THE PHYSICAL CONDITIONS, METALLICITY AND METAL ABUNDANCE RATIOS IN A HIGHLY MAGNIFIED GALAXY AT z = 3.6252^*

2.1.1. Subaru/SuprimeCam

2.1.2. HST/WFC3

2.1.3. Spitzer/IRAC

A summary of spectroscopic observations used in this work is shown in Table 1. In the following sections, we describe the spectroscopic data and their reduction.

2.2.1. Magellan/FIRE

Near-infrared spectroscopic observations were obtained with the Folded-port InfraRed Echellete (FIRE) instrument (Simcoe et al. 2013) on the Magellan-I (Baade) telescope. SGAS J105039.6+001730 was observed on two nights, UT 2011 June 11 and 2011 June 12. A pair of frames with individual integrations times of 602 s were obtained each of the two nights, for a total integration of 2410 s. The echelle grating and the 10 slit were used, resulting in spectral resolution of R = 3600 (83 km s⁻¹). The position of the FIRE slit is shown in Figure 2.

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The A0 V star HD 96781 was observed as a standard star for purposes of fluxing and telluric correction. The star was observed immediately before each pair of science frames; the star was located 14°from the science target, with sec (Z) airmass that differed by less than 0.2.

FIRE data were reduced using the FIREHOSE data reduction pipeline tools,¹³ which were written in IDL by R. Simcoe, J. Bochanski, and M. Matejek, and kindly provided to FIRE users by the FIRE team.

The FIRE pipeline uses lamp flat-fields to correct the pixel-to-pixel variation and sky flats to correct the illumination. The wavelength solution is fit using OH sky lines, and a two dimensional model of the sky is iteratively fit and subtracted following Kelson (2003). The object spectrum is extracted using a spatial profile fit to the brightest emission line, and a flux calibration and corrected for telluric absorption correction are applied using the method of Vacca et al. (2003) as implemented in an adapted version of the xtellcor routine from the SpeX pipeline. The final FIRE spectrum is a weighted average of the spectra that were extracted from the four individual exposures.

2.2.2. Gemini/GMOS-N Nod-and-shuffle

2.2.3. Magellan/IMACS

2.2.4. Magellan/MagE

The MagE spectrum was flux-calibrated more carefully, with several standard stars during the night, whereas the GMOS flux calibration was based on a non-contemporaneous (archival) standard star observation. We therefore extract the GMOS spectrum corresponding only from the slit which covers approximately the same region that was targeted by both the MagE and FIRE observations (see Figure 2), and compare the resulting fluxed spectra against the MagE flux spectrum. In the wavelength range where both spectra have reasonable S/N (i.e., Δλ ∼ 6000–7000 Å), the two data sets have the same continuum flux level to within ∼5%. Having performed this "boot-strap" flux calibration, we feel secure in using the GMOS spectrum to measure line fluxes with a calibration that is accurate to within the uncertainty in the more carefully quantified MagE flux calibration (±20%).

We fit Gaussians to all spectroscopic features of interest; the fits use a single Gaussian profile with three free parameters: the normalization, width, and centroid. For the FIRE data this process is performed directly on the extracted one-dimensional spectrum, in which any continuum emission is consistent with zero flux to within the uncertainties of the data. The regions in the FIRE spectrum in which emission lines appear are shown in Figure 3.

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The GMOS spectrum for SGAS J105039.6+001730 exhibits strong features in both absorption and emission (Figure 4). We begin our analysis of this spectrum by fitting a polynomial continuum model to the continuum. The continuum fitting process begins by identifying regions of continuum emission with good S/N (e.g., λ_obs ∼ 6650–6750 Å, 7250–7400 Å, 7500–7550 Å, 7800–8200 Å, and 8900–9000 Å) and then iteratively add new wavelength ranges to the fit. Our final continuum fit is robust to the exact model parameterization, and is plotted on top of the GMOS data in Figure 4. The residuals of this continuum fit are consistent with the uncertainties in the extracted GMOS spectrum. The continuum fit is subtracted from the GMOS spectrum prior to the measurement of individual line positions and fluxes. We then fit Gaussian profiles to the continuum-subtracted spectrum to measure their wavelength centroids, as well as—in the case of emission features—their fluxes. We incorporate both statistical (measurement) and systemic uncertainties into the emission line flux measurements. We determined the systematic uncertainty contribution from the continuum fit empirically by comparing the line flux measurements that result from different continuum models. The different continuum fits agree well, and the magnitude of the systemic contribution to the total uncertainty is typically ≲20% that of the measurement uncertainty.

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The MagE spectrum also includes continuum emission, though at lower S/N than in the GMOS data. We use the same procedure to fit a continuum model to the MagE data before measuring line profiles. All line flux measurements in the optical are made using the GMOS data, which is much higher S/N. We do measure some line profiles in the MagE spectra, and find centroids that agree well with the GMOS measurements of the same features. All measured line centroids are reported in Table 2.

For measurements and analyses that span different spectra (e.g., comparing line fluxes between the GMOS and FIRE data), we restrict the analysis to the GMOS spectrum extracted only from the slit targeting the same bright knot as the MagE and FIRE observations. The total integration time for this slit was twice as long as the other slits, and the knot in question is the brightest part of the arc, so that the GMOS data from this slit alone provide a spectrum with only marginally lower S/N than a stack of all the GMOS slits. Comparing spectral features measured from this knot minimizes the geometric corrections between the different spectral data sets.

Geometric corrections do not account for the effects of differential refraction, but the differential refraction effects across the GMOS spectrum should be minimal given the wavelengths covered by the observations. Atmospheric dispersion effects are also not a significant problem in spectra in the NIR.

Given the broad wavelength coverage (rest frame UV to optical) and good S/N of the spectra, it is possible to measure systemic redshifts for emission and absorption features with different astrophysical origins within SGAS J105039.6+001730. Typical uncertainties in individual line redshifts for well-detected transitions are σ_z = 0.0006, 0.0002, and 0.0002 in the GMOS, MagE, and FIRE spectra, respectively (some low S/N lines have larger uncertainties, e.g., σ_z = 0.001–0.002). These values include the uncertainties in the individual line centroids, as well as the (negligible) rms uncertainty in the wavelength calibration.

