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Was Theia a planet or an asteroid?
According to an article Theia (from the Giant impact hypothesis) was an asteroid and according to The Wikipedia article about Theia Theia was an Earth trojan (which is an asteroid). Which is dubious, so why it is  dubious?. It feels very clear to me that Theia was a planet since it was 0.40 the Earth's mass, according to this ScienceDirect article.
In the Wikipedia article clicking the dubious - discuss hyperlink, someone said that Theia should be an asteroid since it has not cleared it's neighborhood  according to IAU's 3rd rule. But why couldn't it have cleared it's neighborhood, being 0.40 M⊕ / Earth's Mass while Mercury is only 0.055 M⊕ ?

It obviously did not "clear its neighbourhood"... or it could not have collided with Earth. Wether asteroid, planetesimal, proto-planet, dwarf-planet... it's just a word for the same or very similar things at that time in the solar system.

A dubious link indeed - in actual, reputable science riding this semantic question of 'what is a planet' is not really done - those are mostly armchair experts. Ignore. It's a $0.4 m_{\oplus}$ object.

I am not sure if the IAU definition of planet can be applied to early solár systém bodies.

FWIW, the total mass of the main asteroid belt is calculated to be ~3% that of the Moon.

Thanks, @Fred for correcting the grammar.

Please don't directly paste google search results. Doing so can result (and has resulted) in problems. Instead, visit the found link and paste that page's address. I've fixed that link.

Thanks, @DavidHammen

Was Theia a planet or an asteroid?

Neither. It was, if the giant impact hypothesis is correct, a planetary embryo. Not yet a planet, but bigger than any known asteroid.

It feels very clear to me that Theia was a planet since it was 0.40 the Earth's mass, according to this ScienceDirect article.

That's one article, and it hasn't been cited very often, which suggests it might not be that good. It's best to view recently published peer reviewed articles as potentially suspect. Getting an article published in a peer reviewed scientific journal is where science starts, not ends. It's been estimated that many (maybe even most) peer reviewed papers are wrong. This is a much bigger problem in the soft sciences, but it's a problem with models of star systems as well.
You should not be taking that 0.4 Earth masses as a given. It's a conjecture. Most scientists lean toward a Mars-sized object, or about 0.1 Earth masses. The science is not settled. Nor should you be taking the conjecture in the wikipedia article on Theia that states that Theia formed in the vicinity of the Earth-Sun L4 or L5 point as a given. The wikipedia article does write as if this is a fact. That also is a conjecture.
In fact, the giant impact hypothesis itself is a conjecture. (Hypothesis and conjecture are near synonyms.) The giant impact hypothesis is by far the most widely accepted scientific explanation of the Moon's origin, but there are other explanations out there. In addition, there are many different variants of the giant impact hypothesis.
Take everything you read in wikipedia with a giant grain of salt, and everything published in scientific journals with a smaller grain of salt.

But why couldn't it have cleared it's neighborhood, being 0.40 M⊕ / Earth's Mass while Mercury is only 0.055 M⊕ ?

Theia obviously couldn't clear its neighborhood because the presumably larger port-Earth was in Theia's orbital neighborhood. The larger proto-Earth also had not yet cleared its neighborhood up until the time of the giant impact because Theia  was in the proto-Earth's orbital neighborhood. Impacting one another is one of the multiple mechanisms by which planet sized objects clear their neighborhood.
The IAU definition of a planet pertains to the solar system after it had formed and more or less settled down into its current state. Conjectures abound regarding the mechanisms by which the solar system formed and then settled down. Some have hypothesized a fifth giant planet that was ejected from the solar system. Some have hypothesized that Uranus and Neptune switched places. Some have hypothesized that Jupiter dove deep into the solar system, to about where Mars is now, only to move back out to where it is now. This last one, the grand tack model, is fairly widely accepted, but it is not settled science.
Regarding the origin of the Moon, there is a lot that remains unsettled. The giant impact hypothesis explains a number of mysteries, but leaves several unsolved mysteries. Another yet to be resolved mystery is when the Earth got its water. If this happened mostly after the giant impact such as the late heavy bombardment, it wouldn't be surprising that the Earth and the Moon exhibit different hydrogen isotope ratios.

The IAU definition of "planet" is at best irrelevant here.  The IAU defines a planet as a body that has cleared its neighbourhood. But in the early solar system the 8 bodies that are now classified as planets were in the process of clearing their neighbourhoods.
The classification of certain solar system bodies as "planets" is not arbitrary in the stable solar system in which we live now.  It becomes arbitrary if you go back far enough in time. We can say that we can model the formation of the moon as being the result of a collision between a "proto-earth" and a body with about 40% of the mass of Earth.
Such a body would be far more massive than any current asteroid. It would be planet-sized. The semantics of "is it an "asteroid" or "planet"" are not relevant to that period in the solar system's history.

The only meaningfull definition is the geophysical one (you can categorize a body based on Its properties without reference to neighborhood).

@LeosOndra Many astronomers disagree with what you wrote, including the IAU. There are no crisp boundaries with regard to properties such as roundness. On the other hand, there is a huge gap between the one object in the solar system classified as a star and everything else in the solar system, and another huge gap between the eight objects in the solar system classified as planets and the other smaller bodies. The gap between stars and non-stars gets a bit fuzzy outside of the solar system, and determining roundness outside of the solar system is beyond science's current capabilities.

Maybe the IAU definition is useful for solár systém. But if I understand what you wrote, it would ve enough to define the bodies in solar system by enumeration - stars: Sun, planets: Mercury, ..., Neptune.

If the hypothetical Theia had 0.40 the mass of Earth, it would definitely be in the category of planetary mass objects, or planemos.
A planemo is a geophysical planet, a planetary mass object.
A body massive enough to pull itself into a spheroid shape by its own gravity, but not massive enough to become a brown dwarf (which is about 13 times the mass of Jupiter or about 4,131.4 times the mass of Earth).
The composition of a world will determine what mass is sufficient to make it gravitationally rounded.  An iron object can remain irregularly shaped at a much higher mass than an icy object would become rounded at.
Planetary mass objects in our solar system have masses as low as 0.0001 the mass of Earth.  So the hypothetical Theia would definitely be a planetary mass object and a planet by the the geophysical definition of a planet.
One reason why the International Astrophysical Union adopted a definition of planets which required them to have "cleared" their orbits of other objects was to avoid having to recognize many new Trans Neptunian Objects (TNOs) of planetary mass as planets, which was considered undesirable.
But even mighty Jupiter hasn't cleared its orbit of all other objects.  In fact its orbit has quite a lot of asteroids in the L4 and L5 positions, the Trojan asteroids. Venus, Earth, Mars, Uranus, and Neptune also have Trojan asteroids.  So, at best, there could be only two planets in our solar system which have truly cleared their orbits: Mercury and Saturn.
So think of Theia as a planetary mass object, a planemo, a geophysical planet, or a plain planet, if you want.  Those seem like accurate terms for an object of that mass, whatever its orbital characteristics.

I think you've misspelled "planemo" several times. But that's also semantics. It's all just protoplanets. Nobody in the planet formation literature cares about those labels, because they are not meaningful in the early phases.

Isn't also the geophysical definition of planet / brown dwarf tied to their origin / history? For brown dwarf we assume hydrogen / helium body. Would silicate / iron planet become brown dwarf oř a star if we add enough material?


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Can LIGO distinguish rotating and non rotating black hole collisions?
I am assuming two rotating black holes create gravitational waves as they collide.

Yes it can - well, to some extent. If you look at any of the merging black hole discovery papers you will see that they try and put constraints on the dimensionless spin parameter and orientations of the spins of the black holes, both before and after the merger. There is also a test for the likelihood of spinning versus non-spinning black holes.
Here is an example from Abbott et al. 2020 concerning the analysis of GW190521, a very massive black hole merger. The table reproduced below gives the magnitude of the spin parameters (the "spin magnitude") of the black holes both before an after merger. Subsequent analysis in the paper looks at how those spins might be oriented compared with the orbital plane of the binary. Notice that the error bars on the spin parameters before merger are large and the evidence that the black holes are spinning is quite weak - this is parameterised with the Bayes factor, which is the ratio of likelihoods for models with and without spin. In this case, a Bayes factor of about 8.3 is substantial but not decisive evidence that the spinning model is favoured.
However, after the collision the spin parameter of the merged black hole is much better defined.

It is actually quite difficult to get good constraints on the individual spins of black holes before the merger. The signal instead chiefly depends on something called the dimensionless effective spin parameter of the system ($\chi_{\rm eff}$ in the table above), which ranges from -1 if the black hole spins are anti-aligned with the  orbital angular momentum to +1 if they are aligned (e.g. Vitale et al. 2017).

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Do conjunctions of planets block out the sun and cause measurable cooling of the atmosphere on one of the planets?
Is a significant amount of light energy blocked by one planet such that there is noticeable cooling of the atmosphere of another?

Planets look pretty tiny without a telescope. Why do you think they might block a noticeable amount of light?

From Earth, Venus' max size is about 1 arcmin, compared to the Sun's 30 arcmin.  If you compute the surface area of each circle, Venus blocks .1% of the Suns' disk.  Variations in cloud cover certainly account for much more than that.

@GregMiller that is an answer

For an Earth-centered view see https://xkcd.com/1276/

Jon Custer
xkcd.com/1276.  Voyager has a shadow the size of a bacterium..Wow!

@JonCuster that xkcd would make for an excellent answer

It is detectable, but not substantial.
When Venus transited in 2012, it blocked about  0.1% of the light from the sun, which was unnoticeable.  This is about 10% of the variation in the sun's brightness over it 11 year cycle. It is  much less than atmospheric effects, such as variation in global cloud cover.
The biggest transit would be a transit by Jupiter, viewed from Saturn:

Even this would not cause notable cooling, and would not even be noticeable to someone who was not looking at the sun (our eyes adapt to variations in overall brightness)
Of course a transit by the moon, viewed from Earth, does cause noticeable local cooling.

Actually,  Venus is about 1 arcmin,  and the sun is about 30 arc min,  so 1/30^2 = 1/900 = 0.00111 or about 0.1%

yep I was trying to do arithmetic pre-coffee and forgot that Venus was not actually ON the Sun, but well in front of it.

