---
author:
- Dan Kiselman
- 'Tiago M. D. Pereira [^1]'
- Bengt Gustafsson
- Martin Asplund
- 'Jorge Mel<span>é</span>ndez'
- 'Kai Langhans [^2]'
bibliography:
- 'bib-strings.bib'
- 'svst.bib'
- 'ads.bib'
- 'latitude.bib'
date: 'Received / Accepted '
subtitle: 'An investigation with SST/TRIPPEL'
title: 'Is the solar spectrum latitude dependent?'
---

<span> In studies of the solar spectrum relative to spectra of solar twin stars, it has been found that the chemical composition of the Sun seems to depart systematically from those of the twins. One possible explanation could be that the effect is due to the special aspect angle of the Sun when observed from Earth, as compared with the aspect angles of the twins. Thus, a latitude dependence of the solar spectrum, even with the heliocentric angle constant, could lead to effects of the type observed. </span> <span> We explore a possible variation in the strength of certain spectral lines, used in the comparisons between the composition of the Sun and the twins, at loci on the solar disk with different latitudes but at constant heliocentric angle. </span> <span> We use the TRIPPEL spectrograph at the Swedish 1-m Solar Telescope on La Palma to record spectra in five spectral regions in order to compare different locations on the solar disk at a heliocentric angle of 45. Equivalent widths and other parameters are measured for fifteen different lines representing nine atomic species. Spectra acquired at different times are used in averaging the line parameters for each line and observing position. </span> <span> The relative variations in equivalent widths at the equator and at solar latitude $\sim 45\degr$ are found to be less than $1.5\%$ for all spectral lines studied. Translated to elemental abundances as they would be measured from a terrestrial and a hypothetical pole-on observer, the difference is estimated to be within 0.005 dex in all cases.</span> <span>It is very unlikely that latitude effects could cause the reported abundance difference between the Sun and the solar twins. The accuracy obtainable in measurements of small differences in spectral line strengths between different solar disk positions is very high, and can be exploited in studies, e.g. of weak magnetic fields or effects of solar activity on atmospheric structure.</span>

Introduction {#sec:intro}
============

In recent studies it has been found that the chemical composition of the Sun, as compared with those of very similar stars, so-called solar twins, is systematically different: the Sun is comparatively less rich in refractories, i.e. elements that easily condensed to solids for instance in the solar protoplanetary nebula, than in volatiles . The range of the effect is about $20\%$ for volatiles as compared with refractories. Several possible explanations for this interesting phenomenon have been discussed , including cleansing of the protoplanetary disk by planetesimal formation. A more mundane explanation could be an obvious selection effect: in Earth-based studies the Sun is by necessity observed from a position close to the solar equatorial plane. The solar twins, on the other hand, are presumably observed with aspect angles randomly distributed with respect to their rotation axes. Thus, if the solar spectrum, integrated across the disk, for some reason were somewhat different as seen from a position far from the equatorial plane, the differences interpreted as abundance differences might have this explanation instead. An empirical way of exploring this is to observe solar photospheric spectra at different disk positions, though with a common angular distance from the disk centre so that the first-order centre-to-limb variations can be directly compensated for. Here, such a study is presented.

Studies of centre-to-limb variation of the solar spectrum have been pursued for more than a century [cf. @1873Natur...8...77H; @1907ApJ....25..300H] Some observational studies have been devoted to the question whether there are any differences between spectra from regions along the solar equator as compared with along a meridian. These studies have mostly been concentrated towards variations in line shifts and line shapes (bisectors) [e.g. @1976SoPh...46...29C; @1978SoPh...57...13C; @1980SoPh...68...41B; @1982SoPh...79....3B; @1984SoPh...94...49A], variations that <span>have generally been</span> interpreted as variations in the photospheric velocity fields with latitude. There are few studies of the variations, or constancy, in the line strengths (equivalent widths). One notable example is the study by of the variation along the equator and a meridian of four lines of , , and . In addition to studies of line widths and bisectors, these authors also included measurements of the variations of the equivalent widths. For , and lines they found the lines to be a few percent weaker along the equator than along the meridian at given $\mu\approx 0.6$, while the line showed less variation. Although not very pronounced this tendency has the direction needed to explain the apparently low ratio of refractories/volatiles in the Sun compared to the twins. However, three of the four spectral lines studied by Rodríguez Hidalgo et al. are on the flat part of the curve of growth, while the lines used in the analyses of @2009ApJ...704L..66M and are almost all on the linear part with line strengths insensitive to the velocity fields (among the lines of Meléndez et al. is 538.0322 nm which is the fourth line measured by Rodríguez Hidalgo et al.). Therefore, the qualitative tendency found by Rodríguez Hidalgo et al. cannot be used to infer what could be the effects on abundances derived from solar flux spectra at different aspect angles. Instead, a direct comparison of line strengths of the mostly weak lines used in the Sun–twin abundance comparison is needed.

