A Close Relationship between Lyman Alpha and Mg II in Green Pea Galaxies
Alaina Henry Danielle Berg Claudia Scarlata Anne Verhamme Dawn Erb
 
 
 

1Space Telescope Science Institute,  3700 San Martin Drive, Baltimore, MD,  21218, USA ahenry@stsci.edu 
2Department of Physics & Astronomy, Johns Hopkins University, Baltimore, MD 21218, USA
3Center for Gravitation, Cosmology, and Astrophysics, Department of Physics, University of Wisconsin Milwaukee, 3135 Maryland Ave, Milwaukee, WI 53211, USA
4Minnesota Institute for Astrophysics, School of Physics and Astronomy, University of Minnesota, 316 Church Str. SE, Minneapolis, MN 55455, USA 
5Observatoire de Genève, Université de Genève, 51 Ch. des Maillettes, 1290 Versoix, Switzerland 
*Based on observations made with the NASA/ESA Hubble Space Telescope, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-26555.  These observations are associated with program 12928, 11727, 13744, and 14201.
†Observations reported here were obtained at the MMT Observatory, a joint facility of the Smithsonian Institution and the University of Arizona. 


The  doublet is often used to measure interstellar medium absorption in galaxies, thereby serving as a diagnostic for feedback and outflows. However,  the interpretation of Mg2 remains confusing, due to resonant trapping and re-emission of the photons, analogous to .  Therefore,  in this paper, we present new MMT Blue Channel Spectrograph observations of Mg2 for a sample of 10 Green Pea galaxies at z∼0.2-0.3, where   was previously observed with the Cosmic Origins Spectrograph on  Hubble Space Telescope. With strong, (mostly) double-peaked  profiles, these galaxies allow us to observe Mg2 in the limit of low H1 column density.  We find strong  Mg2  emission and little-to-no absorption.  We use photoionization models to show that nebular Mg2 from H2 regions is non-negligible, and the ratios of / λ5007 vs.  λ5007/ λ3727  form a tight sequence.  Using this relation, we predict intrinsic Mg2 flux, and show that Mg2 escape fractions range from 0 to 0.9.  We find that the Mg2 escape fraction correlates tightly with the  escape fraction, and the Mg2 line profiles show evidence for broader and more redshifted emission when the escape fractions are low.    These trends are expected if the  escape fractions and velocity profiles  of  and Mg2 are shaped by resonant scattering in the same low column density gas.  As a consequence of a close relation with ,  Mg2  may serve as a useful diagnostic in the epoch of reionization, where  and Lyman continuum photons are not easily observed.   

 



§ INTRODUCTION
 
In the spectra of star-forming galaxies, interstellar and circumgalactic medium (ISM and CGM) absorption in the  doublet has been used to study galactic outflows <cit.>.    At z∼ 1,  alongside a complex of near ultraviolet (NUV)  Fe2 lines, the Mg2 lines are redshifted into the rest-frame optical where they are readily observed from the ground.    Consequently, as a diagnostic, Mg2 plays an important role for measuring the evolution of galactic outflows, feedback, and the CGM. 

Despite its potential usefulness, most studies acknowledge that, as a resonance feature, the  doublet can be complicated to interpret.   
The lines are commonly observed with P-Cygni profiles, showing blueshifted absorption and redshifted emission.    This line shape is produced when the absorbed photons scatter in a moving envelope of gas.  The detection of P-Cygni emission implies that the pure absorption profile has been “filled in” by re-emission of absorbed photons.  Hence, absorption-line measurements of outflow velocity, column density, and line saturation can be incorrect <cit.>.   
Nevertheless, the  doublet lines are strong, giving sensitivity to low column densities of gas.  
Modeling of the expanding medium generating the P-Cygni profile  can also constrain the 
geometry, velocity, and density of absorbing and emitting gas (, Carr et al., submitted), thereby providing measurements of mass outflow rates.   Therefore, including Mg2 alongside other UV lines can be useful as we aim to leverage all available information to understand outflows and the CGM. However, these features must be interpreted carefully.  








The interpretation of  is further complicated by  a possible contribution from nebular emission.  
Both <cit.> and <cit.> point out that photoionization models predict appreciable
  emission from H2 regions.  While this emission is erased by absorption in most cases, Erb et al. argue that it may account for the differences in the observed profiles of Mg2 and Fe2 
 in galaxies at z∼2.   
    Remarkably,  nebular  Mg2  has been detected from some regions of Orion <cit.>, 
 and in some SDSS spectra of galaxies at z>0.36 <cit.>.  
   Recently,  <cit.> report Mg2 emission from a  low-redshift Lyman Continuum leaker, and  <cit.> observe that Mg2 profiles transition from absorption to pure emission in z∼ 1 galaxies with M  10^9  M_.  Mg2 emission is even seen in the supernova Refsdal host galaxy <cit.>. 

   
    
 Importantly, the production of nebular line photons, and subsequent resonant scattering in
 neutral/low ionization state gas is  identical to the  line.  In fact, some observations have suggested 
 that we may find similarities between these two features.    First,  studies of galaxies at z∼ 1-2 have reported that  
  Mg2  emission is more common in galaxies with lower masses, higher specific star-formation rates, and blue colors <cit.>. 
  These are the same properties that appear to favor  emission from galaxies  <cit.>.  Second, spatially extended  Mg2  has been detected in two 
intermediate redshift galaxies <cit.>, analogous to the ubiquitous  halos seen at both low and high redshifts <cit.>.    Nevertheless, in the only study that has compared  and  Mg2 to date, <cit.> find no correlations for a sample of five galaxies. 



 cccccccccc[!t]
9
Green Pea Sample 

ID       RA      DEC      za    E(B-V)_MWb        Exposure Timec      SDSS u      Slit Loss Correctiond     COS Gratingse 
 
        (J2000)      (J2000)           (mag)         (seconds)            (mag)      
 
0911+1831     09 11 13.34     18 31 08.2        0.26224       0.025        4 × 1800      19.8     2.0      G130M, G160M 
 
0926+4427     09 26 00.44        44 27 36.5         0.18070       0.017       4 × 1800     19.2    2.4     G130M, G160M  
 
1054+5238     10 53 30.80       52 37 52.9          0.25265      0.013         3 × 1800    19.0     2.0     G130M, G160M  
   
1137+3524      11 37 22.14     35 24 26.7         0.19440       0.016       3 × 900    19.1        1.5      G130M, G160M  

1219+1526     12 19 03.98      15 26 08.5         0.19561       0.024       4 × 1800     19.8      1.9     G130M, G160M 
  
1244+0216     12 44 23.37        02 15 40.4          0.23942      0.021        3 × 1800      19.6        2.1      G130M, G160M  

1249+1234     12 48 34.63      12 34 02.9         0.26340      0.025      4 × 1800     20.2      1.4        G130M, G160M 

1424+4217      14 24 05.72      42 16 46.3         0.18480      0.009       3 × 2000      19.3       1.6      G130M 
 
1440+4619       14 40 09.94       46 19 36.9      0.30076      0.012    3 ×  600     19.8      1.8      G160M  
  
1442–0209f      14 42 31.37       –02 09 52.8     0.29367     0.047       3 × 1800     21.5       2.9       G160M 
 

a The redshifts are determined from SDSS spectra, which have uncertainties of order a few .
bThe Milky Way extinction values are from <cit.>, acquired from the NASA Extragalactic Database.   We use the <cit.> extinction curve to correct the UV spectra for foreground attenuation.  
cAn exposure time specified, for example, as 3 × 1800 implies that three 1800 second exposures were combined. 
dThe slit loss correction is estimated by calculating the SDSS u-band magnitude directly from each spectrum, and comparing this result to the imaged SDSS u-band magnitude.    
eThe COS gratings used for comparison in this paper; low resolution gratings were not considered.
fThis Green Pea galaxy was drawn from the <cit.> sample of Lyman Continuum leakers. 
  