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Does Mars get hit by as many meteors as the Earth?
The Moon gets bombarded by meteors at the same rate as the Earth according to
What the moon's craters reveal about earth's history
Does Mars or any other planet get bombarded at the same rate as the Earth and Moon?

Mars probably gets slightly more, it is closer to the main asteroid belt.

Presumably Jupiter gets the most because it ihas the most mass and gravity?

This is a good starting point: https://astronomy.stackexchange.com/questions/14304/what-explains-the-distribution-of-new-impact-craters-on-mars

Great reference: have they found out yet why there are longitudinally few meteors on either side of mars equator.

Probably more reach the surface also as Mars's atmosphere is ~1% of Earth's - not clear if OP is meaning meteor rate at the top of the atmosphere or at the surface

You misread or misrepresent that article you're quoting: It does not state that the rate of meteor bombardment is the same for Moon and Earth. It implies only that the rate per unit area is comparable, but since Earth has a larger area (which is effectively increased by gravitational focusing), the actual bombardment rate for Earth is larger.

I recently wrote a paper that talked about some of this, so I have a fair bit of info on it.
The canonical number today is that Mars' proximity to the asteroid belt means that, for asteroids, the bolide ratio between Mars and our moon is 2.8, meaning that it gets hit 2.8 times for every 1 time the Moon does, per unit area.  This is from a book chapter by Ivanov et al. (2002).  The reason that we can approximate this based only on asteroids is that asteroids probably account for about 90% of all impactors in the inner solar system, and comets should be about equal between Moon and Mars.
Then, you scale by surface area since bolide rate is per unit area.  Mars has roughly 3.8x the surface area as the Moon, so we would expect about 10 more impacts to form on Mars per unit time as on the Moon, in the current solar system configuration.
Where this becomes really kinda hairy is when you go back in time to maybe the first ~half-billion years or so.  With lots of possible dynamic rearrangement going on and scattering of small bodies (what happens if Saturn and Jupiter move farther out in the solar system?) the impact populations were different, and the bolide ratio was also probably different.  The fraction of comet impacts was higher, leftover planetesimals from planet formation was a population that you have to account for, etc.
And, the dynamical models to not agree.  The best I can give you at the moment is that the bolide ratio was anywhere from about 1 to 5 early in the solar system (review by Bottke & Norman (2017) is reasonably understandable).
We can try to use the impact crater record (what I study) to try to at least constrain the problem, but the impact crater record on Mars has been partially obliterated, including the oldest stuff, so it is hard to use that as a constraint.  That was the topic of my paper (Robbins, 2022) where I lay all this out and tried to write it at a level that a non-technical audience could get the gist of, if you're interested.  This paper approaches the problem from the largest, oldest craters on Mars and the Moon and points out that if you assume today's dynamical models are correct in the ancient solar system, then Mars is missing ~40-80 craters >1000 km across.  I then went through several different ways to reconcile the observation with the models, and I think the most likely explanation is that you really did need to have a very different bolide ratio in the ancient solar system than present-day.


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What kind of nebula was the Sun formed from?
I was just wondering what type of nebula did the Sun form from because mainly there are 5 categories: emission nebulae, reflection nebulae, dark nebulae, planetary nebulae, and supernova remnants, so which of these was the Sun formed from and is there a name for this nebula? Probably M67.

Related: https://en.wikipedia.org/wiki/Star_formation#Stellar_nurseries

What did your search engines leave in doubt, please?

@RobbieGoodwin It talked about the Solar nebula in the nebular hypothesis. However I wanted to know what type is the solar nebula furthermore

@PM2Ring Thanks

Are you seriously suggesting the best you could get from search engines was that something 'talked about the Solar nebula in the nebular hypothesis'? I'm suggesting that with no useful research to justify spending SE's time,  you're asking pretty-much a high-school question. Who thinks I'm out of line here, please say how?

@RobbieGoodwin I know both about Solar nebula and nebular hypothesis. There wasn't much info about the solar nebula itself

@ScienceAJ Good for you. How does your knowledge help, here?

@RobbieGoodwin My current knowledge i.e before asking the question  didn't help to come to the conclusions thus I asked the question. + I'm not yet a High schooler

@ScienceAJ Thanks and if you were a graduate student, much less 'not yet a high-schooler' still, the point would not at all be whether your current knowledge did or should have  helped… simply at what point that knowledge ran out.
Otherwise, your whole exposition is irrelevant and you're Asking SE Astronomy the bald Question, "What kind of nebula was the Sun formed from?"
Such a question is wholly valid on Google or any other search engine and here, what failed before matters much more.

@RobbieGoodwin Thanks

Stars and the planetary systems around them form from dark and dense molecular clouds.
Physically we distinguish

Hot ionized gas (supernova remnants and emission nebulae)
Hot neutral gas (also some parts of supernova remnants, reflection nebulae like outflows and clouds near new stars etc)
Cold neutral gas and molecular gas (this is usually the dark nebula)

In the sky the star forming nebulae are visible as either reflection or dark nebulae. One of the nicest examples is in the Orion Nebula which is a large and close star forming region. In front of the bright nebula (it's partially a reflection nebula, some parts are actually already excited by newly-formed stars so that we see the H-alpha emissions) we see the dark blobs and the dark disks around evolving stars (e.g. here).

But why do emission nebulaes have H-Alpha emissions?

That's a separate question. If hydrogen gas is excited (hot) and has emissions it can only emit radiation in the wavelength it can radiate. Each element has characteristic transition lines. H-alpha is the most prominent one of the Balmer series of hydrogen, the base transition of that is between quantum numbers n=3 and n=2 (Lyman series is to quantum number n=1 and more energetic). Other wavelengths than these discret numbers can only be emitted when you have another partner (e.g. atom) - which is rare in space which is empty in terestrial terms - even in gas clouds.

What emit light (hydrogen spectral lines) in emission nebulae Is not ionized gas but gas which has just recombined.

Stars are formed in molecular clouds: these are gas clouds with conditions for $H_2$ to form.
Molecular clouds are typically dark nebulae, but if there is a bright star near them, then they can reflect the light of that star and be reflection nebulae. There is no actual difference, only in appearance.
Planetary nebulae and supernova remnants are not places where stars form,  as the gas is hot and moving apart. (Sun from SuperNova)  Stars form where cold gas can move together.
Of course you can't see the nebula that the sun formed from, it was turned into stars 4.6 billion years ago. It doesn't exist any more.  The open cluster M67 is very unlikely to be the parent cluster of the sun

But why are Planetary nebulae hot, I know they are Ionized but why is it hot? and can gravity overcome the Hot nebulae

They are ionized by the intensely hot white dwarf at their centre.  There is also a huge difference in size between a molecular cloud dark nebula and a planetary nebula.  Stars do not form in planetary nebulae. "ionized" is another way to say "hot".  It means that the gas has absorbed enough energy to strip the electron from the hydrogen.  If gas is cold, then it isn't ionized.

Thanks, @JamesK for the clarification. So gravity can't overcome the hot planetary nebulae? and what would happen to the White dwarf?

Thanks, @JamesK

It would probably cool down into a black dwarf?

Eventually it will.

Yes, @planetmaker

Are such regions where stars from  $H2$ and are dark nebulas called a Bok Globule?

Bok Globules are a type of molecular (H2) cloud  When a giant molecular cloud starts to form stars, those stars will ionise the gas around them, resulting in an HII region (emission nebula) There will be denser regions which don't have stars yet and are too dense for the UV light to penetrate, these form small dark nebulae within the bright emission nebula, these small dark regions are small molecular clouds called Bok globules.

Thanks, @JamesK.


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Python Program for Synodic months
I am trying to make an astronomical program for celestial bodies in our solar system (and beyond!).
However I want it to show how many Synodic months since New moon. Example: Since last 2022 there happened 0.50794789457 Synodic months.
So is there any API/library to get such data (it's not a necessity that a module would be required)? .

Do you mean https://en.wikipedia.org/wiki/Lunar_month#Synodic_month = 29 d 12 h 44 min and 2.9 s? It's a number that will always be less than about one, correct? Isn't the time between successive new Moons on average one synodic month?

Yes, @uhoh. I am talking about the same Synodic month. Thanks.

@uhoh Yes. However I did not find such Library while Googling

29d12h44min is the mean length of the month.  The actual time between successive new moons can vary (due to perterbations on the moon's elliptic orbit) by 6h either way

Thanks, @JamesK. However What causes those Perturbations on the Moon's elliptical orbit? Is it the gravity of other planets?.

Mostly the gravity of the sun.  If you are serious about any kind of astronomical calculation you need to obtain a copy of  "Astronomical Algorithms" by Jean Meeus. They may not be the be-all-and-end-all of astronomical computation.  But they are everyone's starting point.  Lunar theory, in particular, is complex (far more so than the motion of the planets.)  The Moon's orbit is very significantly non-keplarian.

If you haven't already, look at astropy, there might be something there that would help with what you're trying to do. Not totally sure though.

The previously mentioned Astronomical Algorithms book has an algorithm for computing the times of the phases of the moon.  You could use that to compute the time between two new moons, and then compute how far along you are in the current Synodic period.  An implementation of the moon phase algorithm is here: https://www.celestialprogramming.com/moonphases.html .

As James said, lunar theory is complicated. Wikipedia has some good introductory articles on this topic. Start at https://en.wikipedia.org/wiki/Lunar_precession then look at the "See also" links https://en.wikipedia.org/wiki/Orbit_of_the_Moon & https://en.wikipedia.org/wiki/Lunar_theory

Why are you writing this "astronomical program for celestial bodies"? Is it just a learning exercise? How accurate do you want it to be?

BTW, apart from perturbations, the synodic month length varies because the Earth and Moon orbits are elliptical. The mean anomalistic month is almost 2 days shorter than the mean synodic month, so the speed of the Moon at the time of the Full Moon changes significantly from one Full Moon to the next.

Thanks, @PM2Ring

I am making this program so that I can get real-time data and observe Planets and Moons as per their RA, DEC and See the Moon. Moreover though it's usage is currently for non-commercial uses but I want it to be extremely precise

@PM2Ring What is the accuracy of the Meuss algorithms?

Thanks, @GregMiller

@PM2Ring The eccentricity of the Moon is 0.0549 according to NASA

@GregMiller However the link you shared has the code is in Javascript (I also know Javascript but I want to make this in Python) , So is there any  code for Python?.

