The Magellan Evolution of Galaxies Spectroscopic and Ultraviolet Reference Atlas (MegaSaura). II. Stacked Spectra

The MegaSaura sample and MagE spectra are described in detail in Paper I. The N = 15 galaxies span the redshift range 1.6 < z < 3.6 and are among the brightest lensed sources selected from the Sloan Digital Sky Survey; the brightest have a g-band magnitude of ${g}_{{AB}}\lesssim 21$. By selection, the MegaSaura galaxies are skewed toward galaxies with high rest-frame UV surface brightness, i.e., vigorously star-forming galaxies with relatively low dust content. We are compiling star formation rates and stellar masses for the whole sample; a subset have published physical propert-ies, with stellar masses of (3–$7)\times {10}^{9}$ M${}_{\odot }$, stellar ages of ∼100 Myr, $E(B-V)=0.10$–1.0, and star formation rates of 20–100 M${}_{\odot }$yr⁻¹(Wuyts et al. 2012; Bayliss et al. 2014). Seven of the MegaSaura galaxies have metallicity measurements, which are tabulated in Table 2 of Paper I. The measurements range from $\lt 25 \% \,{Z}_{\odot }$ to $\lt 81 \% \,{Z}_{\odot }$, with a median measured metallicity of $37 \% \,{Z}_{\odot }$.

In brief, the MegaSaura spectra are of high S/N and moderate spectral resolution. They were obtained with the MagE instrument (Marshall et al. 2008) on the Magellan telescopes. The spectra cover the rest-frame ultraviolet ($900\lesssim {\lambda }_{r}\lesssim 3000$ Å). The spectral resolving powers range from R = 2500 to R = 4700. The median–quality spectrum has S/N = 21 per resolution element at ${\lambda }_{\mathrm{obs}}=5000\,\mathring{\rm A}$.

The input spectra have been corrected for Milky Way reddening, using the $E(B-V)$ value derived from from Pan-STARRS 1 and 2MASS photometry by Green et al. (2015), assuming an extinction-to-reddening constant of R_v = 3.1 and the reddening curve of Cardelli et al. (1989). Table 1 of Paper I lists the Galactic $E(B-V)$ values that were used.

We exclude the galaxy SGAS J224324.2−093508 from the stack, as the MagE spectrum reveals it to contain a broad-line active galactic nucleus (AGN; see Section 3.2 of Paper I). This reduces the number of galaxies stacked to N = 14.

As detailed in Table 1 of Paper I, for a few MegaSaura galaxies, we have obtained spectra of multiple distinct physical regions, because we placed spectroscopic slits at different positions along the highly magnified giant arcs. To prevent these galaxies from dominating the stack, we do not include the spectra of each physical region of a lensed galaxy in the stacking process. Instead, we use the spectrum of the physical region with the highest S/N. As the stack is weighted by S/N, such spectra would be the dominant contribution from their input galaxy in any case.

Before stacking, the input spectra must be shifted to rest-frame wavelength. This is done using systemic redshifts from Paper I. For this sample, we have access to both nebular line redshifts and stellar redshifts. The stellar redshift was measured by fitting linear combinations of Starburst99 (Leitherer et al. 1999, 2010) simple stellar population models to each spectrum, while simultaneously fitting for reddening, following the methodology of Chisholm et al. (2015). These fits were made using a linear combination of 10 single-aged, fully theoretical Starburst99 models and 5 different stellar continuum metallicities (0.01, 0,2, 0.4, 1.0, and 2.0 Z${}_{\odot }$). The median light-weighted stellar metallicity is 0.37 Z${}_{\odot }$, and the light-weighted stellar age is 10 Myr. The theoretical stellar continuum models were compiled using the WM-BASIC code (Leitherer et al. 1999, 2010) with the Geneva stellar evolution tracks with high mass loss (Meynet et al. 1994). We used a Kroupa IMF, with a power-law index of 1.3 (2.3) for the low (high) mass slope, and a high-mass cut-off at 100 M${}_{\odot }$. We fully discuss these models in an upcoming paper (J. R. Rigby et al. 2018, in preparation). Given this method of fitting the stellar continuum, the stellar redshift is dominated by the myriad weak photospheric absorption features. The nebular redshift was measured by fitting two Gaussians to the [C iii] 1907, C iii] 1909 Å doublet, except as noted in Table 3 of Paper I. We noted in Paper I that there is no systematic offset between the redshifts of the hot stars and the nebulae; the median offset and median absolute deviation are −1 ± 31 km s⁻¹.