The first line system that we examine is the family of nebular emission lines that appear in both the optical (rest-UV) and NIR (rest-optical) spectra. These lines originate from ionized regions within the galaxy, i.e., H ii regions around massive stars. From 14 measurements of 14 separate nebular emission features we measure a systemic redshift z_neb = 3.6253 ± 0.0008 (O iii] λλ1661,1666 and He ii λ1640 are detected in both the GMOS and MagE data). We exclude the [O ii] λλ3727,3729 doublet lines from inclusion in this systemic redshift due to their coincidence in wavelength with a bright sky line. The sky subtraction residuals from the bright sky line seem to cause an over-subtraction on the blue side of the sky line and an under-subtraction on the red side, which seems to result in a redshift measurements for the [O ii] λλ3727,3729 lines that is slightly biased low (see also Section 4.5 below).

There are also numerous absorption lines in the optical spectra which originate from ionized metals in the ISM of SGAS J105039.6+001730. These include a significant P Cygni absorption/emission profile for the C iv λλ1448,1450 doublet, and similar P Cygni features are also apparent at lower significance for the Si iv λλ1393,1402 doublet. From 20 measurements of 14 individual line features we measure a systemic ISM absorption redshift z_ISM = 3.6236 ± 0.0011. We also compute the systemic redshift for the 7 detected P Cygni absorption features alone, and find z_P-Cyg = 3.6232 ± 0.0011—this is marginally more blueshifted than the complete set of ISM lines, which would be consistent with the P Cygni features tracing regions with stronger outflows, though the offset is not statistically significant.

There are also several spectral features that can arise from a blend of stellar and nebular P Cygni features, including N v λλ1238,1242 and O v 1371, O v 1417, and S v λ1501—where O v 1417 can also be blended with Si iv 1417. We lack the S/N and spectral resolution to disentangle these features in the GMOS and MagE spectra, so we do not use them to compute any systemic redshifts, and flag them as possibly being both stellar and P Cygni (i.e., likely a blend of the two) in origin in (see Table 2). The emission parts of the P Cygni features are difficult to fit because of significant asymmetry due to the neighboring absorption. These features may also originate, in part, from nebular line emission from these transitions (see Section 5.3). Given the difficulties we refrain from measuring line centroids for the P Cygni emission, as it is not clear how to interpret such measurements.

Additionally, in the GMOS spectrum, we note the presence of O iv λ1343, C iii λ1427, and N iv λ1718 in absorption. All of these lines are associated with photospheric absorption in the atmospheres of massive stars (e.g., Pettini et al. 2000), and are therefore likely tracing the stellar content of SGAS J105039.6+001730. These four lines are all weak relative to the much stronger ISM absorption lines, and have a mean redshift z_stars = 3.6258 ± 0.0005.

All of the three systemic redshift measurements agree within 2σ given the measurement uncertainties, but we note that the ISM absorption line redshift is formally blueshifted by 100 ± 70 km s⁻¹. The nebular and stellar photospheric redshifts agree within 1σ, as is expected given that both of these features should trace structures that are gravitationally bound within the galaxy.

To obtain the best possible systemic redshift constraint for SGAS J105039.6+001730, we restrict ourselves to using nebular emission lines in the FIRE spectrum. The FIRE spectrum is high resolution and includes many high S/N lines, whereas the nebular lines in the GMOS and MagE data are much lower spectral resolution and S/N, respectively. Computing the systemic redshift using just the remaining five lines in the FIRE spectrum results in a statistically consistent redshift measurement but reduces the uncertainty significantly. The systemic nebular emission line redshift derived from the FIRE data is z_sys = 3.6252 ± 0.0001.

The telluric A-band absorption feature is prominent in the GMOS spectrum, but at the redshift of SGAS J105039.6+001730, it fortuitously falls between the He ii λ1640 and O iii] λ1661 emission lines without significantly affecting the flux of either line. Because we use archival standard star observations to flux calibrate the GMOS spectrum, we cannot apply a reliable telluric absorption correction and so instead we refrain from using the affected parts of the GMOS spectrum.

All individual line redshifts are all presented in Table 2, and the resulting systemic redshift measurements are given in Table 3.

In addition to the lines that are associated with SGAS J105039.6+001730, we also identify several foreground intervening features. An absorption doublet at λ ∼ 6105 Å is Mg ii λλ2796,2803 from an intervening galaxy at z = 1.1820 ± 0.0002. There is also an absorption doublet at λ ∼ 6330 Å that we identify as the Al iii λλ1854,1862 doublet, along with a an absorption line at 5687 Å that we identify as Al ii λ1670; these Al lines originate from a second intervening galaxy at z = 2.4034 ± 0.0011. Interestingly, both of these intervening galaxies are also strongly lensed by the foreground cluster SDSS J1050+0017 and have redshifts confirmed from spectroscopic data that are not presented in this paper. Several other absorption features that are present in the GMOS spectrum remain unidentified—at least some of these likely result from intervening absorption by the foreground galaxy labeled "Gal1" in Figure 6 for which we do not yet have a spectroscopic redshift measurement. Lines from intervening absorbers are include in Tables 2 and 3.

From the GMOS observations of SGAS J105039.6+001730 we have optical spectra that extend along the length of the arc, which allows us to test for spatial variations in the spectrum. There are several emission lines that are strong enough to be well-detected in spectra that are extracted from sub-apertures along the GMOS slits covering the arc, and we can look for variations in the relative strengths of these lines as a function of spatial position. C iii] λλ1907,1909 and He ii λ1640 are the two highest S/N such lines, and we find no evidence for spatial variation in their equivalent widths in the GMOS data. The seeing during the GMOS observations was 065, and we also note that the emission line features are clearly extended along the GMOS slits, which are between 15 and 2'' long (Figure 5). This spatially extended emission rules out and active galactic nucleus (AGN) as the dominant source of ionizing photons in SGAS J105039.6+001730. There is also a notable lack of emission lines that would be associated with the extremely hard ionizing spectrum of an AGN, such as N v in the rest-UV and [Ne v] in the rest-optical. We can also use the emission lines in the FIRE spectrum to evaluate where SGAS J105039.6+001730 falls in the log([O ii] 3727/[Ne iii] 3869) versus log(O_2Ne3) diagnostic space from Pérez-Montero et al. (2007). With log([O ii] 3727/[Ne iii] 3869) =−0.4 and log(O_2Ne3) =0.9, SGAS J105039.6+001730 resides well within the region occupied by star forming objects in this space. Based on all of the available information, we therefore conclude that AGN activity is not powering a significant fraction of the ionized gas emission, and proceed with the assumption that AGN contributions to the spectrum of SGAS J105039.6+001730 are negligible.