Thanks @JustinT. I will check  Astropy

Let us continue this discussion in chat.

If you want the Ra/Dec of the moon and planets, you're making it too complicated.  As you can imagine, there have been a lot of people wanting to do the same thing, and there are many ways to do it.  The Skyfield API in the answer below can do it, and the link I posted above has a few different methods too.

Thanks, @GregMiller. I already have RA, Dec of planets using the same Skyfield library. I want the Day since last new moon

The Python Skyfield API can do this.  What follows is a brief python program  that will calculate the fraction of time that has passed between the last and the next New Moon.

import pytz
from bisect import bisect
from datetime import datetime, tzinfo, timedelta

from skyfield import api, almanac

def main():

    time_zone = pytz.timezone("UTC")
    time = time_zone.localize(datetime.utcnow())

    ephemeris = api.load("de421.bsp")
    timescale = api.load.timescale()

    start_ts, end_ts = timescale.utc((time - timedelta(days=30),
                                      time + timedelta(days=30)))

    phase_times, phase_indices = almanac.find_discrete(
        start_ts, end_ts, almanac.moon_phases(ephemeris))

    new_moons = [phase_time for phase_time, phase_index
                 in zip(phase_times.astimezone(time_zone), phase_indices)
                 if phase_index == 0]

    index = bisect(new_moons, time)
    prev_moon, next_moon = new_moons[index-1: index + 1]

    lunation_fraction = (time - prev_moon) / (next_moon - prev_moon)

    print(f"Lunation fraction: {lunation_fraction}")

if __name__ == '__main__':
    main()

Incredible script! +n! I've never heard of pytz or bisect but wow how useful. For those new to Python, if you click "install" at https://www.anaconda.com/products/distribution you'll get a nice selection of scientific libraries, but you'll have to install Skyfield separately.

Thanks a lot!. However what does Pytz and bisect do?

@ScienceAJ I use the pytz module to turn an ordinary datetime object into one that contains time zone information that  skyfield's timescale objects are happy with.  bisect takes a sorted list,  and a value and returns the index a value would have if you inserted it in its sorted place;  I used it in this case because in the sixty-day timespan  the code searches for New Moons, there's a small chance of finding three.

@notovny Thanks a lot!. I shall implement the code in my program


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Does the mass-luminosity relation work for brown dwarfs?
There is a mass-luminosity relationship of the form $L \propto M^a$, where $a = 3.5$, that is is applicable to main-sequence stars. Is there a similar relationship that holds for brown dwarfs?

See also https://astronomy.stackexchange.com/questions/32771/is-there-a-way-to-factor-age-into-the-mass-luminosity-relationship-for-stars

Thanks, @ProfRob. I've checked out the link and I found the formula for mass-luminosity-time relation given by you, however this is for Main-sequence only and not for brown dwarfs, right?

The linked question applies specifically to brown dwarfs during their deuterium-burning phase, which lasts from 3-30 million years, depending on the brown dwarf mass. The conclusion there, is that there is a luminosity plateau, akin to the main-sequence, where luminosity is closely-related to mass. However, after that, the luminosity depends on both mass and age so there is no unique relationship between luminosity and mass and no simple relationship that can be written as a formula.
Details:
It is worth showing this diagram again (from Burrows et al. 1997) which shows the luminosity evolution of stars, brown dwarfs (and planets) as a function of age for different masses. The regions where there is a good relationship between luminosity and mass will be horizontal lines on this plot. The luminosity-mass relationship works in main sequence stars (especially low-mass main sequence stars) because their luminosity does not change for long periods after they have initiated nuclear burning.
Thes situation for brown dwarfs is far more complex (the green lines). During deuterium-burning, the green curves are more-or-less flat, implying a close relationship between mass and luminosity. Thereafter you see that brown dwarfs continuously cool and therefore the luminosity is a function of both mass and age. By looking at the wobbling of the cooling curves and the fact that some of the curves meet or even cross at certain ages, you can see that there is no simple mathematical formula that can be written down to represent this relationship - one must use the theoretical curves (and different models can have significant disagreements in detail).
There is probably a luminosity-mass relationship at a given age, but in general, you wouldn't know the age of a brown dwarf.
So, for example, if you know the luminosity is $10^{-4}$ solar luminosities, the plots below show that if you don't know the age, the object could have a mass anywhere between 0.004 - 0.07 solar masses.

Incidentally, it is worth noting that there isn't a single power-law formula relating luminosity and mass across the whole main sequence and that for stars of about 0.8 solar masses or higher, one should also take account of (or correct for) the age of the star. For example, the Sun is about a factor of 1.5 more luminous than when it started on the main sequence, but its mass is almost the same (slightly less actually).

Thanks a lot!. So there isn't a equation for it, Right? and What if the mass  given from the Mass- luminosity relation equation can vary a bit, So that I don't have to supply the age of the star?

@ScienceAJ I don;t understand your comments. You asked if there is a mass-luminosity relationship. No, there isn't. There is some sort of mass-luminosity-age relationship. If you ignore the age, then you can see that at a given luminosity the brown dwarf could have almost any mass within the brown dwarf (or planetary) regime.

So what is the formula for Mass-Luminosity-Age relation for Brown dwarfs?

Thanks a lot!. Moreover what do you mean by a simple formula, by that do you mean that there is not formulated formula at all or there is some complex formula?

@ScienceAJ Not everything can be reduced to a mathematical formula with few parameters/variables. Most work in astrophysics works with actual models of complex systems. I am certainly not aware of any formula in use. You could try to take the models and fit some complicated mathematical function to it.

Thanks a lot!. So can the Main-sequence formula be interchanged with Brown dwarf equation ?

@ScienceAJ NO! There is no simple relationship between mass, age and luminosity for brown dwarfs. I don't know how I can say it any more clearly.

Thanks. Alright, @ProfRob


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Mass range of a sub-brown dwarf
Sub-brown dwarfs are celestial object that have planetary mass or are termed "Planetary mass object/planemos". They do not lie in the range 13-80 MJ that defines "normal" brown dwarfs, which is the range from the boundary for deuterium fusion and the minimum mass of a star. So is there a lower mass limit for a sub-brown dwarf? Wikipedia has it being around 1 Jupiter mass however this is the mass of the nebula a sub brown dwarf can form from.
The maximum would probably be 13 MJ but what is the minimum? I think since the definition of a planemo is "a celestial object massive enough to achieve hydrostatic equilibrium", so it might be calculated using this.
Difference between Planet and Sub-brown dwarf:
Moreover Planemo's are kind of an grey area i.e superposition between a planet and an star
To clarify I am asking what is the lower mass limit for an object of low-mass that forms in isolation from a collapsing cloud and not in a Circumstellar disk where planets form (which is an further form of categorization to resolve  "where planemos are there  thus we can not conclude whether it is a star or an planet")?

Thanks a lot! @ProfRob .I mean a planemo not a planet. I think the difference  between a planet and a sub brown dwarf might be the IAU's 2nd rule which is that in order for an celestial planet to be considered an planet  it would have to be in orbit around a star, so even if it was orbiting a star it may be called an binary star system because brown dwarfs are made of Nebula and Planets are formed from protplanetary disks

I'm suggesting your question is hard to answer because nobody can even decide what is a brown dwarf and what is a planet. Is a gas giant ejected from its planetary system a brown dwarf? Because many are ejected.

But I think sub-brown dwarfs are not formed from "circumplanetary disk", Can you please share any citations so I can further investigate it?


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How do amateur astronomers do stellar spectroscopy?
This question consists of 2 parts:

How can amateur astronomers measure the spectrum of stars?

In addition to diffraction gratings, what equipment do they use (like telescopes, and the focal length and aperture of the telescope)?

@ScienceAJ why don't you do the following to narrow this down and add more focus 1) explain that you have a goal of getting a spectrum from a very dim object but want to start by measuring something bright and easier first, 2) mention if you have a telescope at the moment or not, or if you plan on using a camera. 3) mention a little bit about how accurately you want to measure the spectrum, and if you need to resolve individual spectral lines or not. Then you could ask about the minimum amateur setup that might be able to do it.

It might help you focus your questions to go here: https://www.rspec-astro.com/sample-projects/ and look at spectroscopy examples that some amateurs are doing with telescopes. If you only have a camera and appropriate diffraction grating, then only a few bright objects are suitable. I have no financial connection with the stuff at the link, but I did buy a grating, camera adaptor and the software.

Thanks a lot, @EdV. It pretty much solves all my questions

@ProfRob WISE is an telescope, by WISE system I mean the sub brown dwarfs and brown dwarfs discovered by WISE

You are at the early stages of a possibly life-long love affair with astronomy and I envy that: I am just a retired chemistry professor who did various spectroscopy research projects (lots of blowing stuff up with lasers). So no need for you to rush. Just start simple: what hardware, software and astronomy knowledge do you have and what project would be a good match for an enthusiastic person with that capability? Perseverance really counts, as does curiosity and skepticism. Best of success!

@ScienceAJ if the 16.5 is the magnitude of your object, you will not get lucky unless you have a decent amateur telescope at hand. That is even more true when you want to do spectroscopy. With the 50cm telescope here we can just barely see pluto at 16mag in the best of nights- without any grating. Getting started with spectroscopy I recommend doing spectra of our planets maybe first or of bright stars, and then see what you can identify, comparing it to their known spectra

Thanks a lot, @EdV

@planetmaker I shall have an telescope after a few months, but what is the focal length, aperature size, magnification in order to observe such an object?

Suggestion for a sweet amateur spectroscopy project: create a thin slit, place it parallel to and over the equator of Jupiter, and do spectroscopy there. Use the results to obtain the rotational velocity of Jupiter from the space-resolved spectrum.

@planetmaker I did that a quadrillion years ago, with a photographic plate, and read it with a Mann measuring machine a bit like this. I was really excited by the result! Have you tried it? If so, I think that example would make for an excellent "how to get started in amateur astronomical spectroscopy" answer!

Thanks, @planetmaker. I will implement that technique

Thanks, @uhoh. I've never tried Spectroscopy before

Thanks a lot, @planetmaker. Would I need a telescope in order to do Spectroscopy with Jupiter?