For most redshifts, the wavelengths of Mg2 and  have made comparison between the lines difficult.  Consequently, 
more questions than answers remain about the interpretation of Mg2, its similarities or differences with  and other ISM absorption lines, and its ability to serve as a diagnostic for outflows.    To address these issues, in this paper we present the first observations of Mg2 from z∼ 0.2-0.3 Green Pea galaxies.  With existing high-resolution, high signal-to-noise   and far ultraviolet (FUV) ISM absorption line spectra <cit.>, we are able to compare the Mg2 to other widely-used diagnostics.    This sample allows us to explore Mg2 in the limit of low H1 column density that has been inferred from  profiles  <cit.> and, in some cases, Lyman Continuum (LyC) leakage <cit.>.  By focusing on this select set of rare, nearby galaxies, we can aim to better understand Mg2 under physical conditions that may be common at high-redshifts.  Ultimately, as we will demonstrate, Mg2 observations of these galaxies form a strong motivation for increased samples, covering a greater dynamic range of galaxy properties.    



This paper is organized as follows.  In <ref> we present our sample, observations, and data reduction.    In <ref>  we show that the Green Pea galaxies have consistent strong  emission and almost no absorption.  We present measurements of these emission lines, and predictions for intrinsic Mg2 strength using Cloudy photoionization models <cit.>.    Using this intrinsic Mg2  prediction, we calculate Mg2 escape fractions, analogous to  escape fractions.   In <ref>  we explore how the Mg2 escape fraction, equivalent width, and line velocity structure vary due to radiation transport effects, showing that Mg2 escape fractions form a tight sequence with  escape fractions. Finally, <ref> summarizes these results and discusses their implications, considering the utility of Mg2 as a diagnostic in the epoch of reionzation.  Throughout this paper, we adopt a convention where positive equivalent widths refer to emission, while negative equivalent widths indicate absorption. 






§ SAMPLE, OBSERVATIONS, AND DATA
 
 
Green Peas are a sample of z∼ 0.2 galaxies with extremely high-equivalent width emission lines <cit.>, 
making them compelling analogs for high-redshift objects. 
We have selected ten such galaxies for observations in the  doublet, using two main criteria.  First, we require that the objects have existing observations of  and UV continuum from the Cosmic Origins Spectrograph (COS) on the Hubble Space Telescope, with sufficient sensitivity to measure metal absorption lines.  Second, we chose objects with z>0.18, placing  at observed wavelengths greater than 3300 Å.   We chose eight of the ten galaxies from the Green Peas presented in <cit.>, adding one galaxy from Yang et al. (2017; HST GO 14201), and a LyC leaker from Izotov et al. (2016; HST GO 13744).    All of the supplemental COS observations use the high-resolution G130M and/or G160M gratings.  The sample is listed in Table <ref>.    Figure <ref> shows their COS NUV target acquisition images. 

We observed these ten galaxies using the Blue Channel Spectrograph <cit.>  at the MMT on 28-29 March 2017.    
A 1 slit was used with the 832 lines mm^-1 grating at second order, achieving a spectral resolution of 90 km s^-1. The central wavelength of 3605 Å provided wavelength coverage from 3150 to 4090 Å in the observed frame.    Total exposure times were chosen to obtain an estimated continuum signal-to-noise (SNR) of ten per spectral resolution element, and were divided into three or four exposures per object.  Since atmospheric dispersion is significant at these wavelengths <cit.>, we ensured that the observations were carried out at the lowest possible airmasses (less than 1.25, except for 1442-0209 which reached 1.36).    We also reset the slit position angle for each exposure, choosing the parallactic angle midway through the exposure.  Likewise, because the Blue Channel Spectrograph does not compensate for flexure, arc lamp exposures were taken before the observation of each object.   Finally, we note that observing conditions were non-photometric, with light cirrus and variable seeing around 1. 




The spectra were processed using ISPEC2D <cit.>, a long-slit spectroscopy data reduction package written in IDL,
and then extracted and calibrated using standard IRAF procedures.
A master bias frame was created from 10 zero-second exposures by discarding the highest and lowest value at each pixel and taking the median.
Master sky and dome flats were similarly constructed after normalizing the counts in the individual images.
Those calibration files were then used to bias-subtract, flat-field, and illumination-correct the raw data frames.
Due to faint continuum in individual exposures, the multiple sub-exposures of each target were median combined prior to extraction,
also eliminating cosmic rays in the process.
Extraction of the one-dimensional spectra was performed using a box-car aperture capturing 99% of the light in the Mg2 feature
and a median sky subtraction along each column of the dispersion direction. 
For each object, the wavelength calibration was applied from the HeArHgCd comparison lamps taken at the same telescope pointing.
A sensitivity curve was derived from several standard stars observed during twilight,  and used to flux calibrate the individual 1D spectra. This spectrophotometric data reached 3200 Å, so although our Blue Channel spectra reached 3150 Å, we do not consider these wavelengths in any analysis.   Finally, the spectra were corrected to a heliocentric velocity reference frame, using IRAF's rvcorrect  procedure.   


 
Since we aim to measure Doppler shifts for the Mg2 lines, we tested the accuracy of our wavelength calibration.  For this check, we compared our data to the night sky spectrum from , taken with the Ultraviolet and Visible Echelle Spectrograph (UVES) on the Very Large Telescope (VLT).   This spectrum has an average wavelength accuracy of 17 mÅ (1.5  at 3400 Å).  First, we downgraded this high resolution spectrum to 90 , and rebinned it to match the Blue Channel data.  Then we cross-correlated the spectra in 200 Å segments to derive any residual velocity shifts between the UVES and Blue Channel data.   We find that, for some wavelengths, the VLT and MMT sky spectra show substantial time, airmass and/or site-dependent variations that limit the utility of this method.  Nevertheless, at wavelengths where the spectra appear to have a similar spectral-morphology, this test indicates that the calibration in our data is accurate to 20 .  


In order to compare the MMT spectra with SDSS and COS observations, we calculate slit-loss corrections to place the Blue Channel spectra on an absolute flux scale.  We convolve each spectrum with the SDSS u-band throughput   (λ_center∼ 3600 Å, FWHM ∼ 500 Å), 
calculating a synthetic u-band magnitude for the Blue Channel data.  Comparing to the SDSS photometry, we find that a factor of around two is required to correct for slit-losses and non-photometric conditions.  The SDSS u-band magnitudes and slit-loss corrections are given in Table <ref>, and are applied to the Mg2 fluxes in <ref>.  Although we do not detect Mg2 emission extending beyond the continuum, we acknowledge that these corrections could still be lower limits for the lines, if extended, low surface brightness  line emission is missed by our observations. 


Finally, we combine these observations with COS spectroscopy covering  and FUV absorption lines.  We described the data in detail in <cit.>.   In brief, we estimate  that the spectral resolution is 20-40  for compact continuum emission, degraded only somewhat from the optimal point source spectral resolution.    Measurements of the Milky Way ISM absorption lines and CIII 1175.5 Å photospheric absorption in the Green Peas implies a redshift precision around 30 .    We rebin the spectra in bins of 20 pixels for continuum and absorption lines (around 45 ) and 10 pixels for .   Noise in the binned spectra is estimated by summing the photon counts in each bin and calculating the Poisson noise according to <cit.>.  The Green Peas 1440+4619 and 1442-0209, which were not originally in the <cit.> sample, have been treated in the same manner.    We do not correct the COS spectra for aperture losses, which, for ,  are mostly unknown, but significant when measured <cit.>.   As a result, the  measurements give a sense of the flux that escapes from the central few kpc of these compact galaxies.  






§ ANALYSIS
 
 
The Mg2, , and Si2 spectra are shown in Figures <ref> and <ref>.    The most striking observation in these figures is the strong Mg2 emission and weak (or absent) absorption, similar to the Mg2 emitters reported by <cit.> and <cit.>.    
This finding strongly suggests that Mg2 originates as an emission line, which is not erased by absorption in these galaxies. 