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Photometry of the giant arc is performed using a custom IDL code that lets us construct apertures which follow the ridge-line of the arc. Images are convolved to a common PSF so that the apertures can be defined and applied to the same regions on the sky. This process is described in more detail in Wuyts et al. (2010) and Bayliss (2012). SGAS J105039.6+001730 has a total magnitude of F606W = 21.48 ± 0.05 and i = 21.18 ± 0.06.

3.6.1. Strong Lens Model

In addition to SGAS J105039.6+001730, we identify several different strongly lensed background galaxies around the core of the foreground galaxy cluster; these are labeled in Figure 6. Galaxy A, at z = 2.404, is lensed into a giant tangential arc (A1) and a radial arc (A2), both with similar morphology and colors in the HST and Spitzer data. Galaxy B is a faint tangential arc at unknown redshift. Galaxy D is lensed into four images (D1–4), spectroscopically confirmed to be at z = 4.867 from Gemini/GMOS (D1) and Magellan/IMACS (D2, 3, 4).

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Two images of galaxy C form the giant arc, SGAS J105039.6+001730. One counter image (C3) at (α, δ) = 10:50:41.336, +00:17:23.35 (J2000) was spectroscopically confirmed by IMACS based on the presence of emission line features coincident with He ii λ1640, C iv λλ1448,1450, and C iii] λλ1907,1909 at the same redshift and in the same approximate relative strengths as observed in the GMOS spectrum of the main arc. Another image (C4) is predicted by the lens model and visually confirmed in the HST data, but lacks spectroscopic confirmation.

The positions and redshifts of the spectroscopically confirmed galaxies are used as constraints in the lens modeling process. With the exception of system C (SGAS J105039.6+001730), we use one position per image. For system C, we use the positions of the four brightest knots in C1 and C2, and the two brightest knots in C3. The lens model is computed using the publicly available software, Lenstool (Jullo et al. 2007), utilizing a Markov Chain Monte Carlo (MCMC) minimizer both in the source plane and the image plane. The lens is represented by several pseudo-isothermal ellipsoidal mass distribution (PIEMD) halos, described by the following parameters: position x, y; a fiducial velocity dispersion σ; a core radius r_core; a cut radius r_cut; ellipticity e = (a² − b²)/(a² + b²), where a and b are the semi major and semi minor axes, respectively; and a position angle θ. The PIEMD profile is formally the same as dual PIEMD(see Elíasdóttir et al. 2007).

All the parameters of the cluster PIEMD halo were allowed to vary except for r_cut, which is not constrainable by the lensing evidence and was thus set to 1.5 Mpc. We selected cluster member galaxies in the ∼30' SuprimeCam field of view, as red-sequence galaxies in a color–magnitude diagram. All galaxies within 65 from the brightest cluster galaxy (BCG) and brighter than i = 23 mag were included in the model, with positional parameters (x, y, e, θ) that follow their observed measurements, r_core fixed at 0.15 pc, and r_cut and σ scaled with their luminosity (for a description of the scaling relations; see Limousin et al. 2005). Four foreground galaxies have a more direct influence on the lensed galaxies due to their proximity to the lensed images. We thus allowed their velocity dispersions to be solved for in the lens modeling process. In particular, we note a galaxy at (α, δ) = 10:50:39.704, +00:17:29.14—identified as "Gal1" in Figure 6—that is not on the cluster red sequence, but its perturbation of the lensing potential is key to the lensing configuration of SGAS J105039.6+001730. Since the deflection is linear both with the distance term and the velocity dispersion, we included this galaxy in the same lens plane as the cluster, but note that its best-fit fiducial velocity dispersion scales with its dynamical mass and with its distance term. This approach is described in more detail by Johnson et al. (2014). We are ignoring the second order effects that result from halos residing in different lens planes (D'Aloisio et al. 2013; McCully et al. 2014), including other projected structure which exists along the line of sight toward the cluster lens, SDSS J1050+0017 (Bayliss et al. 2014), but these corrections contribute insignificantly to the uncertainty in the magnification derived from our lens modeling of this cluster.

The distribution of cluster galaxies shows a secondary concentration ∼290'' north of the BCG. Thus another PIEMD halo is included at the position of the brightest galaxy at that position (see Table 4). The inclusion of that structure is also supported by the weak lensing analysis of Oguri et al. (2012).

Table 4. Best-fit Lens Model Parameters

Halo	R.A.	Decl.	e	θ	rcore	rcut	σ0
(PIEMD)	('')	('')		(deg)	(kpc)	(kpc)	(km s−1)
Cluster	$-0.73 ^{+0.21}_{-0.14}$	$3.07 ^{+0.61}_{-1.32}$	$0.10 ^{+0.04}_{-0.03}$	$72.6 ^{+10.5}_{-2.9}$	$81.2 ^{+12.0}_{-20.9}$	[1500]	$1029 ^{+ 32}_{- 55}$
BCG	[0.0]	[0.0]	[0.067]	[-81.3]	[0.19]	[38.2]	$492 ^{+ 43}_{- 48}$
Gal1	[3.37]	[22.33]	[0.0]	[0.0]	[0.08]	[27.1]	$124 ^{+ 18}_{- 10}$
Gal2	[1.56]	[25.42]	[0.081]	[24.1]	[0.14]	[28.3]	$234 ^{+ 19}_{- 17}$
Gal3	[8.37]	[29.13]	[0.083]	[71.2]	[0.09]	[17.1]	$177 ^{+ 40}_{- 35}$
Fixed components
Halo2	[7.11]	[290]	[0.0]	[0.0]	[100]	[1500]	[950]
L* galaxy	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	[0.15]	[40]	[140]

Notes. All coordinates are measured in arcseconds relative to the center of the BCG, at [R.A., decl.] = [162.66637, 0.285224]. The ellipticity is expressed as e = (a² − b²)/(a² + b²). θ is measured north of west. Error bars correspond to the 1σ confidence level as inferred from the MCMC optimization. Values in square brackets are for parameters that were not optimized. The location and the ellipticity of the matter clumps associated with the cluster galaxies and the BCG were kept fixed according to their light distribution, and the fixed parameters determined through scaling relations (see text).