@uhoh no, I didn't yet. But I recently came across that idea in some article (forgot where) and put it on my list of "possibly cool project" - especially in relation to doing this with children, youths or students. :)  @ ScienceAJ: I recon without a telescope such spatially-resolved spectroscopy will fail... you need to measure the velocity at different parts of the equator to get results. Good luck without a telescope.

I admire your ambition and enthusiasm, but it is time for a reality check: you currently have too little knowledge of spectroscopy, diffraction gratings, telescopes, etc. You would be very well served to just pick a simple beginner project. The link I provided previously shows example projects. And that plastic diffraction grating you mentioned, which I happen to have, is just a toy: good in a lecture hall for students to see spectral lines in gas discharge lamps. Don’t be discouraged, just be realistic: you need to walk before you can run.

Thank you so much, @EdV about the valuable inputs. Can you please guide me or provide pointers so that I can get a better understanding and hold on the subject?

I think you need to find a local mentor to help you learn the basics and focus on doing something feasible. Otherwise, you may end up frustrated and spinning your wheels. I cannot provide any better advice than to find a local mentor and I will post no more comments here.

Ad 1) There are multiple options:

A diffraction grating in transmission like the StarAnalyzer 100 or 200, that are conveniently framed in a 1.25“ ring, so it can be attached to a standard ocular.
A grating in reflection in the Star‘Ex an extension of the Sol‘Ex heliospectrograph.
there are a couple of spectrometers commercially available, including Echelle spectometers and even with optical fibres.

Ad 2)
You use what you have available, from refractors with 70/420 as I do up to Schmidt-Cassegrains like the C11 or C14 from Celestron.

Hi, Thanks a lot. Moreover what is C11 and C14? Also how can transmission spectroscopy be done on stars?

Watch this video by Tom Field: https://youtu.be/6MrFuNGLsUE. He tells and shows you exactly how to use the StarAnalyzers to do transmission spectroscopy on stars. There are lots of videos there: have a look at some.

C11/C14 = Celestron Schmidt-Cassegrains with 11“ or 14“ aperture.

Ok, Thanks. Moreover in order to make precise measurements, how do they avoid telluric contaminations?

@EdV Thanks a lot!

If Tom Field does not explain how to get rid of telluric contaminations, I won‘t do that either. (Means: I have no clue ;-)  Theoretically, you can download space-based spectra or prepare extinction spectra yourself. I have not come across infos on that from amateurs on the web.

@ScienceAJ      I know absolutely nothing about correcting telluric lines, sorry to boast, but other people do, e.g., https://www.eso.org/sci/software/pipelines/skytools/ and links therein. It is a separate question anyway.

Thanks, @EdV. No issues


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What caused a huge piece of the Sun to break off?
There seems to be a huge piece of the sun that broke off at approximately 53 degrees. There's at least one article that describes it in these terms.
This, to me, seems to be a CME (Coronal Mass Ejection) – it seems that it cannot be a solar flare because it is just a burst of EM radiation. However before this event, there is a high chance that a solar flare happened.
Coincidentally, now the Sun's 11-year solar cycle has completed and during a solar maximum, we see a lot of sunspots.
So my theory is that this is because we have reached the solar maximum, thus magnetic field lines entangle easily, thus this event happened. Is this correct?

What are you talking about "The Sun's huge piece breaks off approximately 53 degrees"  This doesn't happen.  CME happen all the time.  Has there been one recently? Yes, there is one every day.  Has there been a big one recently? You tell me what you are referring to. The sun is pretty active now.

We are several years off solar maximum.

There is a story in the news about this https://metro.co.uk/2023/02/10/part-of-the-sun-broke-off-and-weve-never-seen-anything-like-it-18259267/

Metro is a pretty much worthless for any kind of science news.

You'll want to cite the source of any claims that seem sensational.

As in @JamesK's good answer, there is a misunderstanding from the news report... very nicely clarified in his answer. :)

I'm guessing it's unlikely the OP will [edit] their question to include the source, but it may well be the article @sno gives a link to – so I'm going to add that link to the question. There are votes to close the post because it's a poor, ill-informed question, but I'd advocate to leave the edited version open, primarily because JamesK's answer is a worthwhile addition to our library for anyone who happens across this article (or any other low-brow "news" article written about this solar event).

@JamesK  I can support the claim that metro is worthless for science news.

Not a CME, but pretty neat.  This is a prominence, the plasma in the prominence got entrailed into a "vortex" that presumably exists at the solar pole.  The wind speeds in the plasma are pretty extreme.
But this is not "a piece breaking off" (the Sun isn't solid so pieces can't "break off").  The whole "Scientists have never seen it before" statement is rather hyperbolic: the Sun is never the same twice, so there is always something new. However prominences aren't new; n55° refers to the latitude of the prominence.
In particular, our knowledge of the solar poles is limited.  We do now have ESA's solar orbiter which will get a better view, but it is not yet in position.
The current  solar cycle (cycle 25) will peak in about 2025, although the sun is already pretty active.
So a pretty neat observation, but treated in a silly way by the news media (as usual).

Thanks a lot!, (I totally forgot a solar prominence could also be an option). In the news (Example: https://www.ndtv.com/feature/huge-piece-of-sun-breaks-off-scientists-stunned-3769985), the title isn't technically accurate, because as you pointed out it isn't really a piece breaking off. Is it entailed due to the centripetal acceleration around the sun?


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Weak force beta + and - decays
What is the role of the weak nuclear force in nuclear fusion, changing a proton to a neutron to produce deuterium and in neutron stars when a fundamental particle, the lepton electron, is fused in to the composite protons?

Welcome to Stack Exchange! Check Wikipedia;s The proton–proton chain and add to your question at what point you are getting stuck by editing your post. At some point your question will probably be migrated to Astronomy SE. That's okay, don't worry, then you can join that site as well.

the particle you're missing is the neutrino.  a proton changes into a neutron plus an anti-electron and an electron-neutrino, and that interaction is mediated by a weak force vector boson.

What is the question?

@ProfRob it seems to be "What is the role of the weak nuclear force in nuclear fusion when the electron is fused in to the composite protons?" I'm not saying that that's necessarily a clear and/or good question. Would something like "Protons cna beta decay to neutrons just as easily as neutrons to protons, as long as there's enough energy available - so the role is the same as it is for neutron decay, except that the electron is now a positron" be an answer perhaps?

Unfortunately we may never know - the user doesn't seem to be active after posting in Space SE.


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Do whirlpools of turbulence exist in stars just like the whirlpools that exist in water?
Is there turbulence  in the hot plasma and gas of stars that is mathematically the same as whirlpools in water?

Yes there is turbulence.  No it's not mathematically the same because plasma is conductive and carries a magnetic field, the motions in the sun are not hydrodynamic, but magnetohydrodynamic -  Obligatory xkcd https://xkcd.com/1851/

This paper https://iopscience.iop.org/article/10.3847/1538-4357/aaf797#:~:text=There%20is%20an%20abundance%20of,occupy%202.8%25%20of%20the%20photosphere. seems relevant


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Do tidal forces on moons cause them to emit gravitational waves?
As moons orbit planets, they get squashed by uneven gravitational forces acting on them. Does this make a moon emit gravitational waves?

@user438383 about the proposed edit, they DO get cyclicly squashed and "unsquashed" so I've voted to reject it.

Yes, but the effect is tiny
Tim Rias (in a comment below) calculates it to be $10^{-18}$ Watts.  (see a paper about doing a similar calculation for neutron stars)
Bodies that have spherically asymmetric acceleration in a gravitational field will emit gravitational waves. Hence if a mosquito does a loop-the-loop it emits gravitational waves.  In practice, the energy in such waves will be negligible.
The moon weighs more than a mosquito, and if it is squashed (in a non-spherically symmetric fashion) then the motion of mass in its gravitational field will necessarily result in some gravitational radiation.
But the energy released in such motions will be negligible, in comparison to the heating effect, and consequent blackbody electromagnetic radiation. It will also be negligible in comparison to the gravitational radiation already emitted by the Earth-moon system as a result of the orbit.  The acceleration of the moon by the Earth is much greater that the acceleration of matter on the moon by tides.
We are able to detect only the most extreme gravitational waves, those which result from black hole collisions. I'd bet that we will never detect gravitational waves from any solar system object.

If an elderly but distinguished scientist says that something is possible, he is almost certainly right; but if he says that it is impossible, he is very probably wrong. - Arthur C. Clarke.

Eg, "For the Earth-Sun system, this works out to be about 196 watts of power." https://physics.stackexchange.com/a/412990/123208

@planetmaker  Is James K an elderly but distinguished scientist?  Does the quote apply to him.  Anyway, from all that I have read, gravitational waves are very weak except for those produced by super energetic events.

@M.A.Golding. Were you reading the work of elderly but distinguished scientists?

I stumbled on the second sentence of your answer. Could you kindly explain what a "spherically symmetric acceleration" is? My best guess is a spherical body, whose individual parts accelerate as $$ \mathbf{r}'' = f(r,t) \mathbf{e}_r $$, is that correct?

The phrase "The moon weighs more than a mosquito" is just begging for an xkcd-style "[citation needed]".

@PM2Ring That number refers to the GWs generated by the changing orbital quadrupole moment. The amount of GWs generated due to the changing quadrupole moment of the Earth due to tidal deformations, is many orders of magnitude smaller.

If I did not make a mistake putting numbers in https://arxiv.org/pdf/0709.1915.pdf, the power produced in gravitational waves due to tidal deformation of the Moon is something like $10^{-18}$ Watt.

Thanks Tim, I've incorporated that value into my answer, with credit, of course.

@Tim Indeed! I assumed that the reader would realise that the GW power emitted by tidal deformation would be many orders of magnitude smaller than my Sun-Earth example, but I suppose I should've said that explicitly...

While JamesK's answer works hard and goes to great effort to emphasize that the effect is really small, so as  to dismiss the effect as (humorous hat tip to Douglas Adams):
The effect is small, You just won't believe how vanishingly, sub-microscopically, mind-bogglingly small it is. I mean, you may think it's a short way down the road to the chemist's, but that's just peanuts to this.
But I think we should stop and think the other way for a moment.
Space is ringing with a quadrillion-zillion-billion voices! Everything makes gravitational waves, and the distortion of space is a tapestry of reality.
It reminds me of Herman Hesse's Siddhartha_ and the sound of the river.