 However, we still see effects of scattering on lines:  in each galaxy, the Mg2 lines are systematically redshifted.   Moreover, the FWHM of the lines range from 100 to 300 ,  in  some cases, broader than we observe in the optical nebular lines.   In contrast, however, we see no evidence that Mg2 is extended beyond the continuum (e.g. ). Remarkably, the Mg2 spectra bear no resemblance to the Si2 lines shown in the bottom rows of  Figures   <ref> and <ref>.   We will return to this puzzling observation in <ref>. 

 


  



 §.§ Measurements
 
To further understand the unusual Mg2 emission, we measure fluxes, equivalent widths, peak velocities, and FWHM from these lines.  Each spectrum is normalized around the Mg2 lines using a linear fit to continuum regions spanning several thousand  around the systemic velocity.   We find
that the statistical uncertainty on the continuum normalization is a few percent or better, although visual inspection of the data suggests an approximately 5% systematic uncertainty.  Next,  we divide the spectrum into two regions corresponding to each line, using the midpoint between the two lines, λ_rest = 2799.1 Å.   Bluer wavelengths are assigned to the 2796 Å line while redder wavelengths are assigned to the 2803 Å line.  Then, we calculate the equivalent width weighted velocity of each line, v_peak, as a nonparametric means of centroiding the emission (see ).   Since some lines show minimal absorption blueward of the 2796 Å line, we measure a  blueshifted velocity where the absorption meets the continuum. For the 2796 Å line, the fluxes and equivalent widths are integrated to this maximal velocity.  In the case of 1440+4619, the emission is mostly erased by this absorption.  
 Finally, errors are calculated through a Monte Carlo simulation where we perturb the spectrum according to its errors, repeat the measurements, and calculate the RMS. 



The Mg2 measurements are likely impacted by stellar Mg2 absorption.   <cit.> highlight how this absorption varies with the characteristic age of the stellar population, showing that weaker absorption corresponds to younger stellar populations.   In order to quantify this absorption for the present sample, we 
measured the absorption equivalent width in the Binary Population and Spectral Synthesis (BPASS v2.0; ) models that we use for photoionization modeling in <ref> (see below).     At the resolution of these models, the Mg2 lines are blended.  Nevertheless, we find a minimum  W_stellar = 0.2 at ages of a few Myr (for both bursts and continuous star-forming models).   An upper limit on  W_stellar can be inferred by considering the maximum plausible ages that can still
produce  W_H α≳ 300 Å, typical for Green Peas.   This requirement implies that the ages can be at most a few hundred Myrs for continuous star-forming models, which corresponds to  W_stellar < 1.0 in the BPASS models considered here.   Therefore, we adopt   W_stellar = 0.6; since the Mg2 lines are unresolved in the stellar models, we apply a 0.3 Å correction to the equivalent width of each Mg2 line, and scale the measured fluxes accordingly. 
The Mg2 measurements are presented in Table <ref>.





 



For the COS spectra, we compile several measurements from <cit.>, repeating that analysis for 1440+4619 and 1442-0209.  First, we include the  escape fractions,   = F() /  (8.7 × F(Hα)_corr),  where F()_corr is corrected for dust (according to ). For this calculation, we use an intrinsic / ratio of 8.7, since these Green Pea galaxies have elevated electron densities (n_e = 100 - 700 cm^-3), which increases  / above the Case-B low density limit of 8.1 <cit.>.   The , Mg2, and Si2 spectra in Figures <ref> and <ref> are shown in order of increasing .   Second, in addition to  escape fractions, we include kinematic measures for the  lines.   We measure the peak velocities,  v_blue^peak and v_red^peak, since peak separation is sensitive to the H1 column density <cit.>, and has been shown to correlate with  <cit.>.   Finally, velocities and equivalent widths of FUV absorption can also be compared to Mg2.    For  1440+4619 and 1442-0209, we either do not convincingly detect the low-ionization  (LIS) metal absorption lines (Si2 and C2)  that trace H1, or we find that the spectra are contaminated by foreground Milky Way absorption.  Therefore, we either set upper limits on the equivalent widths at W_ LIS -0.5 Å, or exclude the lines.   For the remainder, we take the measurements from <cit.>, and do not reproduce that tabular data here.  Since these lines are often weak in Green Peas and similar galaxies <cit.>,  we mostly focus on  in this paper, but we do consider whether Mg2 varies with W_ LIS in <ref>.  To conclude, the Mg2 and  measurements are reported in Tables <ref> and <ref>. 







 §.§ Calculating Mg2 Escape Fractions with Photoionization Models
 
 
In order to understand how the observed Mg2 varies due to scattering and absorption in
the ISM and CGM, we must first account for the intrinsic variations in the Mg2 produced in H2 regions.  Therefore, we aim to predict the intrinsic Mg2 fluxes, using  photoionization models constrained by the physical properties determined from the SDSS spectra (i.e., oxygen abundance and electron density, n_e).   Fortunately, for the Green Peas in our sample,  significant detections of the temperature-sensitive  λ4363 auroral line allow accurate determinations of the oxygen abundance using the “direct” method[While there has been a long-standing debate over the accuracy of the “direct” method, recent studies have shown remarkable agreement between stellar and “direct” method nebular abundances in typical nearby galaxies <cit.>.  Therefore, we judge the gas-phase metallicity calibration as accurate to around 0.2 dex. ].
We follow the procedure described in <cit.>[Specifically, we use the IDL-based IMPRO routines (<https://github.com/moustakas/impro>), along with the atomic data in <cit.>.] to determine electron densities and direct method abundances.   For this calculation, we correct the emission lines for internal dust attenuation using the reddening law of <cit.>, and also use the theoretical  <cit.> relationship to estimate the [O2] electron temperature from the measured [O3] temperature.  The electron densities were measured from the  [S2] λλ6716, 6731 doublet, and ranged from 100-700 cm^-3.  The metallicities are between 12 + log(O/H) = 7.9 to 8.2 (Z_gas = 0.16-0.32 Z_,  where Z_ corresponds to 12 + log(O/H) = 8.69; ), and are listed in Table <ref>. 
 
For photoionization modeling, we use Cloudy version 17 <cit.>, considering a range of ionizing spectra with sub-solar metallicities.   
First, we include fourteen models from Starburst99 <cit.>.  In brief, these are: the Padova models, with and without AGB stars, at  Z_stars = 0.0004, 0.004, 0.008  (Z = 0.029, 0.29, and 0.57 Z_, where Z_ = 0.014); the Geneva models with standard and high mass loss rates at Z_stars = 0.001, 0.004, 0.008;  and the Geneva models with and without rotation at Z_stars=0.002 (Z = 0.14 Z_).   In all Starburst99 models, we use the <cit.> stellar initial mass function (IMF). Second, we consider the Binary Population and Spectral Synthesis models (BPASS v2.0 and  v2.1; ), which include the effects of binary evolution and produce harder ionizing spectra than Starburst99.  For these models, we include metallicities of  Z_stars = 0.001, 0.002, 0.004, 0.008 (Z = 0.07, 0.14, 0.29 and 0.57 Z_) and use the fiducial IMF, which has a slope of -1.30 between 0.1 and 0.5M_ and -2.35 above 0.5M_.  For BPASS v2.1, we also include the Z_stars = 10^-4 and 10^-5 models.  For all BPASS models, we consider the IMFs both with 100 and 300M_.   Finally,  we select both constant star-forming models and bursts aged 1, 3, and 10 Myrs for both BPASS and Starburst99, except for BPASS v2.1, where only the bursts are available. 

Following <cit.>,  the photoionization models were run using a  plane-parallel geometry.  The ionization parameter, U, was varied between -3.3  <  log  U < -1.5 in 0.3 dex increments.  Models were calculated for three gas-phase metallicities, allowing for systematic uncertainties by covering a slightly broader range than our measurements: Z_gas =0.1, 0.25,  and  0.4  Z_.  Likewise, we calculated  models over the range of densities measured for our sample: n_e = 10^2.0, 10^2.4 ,   and 10^2.8 cm^-3.   Finally, we chose the Orion dust grains,  and a solar relative abundance pattern <cit.>.  Here, we  do not require the stellar and gas-phase metallicities to match,  as non-solar α/Fe abundances can give the appearance of decoupled stellar and nebular metallicities <cit.>. 