It is clear from the previous work on the latitude dependence of the solar spectrum that considerable care must be exercised in positioning the spectrometer slit and averaging properly over granulation and other inhomogeneities. A strictly differential approach must be adopted, in order to minimise the effects of stray light and other instrumental issues.

Observations {#sec:obs}
============

The observations were made with the Swedish 1-m Solar Telescope (SST) on La Palma [@scharmer03new] employing the TRIPPEL spectrograph during the period of 3–15 May 2010. Since this instrument has not yet been subject to a detailed description in the literature, we use this opportunity to give a summary of its properties.

The TRIPPEL spectrograph
------------------------

The TRI-Port Polarimetric Echelle-Littrow (TRIPPEL) spectrograph had the following design goals:

-   allow simultaneous observations at three separate wavelengths

-   in principle exploit the full spatial resolution of the SST

-   wavelength range about 380nm – 1100nm

-   good polarimetric properties

-   moderate (for a solar spectrometer) spectral resolution ($R \approx 200,000$)

To achieve this, it is designed as a lens Littrow spectrograph with a ruled echelle grating. The design draws on the experience from the short Littrow spectrograph at the SVST [@scharmer85concepts the predecessor of the SST]. Some relevant numbers are given in Table \[table:trippel\] and a schematic view of the main optical designis shown in Fig. \[fig:trippelsketch\].

The slit is etched on a chromium-coated glass plate that is easily interchangeable and the reimaging lens of the SST could also in principle be changed to give another image scale. The spectrograph optics and the grating can accommodate a beam that is twice as fast as was used in the current setup (f/46). The slit plate can be rotated around a vertical axis to allow the reflected light to be directed towards slit-jaw imagers. It can also be rotated around an horizontal axis orthogonal to the optical axis to adjust the tilt of the slit relative to the dispersion direction. There are two movable jaws behind the slit plate that can be used to cover parts of the slit to minimise the amount of light entering the spectrograph, and to allow dark areas on the spectrum camera for reference.

The Littrow doublet lens is mounted on a translational stage. To get the required large diffraction-limited field-of-view, a meniscus field lens is placed close to the focal plane so that the light passes twice through it. The optical design fixes the Littrow lens position relative to this field lens. The translational stage is thus only used when checking the spectrograph focus and never for focusing the spectrograph cameras.

The grating from Richardson Grating Laboratory has excellent polarization properties, with the maximum difference between S and P efficiency being about 10% in the visual region. The grating is mounted on a rotational stage with 0.01 setting precision.

Three silver-coated mirrors pick off light to the exit ports. For the two ports with horizontal light beams (designated A and B), the cameras are mounted on holders sliding on a rail of the same type as is used for the SST imaging setups, thus allowing freedom in camera choice. The third port (C), which has a vertical light beam, currently uses a special holder for a Redlake Megaplus<span>ii</span> camera (ES1603).

Apart from some image distortion caused by the corrector lens, TRIPPEL has an off-plane design which leads to curvature of the spectral lines (smile) and also of the dispersion direction (keystone). The curvature over the typical CCD size is small, so the greatest effect of the smile is to cause the spectral lines to tilt relative to the axis defined by the direction of the grating grooves. The slit is rotated about 3.5 from the vertical direction to partly compensate for this.

Since all spectral orders fall on top of each other in the focal plane, interference filters placed just in front of the CCDs are used to select the desired order. This also has the advantage of blocking straylight outside the filter passband. The transmission profile of two-cavity filters typically has a base that is too wide to be practical, so three-cavity filters are used. Assuming a profile for a three-cavity interference filter, requiring that the transmission at a distance of a full spectral range from the central wavelength is $10^{-4}$ of its peak value, and applying a significant margin of safety, result in the filter widths in Table \[table:trippelparams\].