“Siddhartha listened. He was now completely and utterly immersed in his listening, utterly empty, utterly receptive; he felt he had now succeeded in learning how to listen. He had heard all these things often now, these many voices in the river; today it sounded new. Already he could no longer distinguish the many voices, could not distinguish the gay from the weeping, the childish from the virile; they all belonged together, the yearning laments and the wise man’s laughter, the cry of anger and the moans of the dying; they were all one, all of them interlinked and interwoven, bound together in a thousand ways. And all of this together—all the voices, all the goals, all the longing, all the suffering, all the pleasure, everything good and everything bad—all of it together was the world. All of it together was the river of occurrences, the music of life. And when Siddhartha listened attentively to this river, to this thousand-voiced song, when he listened neither for the sorrow nor for the laughter, when he did not attach his soul to any one voice and enter into it with his ego but rather heard all of them, heard the whole, the oneness—then the great song of the thousand voices consisted only of a single word: Om, perfection.”

The more sensitive we make instruments, and the wider and more diverse ranges of frequencies those future instruments are optimized for, the more we will learn about the universe!
Just to get the ball rolling:

Expected nature of LISA's data; will it be more like a forest of static peaks, or a series of individual events?
What would a kHz gravitational wave detector look like? (mountains on millisecond magnetars) How would it differ from LIGO/Virgo?
What produces gravitational waves with "periods between about 100 - 8000 seconds"?
Which things can LIGO see that LISA can't, and vice-versa?
Is the difference between LIGO & Virgo and their "Advanced" versions really generational, or were these just planned incremental upgrades?

+1 for the beautiful quote. Astronomy is science, philosophy and art.

Your "space is ringing with" point suggests an analogy: There are sounds being created constantly all around the world. But except for extremely loud sounds, only nearby sounds can be heard even by extremely sensitive microphones.

@Barmar theres a big difference between the way sound pressure in air and  gravitational wave strain decrease with distance. First of all, sound pressure drops as $1/r^2$ whereas gravitational wave strain drops much more slowly as $1/r$. Second, sound has has an exponential attenuation in air, it is damped, there are losses in air - sound converts to heat. This doesn't happen with gravitational waves. Third, there are objects around - we don't always have completely unobstructed line-of-sight to sources of sound.

Fourth, over long distances air is "lumpy" in temperature and density and has turbulence, so sound can be scattered away from line-of-sight trajectories. Elephants have a way of avoiding some of these loss mechanisms of sound pressure level in air, they produce low-frequency noises between 1 to 20 Hertz, known as infrasounds, that help them keep in touch over distances as large as 10 kilometers. You and I can't talk over 10 kilometers, but that only our limited experience.

Basically, gravitational wave astronomy is still in its infancy. There are a huge amount of vibrations out there coming from modest and relatively small phenomena that are theoretically detectable if the right detection system is built. Think of how astronomy changed after optical telescopes were first invented and then grew to what they are today in number, variety and locations (including space).That same explosion in information is going to happen for gravitational waves science.


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Can gravitational waves cause a large asymmetric planet to spin?
As planets orbit Earth it won't be perfectly spherical because of gravity But can gravitational waves make the asymmetrical Earth spin a little?

Planets don't orbit Earth.  They orbit the sun.  How much of "a little" are you willing to accept.  Would a surface motion of 1mm in a billion billion years be "spin a little"?

@DAveTheWave.  There is a difference between not being perfectly spherical and being asymmetric.  For many purposes Earth is an oblate spheroid  and so is symmetrical.  It takes a really close examination to notice Earth's minor asymmetric deviations from the figure of an oblate spheroid.  And of course mountains and valleys, continents and ocean basins make Earth slightly asymmetric.

Any effect would be tiny.  GW have very weak coupling to matter, so any transference of momentum or torque from the wave would be entirely neglible.  It would have far less effect than the proverbial girl spinning anticlockwise to make the night last longer.

potentially helpful Do gravitational waves impart linear momentum to objects? (e.g. Quasar 3C 186)


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When a supernova emits gravitational waves do they have momentum and does the supernova recoil to conserve momentum?
In a perfectly symmetrical supernova explosion presumably the net recoil would be zero.But would there be a recoil due to the emission of gravitational waves in a more realistic asymmetrical explosion?

What do you mean with recoil in this context? Momentum is conserved, regardless of symmetry.

As with your other GW questions, any effect would be utterly neglible.

@JamesK I'm not so sure that it would be negligible. Core-collapse supernovae may be quite asymmetrical, giving the remnant a considerable kick. See https://en.wikipedia.org/wiki/Pulsar_kick So they might produce gravitational waves that are roughly of the strength seen when neutron stars or small black holes merge, give or take an order of magnitude.

Oh yes, a very substantial kick, potentially quite enough to eject the resulting neutron star from the galaxy. They can have velocities in excess of 800km/s. Almost none of that recoil is from gravitational waves. It is due to the explosion and the asymmetric expulsion of matter at extremely high velocity that can impart momentum to the neutron star.  How do I know?  GW are very hard to detect, and yet high velocity pulsars have been know about since the 1990s.  If the mechanism was GW, this would be noted as the first evidence that GW exist.

@JamesK it is not yet decided what causes neutron star recoil - other than some sort of asymmetry. Recoil caused by GWs from merging binaries is a hot topic at the moment. They are more powerful GW emitters, but I'm not sure the question of recoil in supernovae  can be dismissed immediately.

potentially helpful Do gravitational waves impart linear momentum to objects? (e.g. Quasar 3C 186)


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Why is a megaparsec considered to be a useful distance in astronomy?
Is the megaparsec fundamental or man made? I have read that galaxy clusters are megaparsecs wide for example.

This question would benefit from some more background - what was the context in which you ask the question.  Was there a use of megaparsecs that seemed not to be useful? Is there another unit that you would consider better - and why? What do you understand the definition of the megaparsec to be?

Every unit is "man-made". Yet within a given system of units you will end up with a set of 'fundamental units' which can be used to express every other property. There are systems which make conversion and calculations easy, others which make it needlessly complicated.
For SI these fundamental units are kilograms, metres, seconds, mol, Kelvin, candela and Amperes. Everything else can be derived. The megaparsec is as fundamental as is the foot or furlong - yet the megaparsec (thus million parsec) is useful to express cosmological distances, while the foot and furlong are not.

Universal constants can be used as units. And they are not man-made. In relativity, for instance, the speed of light is used as a unit.

@Dieudonné well, yes. Kinda. The SI base units are actually defined in terms of such kind of constants. One surely could devise a system where you express everything in terms of these.... e.g. https://en.wikipedia.org/wiki/Natural_units

Constants are not interchangeable with units. A constant is a quantity (186,000, or 2, or 7.4) which may or may not have an associated unit. A unit is what we're measuring with the number. The speed-of-light label "c" belongs to the constant 299,792,458 m/s. So, no, c is not a unit, but you can pair it with a coefficient so that 2c means "599,584,916 meters traveled in a second", and you may also define other constants in terms of c as long as you express the unit correctly.

@AriLacenski Yes and no. A constant is not the same as a unit, of course. But you can define a unit $\textrm{c}$ so that the speed of light constant is $c = 1 \textrm{c}$. Then $\textrm{c}$ is a unit, but it is by definition not the same as the constant $c$. Nb. I use an italic $c$ to specify the constant and a non-italic $\textrm{c}$ for the unit, to distinguish between them.

A parsec, and by extension a million parsecs, is essentially a multiple of the astronomical unit, which is related to the distance between the Earth and the Sun.
There is nothing fundamental about it, since the distance between the Earth and the Sun varies with time.


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What percentage of galaxies are isolated galaxies and what percentage are members of a cluster?
Some galaxies, such as NGC821 are classified as "isolated galaxies", others form  parts of distinct groups or clusters (relevant link) Although isolated galaxies may be accompanied by small satellites, they are distinct from the three large galaxies in the M66 group or the many galaxies in the Coma cluster. Those galaxies are part of an obvious grouping.
Among large galaxies (and ignoring the many dwarf galaxies) what proportion are isolated, like NGC821, and what proportion are found in groups or clusters?

Define 'partner' - there are very large structures in the galaxy encompassing many (many many) galaxies - are they all partners?

What is a "partner" - I suppose it is clear that the magellanic clouds are partners to the milky way,  What about the Andromeda Galaxy?  Is it a partner, or is it just another galaxy that happens to be nearby.  Then the local group of galaxies can be seen as being on a spur of the Virgo cluster: are all the Virgo cluster galaxies partners to the Milky Way?    NGC 821 doesn't have any obvious partners, but if you look hard enough there are "stellar populations" that are small galaies that are in the the process of merging.
https://academic.oup.com/mnras/article/362/3/857/976947

The notion of isolated galaxies seems to be a reasonable one, and should include galaxies like NGC821, which are not part of a group, even if they have small satellites and so the question could be focussed more on non-dwarf galaxies.  There is an interesting question here.  Relevant definition is given here https://astronomy.swin.edu.au/cosmos/i/Isolated+Galaxies

I've tried adding details and examples to your question.

The question could have been how many fossil galaxies are there since isolated galaxies are suspected to be unions of other galaxies.

It's a bit hard to pick an obvious "large galaxy" threshold. This is partly because most galaxy group catalogs are based on galaxy catalogs that are limited by apparent magnitude, meaning that it includes lower-luminosity galaxies at small distances but only high-luminosity galaxies at large distances. Thus, how many galaxies are in each "group" (this includes massive clusters and groups with only one galaxy, which are "isolated galaxies") will unfortunately depend on how distant the group is.
So, keeping that in mind...
The Yang et al. (2007) group catalog, based on Data Release 4 of the Sloan Digtal Sky Survey, used around 400,000 galaxies with redshifts between 0.01 and 0.2. In their Sample II (more accurate, but possibly missing some groups), there are 369,000 galaxies, of which 271,000 (73%) are isolated. In their Sample III (more complete, but probably erroneously includes some isolated galaxies into groups), there are 408,000 galaxies, of which 250,000 (61%) are isolated.
A much more local group catalog is that of Kourkchi & Tully (2017), which looks at galaxies within 3500 km/s ($z < 0.011$). This includes NGC 821 (classed as a "group" with 1 member, so indeed isolated) and the Leo Triplet ("M66 Group" classed as a group with 15 members). 7290 of the 15,004 galaxies are isolated, for a isolation fraction of 49%. The fact that this is lower than the Yang et al. results is undoubtedly due to Kourkchi & Tully including more dwarf galaxies.
(If I arbitrarily define "cluster" as "group with $> 100$ galaxies -- which correctly gets the Virgo and Fornax Clusters), then in the Kourkchi & Tully catalog there are 1339 galaxies in clusters, for a cluster fraction of $\sim 9$%.)
But, generally, I think you could say that $\sim 50-65$% of "large" galaxies are isolated, with about 9% (maybe less) in proper clusters, and the remainder in groups (mostly small groups).