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The results of preliminary lens models indicated that several parameters are not well constrained by the lensing evidence. These include all the parameters of the secondary cluster-scale halo (a large range in σ is allowed), and the scaling relation parameters for cluster member halos; these parameters were fixed in subsequent models. Table 4 lists the best-fit parameters and uncertainties, and the values of fixed parameters. The model uncertainties were determined through the MCMC sampling of the parameter space and 1σ limits are given. The image plane rms of the best-fit lens model is 031.

The lensing cluster SDSSJ 1050+0017 was first published by Oguri et al. (2012), which included a simplified strong lens model. The model was based on constraints from only one lensed galaxy (A), and assuming z = 2 ± 1 as a best-guess for its redshift, which was not measured at the time. Oguri et al. (2012) report an Einstein radius for the fiducial arc redshift of 161 with large error bars due to the redshift uncertainty. For the same arc, we find that the Einstein radius (defined here as the radius of a circle with the same area as the critical curve) is 175, well in line with the initial model presented by Oguri et al. (2012).

3.6.2. The Magnification of SGAS J105039.6+001730

The lensing magnification depends strongly on the location along the arc. Areas in close proximity to the critical curve (plotted as a red line in Figure 6) have the highest magnification, and the magnification decreases farther from the critical curve. To convert the measurements in this paper to their intrinsic, unmagnified values, we calculate the total magnification inside the relevant aperture within which each measurement was made. The boundaries of the aperture are ray-traced to the source plane; we then measure the area covered by the aperture in the image plane, and divide it by the area covered by that aperture in the source plane, thus averaging over magnification gradients within the aperture. This approach overcomes the problem of pixels very close to the critical curve with extremely high magnification artificially driving the average magnification to a higher value.

To derive the uncertainties in the magnification, we compute many models with parameters drawn from the MCMC sampling which represent a 1σ range in the parameter space. The total magnifications are $27.3 ^{+11.4}_{-6.5}$ in the aperture used for the FIRE spectroscopy, $31.9 ^{+10.7}_{-7.8}$ in the GMOS aperture, and $31.4 ^{+10.8}_{-3.5}$ in the aperture used for the photometric measurement of the arc.

We take the magnification factors that correspond to the slit apertures for the FIRE and GMOS spectrum to correct the line flux measurements described in Section 3.1. The resulting magnification-corrected (i.e., intrinsic) emission line fluxes that result from the brightest knot (observed with FIRE, GMOS and MagE) are reported in Table 5.

Table 5. Emission Line Flux Measurements

		Measured Fluxa	Dereddened Fluxb
Ion	λrest	×10−18	×10−18
		(erg cm−2 s−1)	(erg cm−2 s−1)
He ii	1640.42	0.29 ± 0.04	2.7$^{+1.6}_{-1.1}$
O iii]	1660.81	0.10 ± 0.04	0.9$^{+0.6}_{-0.4}$
O iii]	1666.15	0.29 ± 0.04	2.7$^{+1.6}_{-1.1}$
N iii]c	1750.71	0.08 ± 0.03	0.6$^{+0.3}_{-0.2}$
Si iii]	1882.47	0.26 ± 0.04	2.1$^{+1.1}_{-0.7}$
Si iii]	1892.03	0.15 ± 0.04	1.2$^{+0.7}_{-0.4}$
C iii] d	1907.68	1.14 ± 0.07	9.0$^{+4.6}_{-3.0}$
C iii] d	1908.73	0.69 ± 0.08	5.5$^{+2.8}_{-1.9}$
O [ ii]e	3727.09	2.26 ± 0.06	8.6$^{+2.6}_{-2.0}$
O [ ii]e	3729.88	2.22 ± 0.06	8.4$^{+2.6}_{-2.0}$
Ne [ iii]	3870.16	1.83 ± 0.04	6.7$^{+1.9}_{-1.6}$
Hγ	4341.68	2.96 ± 0.12	9.5$^{+2.5}_{-2.0}$
O [ iii]	4364.44	<0.81	<3.3
Hβ	4862.68	5.71 ± 0.06	16$^{+4}_{-3}$
O [ iii]	4960.29	13.44 ± 0.10	38$^{+8}_{-7}$
O [ iii]	5008.24	46.12 ± 0.12	127$^{+29}_{-23}$

Notes. ^aValues reported here are corrected for the lensing magnification. ^bThese are the magnification-corrected line fluxes after applying a reddening correction using a Calzetti et al. (2000) extinction law with A_V = 1, with reported uncertainties that include the uncertainty in the reddening correction. ^cThis line is only marginally detected at ∼2σ. ^dThese lines are blended in the GMOS spectra; we extract the individual line fluxes by fitting a double Gaussian model to the combined line profile, see Section 4.5. ^eThese lines are blended in the FIRE spectra; we extract the individual line fluxes by fitting a double Gaussian model to the combined line profile, see Section 4.5.

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We model the observed SED using the fitting code FAST (Kriek et al. 2009) at fixed spectroscopic redshift with Bruzual & Charlot (2003) stellar population synthesis models, a Chabrier (2003) initial mass function (IMF), and a Calzetti et al. (2000) dust extinction law. We adopt exponentially decreasing star formation histories with minimum e-folding time log(τ) = 8.5 yr (e.g., Wuyts et al. 2011) and the metallicity is allowed to vary from 0.2 Z_☉ to Z_☉. This results in a stellar mass estimate log(M_*/M_☉) = 11.0 ± 0.15 (statistical) ± 0.2 (systematic) M_☉. We combine this with the magnification acting on the arc as computed from the strong lens models described above (μ = $31.4 ^{+10.8}_{-3.5}$) to recover the intrinsic stellar mass of SGAS J105039.6+001730: log(M_*/M_☉) = 9.5 ± 0.15 (statistical) ± 0.2 (systematic)

Because of the relatively large PSF of the IRAC bands there is possible contamination in the measured flux of SGAS J105039.6+001730 in the IRAC 3.6 and 4.5 μm bands from a nearby foreground galaxy that is separated from the arc by ∼15. As a test we have explored SED fits with the IRAC flux reduced by a factor of two (an extreme case); we find that this factor of two contamination case only weakly affects the best-fit stellar mass, and that the possible contamination is sub-dominant to other systematic uncertainties in the SED-derived stellar mass (Shapley et al. 2005; Wuyts et al. 2011; Conroy et al. 2009, 2010; Conroy & Gunn 2010).