  ----------------------- ---------------------------
               Slit width 25 $\mu$m ($\approx$ 011)
         Grating constant 79.01 mm$^{-1}$
              Blaze angle 63.43
             Grating size $154\times 306$ mm
             Focal length 1500 mm
    Littrow lens aperture 135 mm
  ----------------------- ---------------------------

  : Some properties of the TRIPPEL spectrograph<span data-label="table:trippel"></span>

  ------------------------------------ ----------- ------------------- ----- ---------- --------------- --------
  <span><span>****</span>Line</span>    $\lambda$   <span>fwhm</span>    $n$  Bandpass   $dx/d\lambda$    $W$
                                         \[nm\]          \[nm\]               \[km/s\]     \[mm/nm\]     \[nm\]
                                         393.39            2              57    1.3          14.9         0.93
                                         457.11            2.5            49    1.3          13.0         1.06
                                         517.27            3              44    1.2          11.9         1.16
                                         630.20            5              36    1.2           9.6         1.44
                                         670.78            6              34    1.2           9.3         1.49
                                         866.20           10              26    1.3           6.7         2.05
  ------------------------------------ ----------- ------------------- ----- ---------- --------------- --------

  : Nominal TRIPPEL parameters at the wavelengths of some interesting lines.<span data-label="table:trippelparams"></span>

![Schematic view of the TRIPPEL spectrograph as seen from above. Components from left to right: entrance slit, pick-off mirrors for ports A-C, field lens, Littrow doublet, grating. Spectral port A has a CCD camera with an interference filter. <span data-label="fig:trippelsketch"></span>](trippelsketch){width="\columnwidth"}

The dispersion decreases with decreasing order and thus with increasing wavelength. The theoretical spectral resolution is limited by the slit width and so stays rather constant between different orders: it is between 1.1 and 1.4 km/s or $R={\lambda \over
  \delta\lambda} \sim 220000$. The resolution as found by our straylight-fitting routine is generally lower than this, but there is probably cross-talk between the spectral resolution and the straylight parameter in our model.

The spectral interval recorded by each camera is determined by the turning angle of the grating and the filter. With three ports, many combinations are possible, especially because some freedom of camera movement in the dispersion direction is available.

Table \[table:trippelparams\] lists some nominal <span><span>****</span>instrumental</span> parameters at the wavelengths of some interesting lines.

The spectrograph is focused by pressing a perpendicular slit against the spectrograph slit. This creates a small rectangle that is seen on the spectrum cameras as a very narrow spectrum. The Littrow lens is then moved between two out-of-focus position for a range of camera positions. The camera position where the two lens positions create spectra of similar sharpness is taken as its focus position. With some training it is not difficult to assess the sharpness from the spectrum image displayed on the screen.

The other crucial focusing, that of the solar image on the spectrograph slit, is done with a similar technique. But instead of placing a physical slit crossing the spectrograph slit, an <span>*image*</span> of a slit is placed there by mounting a physical slit in the telescope focus at the exit port of the vacuum system. The adaptive optics is locked on a pinhole next to that slit. The wavefront sensor is then adjusted (which leads to the image moving back and forth) until symmetry in the out-of-focus spectra is achieved.

Finally, TRIPPEL allows some auxiliary instruments. The wavefront sensor that controls the adaptive mirror and the correlation tracker camera are fed via a beamsplitter cube in front of the slit. The reflective slit plate makes slit-jaw imaging possible. For the current observations, we employed up to two slit-jaw cameras fed with reimaging optics. These cameras were equipped with interference filters with central wavelengths close to the spectral regions observed. The slit-jaw imaging was used for pointing control, and for keeping track of the seeing quality and the light-intensity level.