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Do you need to understand the detailed mathematics of general relativity to be a professional astronomer?
Could I become an astronomer by understanding how to use the main results of general relativity such as cosmological redshift or would I need to understand the whole theory?

It's not very clear what you mean by "the whole theory", or what you mean by "professional astronomer".  However (1) all the physical sciences use maths a great deal, and (2) Relativity is now routinely taught in undergraduate classes. It's not exceptionally difficult maths.

I know two people with PhD's in astrophysics who are plummers.  Making a living as a professional astronomer is tough.

@GregMiller Plummers? Are they spherical?

An astronomer maybe (i.e. someone who performs observations), but not e.g. an astrophysicist or cosmologist.

@JamesK Special Relativity is almost always a part of every physics undergraduate's curriculum. However, General Relativity is not. My university doesn't even have an undergraduate course on it.

I guess there are two related but distinct ways of thinking about this question: from a skills perspective (i.e. do you need a functional knowledge of general relativity to perform astronomy research?) and from a requirements perspective (i.e. do paths to becoming a professional astronomer require you to learn the subject?).
The answer to the latter will depend strongly on the institutions you attend. Assuming you work towards a bachelor's (and, in all likelihood, doctoral) degree in physics, astrophysics or astronomy, you may be required to take a full, in-depth class on general relativity at some point. I know of universities where that is the case, usually in their graduate programs. That said, it's not universal; as both an undergraduate (in astrophysics) and a graduate student (nominally in physics, doing research entirely in astronomy), I've been required to take classes that touched on portions of general relativity and adjacent topics but not a full-on GR class. These topics included gravitational time dilation, gravitational lensing and the Friedmann equations. So the answer to this interpretation of the question is a maybe. It depends on where you study.
Regarding the former way of couching the question: in the day-to-day process of research, in many subfields you can certainly get by without knowing much or any general relativity. For example, the majority of work in exoplanets, planetary science and the interstellar medium uses little to no GR. Whether or not you know how to derive the Schwarzschild metric will not make a difference. Frankly, even fields where you would expect GR to pop up on a regular basis won't necessitate a deeper knowledge of general relativity. Half of my research is in pulsars; the other half is in gravitational waves. Believe it or not, I personally have not had to invoke any deep relativity knowledge in a long while; I could, strictly speaking, get by without it and still do good science in my field. (Granted, I work in observational astronomy -- pulsar theorists usually aren't so lucky!)
That said: Knowing general relativity beyond just the surface-level topics I was required to study has certainly served me well because of the research I do. I understand linearizing the Einstein field equations; this is obviously crucial to understanding gravitational waves. I understand (sort of!) the relativistic effects in tight binary systems; this has helped me understand the various phenomena (e.g. the Shapiro and Einstein delays) that are accounted for under the hood, so to speak, of our pulsar timing software. Same goes for post-Keplerian parameters. I do think I'm a better scientist for it.
Could I keep button-pushing each day and succeed in astronomy research? Probably. Have I been required to learn more than these surface-level results, as opposed to the nitty-gritty retails? No. But, given the choice, should you learn more general relativity? This is opinion-based and so beyond the scope of the question, but honestly, I really think the answer is yes.

No, but it depends on what you work on
For example if you work on building telescopes (e.g. Hubble Space Telescope, James Webb) then you don't need to know anything about Relativity.
Some topics might require some GR, although it's not that much. Examples are solar physics, exoplanet searches (since gravitational lensing is part of the methods used), and SETI. You don't need to know GR thoroughly, since you can just use the results that other people derived. Another example is cosmology. Modern cosmology is built on the Friedmann equations. Every cosmologist knows how to use these equations, but there's a good chance they don't know how to derive it.
At the other end there are topics where you need a thorough understanding of GR. Here's an example of such a paper. The first line of the abstract says it all: "We study thermodynamic properties and phase structures of topological black holes in Einstein theory with a Gauss-Bonnet term and a negative cosmological constant". Many (most?) astrophysicists will have no idea what "Gauss-Bonnet term" means, but if you want to work on this topic, you will of course need a thorough understanding of GR.

Communication does due to gravitational red-shift

@planetmaker I assume you mean "cosmology"? It certainly does use GR, but not to the extent where you know it well (at least not for the subfields of cosmology I'm familiar with).

no. I mean telemetry and communications with whatever satellite or space craft. The redshift due to Earth's gravitation in frequency compared to the satellites one in the communication frequency must be taken into account. It is not negligible. That's especially true for deep space where you want to use a very narrow bandwidth to limit power.

Of course if you want to be involved in research directly related to GR effects, then YES, definitely!
You will of course need to demonstrate some degree of understanding in order to get through graduate school - pass exams and candidacy tests - and successfully obtain your Ph.D.
After that, you will certainly need to retain the basics of "what happens when".
You'll probably need to know how to calculate how far the position of one object appears to move when the light passes by a second massive object, what a Schwarzschild radius is, why gravitational waves "chirp", maybe some time dilation equations, at a minimum.
But even if you avoid GR in your research, you will still have teaching duties and some of your students will be frighteningly smart! If you end up having to teach a class that requires you cover General Relativity and you can put off the Math and do some and answer questions about it, depending on the country students will complain about you!
So if you keep your head low and avoid teaching anything beyond Astronomy 101 and choose a field of research that only needs a few simple GR equations for corrections, you may do just fine!
So if you can't understand the basics, then proceed AYOR1!

AYOR:

https://slang.net/meaning/ayor
https://www.slang.org/ayor-meaning-definition/

This brought back memories of taking special and general relativity courses in grad school and getting stuck with a professor, for both courses, who was lazy, cancelled classes without warning and used lecture notes so old, obsolete and yellowed that they were brittle. So I bought books, but that was a black hole experience: all expended effort vanished without a trace.


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Why do planets in our solar system have different chemical compositions?
Was this caused by turbulence in the disc that went on to form the solar system or was the disc itself just endowed with an uneven distribution of elements?

What different chemical composition are you talking about, can you give a reference? It's important to know whether you refer to the refractory or volatile elements, bulk or atmosphere, etc.

From Wikipedia
The elemental composition of Mars is different from Earth's in several significant ways. First, Martian meteorite analysis suggests that the planet's mantle is about twice as rich in iron as the Earth's mantle.[6][7] The planet's distinctive red color is due to iron oxides on its surface. Second, its core is richer in sulphur.[8] Third, the Martian mantle is richer in potassium and phosphorus than Earth's and fourth, the Martian crust contains a higher percentage of volatile elements such as sulphur and chlorine than the Earth's crust does.

Few things to note here. The difference in iron content might be explained by weaker differentiation (i.e. a geological process) due to the weaker gravity. The other statements are more difficult to interpret, "is richer" doesn't say whether it's 10x or only 1% richer, and then we don't have global samples of mars, just about ~10 tiny Martian meteorites. As for the physics of the PP-disc, it is thought that ice lines played a role in controlling the local reservoir of available minerals and ices in the disc. So just the existence of turbulence locally, doesn't mean uniform global mixing.

@planetmaker Yes the link gives a good answer to my question

Why wouldn't they?


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Can the CMB Cold Spot be explained by dark matter redshifting photons?
One explanation for the Cold Spot in the cosmic microwave background (CMB) is that dark matter is redshifting CMB photons; see Fermilab's article "Scientists move a step closer to understanding the “cold spot” in the cosmic microwave background". But this dark matter would affect the orbital speeds of and within galaxies. Can current telescopes detect anomalously high orbital speeds in the direction of the CMB Cold Spot?

Can you cite sources please?  Galaxies hadn't yet formed when the CMB was produced.

@James K   You are right that galaxies hadn't formed when the CMB was produced. There was an article I read that said that dark matter may have been able to account for the redshift. However, the discussion here https://news.fnal.gov/2022/01/scientists-move-a-step-closer-to-understanding-the-cold-spot-in-the-cosmic-microwave-background/#:~:text=To%20make%20this%20discovery%2C%20scientists%20used%20Dark%20Energy,warped%20by%20the%20gravitational%20influence%20of%20dark%20matter.   show there is too little dark matter

Can the CMB Cold Spot be explained by dark matter redshifting photons?

More specifically, the explanation discussed by the linked article is that the CMB Cold Spot is (at least partially) explained by matter redshifting photons as they enter a cosmic void, the Eridanus Supervoid, that is relatively nearby (~2.5 billion light years away). The basis for this explanation is that a cosmic void is a region of below-average matter density, so the gravitational potential is high there. Photons are gravitationally redshifted when they enter and blueshifted when they leave. Over time, cosmic expansion means that voids expand, an effect that weakens the gravitational potential. Their density also drops over time relative to the average, due to a void's weak gravitational attraction compared to that of its surroundings, and this effect strengthens the gravitational potential. However, at recent times, the influence of dark energy causes the first effect (expansion) to win, so the gravitational potential weakens over time. Photons are thus redshifted when they enter the void and blueshifted not as much when they leave at a later time. This effect, known as the integrated Sachs-Wolfe effect, is why a nearby cosmic void can contribute to the appearance of a cold (red) spot in the CMB.

Can current telescopes detect anomalously high orbital speeds in the direction of the CMB Cold Spot?

