The Persistence of Cool Galactic Winds in High Stellar Mass Galaxies Between and
We present an analysis of the Mg ii and Fe ii absorption line profiles in coadded spectra of 468 galaxies at . The galaxy sample, drawn from the Team Keck Treasury Redshift Survey of the GOODS-N field, has a range in stellar mass () comparable to that of the sample at analyzed in a similar manner by Weiner et al. (2009, W09), but extends to lower redshifts and has specific star formation rates which are lower by dex. We identify outflows of cool gas from the Doppler shift of the Mg ii absorption lines and find that the equivalent width (EW) of absorption due to outflowing gas increases on average with and star formation rate (SFR). We attribute the large EWs measured in spectra of the more massive, higher-SFR galaxies to optically thick absorbing clouds having large velocity widths. The outflows have hydrogen column densities , and extend to velocities of . While galaxies with host strong outflows in both this and the W09 sample, we do not detect outflows in lower-SFR (i.e., ) galaxies at lower redshifts. Using a simple galaxy evolution model which assumes exponentially declining SFRs, we infer that strong outflows persist in galaxies with as they age between and , presumably because of their high absolute SFRs. Finally, using high resolution HST/ACS imaging in tandem with our spectral analysis, we find evidence for a weak trend (at 1 significance) of increasing outflow absorption strength with increasing galaxy SFR surface density.
Subject headings:galaxies: absorption lines — galaxies: evolution — galaxies: ISM
Galactic-scale gaseous outflows are a basic element of the process of galaxy evolution, and are observed in galaxies in the local Universe and out to (e.g., Heckman et al., 2000; Frye et al., 2002; Ajiki et al., 2002; Shapley et al., 2003; Martin, 2005; Rupke et al., 2005b; Veilleux et al., 2005; Weiner et al., 2009). They are invoked to explain a wide variety of observational and theoretical results concerning the evolving stellar and gaseous content of dark matter halos. Outflows are a key component of the theory of merger-driven galaxy evolution, in which the primary mechanism driving the observed increase in the number density of “red and dead” galaxies from to today is the merging of gas-rich blue galaxies (e.g., Faber et al., 2007; Tremonti et al., 2007; Hopkins et al., 2008; Sato et al., 2009). The removal (i.e., outflow) of gas is an expected consequence of merging, and is a favored means by which star formation is subsequently quenched in the remnant. Outflows must be incorporated into models of disk galaxy formation which correctly reproduce the observed scaling relations between disk rotation velocity, stellar mass (), and radius (e.g., Dutton & van den Bosch, 2009). Finally, galactic winds may give rise to the Mg ii-absorbing gas in the extended gaseous halos around galaxies observed along QSO sightlines. Several lines of evidence support this idea (e.g., Bond et al., 2001; Bouché et al., 2006, 2007; Ménard & Chelouche, 2009); however, alternative origins for this gas have also been suggested, i.e., multiphase cooling of hot halo gas, accretion of cold gas from the intergalactic medium, or tidal stripping (Maller & Bullock, 2004; Tinker & Chen, 2008; Wang, 1993).
In spite of their importance, the physical processes responsible for driving galactic outflows are not well understood. Energy from supernova explosions or AGN feedback heats the surrounding gas and may displace both hot and cool gas originating in the interstellar medium (ISM), possibly removing it to the galactic halo or beyond. Momentum deposition from radiation or cosmic ray pressure may also contribute to the acceleration of cool ISM gas; the relative importance of these two processes is hotly debated (Dekel & Silk, 1986; Murray et al., 2005; Socrates et al., 2008; Strickland & Heckman, 2009). In galaxies which are known to host outflows in the local Universe, the hot phase is observed in X-ray emission, while the cooler phase is detected via optical emission lines (e.g., H, [N ii] ) and in absorption against the stellar continuum. However, it remains difficult to predict whether galactic winds will form and whether they will affect the kinematics of the ISM in a given galaxy. Theoretical studies propose that there is a “threshold” star formation rate surface density () below which supernova-driven superbubbles cannot break out of a galactic disk and form a wind (e.g., McKee & Ostriker, 1977). Observational constraints on the value of a universal threshold remain merely suggestive (e.g., Lehnert & Heckman, 1996; Martin, 1999; Heckman, 2002; Dahlem et al., 2006).
For instance, several studies have identified outflows in galaxies in which absorption line transitions tracing cool gas are blueshifted with respect to the systemic velocity. The Na i D 5890, 5896 doublet traces the kinematics and column of gas at , revealing outflows in local dwarf starbursts (Schwartz & Martin, 2004) and luminous infrared galaxies (LIRGs) out to (Heckman et al., 2000; Martin, 2005; Rupke et al., 2005b). UV spectroscopy of both low and high-ionization transitions such as Si ii and C iv in Lyman Break Galaxies (LBGs) at has uncovered outflows of hundreds of km s (e.g., Shapley et al., 2003) in these objects. All of these galaxies have high spatial concentrations of star formation, with (Heckman, 2002); the nearby galaxies have values among the largest in the local Universe. If there is a “threshold” required to drive outflows, this suggests that it is likely equal to or below for local galaxies. The value of a threshold for galaxies in the distant Universe remains poorly constrained, although the high () values in LBGs (Steidel et al., 1996; Meurer et al., 1997) suggest a similarly low threshold at .
Not only are outflows expected to contribute to increased numbers of post-merger, “quenched” red galaxies, but they may also influence the gradual decline of star formation since among blue galaxies (Noeske et al., 2007a; Sato et al., 2009), as this decline is likely driven by gas exhaustion. The presence of winds in both distant star-forming and red sequence galaxies has been established (e.g., Sato et al., 2009; Weiner et al., 2009, hereafter W09), although the co-evolution of outflows with the buildup of and the decreasing cosmic star formation rate (SFR) density (e.g., Hopkins, 2004) remains unexplored at .
We use a sample of 468 galaxies at drawn from the Team Keck Treasury Redshift Survey (TKRS; Wirth et al., 2004) of the GOODS-N field to examine the kinematics of cool () gas traced by Mg ii and Fe ii absorption in coadded spectra. Because LIRG-like levels of star formation occur in most massive star-forming galaxies at (Noeske et al., 2007a), and because cool outflows are common among LIRGs in the local Universe, the galaxies in our sample are prime candidates for hosting outflows (Rupke et al., 2005b; Heckman et al., 2000). Indeed, W09 showed via analysis of coadded spectra of blue, star-forming galaxies at that outflows traced by Mg ii absorption are very common among the objects in their sample, and further demonstrated that outflow velocities and absorption strengths increase with both and SFR over the ranges and .
However, additional evidence indicates that the outflows observed in galaxies at by W09 must cease by . W09 suggest that many of the galaxies in their sample will evolve into massive spirals (rather than ellipticals) at (Blanton, 2006; Noeske et al., 2007b). The study of Na i kinematics in both star-forming and quiescent, red-sequence galaxies at by Sato et al. (2009) showed that outflows with velocities traced by Na i are detected in of the blue cloud galaxies in their sample, while the remaining 20% of these galaxies lack outflows. Although the Sato et al. (2009) sample of blue cloud galaxies is incomplete, this suggests that at least some star-forming galaxies at cease to drive winds in the redshift range .