We explored a number of line diagnostic diagrams in order to predict Mg2 from the optical 
spectrum of the Green Peas.  This exercise showed that Mg2/[O3] λ5007 forms a tight sequence with the ratio [O3] λ5007/[O2] λ3727, as illustrated in Figure <ref>.   Here, we show Mg2 λ 2796 /[O3] λ5007.  The same plot with Mg2 λ 2803 /[O3] λ5007 appears similar, with only a factor of two difference set by the intrinsic Mg2 λ 2796 / Mg2 λ 2803 ratio.  

We find that this sequence does not depend  on the stellar model, as harder ionizing spectra move the line ratios down and to the right along the sequence.  This effect can be seen in Figure <ref>,  as each set of colored points (a single ionization parameter) is shown in a cluster of 5 “rows”, each corresponding to a BPASS v2.0 model with a different stellar metallicity.   Likewise, gas-phase metallicity moves the line ratios roughly orthogonally to the sequence.  Hence, metallicity plays a key role in setting the scatter in Figure <ref>.   We have conservatively considered gas-phase metallicities 0.1 dex lower and higher than we have measured, as we will use this scatter below to estimate the uncertainty on the predicted intrinsic Mg2 flux.

 


Figure  <ref>  shows only continuous star-forming BPASS models with n_e = 10^2.4.   Nevertheless, for the ionizing spectra with sub-solar metallicities that we consider here, all reasonable Starburst99 and BPASS models fall along the same sequence, regardless of star-formation history or IMF upper limit.  Still, we verified that this sequence is robust to several other changes in the models.  First, changing n_e shifted the line ratios by only a negligible amount.   
Second, we  considered the effects of reduced dust depletion, as <cit.> show that dust-to-metal ratios may be lower at lower metallicity.  We ran a subset of Cloudy models with no grains, finding that Mg2/ ratios would be higher by around 0.1-0.2 dex over the O32 range covered by our sample.  However, since this limiting case is extreme, we infer that uncertainties in dust depletion probably lead to line ratios that fall within the 0.1 dex scatter in Figure <ref>.    
Third, we explored how an active galactic nucleus  (AGN) may impact the inference of intrinsic Mg2.    We ran Cloudy models, extending to gas-phase metallicity of Z_gas = 2.0 Z_, and using Cloudy's default AGN spectral template: T = 1.5 × 10^5 K for the  “Big Bump” component,  an X-ray to UV ratio, α_ox = -1.4, and the low-energy slope of α_uv  = -0.5.  We find that the O32 range covered by our sample is reached at super solar gas-phase metallicities, with Mg2/ ratios 0.2-0.3 dex lower than the sequence in Figure <ref>.  Therefore, this AGN model would predict weaker intrinsic Mg2 emission by a factor of 1.5-2, possibly even weaker than the observed Mg2 fluxes.  We note, however, that the Green Peas show no evidence for the presence of an AGN.      Finally,  we tested some ionizing spectra with super-solar metallicities, and found a number of model grid-points may fall below the tight sequence in Figure  <ref>.  Likewise, the 10 Myr aged burst, with BPASS v2.1 spectra does not produce realistic line ratios for the Green Peas  (e.g. /< 1).  Hence, we exclude these models from consideration.  We conclude that the sequence in Figure <ref> should be robust for our sample. 


Figure <ref> demonstrates that, with [O3] λ5007/[O2] λ3727 alone, we can predict the intrinsic  Mg2/[O3] λ5007 to within 0.1 dex for these Green Peas. This figure also shows the polynomial fit to our full set of BPASS v2.0 model grids, for the IMF with a 100 M_ upper mass cutoff.  These relations are: 

    R_2796   = 0.079 × O32^2   - 1.04× O32  - 0.54
 
and 

    R_2803   = 0.098 × O32^2   
    
      - 1.02× O32  - 0.84,
  
where  

    R_2796 = log   (Mg II  λ 2796 /[OIII]  λ 5007),  
     R_2803 = log   (Mg II  λ 2803 / [OIII]  λ 5007),  
     and
     O32 =   log ([ O III] λ 5007 / [ O II] λ 3727).
 
We reiterate that these relations are valid over the gas-phase metallicities that we consider here: 12+log(O/H) = 7.8 - 8.3 (Z = 0.1 - 0.4 Z_).  Higher gas-phase metallicities tend to move points down and to the left in Figure  <ref>, increasing the scatter to a value more like 0.2 dex.  In this case, deriving a unique best-fitting Cloudy model for each galaxy may be a better strategy than using the relations given here.
 
 

 


Finally, given the intrinsic  Mg2/[O3] λ5007 ratios, we can calculate the fraction of Mg2 photons that escape the galaxies.    We use the   and  lines  (corrected for dust using )  to predict the intrinsic Mg2 for each line of the doublet, in each galaxy.  Then, we calculate the escape fractions by comparing observed and intrinsic line fluxes: 

    f_esc^2796 = F^obs ( Mg II  2796) / F^int ( Mg II  2796)  
     and
     
    f_esc^2803 = F^obs ( Mg II  2803) / F^int ( Mg II  2803).
 
In this calculation, the observed  Mg2 fluxes are corrected for  slit-losses as described in <ref>.  We also correct for Milky Way foreground extinction, using the <cit.> attenuation curve and the extinction values from (; E(B-V)_MW listed in Table <ref>).   Additionally, we note that the uncertainty on Mg2 escape fraction includes the statistical error on the line fluxes and the 0.1 dex uncertainty on the intrinsic Mg2 prediction.  We do not, however, include an error to account for systematic uncertainties in the internal extinction law, as this error is ill-defined.   Although we chose <cit.>, we note that other attenuation curves (e.g. SMC, LMC; , Milky Way; ) predict smaller absolute dust corrections, leading to lower intrinsic  fluxes and up to 25% higher Mg2  escape fractions.  The Mg2 escape fractions are given in Table <ref>.  


Overall, our calculation of Mg2 escape fractions is analogous to the calculation of  escape fractions in its treatment of dust. The Cloudy models presented in Figure <ref>, and the relations in Equation <ref> and <ref>  use intrinsic line fluxes, rather than dust attenuated.  Likewise, the observed  and Mg2 line fluxes are not corrected for internal dust extinction, since a robust correction is difficult to discern when photons are resonantly scattered.  Therefore, like , an escape fraction less than unity implies that photons are absorbed by dust, or scattered outside the aperture.    

We judge these estimates to be accurate in a relative sense, but acknowledge that photoionization modeling of the intrinsic line fluxes is subject to systematic uncertainties.  Different assumptions about relative abundance ratios, dust depletion patterns, and shocks may predict systematically different intrinsic Mg2 emission.  Hence, we urge caution, and focus on qualitative trends going forward. 




 

 






§ CHARACTERIZING MG2 ESCAPE
  
 
The Green Peas in this sample show a range of Mg2 equivalent widths (0 to 9 Å) and escape fractions  (0 to 0.9).  Figure   <ref> 
explores the cause of these variations.    First, the left-hand panel shows that Mg2 equivalent widths correlate with escape fractions.   This trend implies that 
 higher Mg2 equivalent width emission is not necessarily an indication that Mg2 is intrinsically stronger; rather, the ISM is more transparent to Mg2 
 when the equivalent width is higher.   In fact, the center panel of Figure <ref> shows that the sources with the strongest Mg2 emission have higher O32 values.    In our Cloudy models (and according to Equations <ref> and <ref>), the higher O32  values are an indication of weaker Mg2/ ratios.  
These lower Mg2/  ratios translate directly to fainter intrinsic Mg2 emission for the sources that have the highest equivalent widths and escape fractions (Figure <ref>, right).   In summary, the sources with the strongest observed Mg2 emission are actually those with the weakest intrinsic emission.    