Cosmic voids have less of all matter, not just dark matter. They're places where you expect to find fewer galaxies, not places where you expect galaxies to be dark matter-deficient. Indeed we normally identify voids in the first place as regions where there are fewer galaxies than average.
How do we know that voids are equally underdense in all matter? In general, large-scale variations in the density of the universe are known to be the same in dark and ordinary matter, at least to within a few percent. See the literature on "compensated isocurvature perturbations", e.g. this article, which searches for how such perturbations would gravitationally lens the CMB.
For the CMB Cold Spot in particular, this research article (which is the one associated with the Fermilab outreach publication linked in the question) notes that the Eridanus Supervoid actually appears to have slightly too much dark matter compared to the number of visible galaxies, where the amount of dark matter is inferred from gravitational lensing of more distant galaxies. Note that this is the opposite of what is needed to explain the CMB Cold Spot. However, the excess is not very statistically significant, and they also discuss possible systematic errors that could be responsible for the discrepancy.


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How far away must galaxies be before current telescopes can no longer measure how quickly they are rotating around one another or internally?
What is the distance limit and does it depend on the size of the galaxy and on noise and interference from gas clouds and our own Milky Way?

Here's a report on finding rotation curves of galaxies at z=2~3  https://www.eso.org/sci/publications/messenger/archive/no.125-sep06/messenger-no125-11-14.pdf It describes itself as "First convincing evidence for rotating
discs at z ~ 2" and it also describes rotation in a gravitationally lensed galaxy at z=3.2 and finally notes that the ELT and JWST could make such observations routine.

The galaxies in that paper look really asymmetrical .Presumably they became more symmetrical with time.

Thats an unintuitive conclusion. We'd expect to see more symetry rather than less symetry over distance. Plus on first principles I'd expect it to work the other way around with time smoothing out asymetry.


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Are there any hints in the CMB as to why the James Webb telescope is finding galaxies larger than expected in the early universe?
"James Webb telescope detects evidence of ancient ‘universe breaker’ galaxies | Astronomy | The Guardian" https://amp.theguardian.com/science/2023/feb/22/universe-breakers-james-webb-telescope-detects-six-ancient-galaxies
"First images from Nasa’s James Webb space telescope reveal ancient galaxies | James Webb space telescope | The Guardian" https://www.theguardian.com/science/2022/jul/11/nasa-james-webb-telescope-ancient-galaxy-images

Can you elaborate a bit on what sorts of hint you'd expect, or why you'd expect any hints in the CMB?

@pela Perhaps an anomalously high  redshift in the cmb for this region of space where there was a higher density of matter than usual  or perhaps a CMB in this region with a lower or higher standard
deviation than usual. Or even with a more symmetrical statistical distribution.

The CMB originates from regions that are many billions of lightyears more distant than any galaxy, so they aren't really correlated (except for the SZ/SW effects where later clusters of galaxies leave an imprint in the CMB). Although it's not impossible that the concordance model of the Universe, ΛCDM, is wrong, I can give you a long list of reasons why the JWST galaxies might not have broken ΛCDM just yet.


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Does a photon travelling inside a gravitational wave get stretched and compressed or redshifted?
The photon would be travelling at the same speed as the gravitational wave.


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What is the force that drives electrons along the magnetic filaments of galaxies?
"Milky Way's mysterious filaments have 'older, distant cousins'" https://www.techexplorist.com/milky-ways-mysterious-filaments-older-distant-cousins/54966/?amp=1
Quote from article:
"The seed particles required to form a filament may be provided by the black hole’s jet, but an unknown force must be driving these particles along astounding distances."
Also why do electrons stay together as they move along filaments?

If an article from a non-science source like techexplorist says "but an unknown force must be driving ..." I wouldn't take that too serious. Electrons move along filaments, as their movement perpendicular to them is restricted by the Lorentz force.

@AtmosphericPrisonEscape
Farhad Zadeh astrophysicist at Northwestern University says in article:., “Some of them have great length, up to 200 kiloparsecs. That is about four or five times bigger than our entire Milky Way. What’s remarkable is that their electrons stay together on such a long scale. If an electron traveled at the speed of light along the filament’s length, it would take it 700,000 years. And they don’t travel at the speed of light.” So there is some genuine mystery relating to the motion of the electrons

Perhaps electrons are  displacing each other  from one magnetic field line to another nearby


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Why is it assumed that the universe started out with a size equal to the Planck length?
What if the Planck length is the distance between particles when the universe was very small .
For a spherical ball of 10^ 78 protons that would give the universe a radius of 10^26 X 10^-35 = 10^-9 metres  Is there a reason why this can't be the case? Does the CMB temperature forbid it?

Oh, and who says that? Earliest Universe we can tell anything would be perhaps having density comparable to Planck density - that's completely different situation than you say.

I don't think this assumed.  Indeed the usual assumption is that the universe was always infinite in extent (even if this causes philosophical problems.  If the universe had a start (and there wasn't an infinite period of inflation, for example, which come with their own philosophical problems) then our current understanding of matter has difficulty with times at a scale less than one planck time  We don't really have a model of reality that can deal with such time intervals, so we can't currently talk about what happened in the first planck time.

Don't try to treat protons as "balls", or the universe as a fixed spacetime in which a ball of protons exploded.

The Planck units are not units which are fundamental in some way.  They're just order of magnitude constants that are roughly at levels which mark the range where we don't have good theories.  They feel natural for some purposes - a little easier to manipulate some equations using these units.

There's some relevant info at Did the Big Bang happen at a point? & https://physics.stackexchange.com/a/185943/123208

@James K I should have said a ball of quarks. It is curious though that a black hole of a few solar masses would have a quark ball with radius about the radius of a oroton and the largest black holes a radius about the maximum distance of the strong force. Also that radius for the universe as a whole is not far off some intermolecular bond distances .

@PM2Ring It was interesting to read in that reference that there should be gamma rays scattering off particles at the Planck length now  from cosmic sources . But I think that would only apply if the particles at the Planck length had electromagnetic properties


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Can the distribution of Al28 across the Earth tell us if the solar system formed from a gas cloud that collapsed itself or by a supernova explosion?
A single supernova could have collapsed a gas cloud and left Aluminium 28 on one side of the Earth . If there were many supernovae in all directions that gradually sent material to Earth then the Aluminium 28 would be found  on all sides of Earth .

just fyi I'm guessing that the downvotes are probably for lack of research effort https://i.stack.imgur.com/dQB1z.png

A supernova explosion that collapsed a gas and dust cloud to form the solar system wouldn't leave aluminum 28 on one side of the Earth.
The Earth would have to already be formed in order to receive aluminum 28 on one side. But the speculation in the question is about a supernova explosion collapsing a cloud and starting the formation of the Earth, a process which  no doubt took many millions of years.
If a supernova explosion started the collapse of the cloud of gas and dust which formed the solar system all the atomic nuclei of aluminum 28 would attach to orbiting grains of dust or else orbit around the center of mass of the condensing gas cloud.
And of course the closer an orbiting gas molecule or grain of dust was to the center of mass, the faster it would complete one orbit around the center of mass.
So some particles which eventually winded up on Earth would take days to make one orbit around the center of mass, and others would take centuries or millennia to make one single orbit.
And it would take millions of years for atoms and molecules and grains of space dust to clump into somewhat larger particles, and those to clump into larger objects, and so on and so on.  Eventually objects kilometers or miles in diameter would be colliding and sometimes sticking together to slowly build planets.
And during that time some particles of aluminum 28 which eventually found their way into the forming Earth would orbit the forming Sun thousands of times as often as some other particles of Aluminum 28 did.  The particles of aluminum 28 would be thoroughly mixed in the collapsing nebula long before Earth formed.  The idea that particles of Aluminum 28 would be more common on one side of the nebula which Earth formed out of is false.

Since perfect mixing  in nature is rare I would think Al28 could be  more common on one side  of the nebula than the other but whether or not people can measure the difference is another question.


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Does MOND change general relativity?
Newton's inverse square law appears in General relativity for small masses . Since MOND uses 1/radius instead of 1/radius squared has General relativity been modified to accommodate this?

To incorporate MOND changes do need to be made to the theory of relativity. This is because at small accelerations and speeds, the theory of relativity approximates to normal Newtonian mechanics. Indeed one of the successes for relativity is that at low speeds and accelerations, you can use Newtonian mechanics to get a very good approximation to relativity, thus you can, for example, find the path of a spacecraft in the curved spacetime of the solar system to a very high degree of accuracy by doing Newtonian calculations.
Unfortunately, it isn't at all clear how or why to modify General Relativity to give MOND. The general idea is that at very low accelerations (far lower than anything we get in the solar system, for example) Gravity should be 1/r not 1/r2. But gravity still has to be 1/r2 at everyday accelerations (since this is the rule that the planets obey).  It is possible to "patch" relativistic mechanics so that it gives the 1/r rule for low accelerations, but the patching is completely arbitrary. (and if done in a naïve way it predicts that gravitational waves will propagate at a different speed to light)
This is a problem. Compare with the anomalous rotation of the perihelion of Mercury.  It was shown that it could be explained if the law of gravity was actually 1/r2.00001 (or something, I forget the details) But this patching of Newtonian mechanics is not based on any theory, just fitting a formula to data.  Instead, General relativity account entirely for the anomalous rotation, and it does so in a geometrically elegant way.  General Relativity makes sense.  It may not be intuitive, but it is worked out logically, not by curve-fitting.
In this sense, MOND is more like Kepler's laws.  It does fit the data, but there is no good reason why gravity should behave like MOND.  Newton's laws explain and justify Kepler's laws.  We can say why a planet should orbit in an ellipse in terms of a more basic theory of Gravity.  And this theory of gravity makes specific predictions that can be tested on Earth.  We need something like that for MOND - something that explains why and isn't just an arbitrary patch applied to General Relativity

No, because General Relativity is well-tested (especially on solar system scales) and there is no indication it is incorrect in any way. If anything, it is MOND that needs to be tuned such that it yields general relativistic effects, like how the speed of everything we've seen cannot exceed the speed of light, or how light is bent by mass.
That said, you might want to check out TeVeS, which last I saw is the leading relativistic generalization of MOND.

MOND would be impressive if it yielded quantum gravity or even hinted at how to get quantum gravity done.

The  link says that a TeVes star is unstable after 2 weeks under Beckensteins proposals.Not very promising.


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Could a sheet of plasma ejected from the sun's surface magnetically reconnect with itself and eject bits of itself which then also reconnect?
Could the Corona of the sun be getting heated by large sheets of plasma ejecting smaller sheets and these in turn ejecting smaller sheets ?