We experimented with the choice of systemic redshift for the stacks: nebular or stellar. Unsurprisingly, the nebular emission lines are narrower when the nebular redshifts were used as systemic. The line profiles of the photospheric absorption lines near ${\lambda }_{\mathrm{rest}}=1300$ Å are similar for the two choices of systemic redshift. As the nebular redshifts are more precise, we use the nebular redshifts as the systemic redshifts for all the stacks of the MegaSaura spectra.

Before stacking, we normalize each spectrum, using one of the following methods:

• 1.  
  Divide each input spectrum by its hand-fit spline continuum from Paper I. This normalizes both the zeropoint and shape of each input spectrum and prevents the stack from "ringing" at the edges of the bandpass, due to small numbers statistics and a range of spectral slopes. The output spectrum should have a flat spectral shape, with the exception of the region near and blueward of Lyα, where continuum fitting is extremely challenging. This stack is best suited for measuring the equivalent widths of faint emission lines, as for this application the galaxy's intrinsic spectral shape is not important. It can also be used to study absorption features from the interstellar medium (ISM). We call the composite spectrum that results from this method the shape-normalized stack.
• 2.  
  Divide each input spectrum by the median flux density within a pivot wavelength range: $1267\lt {\lambda }_{r}\lt 1276\,\mathring{\rm A}$. This region was chosen because it is centrally located in the spectra and contains relatively few spectral features. This normalization affects only the zeropoint of each input spectrum and preserves the spectral shape. As a result, when spectra with very different slopes are averaged, the output spectrum may show "ringing" at wavelengths far from the pivot wavelength where the spectra were normalized. As this stack preserves spectral shape, it is the stack to which we can fit stellar population synthesis models. We call the composite spectrum that results from this method the ${\lambda }_{\mathrm{pivot}}$-normalized stack.
• 3.  
  Divide each input spectrum by its best-fit model linear combination of Starburst 99 models from J. R. Rigby et al. (2018, in preparation). This normalization affects both the zeropoint and the spectral shape. This stack may be the best for analyzing ISM absorption profiles, as the stellar wind features have already been removed. We call the composite spectrum that results from this method the S99-normalized stack.

We stack the MegaSaura spectra of N = 14 gravitationally lensed galaxies as follows. Each input spectrum is continuum-normalized using one of the three normalization methods described above. We then shift it to its rest frame, using the nebular line redshift as the systematic redshift. We then resample, using linear interpolation, onto a common output wavelength grid with a sampling of 0.1 Å.

We take steps to keep the composite spectra free of spurious features due to intervening absorption systems. We identified such systems through a systematic search for intervening Mg ii, C iv, and Si iv doublets in all MegaSaura spectra. In each input spectrum, we mask ±200 km s⁻¹around the positions of all transitions from these intervening absorption systems.

The input spectra, after having been continuum-normalized, de-redshifted, resampled, and masked of intervening absorption systems, are then stacked using two methods: weighted average (weighted by the uncertainty spectra), and median (with no weighting). For most applications, the weighted average is preferable to the median, as it has higher S/N.