We next look for signs of resonant line radiation transport on the Mg2 lines.  Figure <ref> presents the Mg2 escape fractions for the 10 Green Peas in this sample, comparing the two lines of the doublet.   The ratio of oscillator strengths describing the ISM absorption on these lines is f_2796 /  f_2803 = 0.61/0.30, or about a factor of two.   Hence, the optical depths are related: τ_2796 = 2 ×τ_2803.  However, since these lines are resonant,  the optical depths do not necessarily translate into differing escape fractions.   Rather,   the top panel of Figure <ref> shows the escape fractions of the lines are mostly consistent within the errors, except for the galaxy with the highest dust extinction and lowest escape fraction in the λ 2796 line: 1440+4619.  In this case, although we detect Mg2 emission, we also detect absorption on the λ 2796 line, so the net equivalent width is near zero (before the stellar absorption correction).   Similarly, the bottom panel  of Figure <ref> shows that the equivalent width ratios,  W_2796/W_2803, are near the intrinsic ratio of about 1.9, inferred from our Cloudy models.     Overall, it appears that the effects of resonant scattering are not significant enough to alter the intrinsic line ratio, or cause the λ2796 line to have a lower escape fraction.   














 
 
 
 
 
 
  
 
 
 






 
 

  



While the Mg2 equivalent width and escape fraction ratios indicate that photon scattering is insufficient to remove λ2796 photons more than λ 2803 photons, kinematic measures, in contrast, show evidence of radiation transport. 
As noted in <ref>, and shown in Figures <ref> and <ref>, the Mg2 lines are systematically redshifted by an average of 70 .  Additionally,  in a few cases the Mg2 lines are broader than the optical nebular lines.  While the SDSS spectral lines are only marginally resolved, we have obtained Keck/ESI spectra for the 8/10 Green Peas in the present sample, achieving 75  spectral resolution (Henry et al., in prep).   
After correcting for spectral resolution,  we find that the Green Pea 1244+0216 has FWHM of 327 ± 44 and 195 ± 119 for the λ 2796 and λ 2803 lines, respectively, whereas its  line has a FWHM of only 94 .  Likewise, 1249+1234 has FWHM around 122 ± 35  in both Mg2 lines, compared to 66  in .   Lastly, the λ 2796 line of 0926+4427 has FWHM of 208± 46, whereas  is substantially narrower at 106 .   For 1440+4619 and 1442-0209, we do not have a high resolution spectrum for comparison, but  we do note that 1440+4619 has Mg2 lines which are among the broadest in our sample, similar to 1244+0216.  

The broad widths and redshifted emission are analogous to the case of .  Therefore, we may expect the lines to be more redshifted and broadened when the column density of Mg2 is higher, and the escape fractions are lower.  The top panels of Figure <ref> test this hypothesis, showing a tentative relation in the expected direction:  higher Mg2 escape fraction may be associated with lower Mg2 peak velocities and smaller FWHM.    The bottom panels of Figure <ref> show the same kinematic measures against the  escape fraction, with a similar tentative correlation.  The Pearson correlation coefficient (ρ), and probability of the null hypothesis (P) are shown in each panel,  indicating a 2-8% likelihood of a spurious correlation.  Additional observations could clarify this relation.  Not only would a broader dynamic range be useful, it is also clear that high-resolution and high signal-to-noise will be needed to measure Mg2 peak velocity shifts of order 100 .  


A more detailed look at the Mg2 line profiles is shown in Figure <ref>.   Here we compare the Mg2 and  lines of two Green Peas, bracketing the range of escape fractions probed by our sample.    This comparison shows clearly that 1244+0216,   which is among the Green Peas with the lowest  escape fractions, widest  peak separations, and lowest Mg2 escape fractions, has much broader Mg2 than .  On the other hand, 1219+1526, which has properties similar to Lyman Continuum leakers <cit.>,  is only marginally broadened on the red side of the Mg2 lines.   The spectral resolution is comparable between the two observations  (90  for the Mg2 spectrum and 75  for the ),  so the broader Mg2 lines cannot be due to instrumental effects.  We also notice in Figure <ref> that 1244+0216  has double peaked Mg2 emission on both lines of the doublet.  Here, we are detecting the same effect that shapes the  profiles of the Green Peas: due to the relatively high optical depth at line center, photons scatter away from the systemic velocity and into the wings of the lines.  Indeed, the somewhat wider peak separation for the λ2796 line (200 ± 20  vs 170 ± 40 ) is consistent with its higher oscillator strength and optical depth to ISM absorption, relative to the λ2803 line.     Overall, we conclude that the changes in the peak velocities and FWHM are consistent  with a scenario of varying column densities of neutral and low ionization state gas. 

Next, we explore the role of dust extinction in establishing the Mg2 emission.   Figure <ref>  shows trends where lower dust extinction is associated with higher Mg2 equivalent width and escape fraction.  Again, the Pearson correlation coefficients are given in each panel, alongside the probability of a spurious correlation.   Although any correlation is only tentative, the trends follow our expectations.  For comparison, we show the starburst dust extinction law from <cit.>, along with the Small Magellanic Cloud (SMC), and Large Magellanic Cloud (LMC) from <cit.>.   While non-resonant lines should follow the appropriate extinction curves, resonant lines are more susceptible to dust attenuation because multiple scatterings increase the likelihood of absorption.   Hence, it is not surprising that many of the Mg2 and  escape fractions fall below the relevant curves in Figure <ref>.    While about half the sample lies near the locus where dust extinction alone could explain the Mg2 escape fractions, the other half appears to have too little Mg2 emission for the amount of extinction.   However, we again caution that the Mg2 escape fractions are uncertain in an absolute sense, due to systematics associated with the photoionization modeling and intrinsic Mg2 flux derivation.  Likewise, as we noted in <ref>, using an SMC, LMC, or Milky Way dust attenuation curve when estimating  intrinsic Mg2 flux (from dust-corrected ) could increase the Mg2 escape fraction by up to 25% in the sources with the most dust.  Nevertheless, since we do see effects of resonant-line radiation transport on the line profiles, we conclude that the less-than-unity Mg2 escape fractions should probably not be explained by dust extinction without resonant scattering. 





Since  and Mg2 are both  shaped by scattering in low-ionization state gas, we might expect their escape fractions to be related.    Indeed, Figure <ref> verifies this hypothesis.  The left panel shows that   W_ Mg II correlates with
W_ Lyα, while the right panel shows a tight relation between and the Mg2 escape fractions. The Pearson correlation coefficient, and probability of the null hypothesis are listed in each panel.   The relation between the escape fractions– where we have included both Mg2 lines in the correlation— is especially robust, with the probability of a spurious correlation around 10^-7.  A linear fit to these data indicates that: 

    f_esc^ Mg II = 0.13 + 1.21 f_esc^ Lyα,
 
 where both Mg2 lines are included in the fit. 
 

These correlations are notable:  they confirm that the  and Mg2 escape are regulated by resonant scattering in the same gas.   Since high  escape fractions can be a sign of low column densities of H1 gas <cit.>, we infer that high Mg2 escape 
must also be a sign of correspondingly low column densities of Mg2.   Remarkably, a link between  and Mg2  (and the column density of low ionization state gas) opens up the potential for a new diagnostic in the reionization epoch,  where  and Lyman Continuum are difficult to observe.  We will return to this point in <ref>. 

 


While a relationship between Mg2 and   escape fractions is sensible, the observation that these quantities are of the same order is counterintuitive.  The  and Mg2 transitions have optical depths
to resonant scattering which differ by orders of magnitude.  Hence, one might expect a  substantially lower   for a given Mg2 escape fraction.  Considering dust attenuation highlights
this puzzling  observation.   Figure <ref> shows the predicted relationship between the  and Mg2, if the lines were non-resonant, for three extinction curves.    All three run through our observations.  Yet, because  scatters much more than Mg2, we expect it to be much more impacted by dust.  This effect would place the measurements to the left of the extinction curves.     Although Figure <ref> suggests that the Mg2 and  emission see more dust than a non-resonant photon would (for at least some of the sample), contrary to our expectation, Figure <ref> suggests that this effect is not more pronounced for  than it is for Mg2. The reason for this observation is unclear.   While similar escape fractions could arise from a scenario where the  and Mg2 photons escape through pathways with negligible column densities of low-ionization state gas (and dust), we previously showed that Green Peas have uniformly high covering and modest column densities (N  > 10^16 cm^-2) in H1 <cit.>.  Similarly,  <cit.> showed that, for z∼ 0.3  emitters, there was no need to invoke a scenario where the  photons escape through dust-free “holes” in the ISM.  Therefore, we conclude that more detailed radiation transport modeling would be helpful.  