We use our sample to explore the dependence of the equivalent width (EW) of outflowing gas on galaxy and SFR and examine the relative importance of these two properties in determining outflow absorption strength among star-forming objects. We follow the co-evolution of outflows, galaxy and SFR in the range and search for the expected decline in outflow EW with increasing galaxy age. Finally, using coadded spectra in concert with the deep HST/ACS imaging available in the GOODS-N field, we study the relationship between and the EW of absorption due to outflowing gas for the first time beyond the local Universe.
We describe our sample, spectroscopy and imaging data in §2. We show evidence for outflow in a few individual galaxy spectra and in a coadded spectrum in §3, and describe the measurements we use to quantify outflow properties in §4. Section 5 describes our derivations of galaxy properties, and §6 examines trends in outflow properties with galaxy SFR, , SFR surface density () and redshift. Section 7 discusses Fe ii absorption properties. Sections 8 and 9 contain a discussion of these results and our conclusions. We adopt a CDM cosmology with , , and . Magnitudes quoted are in the AB system unless otherwise specified, and stellar masses are reported in units of .
2. Data, Sample, and Stacking Technique
We use publicly available spectra from the TKRS (Wirth et al., 2004) for analysis of Mg ii and Fe ii kinematics. In brief, the TKRS is a magnitude-limited spectroscopic survey of galaxies selected to have in the GOODS-N field. Spectra were obtained using one hour exposures with DEIMOS (Faber et al., 2003) on the Keck 2 telescope. The grating blazed at was used with a 1″ wide slit. Spectra have a resolution of Å (Weiner et al., 2006), and cover with . Approximately 1440 spectra of galaxies and AGN were obtained in total.
The spectra were reduced using an early version of the pipeline developed by the DEEP2 Redshift Survey Team (Coil et al., 2004, J. Newman et al. 2009, in preparation). To determine first pass redshifts, the pipeline calculated the best fitting source spectrum at each lag position, or redshift, from a linear combination of several template eigenspectra (Strauss et al. 2002; Glazebrook et al. 1998). The template spectra included stars, galaxy absorption and emission line spectra, and an AGN spectrum. The 10 best fits (i.e., with the smallest values) were saved, and members of the TKRS team then visually checked the best solution, replacing it in some cases, and assigned it a quality code. Wirth et al. (2004) performed a detailed comparison between TKRS redshift determinations and redshifts measured in other surveys, and estimated that the uncertainty in TKRS redshifts is or better.
We limit our sample to spectra with high redshift quality codes, i.e., with confidence level , and with coverage of the Mg ii doublet. We then visually inspect each of these spectra to check for broad Mg ii emission lines; we exclude four objects with broad emission from our analysis (with object IDs 5609, 3660, 1488 and 9377). These cuts limit the sample size to 625 objects.
As noted in Cowie & Barger (2008), some of the TKRS spectra suffer from poor sky subtraction, and spectra of faint objects can have negative continua. This implies that there are large systematic errors not accounted for in the one-dimensional error array for each spectrum. If the distribution of the errors in the estimates of the sky level were symmetric, the sky subtraction errors would not affect our results, as we work primarily with coadded spectra. However, negative continua (i.e., oversubtractions) occur preferentially when there is excess scattered light in a given slit, whereas we do not expect that undersubtraction results from a specific systematic issue. Thus, we expect that overestimation of the sky level is more likely to occur than underestimation in general. Including the objects with oversubtracted sky in coadded spectra will tend to reduce the continuum level of the coadd. We exclude the 96 spectra with a negative median continuum level measured between rest wavelengths 2790 Å and 2810 Å (i.e., 15% of the sample). This method of tagging spectra with poor sky subtraction is almost certainly not comprehensive; however, it likely removes the worst cases from the sample.
Among the remaining 529 spectra, a few have very poor wavelength solutions in the blue due to the paucity of arc lamp lines at Å. This may affect the accuracy of the redshift determination as well as the offset of UV absorption lines from systemic velocity. In order to assess the quality of the wavelength solutions, we fit a single Gaussian to the sky lines at and , which are not resolved in the TKRS spectra. We define to be at the average of the true wavelengths of the two lines () and measure the velocity offset of the sky line complex in each spectrum. Our assumption that the centroid of a single Gaussian fit to the blended lines will be at the average of their central wavelengths holds if the lines have equal strengths. In the extreme case in which one of the lines is completely absent, an additional offset of must be added to the calculated offset. To find the mean velocity offset of the sky line complex for the sample (), we first exclude spectra with sky lines offset by more than from , and then calculate the mean of the velocity offset in the remaining spectra. The resulting is . We then exclude all spectra from the sample (61 objects) with sky lines offset by more than from . Accounting for variations in the relative strengths of the sky lines, this means that all remaining 468 spectra have sky lines offset by no more than from their true central wavelength; these spectra make up our final sample. Figure 1 shows the redshift distribution of the objects in the sample. The median redshift of the total sample is .
The standard deviation of the distribution in sky line velocity offsets for spectra remaining in the sample is (not accounting for variations in the strengths of the sky lines). This dispersion measures the typical wavelength uncertainty in the TKRS spectra at Å. We estimate considerably smaller uncertainties at redder wavelengths, as arc lines are more abundant in this range. For instance, a Gaussian fit to the sky line at 5577 Å yields maximum velocity offsets and a dispersion of for the spectra in the sample.
The errors in the wavelength solution introduces uncertainties in the systemic velocity of the UV absorption lines in each spectrum. Throughout the paper, we assume that the systemic velocity of each galaxy is given by the TKRS redshift. As redshift determinations are most strongly dependent on sections of the spectra redward of observed wavelength Å in the redshift range of our sample, they should not be affected by poor blue wavelength solutions. However, the UV absorption lines of interest are blueward of Å in the redshift range in the case of Mg ii and in the range in the case of Fe ii. We estimate the error in the systemic velocity for these transitions by assuming the wavelength solution is perfect at Å and that it varies linearly to the blue, with absolute velocity offsets at Å between and . At the very bluest wavelengths, the velocity offset is for sky line velocity offsets , and have a maximum of for sky line velocity offsets of . Near the median redshift of the sample (), the velocity offset at Mg ii is for sky line velocity offsets of . These errors in the systemic velocities of UV absorption lines must be considered when interpreting results from coadded spectra, as discussed in §2.3.
We use the high quality HST/ACS imaging available in the GOODS-N field (Giavalisco et al., 2004). The imaging covers a area with the ACS F435W, F606W, F814W and F850LP bands (, , and ). The limiting surface brightness at in a aperture in the F850LP band is (Giavalisco et al., 2004, version 1 release). We use the mosaic data in each band with a pixel scale .
2.3. Stacking Technique
We use code written by J.A.N. to coadd TKRS spectra. The code first masks out bad pixels in each object spectrum. It then renormalizes each inverse variance array so that it has a median equal to 1. Each spectrum and its associated inverse variance array is linearly interpolated onto a grid of rest-frame wavelength, and the spectra are coadded. The flux in each pixel is weighted by the renormalized inverse variance, so that pixels with more noise from sky emission are given less weight, while each spectrum overall contributes to the stack in proportion to its flux and it does not have an extra weighting corresponding to its . This results in a coadd which is “light-weighted”. This method of coaddition is the same as that used in W09.