To understand the uncertainty in the composite spectra, we perform jackknife tests, in which we compute the weighted average n times, each with a different spectrum masked out. For each stack, we compute two estimates of the per-pixel uncertainty: (a) the uncertainty spectrum propagated from the individual uncertainty spectra, and (b) the jackknife uncertainty ${\sigma }_{\mathrm{jackknife}}$, which measures the variation in the n jackknife spectra:

$$\begin{eqnarray}&&{\sigma }_{\mathrm{jackknife}}^{2}=\displaystyle \frac{(n-1)}{n}\displaystyle \sum _{i=1}^{n}{({x}_{i}-{x}_{(.)})}^{2},\end{eqnarray} \tag{ 1 }$$

where x_i is the pixel value in the ith jackknife spectrum, and ${x}_{(.)}$ is the pixel value in the weighted average spectrum. These two uncertainty estimates, which should be independent, are consistent, as Figure 1 illustrates. Used together, the median spectra and the jackknife uncertainty spectra can be used to check whether a particular spectral feature is unduly influenced by a single galaxy.

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To enable an apples-to-apples comparison of the MagE MegaSaura stack to the spectra of galaxies in the nearby universe, we stack the spectra of $z\sim 0$ galaxies with COS/HST spectra using the G130M and G160M gratings from Chisholm et al. (2016). That local sample is comprised of 41 galaxies¹¹ with star formation rates of 0.01–137 M${}_{\odot }$ yr⁻¹. Each galaxy has blueshifted ISM absorption lines at the 1σ significance level. The stack represents the most complete sample of local star-forming galaxies with COS/HST spectra that show galactic outflows.

The input COS spectra requires extra pre-processing. We mask the expected wavelengths of geocoronal and Milky Way emission lines. The spectral resolution of COS is higher than that of MagE: for a point source, it is R = 16000, but it decreases as emission fills the circular aperture of COS. In the COS spectra we are stacking, the Milky Way absorption lines indicate effective spectral resolutions ranging from R = 4000 to R = 14000, with a median of R = 9000 due to the diffuse, extended morphology of these galaxies in the slit. Therefore, we resample the wavelength grid of each input COS spectrum to be Nyquist sampled for the spectral resolution measured from the Milky Way absorption lines, then convolve by a Gaussian kernel to lower the spectral resolution to that of MagE (R = 3300), and then resample the wavelength array once more, to be Nyquist sampled at R = 3300. Downgrading the effective spectral resolution in this way does not meaningfully change the profiles of absorption lines in the stacked spectrum, but it does change the per-pixel S/N, and as such, the measured maximum velocity.

Given the large number of COS spectra, rather than fit the continuum by hand as for the MagE spectra, we fit the continuum automatically, by masking spectral features and then convolving with a boxcar. Tests using the individual MagE spectra show that this automatic continuum fitting process produces continua that closely track our hand-fit continua. We then stacked the COS shape-normalized input spectra in the same way as we stacked the MagE spectra. The result is a shape-normalized COS stacked spectrum whose spectral resolution and S/N closely match that of the MagE stack (as quantified in Table 1).

We compute two metrics of the absorption line velocity profiles: the maximum blueshifted velocity v_max and the absorption-weighted mean velocity v_mean. We used the weighted-average, shape-normalized stack to measure these metrics, for both the MagE stack and the COS stack.

We calculate the absorption-weighted mean velocity of the absorption line, v_mean, within the interval from ${v}_{\max ,\mathrm{blue}}$ to ${v}_{\max ,\mathrm{red}}$. We restrict ${v}_{\max ,\mathrm{red}}$ < 600 km s⁻¹ to prevent runaway fits in the case of doublets and other closely spaced absorption lines (for example, for C iv 1548).

Steidel et al. (2010) defined v_max as the velocity where the blue wing of the absorption returns to the continuum, specifically the first pixel to return. We adopt this definition for both ${v}_{\max ,\mathrm{blue}}$ and ${v}_{\max ,\mathrm{red}}$, with a caveat to the reader that this metric is sensitive to the S/N and dispersion of the spectrum. This is indeed why, when we stack the $z\sim 0$ COS/HST spectra, we downgrade the resolution to create a stack with similar spectral resolution and noise properties to the MagE stack.