Spectral lines
--------------

  ---------------------------------------- --------------------------------------- -------- -------- -------------------------------------
    <span><span>****</span>Spectral</span> <span><span>****</span>Species</span>        CWL    $E_l$ <span><span>****</span>Class</span>
                                    region                                           \[nm\]   \[eV\] 
                                       538                                           538.03     7.58 volatile
                                       616                                           616.08     2.10 intermediate
                                       616                                           616.54     4.14 refractory
                                       616                                           616.64     2.52 refractory
                                       616                                           616.90     2.52 refractory
                                       711                                           711.14     8.64 volatile
                                       711                                           711.32     8.65 volatile
                                       768                                           768.61     7.87 intermediate
                                       768                                           769.90     0.00 intermediate
                                       777                                           777.19     9.15 volatile
                                       777                                           777.41     9.15 volatile
                                       777                                           777.53     9,15 volatile
                                       783                                           783.53     4.02 refractory
                                       783                                           783.61     4.02 refractory
                                       869                                           869.46     7.87 intermediate
  ---------------------------------------- --------------------------------------- -------- -------- -------------------------------------

  : Spectral lines observed <span data-label="table:lines"></span>

  ------------ -------- ----------------------------------- -------- ----------- ---- ---- ---- ------------ ------------ ------------ ----------- ----------- --
                 Port A                              Port C   Port B     DC       N    NW   W        SW           S            SE           E          NE      
          Date                                                        $-3\degr$   42   27   -3   $-32\degr$   $-48\degr$   $-32\degr$   $-3\degr$   $27\degr$  
    2010-05-05      538                                 711      783      5       1    1    1        1            1            1            0           1      
    2010-05-06      538                                 711      783      9       3    3    3        3            3            3            3           2      
    2010-05-07      538                                 711      783      7       3    1    3        1            3            1            3           1      
    2010-05-09      768   <span><span>****</span>...</span>      777      6       5    0    4        0            5            0            5           0      
    2010-05-14      768   <span><span>****</span>...</span>      777      1       1    0    0        0            0            0            0           0      
    2010-05-15      869   <span><span>****</span>...</span>      616      7       4    0    4        0            4            0            4           0      
  ------------ -------- ----------------------------------- -------- ----------- ---- ---- ---- ------------ ------------ ------------ ----------- ----------- --

In the present study we have selected some spectral lines used by @2009ApJ...704L..66M in their analysis of the Sun and solar twins, ensuring that both refractories, volatiles, and intermediate elements were represented and that as many lines as possible were observable simultaneously. The spectral regions were ranked in priority and the setup was changed to the next set of regions when enough data had been secured. Table \[table:lines\] lists the lines observed and Table \[table:obs\] the setup combinations used. Fig. \[fig:EWregions\] shows plots of all the lines in their spectral context of our solar observations.

Observations: strategy and practice
-----------------------------------

We assume that a latitude dependence of line equivalent widths that is strong enough to give a significant effect in the flux spectrum, must be present also at a moderate distance from solar disk centre. We choose a heliocentric distance of 45 degrees or $\mu = \sqrt{2}/2 \sim 0.71$. For the solar meridian, this corresponds to the point that is seen at the same $\mu$ for an observer in the ecliptic plane and one that would observe the Sun pole-on. It is also close to $\mu = 2/3$, which is where, according to the Eddington-Barbier relations, the outgoing intensity spectrum should be characteristic of the flux spectrum and thus relevant for stellar observations.

In order to decrease bias from north-south and east-west systematic differences, perhaps due to random activity patterns, we selected eight different position angles and named these points N, W, S, E, NW, SW, SE, and NE. To test the stability of the results, the solar disk centre was observed frequently and interspersed with the $\mu = 0.71$ pointings. The solar latitudes of the observed points are given in Table \[table:obs\]. The heliographic latitude at the time of observations was approximately $-3\degr$.

An observational sequence consisted of a series of pointings with about 5 min graylisa@example.com. Before and after each sequence flat fields were acquired. The sequence typically started at disk centre and then going to all the eight $\mu=0.71$ points, after which disk centre was observed again. All the time during observations, the Ca<span>ii</span> H imaging camera was used to make sure that the regions observed were quiet.

After the first days of observations when inspection of the data confirmed that the stability of the results was quite high, the intermediate points (NW, SW, SE, NE) were abolished from the observing sequence, and only observations in the N, W, S, and E positions, as well as the disk centre, were made.

The first data sets were taken with fixed pointing. In order to increase the spatial sampling, a procedure where the slit was scanning back and forth over 3was implemented. This was done via the correlation tracker.