Errors in TKRS redshifts as well as errors in the wavelength solution will have the effect of broadening the absorption and emission features located at the true systemic velocity in the coadded spectra. The redshift uncertainties discussed above are , while velocity offsets due to poor wavelength solutions are estimated to be for the 68% of the spectra with the smallest sky line velocity offsets, making the extreme assumption that the UV absorption lines of interest are always at the bluest end of the wavelength coverage. We therefore expect that absorption observed at velocities offset from systemic by in both the Mg ii and Fe ii transitions in the coadd is most likely due to absorption at velocities offset from the true systemic velocity of the galaxies in the sample.
3. Rest-frame UV Metal-line Absorption in TKRS Galaxies
3.1. Detection of Outflowing Gas in TKRS2158
The continuum of a typical TKRS spectrum near Mg ii is . We are therefore not able to visually identify Mg ii absorption in the vast majority of the individual spectra. There are a few brighter galaxies, however, for which rest-frame UV absorption lines are evident.
One example is shown in Figure 2, which includes a color HST/ACS image and the full spectrum of the object TKRS2158. This object has a redshift , has absolute -band magnitude , and has an infrared luminosity (Melbourne et al., 2005). Figure 3 includes sections of the same spectrum showing UV absorption line profiles. The systemic velocity is given by the redshift of the galaxy reported in the TKRS, which was determined from the velocity of the [O ii] doublet. Not only are Mg ii and Fe ii absorption lines detected, but Fe ii absorption is evident further to the blue. We calculate velocity offsets of each line with respect to systemic by fitting a Gaussian to each and finding the offset of its centroid. These measurements are reported in Table 1. All lines are offset from the systemic velocity by , with the exception of the Mg ii 2796 line and the Fe ii 2382 line, which are offset and respectively. These kinematics are a clear indication of cool outflow from this galaxy. Discrepancies in the measurements of the velocity offsets could be due to noise in the spectrum such as poorly subtracted sky emission at the locations of certain absorption lines. Additionally, narrow emission in the Mg ii 2796 transition or in Fe ii* fine-structure transitions may be filling in the some of the absorption profiles and shifting their centers to the blue (e.g., Rubin et al., 2009).
Figure 4 shows the spectral regions around the UV absorption lines for several more individual TKRS objects. Blueshifted absorption lines are evident in a few of these spectra, hinting at the presence of outflows. However, most of the spectra are not of sufficiently high quality to reliably measure velocity offsets or line strengths for individual galaxies.
3.2. Outflow Signature in Coadded Spectra
Figure 5 shows sections of the coadd of the full galaxy sample (468 objects) surrounding the Mg ii and Mg i absorption lines. The spectrum has been normalized by a linear fit to the continuum flux in the continua regions and , where at and for Mg ii and Mg i respectively. This continuum normalization is applied to all coadds presented. The Mg ii line profiles in this figure are asymmetric, with more absorption on the blue side of . The Mg i absorption line is asymmetric in the same sense. Quantitative analysis of these lines will be performed in later sections.
To test whether the properties of the coadd reflect the properties of most of the individual galaxies in the sample, rather than a few of the brightest galaxies, we measure the flux in various velocity ranges with respect to Mg ii in individual spectra. This was done in W09, and our velocity windows match those used in that work: (window 1), and (window 2). Window 1 provides a measurement of the continuum and window 2 probes the flux in the deepest part of the blueshifted 2803 Å line (although this velocity range may not probe blueshifted absorption in all spectra, due to errors in systemic velocity determinations as discussed in §2.3). We plot the average number of counts per pixel weighted by the inverse variance in window 2 vs. window 1 in the top panel of Figure 6. The points are offset below a one-to-one ratio, showing that many of the spectra have a count decrement in window 2 (where blueshifted absorption is expected) relative to window 1 (where we are making a measurement of the counts in the continuum). Approximately of the spectra have average counts lower in window 2 than in window 1, which indicates that a majority of the spectra contribute to the coadded flux decrement.
We also wish to characterize the presence of emission in the Mg ii transition in individual galaxy spectra. This is motivated by the work of W09, who identify Mg ii emission in coadded spectra as well as in % of the individual galaxy spectra in their sample at . This emission may be due to AGN activity, but could also be related to some other physical process. W09 attempt to exclude galaxies which exhibit Mg ii emission from their analysis of outflow properties in coadded spectra, as the complicated continuum shape of these individual spectra makes characterization of the Mg ii absorption line profiles in the coadds difficult. To identify individual spectra with Mg ii emission in our sample, we measure the flux level in the velocity range (window 3) and compare it to our measurements in window 1 in the bottom panel of Figure 6. The placement of window 3 is immediately to the red of the line, and samples the region between the absorption lines where Mg ii emission is likely strongest. Points toward the upper part of this plot have “excess emission” in window 3. There are 7 spectra in our sample with in window 3 greater than 120. Four of these spectra have P Cygni-like line profiles at Mg ii; the three remaining spectra are pushed into the “excess emission” regime because of noise in the window. Removal of these spectra from our sample does not significantly affect the Mg ii line profiles in the coadded spectrum. Their inclusion will therefore not demand careful modeling of emission in the continuum, and we retain them in the following analysis.
4. Analysis of average outflow properties traced by Mg ii absorption
In this section we introduce two measurements which will be used in the remainder of the paper to assess the strength of the absorption due to outflowing gas in coadded spectra. With both methods we attempt to estimate the strength of absorption at the systemic velocity through analysis of the red side of the Mg ii 2803 line. We then “correct” the measurement of the absorption strength on the blue side of the Mg ii 2796 line accordingly. This corrected measurement should then depend on the absorption strength of outflowing gas only. The first method uses boxcar EWs for the measurements in each velocity range and is useful in the case of low coadds, while the second includes more detailed fitting of the line profile. The latter method, however, requires that the red side of the Mg ii 2803 line can be well-characterized by a Gaussian.
Analysis of the absorption strength of outflowing gas is complicated by absorption from stellar atmospheres and the ISM near the systemic velocity. Photospheric Mg ii absorption at the systemic velocity is strongest in F8 - G1 type stars (Kinney et al., 1993), in which the EW of the 2796 Å line can reach Å (see §7). As outlined in W09, very bright late B, A and F stars can exhibit asymmetric or shifted Mg ii absorption due to stellar winds (Snow et al., 1994); these stellar absorption lines may be blueshifted by . There may also be absorption due to the ISM of the galaxies; this gas is in the disks of the galaxies and will rarely be blueshifted by more than a few tens of (i.e., in the case of a rotating disk). The situation for Mg i is simpler; stellar Mg i absorption is not blueshifted and is only found in the photosphere of F stars. It may be present in the ISM, however, and in outflowing gas.