The Hβ and Hγ Balmer lines are detected in the FIRE spectra, which allows us to place a constraint on the reddening due to interstellar dust in the rest-frame. Hβ is well-detected in the FIRE data, but unfortunately the Hγ line falls in a region of poor atmospheric throughput and on top of sky lines, which degrades our ability to precisely measure the line flux. SGAS J105039.6+001730 appears from all indications to be a relatively low-mass galaxy with active ongoing star formation, so we assume a Calzetti et al. (2000) extinction law. The measured Hβ/γ ratio indicates an internal extinction of E(B − V) = 0.14$^{+0.38}_{-0.14}$, which is effectively an upper limit of E(B − V)< 0.52. This agrees with the results of the best-fit SED model, which prefers A_V = 1.0 ± 0.2. From here on out, we proceed with an extinction value of A_V = 1.0 and the Calzetti et al. (2000) extinction law and correct all reddening sensitive measurements accordingly. Achieving better constraints on the internal reddening will be challenging due to Hα being redshifted out of the K band, and Hγ falling into a region of poor atmospheric transmission.

From the GMOS and MagE spectra it also appears as though SGAS J105039.6+001730 is a damped Lyα absorption (DLA) system. The GMOS spectrum is higher S/N and we use it to fit a Voigt profile using the XIDL procedure x_fitdla. Even in the GMOS data the S/N is falling off rapidly in the region of the damped Lyα absorption due to the combination of (1) the throughput of the grating decreasing at bluer wavelengths and (2) the continuum emission being suppressed by the Lyα absorption. We use Δλ ∼ 5600–6200 Å—corresponding to Δλ ∼ 1210–1340 Å in the rest frame—to fit the DLA profile (see Figure 4). In this region of the spectrum, the data fall off from S/N per spectral pixel of ∼6 at 6200 Å to <1 at 5600 Å. The low S/N limits our ability to precisely constrain the centroid of the DLA profile, but we find that the data prefer a high column density, log($N_{{\rm H}\,\scriptsize{I}}) >$ 21.5 cm⁻², independent of the precise redshift centroid of the DLA feature. The width of the velocity broadening component of the profile is also unconstrained. Higher S/N observations of the spectrum blueward of 6000 Å will be necessary to make a precise measurement of the DLA feature, but the available data strongly indicate the presence of a large quantity of neutral hydrogen.

Following the calibrations of Kennicutt (1998), we compute the SFR from the FIRE observations of the brightest knot of SGAS J105039.6+001730 using the Hβ and [O ii] λλ3727,3729 emission lines. Both the Hβ and [O ii] λλ3727,3729 SFR estimates measure the instantaneous star formation, because they probe the integrated luminosity of massive stars blueward of the Lyman limit (i.e., ionizing photons). We correct these SFR measurements by using the strong lens model described in Section 3.6.1 to compute the magnification factor that applies to the region of the arc covered by the FIRE slit. In this case, the FIRE slit measures a region of the arc with a total magnification of μ = $27.3 ^{+11.4}_{-6.5}$, and after correcting for this magnification we compute the SFR (for the knot covered by FIRE only) of SFR_Hβ = 84 ± 24 M_☉ yr⁻¹ and SFR$_{{\rm O}\,\scriptsize{II}} =$ 55 ± 25 M_☉ yr⁻¹, where the large uncertainties reflect a 20% uncertainties in the absolute flux calibration of the FIRE data, as well as measurement errors and a 30% scatter in the calibration between and luminosity in the case of SFR$_{{\rm O}\,\scriptsize{II}}$.

Our spectra include three distinct doublet lines that provide a measurement of the electron density, n_e, in the H ii regions that are responsible for the observed nebular line emission (Osterbrock 1989). The GMOS spectrum contains both C iii] λλ1907,1909 and Si iii] λλ1882,1893, where the Si lines are well-separated and the C iii] lines are blended but resolved. The FIRE spectrum resolves the [O ii] λλ3727,3729 lines. All of these line pairs are located very close to one another in wavelength so that the uncertainty regarding the internal reddening does not factor into the electron density determination. We use the curves from Osterbrock (1989) to convert line ratios into electron density; the reported uncertainties are those associated with the measurement uncertainties in the line ratios and assume no additional systematic uncertainties in the line ratio versus n_e curves of Osterbrock (1989). We compute initial estimates of the electron density beginning with an assumed electron temperature, T_e = 10,000 K, and then iterate the computations described in this section and the following section to arrive at the converged values presented here.

The cleanest lines that we can measure in the available data are Si iii] λλ1882,1892, which are well-separated in wavelength and unaffected by strong sky subtraction residuals. We also measure the line ratios for C iii] and [O ii], though systematic uncertainties from sky lines make them both less robust measurements than the Si iii] ratio. The C iii] and Si iii] lines both probe a relatively higher density range and therefore cannot precisely constrain n_e values below ∼10³ cm⁻²; the [O ii] λλ3727,2729 line ratio provides constraints below n_e ∼ 10³ cm⁻² but are unfortunately limited by a bright sky line residual in our data. The specific n_e constraints from are data are summarized as follows.