To gauge the uncertainty in v_max and v_mean, we scale the continuum by a factor over the range ±2% (as this seemed the maximum plausible error in the continuum), measure the mean and maximum velocities each time, and quote the mean value and standard deviation.

We measure the equivalent widths of emission lines in the shape-normalized stacked spectrum using the following methodology. We fit each group of neighboring spectral lines simultaneously, with one Gaussian per feature, using the nonlinear least-squares method as implemented in the Python tool scipy.optimize.curve_fit. Neighboring lines are defined as being separated by $\leqslant 5$ spectral resolution elements. We use the equivalent width significance criterion of Schneider et al. (1993).

The stacked spectra span a rest-frame wavelength range of $900\lt {\lambda }_{\mathrm{rest}}\lt 3000$ Å, with 0.1 Å pixels. We calculate the median S/N per resolution element in four regions that are free of spectral lines: S/N = 76 for 1440–1450 Å, S/N = 92 for 1460–1470 Å, S/N = 79 1680–1700 Å, and S/N = 101 1760–1800 Å. Figure 1 plots the stacked spectrum, the S/N per resolution element, and the number of galaxies that went into the stack at each wavelength. The average spectral resolving power of the input spectra is R = 3300. Table 1 compares these metrics to those of composite spectra in the literature. The stacked spectra are available online in a supplemental tar.gz archive.

Figure 2 and Table 1 demonstrate that the MegaSaura stacked spectrum has a broader rest-frame wavelength coverage, higher S/N, and higher spectral resolution than previously published composite spectra made from starburst/LBG field galaxies (Shapley et al. 2003; Steidel et al. 2016). The subpanels of Figure 2 show that, unlike previous composites, the MegaSaura stack has the combination of spectral resolution and S/N required to clearly detect faint spectral features and to measure the shapes of absorption lines. The composite MegaSaura spectra therefore provide the best census of rest-frame UV properties of starburst galaxies in the era of "cosmic noon". We publicly release the MegaSaura composite spectra, and encourage their use as templates for understanding $z\sim 2$ star-forming galaxies.

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In Figure 3, we show the shape-normalized stack, highlighting a number of diagnostic lines, including transitions that arise variously in the ISM, nebular gas, and stellar photospheres.

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For those interested in the strengths of faint emission lines, we recommend using the shape-normalized weighted average stack. For those interested in the overall spectral shape, we recommend using the ${\lambda }_{\mathrm{pivot}}$-normalized weighted average stack.

Table 2 reports the equivalent width measurements for N = 18 rest-frame UV emission lines detected in the MegaSaura shape-normalized stacked spectrum. Table 2 also reports upper limits for undetected emission lines that we expect to be generated in the ionized gas in starburst galaxies. The rest-frame UV emission lines should be useful as diagnostics of physical conditions such as the pressure of the ISM (Kewley et al. submitted to ApJ), electron temperature (D. C. Nicholls et al. 2018, in preparation), ionization parameter, metallicity, and the relative abundance pattern (Bayliss et al. 2014, L. J. Kewley et al. 2018, in preparation). By publishing the measured equivalent widths of the composite, we hope to assist observers in estimating the integration times required to detect these lines at high redshift with James Webb Space Telescope (JWST).