4.1. Boxcar Method
In order to characterize the amount of absorption due to outflowing gas in each coadd, we make the assumption that the Mg ii doublet is saturated in our spectra, such that the 2796 Å and 2803 Å lines have the same depths. Mg ii becomes saturated at column densities () of , which occur at relatively low hydrogen column densities of at solar abundance. The ISM and stellar atmospheres typically have columns exceeding this value. See §8.1 for further discussion. We measure , where
quantifies the amount of absorption due to gas that is not outflowing, and we subtract it from to avoid overestimating the outflow absorption strength from the inclusion of absorption due to gas at associated with the ISM and/or stellar atmospheres.
4.2. Decomposition Method
In addition to the boxcar measurement discussed above, we also adopt the method of W09 to first remove the stellar and “stationary” ISM absorption from the line profile before making measurements of any outflow. We use the model presented in W09:
where is the observed flux density, C is the galaxy continuum emission, and and are the line profiles of the symmetric and blueshifted (outflow) absorption. Here we make no attempt to include emission in Mg ii above the continuum in our model; this issue will be addressed in more detail in §4.4. is made up of the sum of two Gaussians centered at the rest velocity of each line in the doublet. In order to calculate , we fit a Gaussian profile to the red side () of the and lines. See Figure 5 for a demonstration of this procedure. Because the Mg ii doublet is blended in our spectra, we simply impose the Gaussian fitted to the line onto the profile of the line. The depths of these two Gaussians are kept the same (), since the Mg ii lines are mostly saturated. It may be that the line is in reality slightly deeper than the line; in this case we will underestimate the strength of the systemic absorption in this line. We divide the coadd by this model, and the resulting blueshifted (or outflow) absorption line profile is plotted in Figure 5 in green.
We presume that this profile contains absorption only from gas that is outflowing. However, if the doublet ratio for the stationary absorption is larger than one, we will measure too much outflowing gas (and the emission to the red of the line will be artificially weakened). Redshifted emission in the line also affects the amplitude and width of the Gaussian we fit to the absorption line profile, and can cause an overestimate of the EW of outflowing gas. Emission in the 2796 Å line (evident in Figure 5) may in turn cause us to underestimate the EW of the outflow (see §4.4 for more discussion of these effects). Finally, we are assuming that little of the absorbing gas is flowing into the galaxies; if we were to detect a substantial inflow, we would overestimate the amount of absorption at the systemic velocity due to deeper profiles on the red sides of the lines, and underestimate the EW of outflowing gas.
As can be seen in Figure 5, no absorption is evident at positive relative velocities in the line profile shown in green, i.e., the “outflow” profile. Some emission occurs on the red side of the line; this will be discussed in §4.4. The EW of the feature on the blue side of the line is (measured between using a boxcar sum). Although the green profile for Mg i is suggestive of an outflow, the outflow absorption is not detected, with a upper limit of Å, possibly indicating that the outflow is dominated by gas densities lower than those needed to contain a significant column in Mg i (Murray et al., 2007).
To compute the error on the outflow EW, we first generate 1000 realizations of the symmetric absorption profile by adding noise to the best-fit symmetric model generated in the above procedure. The level of the added noise is determined by the noise in the coadded spectrum. Each of these realizations is fit with a Gaussian, and a double Gaussian profile () is created as above. We then calculate the standard deviation of the values of these 1000 different models at each pixel, which is an estimate of the error introduced by the model fitting procedure as a function of velocity. This error is combined in quadrature with the error in the coadded spectrum itself, producing an error at each pixel of the outflow profile (). It is then straightforward to use this error to calculate the uncertainty in EW measurements of the outflow profile.
4.3. Sensitivity of and Outflow EW to Winds
We now explore the extent to which these two quantification methods are sensitive to outflows with a range of physical parameters. To do this, we generate a series of model Mg ii absorption line profiles, each with varying amounts of absorption at systemic velocity and offset to negative velocities. We model both the systemic absorption and the outflowing absorption as single velocity components with Gaussian optical depth (). While cool outflowing gas likely consists of multiple absorbing clouds at different velocities (e.g., Martin, 2005), we are coadding our data, and thus we expect that such features will be completely smoothed out. Components are parametrized following Rupke et al. (2005b), with variable Mg ii column density ((Mg ii)), covering fraction (), Doppler parameter (), and central wavelength (). In all of our models, we choose (Mg ii) for the systemic component, such that the profile is completely saturated, and (Mg ii) for the outflowing component. All components (systemic and outflowing) have , close to the 55% absorption depth of the saturated Mg ii profiles in W09 (which in coadded spectra corresponds to the detection frequency of outflows times the of cool outflowing clouds). Outflowing components are given relative velocities of -100, -200, and -300 km s; we also create models with no outflowing component. In each model, the systemic and outflowing components have the same ; however, we allow this parameter to have the values , 150, and 250 km s in different models. We therefore have a grid of models in and outflow velocity space.
We smooth each of these models to the velocity resolution of the individual spectra, Å (Weiner et al., 2006), adjusted to the rest-frame at the median redshift of the sample (). A velocity resolution element in the coadded spectra is larger than this, due to uncertainties in the redshift determinations and wavelength solutions for the individual spectra (see §2.1); however, the results are similar if we repeat the analysis using a velocity resolution that is . After smoothing we add different levels of noise such that the resulting spectra have , 6, and 9 , consistent with the range in levels of coadded spectra we create in §6 (see Table 1). We generate 1000 realizations of each model at each level, and then measure and perform our decomposition analysis for each realization.
Figure 7 shows the distribution in the measured outflow EW and values for all models as a function of the model outflow velocity. The points have been offset by an arbitrary amount in velocity so that they do not overlap. The mean outflow EW and for models with , and are shown with cyan diamonds, blue circles, and black squares respectively. The point size increases with . The error bars show the 90% confidence intervals in the measured quantities. The size of these intervals and the central values indicate the degree to which outflow EW and are successful in characterizing the underlying physical absorption profile. For instance, at , and outflow EW have very broad distributions for all models. For models with no outflow, both of these measures exceed values of 0.5 Å in between 12% and 40% of realizations, with outflow EWs for models with and exceeding Å in 6% and 12% of realizations, respectively. Likewise, models with outflows can have or outflow EW Å, although in general the distributions shift to higher values of these quantities as outflow velocities increase. We conclude, however, that in the case of coadds with , we are able to confirm the presence of outflows only if the measured values of outflow EW are Å and values are Å. These values are recovered for outflow velocities , and occur more frequently with higher . If lower values are measured, the presence or lack of outflows remains ambiguous.
These measurements become more sensitive with increasing . At , and outflow EW can be as high as 0.5 - 0.9 Å for models with no outflow. However, models with outflows yield mean values higher than these if or 250 km s. Values of outflow EW Å are measured for at least 95% of realizations of models with high values of and outflow velocity. At , models with no outflow have and outflow EW Å, while models with outflows and or 250 km s again yield higher values in at least 92% of realizations. Models with km s have higher mean values if the outflow velocity km s.
Although this modeling relies on a very simplistic parameterization of the Mg ii absorption profiles in our coadded spectra, it suggests that we are sensitive to saturated Mg ii-absorbing outflows with velocities on the order of 100 km s in coadds with . We are sensitive to outflows in coadds only with large velocities and . These findings will be discussed further in §8.
