DIFFUSE LYMAN ALPHA EMITTING HALOS: A GENERIC PROPERTY OF HIGH REDSHIFT STAR FORMING GALAXIES1

Diffuse Lyman Alpha Emitting Halos: A Generic Property of High Redshift Star Forming Galaxies1

Charles C. Steidel2, Milan Bogosavljević2,3, Alice E. Shapley 4,5,6,
Juna A. Kollmeier7, Naveen A. Reddy8,9, Dawn K. Erb10,11,12, & Max Pettini13
Abstract

Using a sample of 92 UV continuum-selected, spectroscopically identified galaxies with , all of which have been imaged in the  line with extremely deep narrow-band imaging, we examine galaxy  emission profiles to very faint surface brightness limits. The galaxy sample is representative of spectroscopic samples of LBGs at similar redshifts in terms of apparent magnitude, UV luminosity, inferred extinction, and star formation rate and was assembled without regard to  emission properties. Approximately 45% (55%) of the galaxy spectra have  appearing in net absorption (emission), with % satisfying commonly used criteria for the identification of “Lyman Alpha Emitters” (LAEs) [ Å]. We use extremely deep stacks of rest-UV continuum and continuum-subtracted  images to show that all sub-samples exhibit diffuse  emission to radii of at least 10 ( physical kpc). The characteristic exponential scale lengths for  line emission exceed that of the Å UV continuum light by factors of . The surface brightness profiles of  emission are strongly suppressed relative to the UV continuum light in the inner few kpc, by amounts that are tightly correlated with the galaxies’ observed spectral morphology; however, all galaxy sub-subsamples, including that of galaxies for which  appears in net absorption in the spectra, exhibit qualitatively similar diffuse  emission halos. Accounting for the extended  emission halos, which generally would not be detected in the slit spectra of individual objects or with typical narrow-band  imaging, increases the total  flux [and rest equivalent width ] by an average factor of , and by a much larger factor for the 80% of LBGs not classified as LAEs. We argue that most, if not all, of the observed  emission in the diffuse halos originates in the galaxy HII regions but is scattered in our direction by HI gas in the galaxy’s circum-galactic medium (CGM). The overall intensity of  halos, but not the surface brightness distribution, is strongly correlated with the emission observed in the central - more luminous halos are observed for galaxies with stronger central  emission. We show that whether or not a galaxy is classified as a giant “Lyman Blob” (LAB) depends sensitively on the  surface brightness threshold reached by an observation. Accounting for diffuse  halos, all LBGs would be LABs if surveys were sensitive to 10 times lower  surface brightness thresholds; similarly, essentially all LBGs would qualify as LAEs.

cosmology: observations — galaxies: evolution — galaxies: high-redshift

1 Introduction

Although the Lyman () emission line of neutral H is expected to be produced in prodigious amounts by star-forming galaxies (e.g. Partridge & Peebles 1967; Meier 1976), it has long been appreciated that the astrophysics affecting observations of  are far more complex than for other lines of abundant species due to resonant scattering (Spitzer 1978; Meier & Terlevich 1981; Charlot & Fall 1993). The very large cross-section in the  transition means that emission from a gas cloud or nebula may have been strongly altered in intensity, kinematics, and apparent spatial distribution by the time it reaches an observer. Similarly, information about the initial source of observed  emission may be lost or obscured, with the apparent source simply being HI gas responsible for scattering in the observer’s direction. Consequently, the dominant process producing  emission may often be ambiguous; possibilities include photoionization by young stars or AGN, line emission following collisional excitation of H atoms, or simply scattering from intervening HI gas that happens to favor the observer’s direction.