• 1.  
  Si iii] λλ1882,1892. We measure this line ratio to be 1.6 ± 0.2 in the GMOS spectrum. This value corresponds to an electron density n_e = 10³ cm⁻² for nebular line emitting regions within SGAS J105039.6+001730. Incorporating the uncertainty in the Si iii] line ratio results in an upper limit, n_e ⩽ 2 × 10³ cm⁻². This is fully consistent with SGAS J105039.6+001730 being in the low-density regime, though the Si iii] doublet ratio transitions at higher densities and therefore does not provide as powerful a constraint on low density values of n_e as well-measured [O ii] 3727,2729 line ratio would.
• 2.  
  [O ii] λλ3727,2729. The measurement of [O ii] λλ3727,3729 is complicated by the unfortunate fact that the lines are redshifted onto the location of a bright sky line in the NIR. In order to attempt to recover the line ratio from the FIRE data we fit a double Gaussian profile to the resolved [O ii] λλ3727,3729 lines, holding the redshift fixed to the values taken from the mean of the other nebular emission lines apparent in the FIRE data (see Table 3). This line profile fitting method allows us to recover an estimate of the true line strengths, ignoring contamination from the bright sky line residuals. We measure a line ratio of 1.0 ± 0.4; the central value implies an electron density of n_e ∼ 2–3 × 10² cm⁻², though the large uncertainty effectively encompasses all physically plausible density values.
• 3.  
  C iii] λλ1907,1909. The C iii] λλ1907,1909 line ratio is fit in the same way as the [O ii] λλ3727,3729, and we find a line ratio of 1.65 ± 0.14, which is non-physical but less than 1σ from the maximum value for the line ratio in the low-density limit (∼1.55), and implies a 2σ limit of n_e ≲ 3 × 10³ cm⁻². We also note that the line measurements for C iii] suffer from a similar source of uncertainty as the O ii] λλ3727,2729 doublet due to the lines being redshifted to fall on to a bright sky line. However the nod-and-shuffle strategy employed with the GMOS data helps significantly in limiting the sky line subtraction uncertainties to the Poisson minimum.

The two Gaussian profile fits to each of the [O ii], C iii], and Si iii] doublets are shown in Figure 7. From the three electron density indicators, there is a strong preference for the low-density regime, with n_e ⩽ 10³ cm⁻². We also note that the apparent offset in density values preferred by the [O ii] and C iii] doublets may simply reflect the fact that these doublets trace the electron density of the low and medium ionization zones, respectively (Quider et al. 2009; Christensen et al. 2012a; James et al. 2014).

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There is very strong [O iii] λλ4960, 5008 emission, but no detection of [O iii] λ4364 in the FIRE spectrum. We use the non-detection of [O iii] λ4364 to place a limit on the electron temperature in the nebular line emitting regions following the method of Izotov et al. (2006, Section 3.1, Equations (2) and (3)). Izotov et al. (2006) point out that the electron density becomes unimportant to the electron temperature determination for values of n_e ≲ 10³ cm⁻², and our constraint on n_e from the previous section places SGAS J105039.6+001730 in that regime. From the [O iii] λλ4960, 5008 lines and the [O iii] λ4364 limit, we place a limit on T_e (O iii) ⩽ 1.4 × 10⁴ K.

An alternative method for estimating the electron temperature is available to us by measuring the flux ratios between the O iii] λλ1661,1666 and [O iii] λλ4960,5008 (Villar-Martín et al. 2004; Erb et al. 2010). We have good detections of all the relevant lines, so this method allows us to measure a precise temperature rather than a limit. However, this measurement has its own caveats, primarily a large sensitivity to the intrinsic extinction, and a large uncertainty between the absolute flux calibrations of the optical (GMOS) and NIR (FIRE) spectra. With these caveats in mind, we measure T_e = 11300$^{+1400}_{-1000}$ K (measurement uncertainties only), which agrees well with the T_e constraint from the FIRE spectrum alone. When we fold in the additional uncertainty between the relative flux calibrations of the GMOS and FIRE data, as well as the uncertainty in our best-fit value for the dust extinction (A_V = 1 ± 0.2) we find that T_e constraint from the O iii] λλ1661,1666 to [O iii] λλ4960,5008 line ratio is quite broad: 4000 < T_e < 15,000 K. This is less constraining (for physically plausible values of T_e) than the limit derived from the non-detection of [O iii] λ4364. From here on out we proceed with the T_e ⩽ 1.4 × 10⁴ K constraint on the electron temperature.

In the next two subsections, we apply several different oxygen and ionic abundance indicators to our observations of SGAS J105039.6+001730. The results are summarized in Table 7. For all of these calculations we include a systematic uncertainty term that results from the uncertainty in the extinction correction (A_V = 1 ± 0.2) that is applied to the oxygen lines.

4.7.1. T_e Direct Oxygen Metallicity

4.7.2. R₂₃

4.7.3. Ne3O2

4.7.4. Average Oxygen Abundance Metallicity

4.8.1. Ionization Parameter, log(U)

4.8.2. Ne⁺⁺ Abundance

4.8.3. C⁺⁺/O⁺⁺ Abundance Ratio

4.8.4. N⁺⁺/O⁺⁺ Abundance Ratio

4.8.5. Si⁺⁺/C⁺⁺ and Si⁺⁺/O⁺⁺ Abundance Ratios

The P Cygni ISM absorption/emission features that we observe in the rest-UV are the byproduct of powerful winds that are typically associated with Wolf–Rayet (W-R) stars. To try and understand the physical implications of the wind features in the spectrum of SGAS J105039.6+001730, we compare our data against Starburst99 models (S99; Leitherer et al. 2010).

Both our GMOS and MagE data include each of the N v λλ1238,1240, Si iv λλ1393,1402, and C iv λλ1548,1551 doublets, though the N v λλ1238,1240 feature is never detected at high S/N. The MagE spectrum is much higher spectral resolution than the GMOS spectrum, and would be the ideal data set for comparison against synthetic spectra. However, we were limited to collecting one hour of integration time with MagE, and that taken at relatively high airmass and in highly variable seeing. As a result, the MagE data do not provide a superior comparison against the S99 model spectra than the GMOS data, and so we focus on S99 model-GMOS comparisons from here on out.