4.4. Mg ii in Emission
We observe emission in the Mg ii transition in both individual galaxies (see the P-Cygni profile in Figure 3) and in coadded spectra (e.g., Figure 5). Emission in the latter is obvious after the decomposition of systemic and outflow profiles is performed and one can identify the decrement of absorption on the red side of the 2796 Å line as compared to the red side of the 2803 Å transition. This emission is observed in star-forming galaxies (W09), a luminous starburst galaxy at (Rubin et al., 2009), as well as in narrow-line Seyfert galaxies such as two of the ultraluminous infrared galaxies (ULIRGs) studied in Martin & Bouché (2009). A similar P-Cygni-like profile in the Na i transition was observed in NGC 1808, a starburst galaxy driving an outflow (Phillips, 1993). While the origin of this emission remains unclear, we suggest it may be at least in part due to resonance-line scattering off of the receding side of an expanding shell related to the observed outflow, as in the case of Ly emission in LBGs (Pettini et al., 2001, K. Rubin et al., 2009, in preparation).
To better understand the effect of this emission on our outflow EW measurements, we develop a alternative method of characterizing the Mg ii doublet profiles in coadded spectra. We again assume that the absorption at the systemic velocity produces a saturated Gaussian absorption profile as in Equation 5. We then further assume that there is additional emission on top of this continuum on the red side of each line with a Gaussian profile. The amplitudes of the emission lines have a ratio 2:1, and the lines have a variable velocity offset with respect to systemic. In a true P-Cygni profile, the velocity at the peak of the emission (and the shape of the profile in general) depends on a number of factors, e.g., the outflow geometry and , and the velocity dispersion of the outflowing gas. Our model can be written as follows:
where is emission in excess of the continuum and . We may then fit this model to the red sides of both lines in the doublet simultaneously (where ), in the velocity ranges and for the 2796 Å and 2803 Å lines, respectively. We subtract the fitted emission model () from the coadd, divide out the model symmetric absorption, and measure the boxcar EW in the range for the resulting profile.
Because of the number of free parameters in this model (5), this method does not generally produce acceptable fits for the coadded spectra in our study, as the results are often driven by noise features in the line profiles. However, the model does successfully characterize the red sides of the doublet lines in the much higher- coadds of W09. We find that in the W09 coadds with the strongest emission features (e.g., the lowest- and middle- subsamples), the outflow EW we calculate using this method is % lower than the outflow EW calculated in W09 (and described above in §4.2). In coadds such as the high- W09 subsample, the difference in outflow EWs calculated with the two methods is %. While this model is quite simplistic, these results indicate that Mg ii emission causes an overestimate of the outflow EW calculated using our standard method (§4.2). A more complete, physically-motivated model including radiative transfer is required to fully quantify this effect, and additionally may more tightly constrain other characteristics (e.g., radial extent, density) of the cool gas outflow.
5. Properties of sample galaxies
We wish to characterize outflow absorption strength at in galaxies with a range in SFR, and as well as explore the evolution of outflows. To do this, we create subsamples of the galaxies with similar SFRs, s, etc., and coadd spectra within a given subsample. We then compare outflow properties among these coadds. Here we describe how photometry, sizes, , SFR, and quantitative morphologies are derived for our sample.
5.1. Rest-frame Colors and Luminosities
We use photometry from Weiner et al. (2006) derived from ACS imaging (Giavalisco et al., 2004) and Capak et al. (2004) ground-based photometry, and converted to absolute and rest-frame color using the K-correction routine of Willmer et al. (2006). Errors in the observed optical magnitudes and colors are 0.05-0.07 mag and 0.07-0.1 mag, respectively. The errors introduced by the K-correction procedure are 0.12 for and 0.09 in (Weiner et al., 2006). The left-hand side of Figure 8 shows a color-magnitude diagram (CMD) for our sample. The solid line is from Willmer et al. (2006), and marks the division between the red sequence, or the narrow region populated by early-type E/S0s in the CMD, and the blue cloud, or the wider area in the CMD populated by bluer spirals and separated from the red sequence by a narrow “valley” in the surface density of objects.
We wish to measure for our sample, where , for comparison with the suggested local threshold for driving outflows, . In the local Universe, measurements of the SFR from H, far-IR or extinction-corrected UV fluxes are combined with measurements of the sizes of star-forming regions () to determine (e.g., Meurer et al., 1997; Lehnert & Heckman, 1995). The sizes are constrained using measurements of the half-light radius from H or UV (e.g., 2200 Å) imaging, which are direct tracers of nebular emission or emission from young stars. Local starburst galaxies with high values of SFR per unit star-forming surface area (several ) have values of SFR per unit surface area in the optical disk, i.e.,
We use the half-light radii of the TKRS galaxies measured by Melbourne et al. (2007) to parametrize galaxy size. These authors fitted successively larger elliptical apertures to the ACS images for each galaxy and calculated the fluxes and intensities within each aperture. An iterative curve-of-growth analysis was used to determine the flux level of the sky. From these measurements, the total flux of the object was calculated. Apparent half-light radii are equal to the semimajor axis of the ellipse that contained half of the total flux, and were corrected for the point-spread function of the image. To determine half-light radii at 2200 Å in the rest-frame, we interpolate between the radii measured in the passbands to the red and blue of 2200 Å in the rest-frame of each object, assuming that all of the light measured in each band is observed at the central wavelength of the filter (4297 Å for the band and 5907 Å for the band). In cases in which 2200 Å in the rest-frame is blueward of the -band filter, we simply adopt the -band radius. We then use the angular diameter distance to compute the rest-frame UV half-light radius in kiloparsecs (). Melbourne et al. (2007) estimate that they obtain accurate radii to within %. This level of uncertainty applies strictly to the rest-frame -band half-light radii they derive by combining the radii measured in the observed bands in a weighted mean, with weights dependent on the overlap of each observed passband with the rest-frame -band. We assume this level of uncertainty applies to our as well.
We choose to use to parametrize the sizes of the star-forming regions in our galaxies for its simplicity; however, this measure may in fact significantly overestimate the size scales relevant for driving outflows. Many of the galaxies have extended and clumpy morphologies, such that is quite large (), while much of the UV emission arises in a few small but widely separated bright knots. On the other hand, the distance between star-forming knots may be intimately connected to the morphology of the outflowing gas itself (see, e.g., Heckman et al., 1990; Martin, 2006, for some discussion of outflow morphology). Future studies of outflows in individual galaxies will warrant more careful analysis of the size scale and distribution of star formation.
5.3. Stellar Mass
Near-IR photometry of the GOODS-N field was published by Bundy et al. (2005), who derived for 202 objects in our sample (out of a total of 468 ). As we did not wish to limit this study to only objects with K-band derived , we use a calibration derived in W09 to convert rest-frame color and magnitudes into . Bell et al. (2003) compute the relation between rest-frame color and using SDSS and 2MASS photometry of local galaxies. They give this relation for a “diet Salpeter” IMF:
This must be adjusted according to the redshift of each galaxy. W09 derive a redshift correction to this relation using the -band magnitudes and (with Chabrier IMF) available for 11924 objects in the DEEP2 redshift survey (Davis et al., 2003; Bundy et al., 2006). These objects lie in a redshift range . W09 performed a least-squares fit between derived from rest-frame color and those derived from -band photometry, and give a correction term :
The authors find a scatter of 0.25 dex about the fit for . We apply this correction to our data, and compare -band to the corrected color-derived masses where possible (for 202 objects). We find there is a 0.09 dex mean offset and a dispersion of 0.22 dex between the two stellar mass estimates. We use the corrected color-derived masses with a Chabrier IMF for the full sample in the following analysis.