Could the Corona of the sun be getting heated by large sheets of plasma ejecting smaller sheets and these in turn ejecting smaller sheets?

I will rephrase the question to:  Could magnetic reconnection be responsible for the heating of the solar corona?
The answer is yes, it is likely a major source of the energy conversion from electromagnetic to particle random kinetic energy (i.e., heat).  Is it the only mechanism?  No, most likely not.

Could a sheet of plasma ejected from the sun's surface magnetically reconnect with itself and eject bits of itself which then also reconnect?

Well, there are large blob-like eruptions of plasma from the Sun on a semi-regular basis called coronal mass ejections (CMEs).  These are known to have regions within undergoing magnetic reconnection (e.g., see https://ui.adsabs.harvard.edu/abs/2023ApJ...953...15F/abstract).


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Visibility of solar flaring region from Jupiter
I numerically calculated the following numbers.
The geocentric longitude of the Sun on 25 November 1999 at 00:00 UT was 243.52 degrees (numerically calculated with an error of 1 degree).
On this date (25 November 1999), from sunspot number 8771, an M2.0 class of flare started occurring at 18:59 hours and ended at 19:29 hours. This sunspot was located at S15W40.
On this date (25 November 1999), the ecliptic longitude of Jupiter was 32.92 degrees and its geocentric longitude was 26.20 degrees (numerically calculated with an error of 1 degree).
Help me to understand the geometry of the alignment of the location of the sunspot 8771 w.r.t. the position of Jupiter. Would the solar flares from the flaring region be visible from Jupiter?


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What courses should one take for working towards Astronomy from an AI / Data Analysis perspective?
Note:- This is a suggestions seeking question
As a prospective student about to embark on pursuing the MEngg. in Applied AI program, I am eager to align my education with my passion for Astronomy. I would appreciate guidance on selecting subjects that would enable me to contribute to advanced research in exploring galaxies, stars, and other celestial phenomena. How can I tailor my coursework to best support my aspirations in merging AI and Astronomy for groundbreaking discoveries?
I'm really looking forward to make the best use of AI by applying it in my passion, Astronomy. Would appreciate if someone could share their preferred course list from below if you were to make this decision. Following is the course sequence screenshot for your reference. Thanks

2 Electives can be taken from any department. Following is a list from the Space Engineering program. This is more of an Aerospace level program, but what would be more relevant:-


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Does the Drake equation consider how far a planet must be from gamma ray bursters, black holes supernovae etc for life to survive?
Can we use these dangerous phenomena to predict where life can't exist?

The Drake Equation doesn't explicitly consider anything that detailed. But you are free to use things like that in attempting to estimate some of its terms e.g., fractions of life-supporting planets that develop life, or fraction of the latter where life develops intelligence.

The Drake equation, as it currently stands, was never meant to be a definitive equation. It was meant to be used as a discussion point for a conference that Drake was attending.

Comments are for comments and answers are where answers go...

The Drake equation is a rough steady state model of the number of civilizations that can communicate at a typical time. There is no spatial model: it assumes an average over a large galaxy, so it will not tell you anything about where life may not exist. The way the danger shows up in the equation is the last term, how long a civilization remains able to communicate, and in the life/intelligence terms (a dangerous universe has low values for them).
You could imagine running the equation for local volumes with different parameters, but setting these parameters to depend on e.g. local supernova rate is most of the work anyway. It would only be a meaningful exercise if you think there are predictable patterns for how different terms change across space.

Does the Drake equation consider how far a planet must be from gamma ray bursters, black holes supernovae etc for life to survive?

It never explictly says anything about it.

Can we use these dangerous phenomena to predict where life can't exist?

Not with the Drake equation. But absoultely. For example, we know for a fact no life could exist within the event horizon of a black hole (if it did it would be "sucked in" very quickly)

We don't have a quantifiable definition for "life".  All we generally say is that e.g. it's possible liquid water could exist in a region, but we can't even necessarily say that liquid water actually does exist there or that life (as we know it) would inevitably develop as a result.  We cannot say that life would or would not exist in other conditions without liquid water.
You can probably rule out life (again as we know it) existing in close proximity to certain objects, but even this isn't definitive because we don't have a definition of life that makes this certain.
The Drake equation is just a "back of the envelope" toy for discussion purposes.  It should not be taken as the basis for predicting life beyond that extremely limited purpose.


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Is the mass function of dark matter halos fundamental or an approximation based on experimental data?
Can the halo mass function be derived from existing physics or is it just a best fit of some data?

Assuming you know the statistics of the cosmological initial conditions (e.g. the matter power spectrum), the halo mass function can be predicted from first principles using so-called excursion set theory (the simplest form of which is Press-Schechter theory). Consider the cosmological initial conditions -- that is, the density field at a time when fractional variations in the density of the universe are tiny. The basic idea of excursion set theory is to say that if the average density of a region (typically a sphere) in the initial conditions exceeds a set threshold, then that region is part of a halo at the present time (or some other chosen time).
The procedure is to start at some arbitrarily large scale, such that nothing of that scale exceeds the density threshold. For example, if you are considering the whole universe, it has zero excess density, with respect to the cosmological average. Then you can consider successively smaller regions in the initial conditions. Eventually, you might find that the region you are considering exceeds the density threshold. If that happens, you've identified a portion of the initial field that becomes a halo at the later time. The mass of that initial region is the mass of the halo.
Mathematically this can be modeled as a random walk. The density contrast, relative to the mean, is essentially zero for a region of arbitrarily large mass. As you decrease the size of the region, the density could randomly go up or down. The goal is to find the statistical distribution of masses at which your regions first cross the density threshold. This leads directly to the halo mass function.

Doesn't this all assume that before inflation vacuum fluctuations produced dark matter with a statistical probability the same as for quarks leptons etc. How is it known that the density contrast field is Gaussian at large scales? I think I have understood the links in your post Let me know if I haven't.

@DaveTheWave Those two assumptions -- that initial fluctuations are gaussian and adiabatic -- are not required by excursion set theory in principle, although they are commonly made when applying it. They are very well tested anyway; see for example Constraints on primordial non-Gaussianity and Baryons still trace dark matter.


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What causes the filaments of the cosmic web to spin?
The cosmic web is made from galaxies and dark matter  clustered together forming long thin filaments up to 80 Megaparsecs long. The filaments border voids where there is much less mass density and fewer galaxies .Our milky way is on a filament bordering a large void .
"Possible observational evidence for cosmic filament spin | Nature Astronomy" https://www.nature.com/articles/s41550-021-01380-6.
"Cosmic filament spin from dark matter vortices - ScienceDirect" https://www.sciencedirect.com/science/article/pii/S0370269322004324.
"Galaxy filament - Wikipedia" https://en.m.wikipedia.org/wiki/Galaxy_filament


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Is there any observational evidence for dark matter vortices?
The paper here "Vortices and waves in light dark matter" https://arxiv.org/abs/2004.01188
says that in dark matter halos vortices arise. In a vortex some particles move faster than others - the velocity depends on 1/r according to the paper.
This should lead to an uneven relativistic mass increase increase. Is this enough to bend light from stars as it approaches the Earth so telescopes detect it?

Because particles closer to the centre of the vortex move faster and  so would increase their mass more under special relativity.

@Rory Alsop I have reworded the question because you were right about it being unclear what I meant.

I found out from one of the authors of the paper that the vortices need a telescope resolution of 10^-10 arcsecs to detect light bending and even Gaia satellite only has 10^-6 arcsecs .


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If a supernova explodes close to the centre of the milky way does its light get blueshifted by dark matter by the time it reaches the Earth?
Does the dark matter halo of the milky way cause most of the change in wavelength or is baryonic matter responsible?

Why do you have the idea that a supernova's light would be "blueshifted" in the first place? (Are you somehow confusing "interstellar reddening" with blueshifting?)

@Peter Erwin I thought the dark matter halo with more mass than stars might dominate with most of its mass on the galaxy perimeter.

@DaveTheWave You are thinking that the dark matter halo should exert a gravitational pull outward? This does not happen, per the shell theorem.

@Sten I wasn't aware the halos are spherically symmetric shells

@DaveTheWave Halos are not exactly spherically symmetric, but they are close. Although the gravitational pull of a nonspherical shell is not exactly zero, the point stands that no outward force is expected. This is even true in highly nonspherical configurations, like galactic disks. A ring of mass can exert an outward pull, but a disk does not. Galaxies and dark matter halos almost invariably have more mass at lower radii than at higher radii.

Light from the Galactic Center is gravitationally redshifted (not blueshifted) by a little over one part in a million as it climbs the Galactic potential to reach us. While dark matter contributes, stars are the dominant component of the Galaxy's mass below about the Sun's orbital radius (see for example figure 11 of this article).
Note that the great quantity of dark matter above the Sun's radius has no net gravitational influence, because the contributions of the portions of the dark matter halo that lie in different directions all cancel each other out. See the shell theorem.
It should also be noted that gravitational frequency shifts in nonrelativistic orbiting systems tend to be dwarfed by the kinematic Doppler shifts arising from the orbital motion. Although the specific configuration matters, the general scaling is $v^2/c^2$ for gravitational shifts and $v/c$ for kinematic shifts, where $v$ is the orbital velocity and $c$ is the speed of light.


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When gravitational waves pass through a star or gas cloud do they cause mixing of plasma and gas?
Does the compression and stretching of space stir up molecules and atoms?

The compression of space is extremely weak, so no.

@AtmosphericPrisonEscape Please don't answer in comments.  Write  an actual answer that can be voted on and possibly accepted by the OP.

The strain of typical gravitational waves from black hole mergers is on the order of $10^{-21}$. This means that a length of 1000km is compressed and stretched by about the size of one proton.
That is absolutely minute. There is no significant or measurable "mixing", or "stirring up".
If you are much closer to the source of the wave, so that they have a significant macroscopic effect, gravitational waves are not your main problem (your main problem is that you are about to fall into a black hole)

Interestingly, this would mean that a large atomic nucleus like uranium would stretch by a Planck length for a strain of 10^-21. If the Planck length is the smallest possible distance a proton at one femtometre diameter wouldn't  stretch . Quantum gravity of some kind!

@Dave Please see Does the Planck scale imply that spacetime is discrete? & Is the Planck length the smallest length that exists in the universe or is it the smallest length that can be observed?