In the absence of dust, the standard expectation for  emission produced in HII regions for “Case B” (i.e., ionization-bounded) recombination (Brocklehurst 1971) and a Chabrier (2003) stellar initial mass function (IMF) for high mass stars 111Note that this value is a factor 1.8 higher than would be obtained assuming a Salpeter (1955) IMF because a given number of ionizing photons is associated with a smaller total SFR for the Chabrier IMF. is that each solar mass of star formation produces a  luminosity ergs s. For the same IMF, the far-UV continuum light produced per solar mass of SFR near the wavelength of  has an expected monochromatic luminosity in the range ergs s Å (Leitherer et al. 1999). The predicted rest equivalent width of  emission is then given by Å (see also Charlot & Fall 1993), with values near the lower end of this range expected for continuous star formation lasting more than yrs, roughly the minimum dynamical timescale for L* LBGs at (e.g., Erb et al. 2006b). Under the above assumptions, the period of time over which  emission has Å would be very brief, after which the line-to-continuum ratio reaches an asymptotic value of Å. Thus, for a UV continuum-selected sample, one would expect only a small fraction of galaxies to be caught during a time when their intrinsic exceeds 100 Å222For a sample selected by  (as opposed to continuum) emission, this may not be the case..

When dust is mixed throughout the scattering medium, one expects selective extinction of  photons compared to those in the nearby UV continuum due to the much larger effective path length traversed by a line photon before escaping into the intergalactic medium (e.g., Meier & Terlevich 1981; Hartmann et al. 1984; Neufeld 1990). This effect is often cited when observed  emission lines are much weaker than the Case B expectations discussed above (e.g., Charlot & Fall 1993; Shapley et al. 2003; Hayes et al. 2010; Kornei et al. 2010). Since most continuum-selected high redshift galaxies in current spectroscopic surveys appear to have at least some dust, and the vast majority have  equivalent widths Å (e.g., Shapley et al. 2003; Kornei et al. 2010), this conclusion would seem reasonable. On the other hand, it is also possible, at least in principle, for  photons to experience less attenuation by dust than continuum photons, in the case of a clumpy ISM in which dust is located only within the clumps which are rarely penetrated by  photons (Neufeld 1991; Finkelstein et al. 2008). There is no reason to believe that the two competing effects could not both be at work within different regions of the same galaxy.

Even without dust, however, resonant scattering produces spatial and/or spectral diffusion of  photons leading to emergent line emission whose properties depend on the geometry, kinematics, and HI optical depth distributions within the gaseous circumgalactic medium (CGM) surrounding a galaxy (Steidel et al. 2010 [S2010]). In the zero-dust case, the total  luminosity would be unaltered by resonant scattering, but, as we detail below, the detectability of  could be very strongly affected.

  Fig. 1.—: Comparison of  line equivalent widths measured from spectra compared to those inferred from Cont-NB colors in deep imaging. The imaging measurements use isophotal apertures defined by the extent of  flux to a surface brightness limit of ergs s cm arcsec, which is typical of the deepest  narrow-band imaging surveys.

  Fig. 2.—: Comparison of the  line equivalent width distribution from spectroscopic measurements versus that inferred from CB-NB colors in  imaging. The imaging measurements use colors within isophotal apertures defined by the extent of  flux to a surface brightness limit of ergs s cm arcsec, which is typical of the deepest  narrow-band imaging surveys. The statistics are for the mean and standard deviation (left) of individual values (left), and the median and inter-quartile range (right) for each set of measurements.

In S2010, we characterized the distribution of cool gas in the CGM of star-forming galaxies with redshifts and attempted to understand the kinematics and line strength of the ISM absorption and  emission in the context of galaxy-scale gaseous outflows. In brief, we found that UV-selected galaxies within a factor of a few of L* in the far-UV continuum luminosity function (corresponding at to apparent magnitudes – see Reddy & Steidel 2009) have a CGM that can be traced by HI ( and Ly absorption) and several strong absorption lines of metallic species (e.g., CII, CIV, SiII, SiIV) to galactocentric distances of kpc using the spectra of faint background galaxies. The measurement used more than 500 galaxy pairs on angular scales  to map out the absorption line strength as a function of galaxy impact parameter (i.e., the physical separation of the two lines of sight at the redshift of the foreground galaxy) for each observed species. In slit spectra of the CGM “host galaxies”, the bulk of observed  emission, when present, is almost always strongly redshifted, while the strong interstellar (IS) absorption lines are strongly blue-shifted. S2010 presented a geometric and kinematic model that reproduces many of the observed trends.