  


Even with Mg2 showing showing similarities to , it is surprising  how little it resembles the Si2 λλ 1190, 1193 profiles that we show in Figures <ref> and <ref>.   With similar ionization potentials and abundances (assuming a solar relative abundance pattern; ) the column densities of Mg2 and Si2 should be comparable. However, there are two notable differences between these spectral features.  First,  Si2  λλ 1190, 1193  is not produced appreciably in H2 regions.  The Cloudy models presented in <ref> show that Si2 λλ 1190, 1193  is 1-3 dex fainter than Mg2  λλ 2796, 2803  in almost all cases. Only the 10 Myr aged instantaneous bursts with 
log U > -2.0 can have Si2 lines comparable in strength to Mg2; however, this combination of parameters is probably unphysical, as such high ionization parameters are implausible for models that lack O stars.   So we can conclude that the nebular origin for Mg2 is not matched by Si2.  The second  difference between Mg2 and Si2 is resonant trapping of the line and continuum photons.  For the Si2 feature, fluorescent fine structure Si2*  lines at λ1194 and λ1197 Å are  coupled with the  Si2 λλ 1190, 1193  lines.  Photons absorbed in the resonant line can escape through a non-resonant channel,  rather than filling in the absorption in the resonant line. Since Mg2 lacks this non-resonant channel, the absorption is entirely filled by re-emission (as with ).   Given these two major differences, we can understand that the line profiles will appear very different in some cases. 
Still, a single, self-consistent model (e.g. ) should be able to reproduce the Mg2, Si2, and Si2* when these considerations are taken into account.


Despite the lack of any qualitative similarities between the Si2 and Mg2 line profiles in Figures <ref> and <ref>, a quantitative relationship may be expected when we take
the Mg2 escape fractions into account.  Figure <ref> takes the analogy between  and Mg2 one step further. 
Equivalent widths in the  low-ionization interstellar (LIS) metal absorption lines have been shown to correlate 
with  equivalent width or escape fraction <cit.>.
For high redshift  populations,  the interpretation is that the equivalent width of the LIS lines measures the fraction of the 
 background source covered by absorbing ISM <cit.>.  Hence, weaker LIS lines may indicate lower covering fractions, which facilitate higher  escape fractions and equivalent widths.  On the other hand, <cit.> has argued, using COS spectroscopy of low redshift galaxies, that the same trend (albeit, at a different redshift) can be explained by changing column densities and optically thin LIS lines.  Regardless of the origin, Figure <ref> tests for a relation by comparing  and f_esc^ Mg II  to the equivalent widths of four LIS lines: Si2 λ 1190, λ 1193, λ 1260, and C2 λ1334. This analysis shows that, while the higher escape fraction objects are among those with weaker LIS absorption, any trend is only tentative.   We calculated the Pearson coefficient for a correlation between 
 f_esc^ Mg II with the equivalent width of each LIS line,  finding that the probability of the null hypothesis ranges from a few to 30%.  We note that small samples, covering a small dynamic range cannot always detect a correlation in these quantities <cit.>.  We also do not detect a correlation between   and the equivalent widths of the LIS lines in Figure <ref>, even though it has been seen in larger samples (using W_Lyα as a proxy for ; e.g. ).      Therefore, the large scatter in Figure  <ref> is not surprising; more observations are needed to determine how f_esc^ Mg II varies with the equivalent widths of the LIS lines.

 
 
Finally, if  and Mg2 profiles are shaped by radiation transport in the same scattering gas, we might expect some kinematic measures from the line profiles to correlate.   This idea is supported the fact that our observations were able to resolve double-peaked Mg2 profiles for 1244+0216, which
 has a relatively large   peak separation for the Green Peas in this sample.   Since we expect broader, more redshifted emission when the column densities of gas are higher,  we checked for a relation between the Mg2 peak velocities, and the velocities of the red  and blue  peaks.   Similarly, we compared the FWHM of the  and Mg2 lines.    In these cases, we see no evidence of a correlation.   
 It is possible, as with the (lack of) correlation between the f_esc^ Mg II  and the equivalent width of the LIS lines, that a larger sample and more dynamic range is needed.




  









 





  


















  







§ SUMMARY AND IMPLICATIONS
 

We have shown that Mg2 appears in emission instead of absorption in Green Pea galaxies.  Previous studies that aim to constrain 
outflows from this spectral feature have noted emission in some cases <cit.>, but the origin of this emission has been unclear. 
 Nevertheless, we showed that Cloudy models predict appreciable emission  from H2 regions (previously noted  by  and ) that can easily explain the spectra of these Green Pea galaxies.   


Because we have a wealth of other information about the Green Peas, we have characterized their Mg2 emission to 
better understand its use as a diagnostic.  
 Since Mg2 photons are resonantly trapped like , it is not surprising that 
we detect some effects of radiation transport on the lines.   We show that photoionization models can be used to predict the intrinsic Mg2 line fluxes, thereby allowing measurement of Mg2 escape fractions (analogous to ).    These escape fractions vary between 0 and 95%,  and are often lower than the prediction for simple dust extinction without resonant scattering.  We show that lower escape fractions are tentatively associated with Mg2 lines that are broader and more redshifted, which can be an indication of higher column densities of scattering gas.   In particular, the line profiles of the  Green Pea 1244+0216  are remarkable in the sense that they are double peaked and substantially broader than .  This observation makes sense qualitatively, since 1244+0216 is among the objects with the broadest  peak separations and lowest Mg2 and  escape fractions.   

At the same time, however, the effects of radiation transport that we observe are substantially weaker than we see for .   First, the line fluxes remain close to their intrinsic ratio.  Likewise, the escape fractions of the λ 2796 and λ 2803 are mostly consistent within the errors (except for one case), despite the fact that the blue line has twice the oscillator strength (scattering optical depth) of the red line. Finally, we do not see any evidence of scattered Mg2 emission extending beyond the stellar continuum, in contrast to cases seen by <cit.> and <cit.>.   We acknowledge, however, that this constraint is not particularly strong.  <cit.> measure the spatial extent of the  and UV continuum in 9/10 of the Green Peas in the present sample, and while the  is 1.3 to 1.9 times more extended than the continuum, the  sizes are still sub-arcsecond. Since the size of the Mg2 should not exceed , we conclude that our ground-based observations would be unlikely to detect extended Mg2.  Overall, we conclude that in comparison to , weaker radiation transport effects on Mg2 are sensible, since the column density of Mg2 is orders of magnitude lower than that of H1.  Still, we are puzzled that resonant scattering in a dusty ISM produces 
 and Mg2 escape fractions that are of the same order of magnitude.  Since  photons scatter much more than Mg2 photons, we might expect the  escape fractions to be substantially lower than Mg2 escape fractions. 

Intriguingly, the Mg2 escape fractions show a tight correlation with the  escape fraction.   This relation suggests that the same
gas that scatters  photons and sets their escape is also regulating the Mg2 output. In some ways, this result it not surprising: Mg2 is a low ionization line that serves as a proxy for H1.    However, in other ways, it is noteworthy.   In spectra of high redshift galaxies, the ISM metal absorption lines have been postulated to trace dense clumps in an outflow <cit.>, possibly different from the pervasive H1 component that is indicated by Lyman series absorption lines <cit.>.  If the Green Peas are like high-redshift galaxies, it is not obvious that the dense gas which is most effective at scattering Mg2 photons is co-spatial with large H1 reservoir that scatters  photons <cit.>.  
Nevertheless, Mg2 appears to serve as an effective tracer of H1 since the correlation between the escape fractions is surprisingly tight.    More detailed radiation transport modeling will be required to understand the properties of outflows and the ISM/CGM that can produce this relation. 