5.4. Star Formation Rate
The rich multi-wavelength data set in the GOODS-N field makes several different methods available for the derivation of the total SFR for the galaxies in our sample. [O ii] line luminosities have been measured for TKRS galaxies (Weiner et al., 2006). 24 m fluxes and IR-based SFRs for a subset of objects in our sample are available from Melbourne et al. (2005). In order to make comparisons with W09, we adopt their method of determining SFR. The photometry of Capak et al. (2004) measures the flux at 1800 Å - 2800 Å and 2200 Å - 3400 Å in the rest-frame for our redshift range. We use these measurements to derive absolute magnitudes at Å and Å using the K-correction code described in Willmer et al. (2006) and Weiner et al. (2005). Using these luminosities we find the slope of the UV continuum, , and calculate the attenuation from this slope using the relation (Seibert et al., 2005; Treyer et al., 2007). There is a mag scatter in this relation, which results in a 0.36 dex uncertainty in the SFRs. We use the values of to calculate an unextincted UV luminosity, and in turn calculate the SFR (Kennicutt, 1998) for a Kroupa IMF:
To investigate systematic errors in these SFR estimates, we compare them to SFRs derived from the IR luminosities of Melbourne et al. (2005). These authors used the publicly available MIPS imaging of the GOODS-N field to measure 24 m fluxes to a limit of 25 Jy, and used the Le Floc’h et al. (2005) prescription to convert 24m flux to total IR luminosity (). 213 of the 407 blue cloud galaxies in our sample have estimates available. We use the Bell et al. (2005) relation between and SFR with a Kroupa IMF to calculate SFR(IR) for these galaxies, ignoring the contribution from unextincted light from young stars in the UV, which we expect to be small (Bell et al., 2005, W09). We find that for IR-selected galaxies, which may have slightly larger IR-to-UV emission ratios than is typical (W09), -derived SFRs are 0.21 dex higher than the UV-derived SFRs, with a dispersion of 0.43 dex. The expected offset will likely be smaller for galaxies not detected in the MIPS imaging. For consistency with W09, and because we lack measurements for nearly half of the blue cloud galaxies in our sample, we adopt the UV-derived SFRs described above in our analysis. However, these uncertainties must be considered when absolute SFRs are discussed, as in §6.2. Bell et al. (2005) report systematic and random errors in their IR / UV derived SFRs of 0.3 and 0.4 dex; we must account for these errors in addition to those introduced from using purely UV-derived SFRs.
The right-hand side of Figure 8 shows a plot of vs. for all objects in our sample with UV SFR measurements. Upper limits on the SFRs in red sequence galaxies are marked in red. While our sample includes galaxies in a range of comparable to the sample of W09, the mean SFR in W09 is dex higher than in this study.
We use the Gini (G) and measurements made for TKRS galaxies in the -band by J. Lotz (2008, private communication) to quantify galaxy morphology. These are nonparametric measurements described in Lotz et al. (2004, 2006). G quantifies the relative distribution of light among a galaxy’s pixels, and is high if there are only a few very bright pixels. is the second-order moment of the brightest 20% of a galaxy’s pixels; it is larger in galaxies in which the brightest pixels are furthest from each other. Figure 9 shows the distribution of these parameters for our sample (excluding 115 which lack high-quality measurements). The dividing lines for different morphological types are taken from Lotz et al. (2008), who applied these divisions to galaxies at . There are 63 mergers, 226 late-type objects, and 64 early-type objects in our sample.
6. Division of sample by galaxy properties
6.1. Division by , , and Morphology
To examine trends in (where ) with , , and morphology, we have divided our spectra into several different subsamples and coadded them. We calculate for each subsample. These subsamples and measurements are listed in Table 1.
First, we coadd only galaxies on the red sequence. The coadd has a very low in the continuum surrounding Mg ii, and so cannot be used to examine outflows in these objects. Because of their low , we exclude all red sequence galaxy spectra from the subsamples described in the following, with the exception of the morphologically divided subsamples.
We choose to divide the TKRS galaxies by the 25th and 75th- percentile values of (0.555, 0.942) and (9.86, 10.49). Coadds of the spectra for these subsamples are shown in Figure 10. Figure 11 shows for the -divided and -divided subsamples. The outflow absorption strength (as quantified by ) rises significantly with and between the middle and highest and subsamples. There appears to be detected outflowing gas in the lowest- subsample; however, this coadd has , and thus is unlikely to yield reliable measurements (see §4.3 for a discussion of this issue). We also perform our decomposition analysis on each of these coadds, shown in Figure 10. Measurements of outflow EW for each coadd are shown in Figure 11, and show consistency with the measurements. Outflow EW results from W09 are shown in blue. Note that measurements of outflow absorption strength are significantly higher for the W09 galaxies than for the middle- TKRS galaxies. As discussed in §5.4, while the TKRS and W09 galaxies have a similar range in , on the whole the TKRS galaxies have a mean that is lower by dex. In addition, the highest- TKRS galaxies include objects with the highest SFRs in the sample. This suggests that either outflow absorption strength is most closely correlated with SFR, or that there is evolution of outflows in galaxies between and 1. This will be discussed in greater detail in §8.
The coadd of early-type galaxies (as classified by G-) has very low and is not useful for measuring outflow absorption. for the merger candidate and late-type subsamples are the same within the errors, at Å; i.e., there does not appear to be a significant difference in the strength of outflow absorption in late-type galaxies and merger candidates (see Table 1). However, it is difficult to disentangle the effects of morphology and on outflow strength in this analysis. Studies of galaxy mergers (i.e., LIRGs and ULIRGs) in the local Universe show that they host exceptionally strong outflows (Martin, 2005; Rupke et al., 2005b) in comparison to local late-type galaxies. On the other hand, these merger remnants also have some of the highest SFRs at . This degeneracy between morphology and SFR is broken at , where the majority of LIRGs have disk-like morphologies (Melbourne et al., 2008); thus galaxies at may provide the ideal laboratory for investigating the effects of these two parameters on outflows. Higher spectra are required to examine these effects in greater detail.
6.2. Division by
To test for a dependence of outflow strength on SFR surface density () at , we assume that , and combine this with our measure of to calculate the global (i.e., flux averaged) for each object. Figure 12 shows the distribution of and for the blue galaxies in the TKRS sample. The lines show the 25th and 75th percentile values of (-1.36, -0.66), which we use to subdivide the sample. Figure 13 shows the coadds of the spectra in these subsamples and the results of the decomposition procedure.
Figure 14 shows and outflow EW vs. in each coadd. There is a slight increase in outflow absorption strength with evident between the middle- and high- subsamples. The lowest- subsample has , and so here we are sensitive only to high velocity outflows with large velocity widths. As discussed in §4.3, we can be confident that outflows are present in subsamples with low coadds only when the measured outflow EW Å. The outflow EW we measure for the lowest- bin is only slightly below this limit, and is therefore only suggestive of the presence of outflow. Comparing Figures 11 and 14, it appears that the outflow absorption strength is higher in the high- subsample than in the high- subsample, suggesting that outflow absorption strength is more strongly correlated with absolute than with .