Data reductions
---------------

The data reduction procedures follow those described by with few deviations. Each data set requires a set of flat-field and dark exposures. The flat-fields are acquired by taking many exposures while the telescope is scanning over a designated area around disk centre that should be devoid of spots. For the current observations, a new procedure was used where the adaptive mirror of the SST is fed with random voltages in order to smear out spatial structures even more. The darks are acquired with the light beam blocked close to the telescope exit window.

The flat-field exposures are used to compute <span>*gain tables*</span> and mapping the <span>*geometric distortions*</span> of the spectrograms. They are also used for wavelength calibration and scattered-light corrections in a procedure similar to that of , thus comparing the observed spectra with the Fourier Transform Spectrometer at the McMath-Pierce Telescope (hereafter called the FTS atlas) of @fts-atlas.

<span>*Wavelength calibration*</span> is done by fitting line cores. The resulting wavelength scale is thus that of the FTS atlas.

<span>*Straylight*</span> inside the spectrograph is treated as a constant which is determined simultaneously with the spectral resolution by a least-squares fit to the reference spectrum. Typical values are 5-6 % of the spectral continuum.

<span>*Telluric lines*</span> are identified and excluded from the fitting procedures.

Remaining artefacts in the continuum level – caused for example by residual components of fringes perpendicular to the dispersion direction– are also removed with the help of the reference spectrum. The result is a set of parameters that maps the observed disk-centre average spectrum to that of the atlas.

The process described above produces spectrograms ready for analysis. In the current work, we proceed by coadding each spectrogram over the spatial direction to get a one-dimensional spectrum that is the average spectrum under the spectrograph slit. A number of these spectra are then coadded, thus forming an average also over time. Various quantities for the spectral lines of interest are then calculated from such average spectra: <span>*Line centre*</span> is the velocity difference between the local line core and the calibration spectra –it is thus relative to the FTS atlas; <span>*FWHM*</span> is the usual full width at half maximum line depth; <span>*Line asymmetry*</span> is the distance between the local line core and the line bisector at half maximum line depth; <span>*Equivalent widths*</span> are measured by direct integration over a predefined interval which is centred on the line core and thus follows any local Doppler shift – this is illustrated in Fig. \[fig:EWregions\].

Data selection and error discussion
-----------------------------------

Sources of errors and other effects that would undermine the observational strategy could be imprecise and non-reproduceable pointing, seeing, variations on the Sun from granulation, oscillations, or activity, and instrumental drifts. Figures \[fig:CI538\]–\[fig:AlI783\] illustrates this by showing several disk-centre spectral profiles of three lines.

### Pointing

The exact pointing of the telescope is of utmost importance since the equivalent width of the most sensitive lines in our sample – the lines at 711 nm – is predicted to change by 5% for a 1shift ($\Delta \mu \approx 0.05$) along the radius vector. We used the solar limb in four positions to calibrate the telescope pointing before each sequence. After such a sequence we returned to the solar limb to estimate the drift in pointing during the sequence. Sometimes this error was found to be small but it could typically amount to 25.

The spectrograph slit is fixed in the laboratory frame and its orientation in the sky plane will change during the day. No effort was made to measure the orientation. The finite slit length ($\sim 50\arcsec$) thus adds to the positional <span>coverage of each spectrum, but does not affect the mean position of the slit.</span>

### Telluric lines

If a line is significantly blended with a telluric line, its measured properties will be a function of the airmass and thus the time of the observations. This is obvious for the  711.14 nm line as seen in Fig. \[fig:CI711\] <span>(where the standard deviation of $\Delta W/W
= 2.8\%$)</span>, but still this airmass dependence drowns in the noise for this weak line since no clear trend with time is visible in Fig. \[fig:plotw\].

### Impact of seeing

The ever-changing seeing causes the spatial resolution to vary with time. Because the current project does not require very high spatial resolution – indeed some spatial averaging is necessary and beneficial – one might surmise that seeing is irrelevant. We did not take that approach. Bad seeing implies that light from far away on the solar disk will be scattered into the spectrograph slit without any control. We therefore compared results from periods with different seeing but could not discern any significant differences in the measured line properties. Still we excluded the data sets with the worst seeing, and for those that were included, we kept the 50 best frames (100 for disk-centre spectra) as selected from continuum contrast values. We note that really bad seeing can cause tracking loss which itself is a source of error.