Table 2.  Emission Lines

Line	${\lambda }_{\mathrm{vac}}$ (Å)	Wr (Å)	Uncertainty Wr (Å)	Significance
C iii 977	977.0200	>−0.1461	⋯	⋯
He ii 1084	1084.9420	>−0.0758	⋯	⋯
Lyα	1215.6700	−1.2654	0.04	50.65
O i 1304	1304.8576	>−0.0352	⋯	⋯
O i* 1306	1306.0286	>−0.0348	⋯	⋯
Si ii 1309	1309.2757	−0.2441	0.02	21.26
C ii 1335a	1334.5770	>−0.031	⋯	⋯
C ii* 1335b	1335.6630	>−0.0349	⋯	⋯
C ii* 1335c	1335.7080	>−0.035	⋯	⋯
N ii] 1430	1430.4100	>−0.0306	⋯	⋯
N ii]1431	1430.9730	>−0.0306	⋯	⋯
N iv] 1486	1486.5000	−0.0428	0.02	4.12
Si ii* 1533	1533.4312	−0.0367	0.01	3.41
He ii 1640 broad	1640.4170	−0.98	0.1	–
He ii 1640 narrow	1640.4170	>−0.22	⋯	⋯
O iii] 1660	1660.8090	−0.0634	0.01	6.37
O iii] 1666	1666.1500	−0.1716	0.02	13.98
N iii] 1750	1749.7000	>−0.0286	⋯	⋯
Si iii] 1882	1882.7070	−0.0673	0.01	5.70
Si iii] 1892	1892.0290	>−0.0357	⋯	⋯
[C iii] 1906	1906.6800	−0.5214	0.02	38.37
C iii] 1908	1908.7300	−0.3956	0.02	30.26
N ii] 2140	2139.6800	−0.0649	0.02	4.46
[O iii] 2320	2321.6640	>−0.0571	⋯	⋯
C ii] 2323	2324.2140	>−0.0533	⋯	⋯
C ii] 2325c	2326.1130	−0.4034	0.09	19.61
C ii] 2325d	2327.6450	−0.2055	0.07	10.35
C ii] 2328	2328.8380	−0.064	0.04	3.17
Si ii] 2335a	2335.1230	>−0.0608	⋯	⋯
Si ii] 2335b	2335.3210	>−0.0625	⋯	⋯
Fe ii* 2365	2365.5520	−0.183	0.02	9.40
Fe ii* 2396a	2396.1497	>−0.0578	⋯	⋯
Fe ii* 2396b	2396.3559	>−0.0576	⋯	⋯
[O ii] 2470	2471.0270	−0.3584	0.02	18.77
Fe ii* 2599	2599.1465	>−0.0596	⋯	⋯
Fe ii* 2607	2607.8664	>−0.0659	⋯	⋯
Fe ii* 2612	2612.6542	>−0.0665	⋯	⋯
Fe ii* 2614	2614.6051	>−0.0575	⋯	⋯
Fe ii* 2618	2618.3991	>−0.0632	⋯	⋯
Fe ii* 2621	2621.1912	>−0.0627	⋯	⋯
Fe ii* 2622	2622.4518	>−0.0676	⋯	⋯
Fe ii* 2626	2626.4511	>−0.0656	⋯	⋯
Fe ii* 2629	2629.0777	>−0.068	⋯	⋯
Fe ii* 2631	2631.8321	>−0.0672	⋯	⋯
Fe ii* 2632	2632.1081	>−0.0655	⋯	⋯
Mg ii 2797b	2798.7550	−0.367	0.04	14.58
Mg ii 2797d	2803.5310	−0.3522	0.04	14.20
He i 2945	2945.1030	>−0.1063	⋯	⋯

Note. Rest-frame ultraviolet emission lines in the shape-normalized stacked spectrum. Columns are: (1) line identification, (2) vacuum wavelength (Å), (3) measured rest-frame equivalent width (Å) (with negative sign indicating absorption), (4) uncertainty on the previous column, and (5) significance of the detected feature, in σ, according to the Schneider et al. (1993) significance criterion. Non-detections are quoted as $3\sigma$ limits. Note: The C ii 232X complex is challenging to fit given the close spacing of the four emission lines. The total equivalent width of the complex is well-measured, at ${W}_{r}=-0.68\pm 0.14$, but the fit is degenerate as to which components contain most of the flux. We therefore fit the complex by fixing the relative strengths of the lines to the predictions of MAPPINGS V.

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Narrow He ii 1640 Å is not detected in the stacked spectrum. However, a broad (FWHM ∼ 2800 km s⁻¹) excess of emission is seen over the continuum level—this may be stellar in origin. Table 2 quotes an equivalent width limit for the undetected narrow component and an equivalent width measurement for the broad component.