We also consider our results in the context of the suggested local “threshold” for driving outflows, . Because the existence of and a precise value for a strict threshold for driving outflows have not yet been observationally established (see, e.g., Strickland et al., 2004), it is interesting to search below the suggested threshold for evidence of winds. Given the uncertainty in our absolute SFR determinations, it is difficult to differentiate which of our individual galaxies have above or below . The solid green line in Figure 12 shows a line of constant for comparison with the distribution of our sample in - space. From the placement of this line, it appears that many of the galaxies in the middle- subsample have values below the threshold. If we shift this line by -0.21 dex in to reflect our possible systematic underestimate of SFR (see §5.4) as indicated by the dashed green line, a smaller fraction of the sample falls below the threshold. A 0.21 dex correction to the values of the sample is likely too large, as this offset is derived from a comparison between IR- and UV-based SFRs for the IR-detected galaxies only. However, we apply this correction and create a new subsample with “corrected” . The coadd of these spectra (referred to as the sample in Table 1) yields , Å and outflow Å. This implies that some galaxies below a flux averaged drive outflows. Because there is a dispersion in the comparison between and of 0.43 dex, some fraction of galaxies in this subsample do have true values above the threshold; however, the absorption line profile in the coadded spectrum reflects the mean absorption properties of the subsample, which has below the threshold in the mean.
6.3. Redshift Dependence
As noted in §5.4, the TKRS and W09 samples span a similar range in , but the TKRS sample is offset to lower SFRs by dex. To examine evolution in outflow properties with redshift, we compare our outflow measurements to those from W09. The 25th and 75th-percentile divisions of our sample are quite close to the divisions used in W09 (, and ). To further investigate similarities between the two sets of subsamples, we compare the distributions of specific SFR (; SSFR). Figure 15 shows the SSFR distribution of TKRS (solid line) and DEEP2 (dotted line) galaxies in each bin. Each subsample has a symmetric distribution in SSFR at both redshifts; these distributions are simply offset from each other because of the decline in global SFR with decreasing redshift. The symmetry of the distributions suggests that none of the subsamples are severely contaminated with non-star-forming galaxies. See §8.4 and Figure 19 for further comparison of the SSFR- relations of the W09 and TKRS samples and a discussion of the evolutionary connection between the galaxies at the two redshifts.
Although the TKRS and W09 samples are nearly disjoint in - space, we may construct a comparison subsample of 43 TKRS galaxies which lie above the lower envelope of the SFRs for the W09 galaxies. Figure 16 shows the TKRS (black circles) sample and a random selection of half of the W09 (green crosses) sample in - space. We include all TKRS galaxies above the solid line in a high-, “DEEP2-like” sample. Figure 17 shows the coadd and decomposition analysis of this subsample.
The red point in Figure 11 shows results for this DEEP2-like sample. This sample as well as the high- TKRS subsample have outflow EWs similar to or larger than the W09 coadds. This confirms our previous finding that galaxies at and 1 with similar SFRs have strong outflow absorption, and that galaxies with lower SFRs have weaker outflows. We note that the galaxies in the highest- TKRS subsample have a median , with 68% of the subsample in the range . These galaxies therefore have values in a range similar to the W09 sample; the high outflow EW for this subsample is consistent with the measurements for our other high- subsamples.
7. Fe ii 2586, 2600 Absorption
We now focus on measurements of Fe ii absorption in our spectra. A constraint on the extent to which Fe ii 2586, 2600 absorption is detected with Mg ii in outflowing gas is valuable for a number of reasons, as discussed in Martin & Bouché (2009). While Mg ii is found in a wide range of gas densities, Fe ii is present only at higher densities (in more neutral gas), and so may provide information about outflow gas density. Second, the Fe ii 2586, 2600 transitions have oscillator strengths 0.11 and 0.39 times that of Mg ii 2796, and Fe is less abundant in general than Mg; thus Fe ii absorption lines are generally less strongly saturated than Mg ii lines. They may therefore be used to place more stringent constraints on the cool outflow column density. For instance, Martin & Bouché (2009) find that the Fe ii absorption in ULIRG outflows at requires optical depths 2-3 times larger than those derived from analysis of Mg ii. Finally, because Mg is generated in Type II supernovae in younger stellar populations than Fe, comparison of the relative abundances of Mg ii and Fe ii in the outflow may constrain the enrichment history of the gas.
The Fe ii 2600 transition is always weaker than Mg ii 2796 in QSO absorption line systems, with at most the EW of Mg ii 2796 (Churchill et al., 2000). This is also true in stellar atmospheres. Fe ii 2600 reaches its maximum absorption strength in F9 - G2 stars, while Mg ii reaches its maximum strength in F8 - G1 stars (Kinney et al., 1993, although asymmetric Mg ii absorption is found in B-F stars as mentioned in §4). In early type stars, Fe ii lines do not exhibit P-Cygni profiles or asymmetric absorption; instead if mass-loss effects are observed the lines are simply blueshifted (Snow et al., 1994).
We use UVBLUE theoretical stellar spectra (Rodríguez-Merino et al., 2005) to measure the relative EWs of these transitions in stellar atmospheres. We first normalize these spectra, calculating the continuum in the same regions used for our galaxy coadds. We measure EWs between for Fe ii 2600 and between for Mg ii 2796. Note that these spectral regions contain absorption not only from the named transitions, but from several weaker transitions also found in stellar atmospheres (the Fe ii* 2599 transition, for example). Using solar metallicity models, we obtain Å and Å for a solar type star, yielding a ratio of . As the atmospheres become hotter, the of both ions decrease, although the value decreases much faster with increasing temperature than .
We now measure Fe ii EWs and analyze Fe ii line profiles to constrain the origin of the Fe ii absorption in our spectra.
7.1. Fe ii Absorption in TKRS2158
As noted in §3.1, we observe blueshifted Fe ii lines in the spectrum of TKRS2158. Velocity offsets are given in Table 1. Velocities are slightly inconsistent among the various Fe ii transitions; this may be due to poorly subtracted sky emission, intrinsic Fe ii* emission, or other sources of noise in the spectrum. In general, Fe ii velocities are slightly lower than the offsets measured for Mg ii. This may occur if Fe ii absorption is weaker at the highest velocities, and / or if Mg ii emission fills in the line profile near systemic velocity and effectively shifts the line center further to the blue. From Figure 3 we see that a few of the Fe ii lines extend to the same depth as the Mg ii lines. We conclude that Fe ii traces outflowing gas in this object, although we cannot confirm that it traces gas in the same velocity range as Mg ii.
7.2. Fe ii Absorption in Coadded Spectra
To analyze Fe ii absorption in our galaxy spectra, we create a new subsample, selecting objects with such that spectral coverage of Fe ii is available, and further selecting objects with , for a final subsample size of 66 objects. This latter cut selects objects with the bluest colors and the strongest continua near 2600 Å, which minimizes unphysical effects due to poorly determined sky levels. Coadding spectra of fainter galaxies in the sample yields Fe ii absorption with unphysical line profiles, and thus are excluded from this analysis.