We caution, however, against assuming that seeing is unimportant in studies like this. We note that in our case the observed points were far from the limb, that the centre-to-limb variation of the equivalent widths are rather linear (thus symmetric blurring will still give the same results), and that the intensity spectrum at this $\mu$ should anyway be similar to the flux spectrum.

A similar comparison of data from periods where thin high clouds were intermittently in view gave a different result. Here the spectra did change significantly and any cloud-affected observations were subsequently excluded from analysis.

### Solar variations and instrumental stability

Intrinsic variations of the solar target and instrumental drifts can in principle be difficult to disentangle. Figure \[fig:long\] shows the result of a run where the telescope was pointed at disk centre for more than 20 min. Each point in the plot corresponds to one exposure. Pointing errors should be negligible here. As seen from the continuum contrast, the seeing was varying but improved during the period. The line-centre variations show clear evidence of 5-minute oscillations. The continuum intensity is clearly correlated with these. The variations of the other line parameters do not seem to correlate with oscillations but seem consistent with being caused by granulation – mainly from its time evolution but probably with contribution from slit drifts and rotation relative to the solar image. There is a noise envelope, probably caused by a combination of photon noise and seeing jitter, totally amounting to about 1% in equivalent width.

### Summary

All in all, the differential approach taken here should minimise many systematic errors. The results from the tests are consistent with the dominant errors being from solar variations and from pointing. These are random in nature, and given the number of data sets, it seems reasonable to use the spread of the individual data points – graphically shown in Fig. \[fig:plotw\] – to estimate the uncertainties in the mean values using the standard error of the mean <span>computed separately for the S+N data points and the W+E datapoints.</span>

![image](EW_regions){width="\textwidth"}

![Disk-centre spectra for 538 nm. Black 2010-05-05, Blue 2010-05-06. Red 2010-05-07. <span data-label="fig:CI538"></span>](CI538n){width="\columnwidth"}

![Like Fig. \[fig:CI538\] but for 711.14 nm. Note the presence of telluric lines whose strengths varies with the air mass.<span data-label="fig:CI711"></span>](CI711n){width="\columnwidth"}

![Like <span><span>****</span>Fig. \[fig:CI538\]</span> but for the two lines of at 783 nm. <span data-label="fig:AlI783"></span>](AlI783n){width="\columnwidth"}

Quiet Sun results {#sec:qsresults}
=================

Figure \[fig:plotw\] displays the equivalent widths from all data sets. Different symbols are used for the four different disk positions. From the plots alone, no clear difference between the different disk position is obvious for any line, with one possible exception. We note that for the three lines, four of the S points lie below all of the N points. The fact that the fifth point does not indicates that this N-S divergence may be due to activity or erroneous pointing since the four deviating data sets were recorded on a different day.

Figure \[fig:lat\_var\] illustrates the data points by showing examples of line profiles for the different disk position for four lines as recorded during the same day. Computing the mean values separately for the S+N and E+W disk positions, and using the standard error in each mean value as error estimate, gives the result in Figure \[fig:wdiff\]. Here, the relative difference in low-latitude (average of E and W) and high-latitude (average of N and S) equivalent width, $${\Delta W\over
      \langle W\rangle} = {(W_{low} - W_{high})\over \langle W
      \rangle},$$ is plotted for each line. The error bars are the standard errors in the mean values (1 $\sigma$). The departure from zero of the relative differences $\Delta W/\langle W\rangle$ must be considered insignificant.

Our initial goal was to estimate the difference between the spectral analysis an observer close to the equatorial plane of the Sun and one who sees the Sun pole on. The polar observer will see a flux spectrum which is characterised by our high-latitude spectra. The equatorial – or terrestrial – observer will see a flux spectrum that is a mix of low-latitude and high-latitude contributions. We approximate this mix to be 1:1. Thus the effective relative difference in flux equivalent width is $${\mathbf{ \Delta W^{eff } \over \langle W\rangle} = {1\over 2}{\Delta W\over  \langle W\rangle}} .$$

The final result is shown in Fig. \[fig:adiff\] where the difference in derived abundances per element is plotted as a function of condensation temperature. The average values used for this plot were computed without any weights.