 §.§ Implications for the Epoch of Reionization
 
The close correspondence between  and Mg2 could have great utility in the epoch of reionization, where observations of  are 
difficult or impossible.  Two diagnostics stand out.  First,  Mg2 may be useful for predicting the  that emerges from the ISM, before it is 
diffused and rendered unobservable by a partially neutral IGM.  Significant efforts have 
been made to measure the neutral hydrogen fraction in the IGM from weakened or absent  emission at z>6 (e.g., , and references therein).  However, it is unclear how  would evolve over these redshifts in a completely ionized IGM;  hence, the high-redshift   deficit is ill-defined, and inferred IGM neutral fractions are uncertain. Importantly,  Mg2 emission from galaxies would not be impacted by a neutral IGM in the same way.   We can estimate the optical depth for 
scattering Mg2 photons in the IGM at early times, using metallicity measurements from Damped  Absorber  (DLA) observations.   Observations have indicated  
 [Mg/H] ∼ -2.0 at z∼5, with  probably declines to higher redshifts <cit.>.  Taking this value as an upper limit, and conservatively assuming that all Mg in a neutral IGM would be in  Mg2, we estimate that Mg2/ H  10^-6.4, where the solar abundance scale as been adopted <cit.>. 
 Since the column density where  becomes optically thick at line center (τ_Lyα^IGM = 1)  is around 3× 10^13 cm^-2 (the precise quantity depends on the Doppler parameter; ), the column density of Mg2 is at most 10^7 cm^-2 when  photons start to see the effects of a neutral IGM.  Hence, the optical depth of Mg2  at line center will be τ_Mg II^IGM∼ 10^-6,   completely optically thin and unaffected by the neutral IGM. Critically, this means that we could use Mg2 to predict the  that emerges from the ISM and CGM, before it is impacted by the neutral IGM.   Comparison with observations could then allow more robust measurements of the  deficit and IGM neutral fraction at very high-redshifts. 

The second reionization-epoch utility for Mg2 is as a diagnostic for Lyman Continuum  (LyC) leakage.   High  escape fractions have been associated with narrowly spaced  peaks, low H1 column densities, and direct detection of escaping LyC <cit.>.   Because  and Mg2 escape appear to be governed by radiation transport in the same gas, we postulate that Mg2 may also be used to predict LyC emission.   This hypothesis is supported by the detection of Mg2 in the SDSS spectrum of the LyC emitter, J1154+2443 <cit.>, although a higher signal-to-noise spectrum will be required for a detailed comparison to the sources presented here. Ultimately, Mg2 may be particularly useful at z>6-7, where  becomes unobservable due to the  neutral IGM.  With NIRSpec on JWST,  these observations will soon be possible. We can estimate the required exposure time to detect Mg2 from a 26.5th magnitude galaxy with W = 7 Å (rest)  on each of the Mg2 lines.  For this calculation, we simulate a 1D spectrum, assuming NIRSpec's G235H disperser with varying levels of noise, and measure the significance of the simulated line.  We  find that a continuum signal-to-noise of 1.5 per pixel is required to detect the Mg2 lines with a signal-to-noise of 5.   Using the JWST Exposure Time Calculator[https://jwst.etc.stsci.edu/], we find that 48 hours of observation should meet this goal.  While expensive, 
detections of Mg2 in the reionization epoch should be possible as part of a comprehensive, deep spectroscopic survey.   Clearly, before we can confidently use Mg2 as a diagnostic for reionization,  more work will be needed to characterize its emission and relationship with  in an ionized IGM.  Nevertheless, the trends that we have presented here appear promising. 




 §.§ Implications for the  properties of galaxies and outflows
 
We have shown that the Mg2 feature originates from nebular line photons, which resonantly scatter to escape galaxies, analogous to .
This finding implies that studies which aim to use Mg2 for constraining outflows  must account for the emitted line photons.  Models which seek to reproduce the Mg2 line profiles with only scattered continuum photons should struggle to reproduce observations (, Carr et al., submitted).  Indeed, in <cit.>, significant differences between Mg2 and Fe2 line profiles were attributed to a contribution from nebular Mg2 emission.  Our Green Pea observations confirm this interpretation.   In short, when Mg2 is used, measurements of galaxy outflow velocities, column densities, and mass-loss rates will require more sophisticated modeling than has yet been attempted for this spectral feature. Fortunately,  these radiation transport models have already been developed for interpreting  emission <cit.>. 

The observations that we report  here provide further context for interpreting higher redshift observations. 
Notably, <cit.> report Mg2 emission is common among low mass galaxies (M < 10^9 M_)   at
z∼ 1, but less common at high masses.   Within this sample, the lower mass galaxies will have relatively lower metallicities than the high mass galaxies, so they should also have correspondingly higher O32.  Hence, following our photoionization models, we expect that the intrinsic Mg2/ ratio (and possibly the intrinsic Mg2 flux), weakens at lower masses.  Therefore, the strongest Mg2 emitters in <cit.> probably have 
high Mg2 (and ) escape fractions.    These trends among the Green Peas and z∼ 1 galaxies could be an indication that a highly ionized ISM (high O32) results in low column densities of neutral and low-ionization state gas, allowing high Mg2 and  escape fractions. 
Additionally, given our understanding of Mg2 escape, it makes sense that the z∼1 galaxies with  Mg2 emission tend  not to have fluorescent Fe2* emission <cit.>. 
While nebular Mg2 emission favors ISM with low column densities of gas, fluorescent Fe2* is the opposite.  Non-negligible absorption in resonant Fe2, from higher column densities of gas, is required to produce Fe2* emission.    The opposite trend– stronger Fe2* emission when Mg2 is strong– reported by <cit.> is somewhat puzzling.  However, these results are based on composite spectra, and aperture losses on the scattered emission would also tend to correlate the strength of these emission features. 


Our analysis of Mg2 also points to an important warning about the use of resonant lines for constraining the physical conditions in H2 regions.  
For example, observations of nebular C4 have been reported from galaxies at both high and low-redshifts <cit.>, and used to quantify the number of hard ionizing photons from young stars. However,   by analogy with Mg2, we infer that escape fractions may be anywhere between zero and one.    Indeed, at low impact parameter in the CGM of low-redshift galaxies, <cit.> find  C4 column densities around N  = 10^14, which implies C4 optical depth at line center of τ≳ 1-2. Hence, we expect resonant-line radiation transport to be significant; this may explain the apparent redshifting of C4 in some low-redshift galaxies with high-signal to noise UV spectra and known systemic redshifts <cit.>.   Although C4 is commonly used as a diagnostic for the physical conditions in HII regions (e.g. ) we conclude that this approach is probably unreliable, even when the C4 stellar wind feature can be confidently subtracted.    Despite this complication, the resonant nature of C4 could prove useful for understanding the CGM, similar to  and Mg2.   It would be curious to test whether C4 emission and escape[We acknowledge that photoionization modeling to predict intrinsic C4 may not be as straightforward as with Mg2.] correlate with  as Mg2 does.   The C4  traces different gas than Mg2 and , so we would not necessarily expect the same close relationship that we see between Mg2 and .  Still, any correlation, or lack thereof, could place constraints on the multi-phase nature of the ISM and CGM. 




 §.§ Future Work
 
Finally, we conclude that these observations mark an important first step in the 
characterization of Mg2 and its relation with .   We have shown that simultaneous observations of multiple resonance lines probing neutral and low-ionization state gas can give qualitatively consistent results.    We provide evidence that Mg2 may be able to predict the  that emerges from galaxies, before it is impacted by a neutral IGM at high redshifts.  As a consequence of its close correlation with , Mg2 may also serve as a useful LyC diagnostic at high redshifts.   Overall, larger samples at all redshifts will be useful for strengthening our conclusions about the physical processes that allow , Mg2, and LyC escape. Indeed, at z≳ 3, Mg2 and the full rest-frame optical spectrum can be observed with JWST/NIRSpec, and ground based-data can cover  at z<6.  Hence, the data to test these theories at high redshifts will soon be available.  In the mean time, simultaneous radiation transport modeling of the  and Mg2 lines will be an intriguing test of models for outflows and the CGM. 