We now consider the velocity profiles of galactic and stellar winds as seen in the stacked MegaSaura spectra. The MegaSaura stacks have the high S/N that is required to probe outflows at the highest velocities, where the absorption deficit drops to the order of a few percent of the continuum, and are of sufficient quality to enable apples-to-apples comparisons between distant lensed starburst galaxies and some of the most vigorously star-forming galaxies in the nearby universe.

Figure 4 compares the velocity profiles of strong absorption features in two different stacks: the shape-normalized stacked spectrum of the MegaSaura galaxies and our stack of the $z\sim 0$ galaxy COS spectra from Chisholm et al. (2016). The velocity profiles of the $z\sim 2$ stack are remarkably similar to those of the $z\sim 0$ stack, suggesting gross similarity between the galactic winds at these two very different epochs.

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Table 3 quantifies this similarity; it tabulates absorption-weighted mean velocity and maximum velocity measurements for the MegaSaura shape-normalized stack, and for the COS/HST stack for the major absorption lines in the spectra. The next three subsections analyze the measurements in Table 3.

Table 3.  Absorption Velocity Measurements

transition	IP	vmean	σ	vmax	σ	vmean	σ	vmax	σ
	(eV)	(km s−1)	(km s−1)	(km s−1)	(km s−1)	(km s−1)	(km s−1)	(km s−1)	(km s−1)
MegaSaura MagE/Magellan shape-normalized stack
		Measurements of weighted average stack				Measurements of median stack
O i 1302	13.6	...	...	$\lt -500$ a	...	...	...	$\lt -500$ a	...
Mg ii 2796	15.0	−310	3	−885	0	−271	10	−721	72
Fe ii 2344	16.2	−225	20	−965	111	−178	15	−741	50
Fe ii 2383	16.2	...	...	$\lt -840$ b	...	...	...	$\lt 840$ b	...
Si ii 1260	16.35	−97	1	−772	37	−203	1	−740	24
Si ii 1526	16.35	−92	1	−632	30	−138	4	−606	39
Al ii 1670	18.8	−128	18	−707	40	−145	34	−634	27
C ii 1334	24.4	−53	13	−938	183	−163	25	−971	227
Al iii 1854	28.4	−568	136	−2268	494	−275	148	−984	513
Si iv 1393	45.1	−260	76	−1327	406	−419	67	−2097	290
C iv 1548	64.49	−517	43	−2696	159	−535	41	−2513	150
COS/HST R = 3300 shape-normalized stack
		Measurements of weighted average stack				Measurements of median stack
O i 1302	13.6	...	...	$\lt -500$ a	...	...	...	$\lt -500$	...
Si ii 1260	16.35	−189	6.0	−815	20	−179	6	−906	48
Si ii 1526	16.35	−107	3.0	−574	0	−114	0	−532	0
Al ii 1670	18.8	−64	34.0	−431	51	−88	61	−399	0
C ii 1334	24.4	−191	17.0	−1561	86	−104	2	−684	34
Si iv 1393	45.1	−345	49.0	−1833	329	−371	10	−1733	51
C iv 1548	64.5	−355	27.0	−2386	172	−516	28	−2441	154

Note. Columns are: (1) line label; (2) ionization potential in electron volts; (3) absorption-weighted mean velocity v_mean for the weighted average stack; (4) uncertainty in v_mean; (5) maximum velocity v_max for the weighted average stack; (6) uncertainty in v_max; and (7)–(10) same as (3)–(6) but for the median stack. N v 1238 is not listed because absorption was not clearly detected.

^aBlend with photospheric absorption. ^bBlend with Fe ii 2374 absorption.

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The wavelength coverage of the MegaSaura stacked spectra is sufficiently broad ($900\lt {\lambda }_{\mathrm{rest}}\lt 3000$ Å) to cover a large number of transitions, spanning a large range of ionization potential, which can be used to characterize the galactic and stellar winds. In Figures 5(a)–(c), we plot the absorption profiles for several absorption lines of interest.