In the context of the model,  photons escape the galaxy in an observer’s direction mainly by scattering from optically thick HI gas located on the far side of the galaxy’s stars, but having the same overall (outflowing) kinematics as the IS gas seen in blue-shifted absorption. We used the transverse information from the galaxy pairs combined with line-of-sight information available from the galaxies’ own far-UV spectra to construct a consistent geometric and kinematic model of galaxy scale outflows in the context of a very well-studied population of high redshift star-forming galaxies. That is, we combined the line profiles of IS absorption lines and  emission in the galaxy spectra themselves (sampling the kinematics and line strength for galactocentric impact parameter ) with IS line strength measurements at (using close angular pairs of galaxies) to infer the 3-dimensional distribution of CGM gas surrounding an average galaxy in the spectroscopic sample. We suggested that the CGM gas seen in absorption would also constitute a scattering medium through which  photons must traverse in order to be observed. High velocities and large velocity gradients together with gas covering fraction through much of the CGM allow  photons to diffuse spatially outward, favoring escape of  photons last scattered (in the observer’s direction) from atoms with velocities well off resonance with respect to any HI that remains between the location of the last scattering and the observer. If true, one might then expect to observe scattered  emission over the same spatial scales for which strong HI and low-ion metallic absorption is seen, i.e., kpc, even if all  photons originated in the galaxy’s HII regions.

Clearly, scattering will substantially modify both the spatial and spectral distribution of  photons emergent in a particular direction, and at the very least may cause  emitting regions to appear distinct from the UV continuum emission even if both share a common origin. Slit spectra commonly optimized for the compact size of the continuum emitting regions of typical star-forming high redshift galaxies may encompass only a fraction of emergent  emission. The relevant angular scale for the optically-thick CGM HI gas is  ( physical kpc at ), whereas a typical extraction aperture for a slit spectrum is – a difference of a factor of more than 180 in solid angle. Thus, even if the Case B-expected production rate of  photons were to escape the CGM of a galaxy, it is likely that the emission would be distributed over such a large region that a narrow slit would miss most of the  flux; even very deep narrow-band images might leave much of the flux unaccounted-for due to limited surface brightness sensitivity.

In this paper, we present direct observational evidence showing that extended  scattering “halos” are a generic property of high redshift star-forming galaxies, including those that have no apparent  emission lines in their far-UV spectra. In §2 we describe a sample of 92 UV-continuum-selected galaxies for which both rest-far-UV spectra and deep narrow-band  images are available, and discuss the relationship between  properties measured using both techniques. In §3 we use composite UV spectra, as well as  and continuum image stacking, to measure  emission extending to very low surface brightness thresholds for various galaxy sub–samples. The results and their implications for the nature of  emission in star-forming galaxies are described in §4, discussed in §5, and summarized in §6.

Throughout the paper we assume a Lambda-CDM cosmology with , , and .

2 The Galaxy Sample

The galaxies used in this paper are drawn from 3 survey regions where we used UV-color selection to select galaxies with for spectroscopy (Steidel et al. 2003, 2004; Shapley et al. 2005). In addition to completing extensive “Lyman Break Galaxy” (LBG) spectroscopic follow-up, we have also imaged the 3 regions using narrow-band (NB) filters centered at the observed wavelength of  at the redshift of galaxy over-densities we had previously identified from the continuum-selected spectroscopic sample. Table LABEL:tab:obstable summarizes the NB observations in these fields, all of which are among the deepest NB images ever obtained for  at redshifts . The number of continuum-selected galaxies with spectroscopic redshifts falling within the redshift range subtended by the NB filter bandpass in each field are also summarized in Table LABEL:tab:obstable.