The authors thank the anonymous referee for insightful comments, which improved this work.  AH thanks Marc Rafelski,  Nicolas Bouché, Tim Heckman and Molly Peeples for useful suggestions, Anne Jaskot for help with Cloudy models, and James White for reducing  the Keck/ESI spectra.  The authors also
wish to thank the Lorentz Center for facilitating collaboration during the “Characterizing Galaxies with Spectroscopy with a view for JWST” workshop.    This work was supported in part by HST GO 13654. 



 


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 cccccccccc[!t]
10
Comparison Data for the Green Peas 

ID       E(B-V)_gas      O32     F([OIII] 5007)         12 + log(O/H)      F()      f_esc^Lyα     W_Ly α      v_blue^peak     v_red^peak    

                        (10^-14 erg s^-1 cm^-2 )            (10^-14 erg s^-1 cm^-2 )           (Å)      ()      ()       
 
      (1)     (2)     (3)         (4)     (5)     (6)      (7)     (8)     (9)      (10)     
      
      0911+1831     0.17     0.26     1.57        7.90       3.3 ± 0.1         0.16      59 ± 12         -280       90  
 
0926+4427     0.10     0.51      4.60       7.95       6.0 ± 0.3        0.20      40 ± 8            -250      160 
 
1054+5238     0.08      0.40      3.29        8.22      1.7 ± 0.2          0.07      12 ± 3         -250      160 
 
1137+3524      0.06      0.45     5.24         8.14     3.8 ± 0.2         0.12       35 ± 7        -400     150 
 
1219+1526     0.00      1.02       5.71         7.86    13.7 ± 0.2      0.62       164± 33      -100     140 
 
1244+0216      0.07      0.56      5.74        8.12       2.0 ± 0.1      0.07     48± 10           -280      250 
 
1249+1234     0.07       0.55     2.52         8.10        5.4 ± 0.1       0.41      98 ± 20             70 
 
1424+4217      0.04      0.79     7.92         7.99         8.5 ± 0.2      0.25     95 ± 19       -150     230
 
1440+4619      0.16       0.25       2.05       8.17      2.3 ± 0.2      0.11      33 ± 7        -470     70  
 
1442—0209      0.12       0.83       2.05        7.93      5.1 ± 0.2       0.41      115 ± 23      -230      100   
 
Comparison data for the Green Peas are drawn from SDSS and HST/COS spectroscopy.   measurements are either taken from <cit.>, or, in the case of 1440+4619 and 1442-0209 measured in the same way.   Column descriptions: (1) object ID; (2) nebular dust extinction, calculated from /, using the <cit.> extinction curve; (3) O32 ≡ log( λ5007 /  λ3727),corrected for dust; (4)  λ5007 flux, corrected for dust; (5) gas-phase metallicity, calculated following <cit.>.  The values given here differ slightly from those in <cit.>, where they were instead taken from <cit.>;   (6) The  flux measured from the COS spectra, corrected for Milky Way foreground attenuation using  extinction
 measurements and the  extinction law; (7) the  escape fraction; (8) the rest-frame  equivalent width; (9) the velocity marking the blue peak of the  line profile; (10) the velocity marking the red peak of the  line profile.  
  



 
 crcccccccccccc[!t]
14
Mg2 Measurements from Green Peas 

ID       W_2796      W_2803           F_2796    F_2803             v_2796     v_2803     FWHM_2796     FWHM_2803            f_esc (2796)       f_esc (2803)  
 

 
2-3  5-6   8-11 13-14  
 
          2c(Å)            2c(10^-16 erg s^-1 cm^-2)          4c()                 
 
 (1)     (2)     (3)              (4)     (5)         (6)       (7)     (8)     (9)          (10)    (11)
 
0911+1831     2.9 ± 0.4     1.9  ± 0.3               5.5 ± 1.0     3.7 ± 0.8            67 ± 12      94  ± 28     122 ± 59       121 ± 68        0.21^+0.07_-0.06     0.29^+0.08_-0.08  
 
0pt3ex
0926+4427     5.1  ± 0.5     2.9 ± 0.5               21.7 ± 3.4      12.2 ± 3.3          91 ± 10      65  ± 32     208 ± 46      93 ± 69           0.53^+0.16_-0.13       0.57^+0.21_-0.19  
 
0pt3ex
1054+5238     3.0  ± 0.3      1.6 ± 0.2               8.4 ± 1.7     6.9 ± 1.1           113 ± 9      122  ± 22     193 ± 38     159 ± 46          0.23^+0.07_-0.05      0.36^+0.11_-0.09   
   
0pt3ex
1137+3524      2.7 ± 0.4     1.8± 0.4             10.8 ± 4.1      7.2  ± 2.9           123 ± 9     138 ± 44      <90      91 ± 59            0.20^+0.07_-0.07      0.26^+0.11_-0.08 

0pt3ex
1219+1526     6.2± 0.5      3.7 ±0.3              14.1 ± 2.0       8.6 ± 0.9           34  ± 7    86 ± 17      132 ± 45    90 ± 40            0.80^+0.24_-0.21      0.90^+0.25_-0.22   
  
0pt3ex
1244+0216     4.4 ± 0.4      1.6 ± 0.3              10.6  ± 1.2      3.8 ± 0.9           72± 8      55  ± 38     327 ± 44      195 ± 119          0.24^+0.07_-0.04     0.16^+0.06_-0.05 

0pt3ex
1249+1234     9.1  ± 0.4     5.3 ± 0.4             12.0  ± 0.5       7.1 ± 0.5             44± 4    60 ± 23      122 ± 31       121 ± 38          0.58^+0.16_-0.13     0.65^+0.17_-0.13  

0pt3ex
1424+4217      5.4 ± 0.3      4.3 ± 0.3             18.1  ± 1.1     14.1 ± 0.9            29 ± 5     50 ± 13      92 ± 41       133 ± 52         0.46^+0.13_-0.10     0.68^+0.18_-0.15 
 
0pt3ex
1440+4619       0.4 ± 0.5       1.4  ± 0.3          1.0^+17.2_-1.0a       4.3  ± 1.4         87 ± 21     24  ± 42     311 ± 110     151 ± 148          0.03^+0.54_-0.03     0.25^+0.11_-0.11  
  
0pt3ex
1442–0209      6.3 ±  0.7      2.7± 0.6           7.2 ± 2.5      3.1 ± 2.0           24± 14     9 ± 25        153 ± 37       116  ± 44           0.78^+0.34_-0.30     0.61^+0.42_-0.40  
 
Measurements of the Mg2 emission lines from our MMT spectra.  Column descriptions: (1) object ID; (2-3) rest frame equivalent widths for the λ 2796 and λ 2803 lines.   A stellar absorption correction of 0.3 Å is added. The λ2796 line is measured including any blueshifted absorption, hence, 1440+4619 has W_2796∼ 0 Å before the stellar absorption correction.   (3-4) line fluxes are corrected for stellar absorption,  slit-losses (see <ref>),  and the Milky Way foreground attenuation.  The latter correction uses the <cit.> extinction measurements and the <cit.> extinction law.   (5-6) velocities marking the peaks of the lines, (7-8) FWHM of the lines, corrected for instrumental resolution (9-10) Mg2 escape fractions, calculated by correcting for stellar absorption, slit losses and Milky Way extinction, but not  corrected for internal dust extinction. Errors on the Mg2 escape fraction include the measurement uncertainty on the observed flux and a 0.1 dex uncertainty on the predicted intrinsic Mg2 flux.
aThe measured equivalent width on this line is small compared to the stellar absorption correction, so the flux is multiplied by a factor of 6.2.   Prior to this correction, we measure F_2796 = 0.16^+2.8_-0.16 × 10^-16 erg s^-1 cm^-2. 

 






