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In Figure 5(a), we consider the transitions of Mg ii 2796, Fe ii 2344, and Fe ii 2383.¹² These transitions have ionization potentials of 15.0 eV (Mg ii) and 16.2 eV (Fe ii) and are associated with spatially resolved, large-scale outflows in galaxies at $z\sim 1$–2 (Martin and Bouché 2009; Weiner et al. 2009; Rubin et al. 2010, 2011; Giavalisco et al. 2011; Erb et al. 2012; Kornei et al. 2013; Bordoloi et al. 2014; Rigby et al. 2014; Rubin et al. 2014). In the MegaSaura weighted-average shape-normalized stack, these transitions have a maximum velocity of $| {v}_{\max }|$ = 900 km s⁻¹ (Table 3.)

Bordoloi et al. (2016) analyzed the velocity profiles of four regions within one of these galaxies, RCS-GA 032727−132609, and found 95th percentile velocities of 460–610 km s⁻¹ for these transitions. Mg ii is at the extreme red end of the MegaSaura stack and so only four galaxy spectra went into the stack; seven galaxies contribute to the stack for Fe ii 2344 and Fe ii 2383. Knot E of RCS-GA 032727−132609 contributed to the stack for both Mg ii and Fe ii. Despite those small numbers, the maximum velocities we measure for Mg ii and Fe ii confirm and extend the conclusion of Bordoloi et al. (2016): a substantial fraction of the Mg ii and Fe ii gas column has velocities far exceeding the plausible escape velocity of their galactic hosts.

We next analyze the absorption velocity profiles of other low-ionization transitions, plotted in Figure 5(b). The main transitions that trace the neutral gas are Lyα and O i 1302, as they have low ionization potentials (13.6 eV). However, a maximum wind velocity cannot be measured for O i 1302 because of nearby photospheric absorption lines, and Lyα is difficult to interpret due to resonant scattering. Instead, we must estimate the wind velocity from Si ii, Al ii, and C ii, which have ionization potentials of 16.3, 18.8, and 24.4 eV, respectively, and therefore trace a mixture of neutral and ionized gas. This absorption has $| {v}_{\max }|$ ∼ 630–940 km s⁻¹ in the MegaSaura weighted-average shape-normalized stack.

The maximum velocities we measure, for both the MagE and COS stacks, are comparable to the $| {v}_{\max }|$ $=\,\sim 700$–800 km s⁻¹  measured for Si ii and C ii in the composite stacked spectra of $z\sim 2.3$ galaxies of Steidel et al. (2010) and comparable to the value of $| {v}_{\max }|$ = 900 km s⁻¹  measured in Si ii 1260 for the $z\sim 0$ stack of Alexandroff et al. (2015) (see Figure 1 of Heckman et al. 2015).

In Figure 6, we plot the maximum velocity (blue points) and mean velocity (red points) versus ionization potential for the MagE and COS stacks. For the low-ionization lines (${IP}\,\lt 25$ eV), we find that the velocity does not strongly depend on ionization potential. Rather, the mean velocities for both samples are between −50 and −300 km s⁻¹, and the maximum velocities for both samples cluster between −500 and −1000 km s⁻¹. These results are consistent with those of Chisholm et al. (2016), who found that the overall strength of the transition, not the ionization potential, determines the measured velocity. The maximum and mean velocities are very similar between the MagE and COS samples for are very similar for each low-ionization transition. Further, the velocity profiles are very similar for these two very different epochs (see Figure 4.) We conclude that the average galactic outflow does not appreciably change from $z\sim 2$ to $z\sim 0$, which suggests that similar physical processes (acceleration mechanisms, for example) establish the outflow profiles.

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Thus, the galactic wind in the MegaSaura stacked spectrum shows a maximum blueshifted velocity that approaches but does not exceed 1000 km s⁻¹. Having established the maximum velocity of the galactic wind as traced by low ionization lines, we now examine the maximum velocities seen in high ionization transitions.