We generate an array of S99 models assuming both continuous and instantaneous star formation scenarios. The continuous star formation models also spanning a range in metallicities from solar to 2% solar, and a range in ages of 2–40 Myr. Our instantaneous models all assume a metallicity of 0.4 Z_☉ and span the range in ages (2–100 Myr), and also allow for variation in the maximum stellar mass formed, ranging from 30 to 120 M_☉. In Figure 8, we plot two of the continuous star formation model synthetic spectra on top of the GMOS data in the regions surrounding the three strong P Cygni features noted previously (N v, S iv, and C iv). The specific models plotted have metallicities of 0.4 Z_☉—in line with the metallicity we measure from nebular line diagnostics—and ages of 2 Myr and 40 Myr. The S99 synthetic spectra assuming an instantaneous burst of star formation are shown in Figure 9, also plotted for two stellar population ages (2 Myr and 10 Myr). None of the models with either continuous or instantaneous star formation can reproduce the combination of narrow and deep absorption features, the shape of the absorption trailing off blueward of the C iv line center, or the narrow and strong emission from Si iv and the broader strong emission from C iv. The strength of the observed Si iv and C iv emission could imply that these features are at least partly nebular in origin, rather than resulting entirely from the winds and atmospheres of massive stars.

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He ii λ1640 emission appears in the GMOS and MagE spectra of SGAS J105039.6+001730. This feature appears in composite spectra of z ∼ 3 galaxies (Shapley et al. 2003) and in the spectrum of individual strongly lensed z ∼ 2–4 galaxies (e.g., Cabanac et al. 2008; Dessauges-Zavadsky et al. 2011), but typically appears as a broad emission feature that is associated with the winds of W-R stars, and exhibits velocity widths of ∼1000 km s⁻¹. However, the He ii λ1640 detected from SGAS J105039.6+001730 has a width of ∼330 km s⁻¹ in the GMOS spectrum, which matches the resolution of that data. The feature is too low S/N in the MagE spectrum to inform a multiple component fit to the velocity profile, but a simple Gaussian fit to the line prefers an FWHM that is consistent with the resolution of the MagE spectra (∼75 km s⁻¹), implying that a significant fraction of the emission does indeed originate from a narrow distribution in velocity space, and therefore is likely resulting from nebular emission rather than W-R winds.

Explaining such strong, narrow emission from He ii requires extreme ionization. The He ii λ1640 line is extremely bright in SGAS J105039.6+001730, with a total flux ratio of He ii λ1640/Hβ ∼ 0.17 after applying the extinction correction, and likely originates in part from nebular emission. Erb et al. (2010) note the presence of significant nebular He ii λ1640 emission in a bright field-selected LBG at z = 2.3, and find that high ionization parameter values are required to explain the ratio that they measure for He ii λ1640/Hβ of 0.3, and an equivalent width of 2.7 Å.

We also compare the equivalent width, W₁₆₄₀, of He ii λ1640 in SGAS J105039.6+001730 against predictions for the W-R wind He ii λ1640 emission strength in the S99 models described above; we measure W₁₆₄₀ = 1.5 ± 0.15 Å. The S99 models only generate values this high for an extremely short-lived stretch (t_age ∼ 5–7 Myr) and only in models with solar metallicity (in strong disagreement with all of the metallicity diagnostics measured in Section 4.7). As noted previously, He ii λ1640 emission originating from W-R winds would be much broader than the unresolved line that we see in the GMOS spectrum. Finally, we also see no evidence of a P Cygni blue shifted absorption feature in the He ii λ1640 feature, which further argues against this line as originating entirely from W-R winds.

HST imaging enables us to examine the morphology of SGAS J105039.6+001730 via both the internal structure of the arc itself, as well as the much less distorted counter image. The counter image appears extremely irregular, and contains several distinct emission knots. The giant arc also includes multiple images of three distinct knots of emission, one of which is considerably redder than the rest of the arc. The central emission knot in the counter image also appears notably redder. While the knots have different IR-optical colors, all are extremely bright in the optical (rest-UV). This suggests that there is active star formation throughout SGAS J105039.6+001730, but that the redder central knot likely has a larger underlying population of older stars. It is possible that the redder knot corresponds to the core of the galaxy, which possibly hosts the early stages of an assembling bulge, and that the bluer emission from the outskirts of the galaxy is preferentially tracing small but intense star forming regions.

5.2.1. Strength of the C iii] Feature

Strong C iii] λλ1907,1909 emission is not ubiquitous in star forming galaxies at moderate redshift (e.g., z ∼ 2 composite; Shapley et al. 2003). It is therefore interesting to compare SGAS J105039.6+001730 against individual low redshift star forming galaxies with good UV spectra to try and understand the astrophysical conditions that are conducive to producing strong C iii] λλ1907,1909. The galaxy sample compiled by Leitherer et al. (2011, hereafter L11) is an excellent comparison set, with HST UV spectra of 46 star forming regions within 28 galaxies with z < 0.06.

We examine the individual spectra that were analyzed in L11, and measure the equivalent width, W₁₉₀₉, of the C iii] λλ1907,1909 line in the L11 spectra. In Figure 10, we show the relationship between W₁₉₀₉ and metallicity in the L11 sample; there is a dearth of galaxies with both a large W₁₉₀₉ and high metallicity, indicating that C iii] λλ1907,1909 emission may be suppressed in high metallicity star forming galaxies. SGAS J105039.6+001730 has a larger W₁₉₀₉ than all but 2 of the 25 L11 galaxies, yet it has a metallicity, 12 + log(O/H) = 8.3, which coincides almost exactly with the apparent turn-off of strong C iii] emission in the L11 sample. The C iii] lines are forbidden and semi-forbidden transitions, so any such suppression must be the result of one or more indirect mechanisms, unlike the suppression of resonant lines such as Lyα.

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A similar relationship has also recently been observed in low-mass high redshift galaxies (D. P. Stark 2014, private communication; D. P. Stark et al. 2014, in preparation), where W₁₉₀₉ appears to be correlated with the strength of Lyα emission. In this context SGAS J105039.6+001730 is puzzling, in that it exhibits a strong DLA feature, which is opposite of what one should expect given a correlation between W₁₉₀₉ and W_{Ly − α}. The strength of C iii] emission in SGAS J105039.6+001730 is difficult to understand in light of this galaxy's other observable properties and the apparent tendency for strong C iii] emission to coincide with strong Lyα emission and low metallicity. It would seem that the physics which dictate strong C iii] cannot be summarized according to a simple correlation against a single fundamental physical quantity (e.g., metallicity).