Figure 18 shows Fe ii and Mg ii line profiles for this subsample. We note that the Fe ii lines are slightly deeper than the Mg ii lines in the coadd, in contrast to examples from QSO absorption line systems (Churchill et al., 2000) and stellar atmospheres. This inconsistency suggests that a) the depth of Fe ii is affected by unphysical artifacts resulting from poor sky subtraction even in this subsample of the brightest galaxies, b) Fe ii-absorbing gas has a larger than Mg ii, or c) the Mg ii absorption is being filled in by emission in the same transition.
We measure the EW in the Fe ii lines in the coadded spectrum between , as well as on the blue () and red () sides of each. The total EWs for each line are approximately the same ( Å and Å), indicating that Fe ii is completely saturated in this coadd. The total EWs of the Mg ii absorption lines in the same velocity range are significantly larger ( Å), yielding , a slightly smaller ratio than expected from stellar atmospheres and QSO absorption lines. This again may be due to emission filling in the Mg ii absorption line profiles. We measure a larger EW on the blue side of the 2600 Å line than on the red side ( Å and Å). This in consistent with a scenario in which the Fe ii absorbing gas is outflowing. We find that the EW on the blue and red sides of the 2586 Å line in the coadd are consistent within the errors ( Å and Å). We cannot conclude that Fe ii absorbing gas is outflowing from analysis of this line alone; however, the symmetry of the profile does not rule out an outflow scenario. The oscillator strength of this transition may simply be too low for it to obviously trace blueshifted gas. In contrast, Martin & Bouché (2009) find that both the Fe ii 2586 and 2600 Å lines are saturated and have similar line profiles in ULIRG outflows. See §8.1.2 for a discussion of the upper limit on (H) in the outflow derived from Fe ii EWs.
We also examine the relative velocity extent of the Fe ii and Mg ii absorption lines. In Figure 18, the Mg ii 2796 absorption extends to larger velocities than the Fe ii 2600 absorption. The Mg ii 2796 line has a high velocity tail which decreases in strength gradually with increasing velocity offset, whereas the Fe ii 2600 line has no “tail” to high velocities. If the Fe ii absorbing gas is indeed outflowing, this suggests that the majority of this gas does not attain velocities as high as the Mg ii absorbing gas.
To quantify this, we measure the relative velocities where the profiles of each of these lines reaches a threshold amount of absorption. We first smooth the coadds, and calculate the velocity at which the absorption decreases to 80% and 60% of the continuum level. These velocities are marked in Figure 18, and are closer to the center of the line in the case of Fe ii, confirming our finding that Mg ii absorption extends to higher velocities. If we make the assumption that Fe and Mg have the same relative abundances and at all gas velocities, this suggests that the density of the outflowing clouds decreases with increasing velocity, as the Fe ii column decreases with density (see, e.g., Narayanan et al., 2008, for ionization modeling of Mg ii absorbers).
8.1. Physical Characteristics of Outflows
Similarly to W09, we use the ratio of the EWs on the blue sides of the Mg ii lines to estimate a lower limit on the column density () in the outflowing gas. The oscillator strengths of the lines in the Mg ii doublet are in the ratio , and in the optically thin case the ratio of the EWs of the lines will also be . As the optical depth at line center () increases and the lines become saturated, the EW ratio approaches ; therefore the EW ratio can be used to constrain . Once is known, can be calculated using the equation (Spitzer, 1968)
adjusted to include the effect of the covering fraction, , where and are in Å, and is in atoms . is given by:
The EW ratio in the Mg ii doublet is almost exactly equivalent to the “doublet ratio”, . After this doublet ratio is calculated by taking the ratio of the EWs, one may numerically solve for . This method is strictly appropriate only when one absorbing cloud is considered. However, it has been found to yield good results even when the absorption is caused by a number of clouds if the optical depth in the weaker line is (Jenkins, 1986).
We measure the EWs for the coadds in the interval for each line in the doublet; these measurements are listed in Table 1. We choose this interval to avoid measuring absorption at the systemic velocity, which is uncertain to within (see §2.3), and to avoid including absorption from the red side of the 2796 Å line in our 2803 Å line measurement. For the coadd of the entire sample, the EW ratio is . This yields , where the lower limit corresponds to the upper limit on the EW ratio. In the case of the high- coadd, the doublet ratio is , which results in . Using the equation for above, and assuming , we find for both the full sample and the high- subsample. Assuming increases by 0.3 dex.
To estimate a lower limit to in the outflow, we assume a more conservative value of , and we assume ; i.e., we do not apply an ionization correction. We assume the solar value for the abundance of Mg, , and a factor of -1.2 dex Mg depletion onto dust, measured in the local ISM (Savage & Sembach, 1996). This results in the estimate . We emphasize that this is a very conservative lower limit on the column of outflowing gas because of our assumption about , our neglect of ionization corrections, and because our method underestimates for highly saturated Mg ii-absorbing velocity components. In addition, the effect of emission from the Mg ii 2796 transition is to reduce the EW measured blueward of the Mg ii 2803 transition, further reducing the calculated . These results are nearly an order of magnitude smaller than the outflow column obtained in W09 (); however, this latter measurement was calculated using the EW ratio in the outflow line profile rather than in the observed profile, and used a wider range of velocities (). This yielded higher EWs in each line and generally higher optical depths than our lower limits on .
We estimate the mass outflow rate by assuming a specific geometry for the outflowing gas. For a thin shell, the mass outflow rate is given by
from W09. The assumption for is unimportant here, so long as it matches what was assumed for the calculation of (i.e., the factor of cancels out). We have no constraint on the radial extent of the wind from our data (), except that it is likely comparable to the size of the galaxies, because is high. For these purposes, we assume a minimum radius for the shell equal to the median half-light radius for the galaxy sample, 4.1 kpc. We use the velocity at 80% of the continuum in the coadd of all galaxies calculated as described in §7.2, . Note that this is not the same velocity measurement used in W09, who measured the velocity at 50% opacity in the outflow component after decomposing the line profile. The resulting mass outflow rate is . As in previous work (e.g., Martin, 1999; Rupke et al., 2005b; Martin, 2005), we find an on the same order as the SFR of the sample (). We note that in this sample is lower than in the W09 sample at , and that this is due to lower outflow at the lower redshifts. This suggests that the galaxies at lower are less effective in driving outflows than at . However, we reiterate that the outflow in both this work and in W09 may be substantially underestimated.
Because the profiles of the two Fe ii lines do not have an asymmetric blue wing, we hypothesize that either these lines are too weak to trace outflows at velocities , or alternatively that Fe ii simply is not present in outflowing gas at these velocities. However, assuming the absorption on the blue sides of these lines at lower relative velocities is due to outflowing gas, we again use an EW ratio, this time in the velocity range , to calculate a lower limit on the outflow column in the Fe ii transition. The EWs of the two lines in this velocity range for the coadd we use to analyze Fe ii are both , yielding an observed EW ratio of . The two Fe ii lines have oscillator strengths in the ratio 3.475:1. We numerically solve the equation