The difference in derived abundance is computed with the help of theoretical LTE curves of growth <span><span>****</span>using</span> $\mathbf{\Delta W^{eff}/ \langle  W\rangle}$ as input. The difference between "polar" and "equatorial" abundances is within 0.005 dex for all elements and to within 0.002 dex for the refractory elements. The error bars are computed directly from those in Fig. \[fig:wdiff\]. It is clear that there is no significant difference and that, in particular, no trend with condensation temperature is present.

Solar activity {#sec:activ}
==============

The principal goal of this work was to look for possible latitude-effects in the quiet Sun and efforts were made to avoid any activity. The result was negative, but that leaves the possibility that the Sun, or a star, could have significant inclination-dependent spectra due to activity. The point is that even if two stars have the same level and kind of magnetic activity as the Sun, the active regions tend to keep to lower latitudes. Alternatively, one could argue that the studies by @2009ApJ...704L..66M and were made when the Sun was in an unusual deep activity minimum. It the solar twins happened to have systematically higher levels of activity, perhaps their spectra would be different, regardless of inclination angle.

An investigation of this possibility is beyond the scope of this paper. (During our observing run, some data were in fact acquired from regions of moderate activity but the amount of data is not enough to allow any conclusions.) However, some tentative remarks can be made based on the existing literature.

It seems likely that lines that are strongly affected by activity also would display a variation with the solar cycle. Indeed, the long-term monitoring of solar spectral features of @2007ApJ...657.1137L shows that some strong lines with chromospheric contributions display variations in phase with the solar cycle. But among weaker, clearly photospheric, lines only 539.47 nm shows equivalent-width variations of 2 % during the cycle. The reason why this line is special is explained by as due to its strong hyperfine broadening leading to a lack-of-broadening-in-granules effect and very high contrast of magnetic structures in the line. Otherwise, 538 nm was found to be constant by @2007ApJ...657.1137L within 1.5% ($\Delta \log \epsilon < 0.006$dex) with no signs of cycles or trends as were other photospheric lines, e.g. the 777-nm triplet whose equivalent widths all lie within their noise envelope of 1%.

So, while the influence of magnetic activity on lines used for abundance analysis is well worth more investigations, it is unlikely to explain abundance patterns like those found by @2009ApJ...704L..66M and .

Discussion and conclusions {#sec:concl}
==========================

We draw the following conclusions:

The TRIPPEL Spectrograph performs well and has a high stability suitable for comparative studies of the kind presented here.

The method of differential comparison is precise and insensitive to, e.g., seeing variations.

The difference in equivalent widths for the lines observed at the equator and at latitudes around 45is less than $1 \%$ at $\mu = \sqrt{2}/2$, <span>except for the telluric-afflicted  711.1 nm line</span>. Our results exclude the possibility that the effect found by @2009ApJ...704L..66M in the comparison of the composition of the Sun with those of the solar twins, for refractories relative to volatiles and amounting to about $20\%$ in elemental abundance, could be due to the systematically different aspect angles when observing the Sun relative to the twins.

Finally, we note that while we have argued that it is unlikely that solar activity could modify our qualitative conclusions, the effects of magnetic activity on abundances derived from high-resolution spectra need further investigation. A natural follow-up study to the current work would be to apply the same methods to explore in detail the differences between photospheric spectra in solar active regions, as compared with inactive regions. In the present age of high-precision spectroscopy, in particular in detailed differential work, it may be important to take the activity state into consideration when detailed abundance analysis is made.

The Swedish 1-m Solar Telescope is operated on the island of La Palma by the Institute for Solar Physics of the Royal Swedish Academy of Sciences in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrof<span>í</span>sica de Canarias. BG acknowledges support from the Swedish Research Council, VR. J.M. thanks support from FAPESP (2010/17510-3). K.L. was funded by the European Community's Human Potential Program through the European Solar Magnetism Network (contract HPRN-CT-2002-00313).

[^1]: Current Address: NASA ARC, Mail Stop 245-3, P.O. Box 1, Moffett Field, CA 94035, USA

[^2]: Current address: Gothmunder Weg 8, 23568 L<span>ü</span>beck, Germany

{'source': 'arXiv_out/1108'}