5.2.2. Relative C/O, N/O, Si/O Enrichment

Based on the strength of the P Cygni features in SGAS J105039.6+001730, we expect the extremely low metallicity models to do a poor job of reproducing the observed features, and this holds true. Models with metallicities of 0.4 Z_☉ result in the best agreement with our data, which is encouraging given that we measure the metallicity to be ∼0.4 Z_☉ from nebular emission line diagnostics. However, none of the synthetic spectra that we generate using S99 produce the combination of P Cygni features that we observe in of SGAS J105039.6+001730. The most challenging features to explain are the narrow shape and exceptional strength of the blueshifted absorption features, as well as the strength of the redshifted C iv emission and the odd, strong emission from S iv λ1393. Qualitatively these features indicate the presence of an extremely young population of massive stars. Some recent work has also explored the ways in which stellar rotation can affect the spectra of massive stars, and find that including rotation effects in the modeling of stellar spectra can result in a increase in the amount of ionizing radiation, hardening of the ionizing radiation, and stronger profiles for some lines, including the UV Si iv and C iv P Cygni features (Levesque et al. 2012; Leitherer et al. 2014).

Our results here are reminiscent of the difficulty that other studies have encountered comparing synthetic spectra against observations of galaxies at z ≳ 2 (Pettini et al. 2000; Shapley et al. 2003; Quider et al. 2009; Erb et al. 2010). As suggested by Erb et al. (2010), the excess emission features could be explained, at least in part, by nebular emission. The presence of nebular emission from these transitions does, however, agree with the properties of the He ii λ1640 emission line discussed above, and would imply an extremely hard ionizing radiation field from massive O stars.

One possible explanation for what we observe in SGAS J105039.6+001730 is that the integrated spectrum that we measure across a wide range of wavelengths is a blend of the properties from several different star forming regions embedded within the galaxy. Different star forming regions could be generating extreme spectral features that dominate the observable signal in some regions of the spectrum (e.g., the rest-UV) while only contributing in part to other parts of the spectrum (e.g., the rest optical). The superposition of a "normal" star forming galaxy with small, highly magnified regions of intense and short-lived star formation could be responsible for generating the complex spectral features that defy reproduction by a simple monolithic synthetic population of stars. There is, in fact, a body of published work that uses real (Kobulnicky et al. 1999; James et al. 2013a, 2013b) and simulated (Pilyugin et al. 2012) observations of well-studied low-redshift star forming galaxies to explore the biases that can result from simple analyses of the integrated spectra of distant galaxies. Recent observations of different line of sight within a single lensed star forming galaxy also shows clear evidence of different physical conditions in different star forming regions (Rigby et al. 2014). There is clear evidence to suggest that spatially resolved spectroscopy will be essential for constraining some of the physical properties of high redshift star forming galaxies.

It is physically unlikely that all of our measured He ii λ1640 line flux is nebular in origin, as that would require ionization parameters > − 1 according to the models explored by Erb et al. (2010). Even assigning only ∼25% of the flux to nebular emission requires an ionization parameter of log(U) > −2 for metallicities in the range that we measure for SGAS J105039.6+001730, according to the models explored by Erb et al. (2010). A physical picture in which there are one or more extreme star forming region(s) within SGAS J105039.6+001730 is also consistent with evidence that unresolved starbursts have a maximum ionization parameter, log(U) ∼ −2.3 (Yeh & Matzner 2012), implying that diagnostics indicating significantly larger values of log(U) are likely to be sampling individual extreme star forming regions within galaxies (e.g., Snijders et al. 2007; Indebetouw et al. 2009).

Another possible explanation for the strong He ii λ1640 line is the presence of an exceptionally hard ionizing spectrum. The ionization parameter, U, only describes the intensity of ionizing radiation; a very hard ionizing spectrum with relatively low intensity can generate a large amount of nebular He ii emission even given a low ionization parameter. An IMF that generates more of the hottest, most massive stars, for example, could account for a harder ionizing spectrum than considered by the models of Erb et al. (2010). However, arguments that are based on the vague, qualitative implications of varying the IMF are distasteful and presumptive when one considers that the spectral properties of the most massive stars are not well understood, especially at low metallicity (e.g., Rigby & Rieke 2004).

The strong, narrow, He ii λ1640 emission that we detect in SGAS J105039.6+001730 presents a puzzle. It either casts serious doubt on the ionization parameter diagnostics that we compute and rely on throughout Section 4.8, or it suggests a hard ionizing spectrum that is difficult to reconcile with the electron temperature constraints available from rest-frame optical emission lines.

Returning to the explanation that we put forth in the previous subsection, it seems likely that the integrated spectrum of SGAS J105039.6+001730 is too complex to be described by a simple stellar population, or a single list of parameters (i.e., a single ionization parameter, electron temperature, metallicity, etc.). Rather, it is possible that the [O iii] λλ4960,5008, [O ii] λλ3727,3729, [Ne iii] λ3869, and He ii λ1640 lines are in fact blends of multiple components which are originating from different physical regions within the galaxy. A relatively small but extreme region of recent star formation with a large population of hot massive stars could, for example, produce strong He ii emission, while other more "normal" regions within the galaxy could be responsible for weighting the measured [O iii]/[O ii] and [Ne iii]/[O ii] line ratios toward more typical values.

In cases where we are studying the physical properties of strongly lensed star forming galaxies, it is easy to imagine that differential magnification effects across the surface of the background galaxy can generate integrated observable quantities that are weighted toward the highest surface brightness regions within the lensed galaxy, which would naturally tend to be the regions of most intense unobscured star formation (e.g., Er et al. 2013). This issue is not, of course, unique to strongly leaned galaxies at high redshift. Studies of the integrated properties of any distant galaxy must, ultimately, account for the fact that properties such as metallicity, SFR and ionization are not held uniform throughout a given galaxy. The fundamental scale of star formation in the universe is much smaller than a galaxy, and individual galaxies can (and should) therefore host a range of star forming regions with physically different properties. This point is emphasized by the few published studies of lensed galaxies with IFU units in the NIR (e.g., Stark et al. 2008; Wuyts et al. 2014). Spatially resolved/IFU spectroscopy of distant sources is a powerful tool for confronting some of the dangers that result from analysis (or over-analysis) of integrated spectra of these galaxies. It is also sensible that the diversity of properties within an individual galaxy could vary more dramatically in the earlier universe, when star formation was still ramping up to its peak and galaxies had yet to assemble a majority of their stars relative to galaxies in the present epoch.