In Figure 5(c), we plot the absorption profiles of transitions with high ionization potentials, 28.4–97.9 eV. These include transitions that show classical P Cygni line profiles and are assumed to arise in stellar winds. Surprisingly weak are the emission components of N v 1238, Si iv 1393, and C iv 1548. The weakness of this emission indicates that Wolf Rayet stars and/or the most massive O stars are present, but rare.

We consider the absorption profiles of these high ionization lines. N v 1238 is difficult to measure given the complexity of the continuum near Lyα. C iv 1548, Si iv 1393, and Al iii 1854 all show similar velocity profiles: strong absorption at velocities close to systemic, presumably from the ISM, as well as a blueshifted absorption tail extending to $| {v}_{\max }|$ =1300–2700 km s⁻¹. In C iv, this blueshifted absorption tail is detectable in individual MegaSaura spectra with high S/N, namely RCS-GA 032727−132609, SGAS J010842.2+062444, SGAS J003341.5+024217, SGAS J090003.3+223408, the Cosmic Horseshoe, and SGAS J152745.1+065219.

Al iii 1854, with an ionization potential of 28.4 eV, is variously considered in the literature to be either an ISM or a stellar wind line. In the stacked spectrum, the high $| {v}_{\max }|$ and shape of its high-velocity tail strongly suggest that at least a substantial portion of Al iii 1854 absorption has a similar origin to C iv and Si iv. This is supported by the fact that Al iii 1854 has been observed with a P Cygni profile in certain B supergiants of spectral and luminosity classes: B0.7 Ia to B2.5 Ia; B1–B3 Ia+/Iap; and BC1.5 Iab (Walborn et al. 1995). Thus, the Al iii profile further underscores the large contribution to the spectra from B stars.

In Figure 6, we plot the maximum and mean velocities of the high-ionization absorption lines. For both the MagE and COS samples, there is a trend where the maximum velocities increase with increasing ionization potential, but the absorption-weighted mean velocities remain nearly constant for all ionization potentials. This indicates that the high-ionization lines have a weak blue-velocity tail extending to more than ∼2000 km s⁻¹, but that the majority of the absorption has similar velocities to the low-ionization gas. This supports our hypothesis that the blue-velocity wings arise in the hot photospheres of massive stars, while the stronger absorption component at redder velocities arises from a multi-phase galactic outflow. Properly accounting for the stellar winds is important when measuring the maximum outflow velocities of high-ionization lines.

The absorption in this high-velocity tail is only 6%–10% below the continuum level for Al iii and Si iv and only 15% for C iv. As such, detecting it requires high S/N spectra like those of the MegaSaura stacked spectrum. This high-velocity absorption tail is not seen in the profiles of transitions with lower ionization potential, as quantified in Sections 3.4 and 3.5. This correspondence supports our hypothesis that the blue absorption wings of the high ionization lines are likely due to the stellar winds of massive stars.

We now consider the extent to which Starburst99 stellar population synthesis models can reproduce these high-velocity stellar wind features. Thus far, we have considered the shape-normalized stack, which minimizes undesirable ringing and is therefore ideal to study these low level features. However, for spectral synthesis fitting, we use the ${\lambda }_{\mathrm{pivot}}$-normalized stack, as it preserves the spectral shape. We plot the low-ionization features in the ${\lambda }_{\mathrm{pivot}}$-normalized stack in Figure 7(a) and the high-ionization features in Figure 7(b). For both Figures 7(a) and (b), we overplot the best-fitting linear combination of Starburst99 models. The Starburst99 fit decently matches the N v, Si iv, and C iv emission features, as well as the high-velocity tail of C iv.

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As a cross-check, we examine the profiles of these stellar wind lines in the S99-normalized stack. Because each input spectrum was continuum-normalized by its Starburst99 fit before stacking, the S99-normalized stack provides a different way to test whether the Starburst99 models can match the the observed high-velocity absorption profiles. Figure 8 shows negligible residual absorption at high velocities, indicating that the Starburst99 models can indeed reproduce the high-velocity tail of absorption from stellar winds.

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