TABLE 1: HS1549195 4667/88 27 Keck 1/LRIS 2010 May 18,000 HS1700643 4018/90 43 Palomar 5m/LFC 2007 Jul 80,280 SSA22ah 4980/80 22 Keck 1/LRIS 2005 Aug 33,880 Subaru/SuprimeCam 2002 Sep 25,800 \@ifx@empty\@ifx@empty a Central wavelength/bandwidth of NB filter, in Å. b Redshift range included between NB filter half-power points. c Number of continuum-selected, spectroscopically identified galaxies with NB measurements. d Total integration time, in seconds. e Stellar FWHM in arc seconds after smoothing to match the CB and NB PSF prior to photometry. f Observed surface brightness isophotal threshold (1.5), in units of ergs s cm arcsec. g Isophotal surface brightness threshold, corrected to , in units of ergs s cm arcsec. h The field imaged with Keck/LRIS is a subset of the LBG survey field from Steidel et al. (2003, 2000). The NB image is a combination of the LRIS images and archival Subaru images, discussed by Nestor et al 2011.

We now briefly comment on each of the fields observed:

  • SSA22a has a redshift “spike” centered at (Steidel et al. 1998, 2003) which was first identified from the spectroscopic follow-up of LBGs. It was first imaged in  at the same redshift by Steidel et al. (2000), who discovered two very large ( kpc)“ Blobs”, prompting several subsequent studies of -selected objects using deeper narrow-band data (e.g., Matsuda et al. 2004; Hayashino et al. 2004; Nestor et al. 2011). Here we include the 22 continuum color-selected LBGs with spectroscopic redshifts (Steidel et al. 2003; Shapley et al. 2006) lying within a region with especially deep  NB observations (Table LABEL:tab:obstable)

  • HS170064 is a survey field centered on the the position of a hyper-luminous (, or ) QSO. A galaxy over-density was again identified from spectroscopic follow-up, with (Shapley et al. 2005; Steidel et al. 2005). We have subsequently obtained very deep NB imaging in both  and  at this redshift (Erb et al 2011, in prep.). We include in the present sample the 43 continuum-selected galaxies with spectroscopic redshifts placing the  transition within a NB filter designed for follow-up of the proto-cluster.

  • HS1549195 is another survey field centered on the position of a hyper-luminous QSO (, or ), with . Once again a galaxy over-density was identified from the LBG spectroscopic follow-up, in this case centered on the redshift of the QSO itself 333 As we will show below, there is no evidence that the presence of the QSO has significantly altered the overall  emission of the galaxies at the same redshift.. The NB4670 filter was designed to follow-up on the galaxy over-density, and in response to the serendipitous discovery of spatially offset (and plausibly fluorescent)  emission associated with a damped  absorption (DLA) absorption system identified in the spectrum of a faint background QSO (Adelberger et al. 2006).

In all 3 fields used in the present paper, galaxies were selected using rest-UV (LBG) color selection and observed spectroscopically using the Keck 1 10m telescope and LRIS spectrograph (Oke et al. 1995; Steidel et al. 2004) prior to the  imaging, so the resulting sample should be relatively unbiased with respect to  properties. The full sample of 92 galaxies with mean redshift is broadly representative of UV-selected spectroscopic samples (e.g., Steidel et al. 2003; Shapley et al. 2003; Steidel et al. 2004; Adelberger et al. 2004) in terms of both continuum and  properties: for example, they have with median (mean) of (24.50), and spectroscopically-measured in the range Å (absorption) to Å (emission) with median Å (cf. Shapley et al. 2003; Reddy et al. 2008; Kornei et al. 2010). The spectroscopic measures of  are based on extraction apertures of angular size (the slit width) by , independent of wavelength, so that  and the UV continuum light are measured over identical spatial regions. We used a method similar to that described by Kornei et al. (2010) to measure directly from the galaxy spectra.

 equivalent widths (and fluxes) were also measured for the same set of 92 galaxies using a comparison of deep narrow-band (NB) and continuum (CB) images. As discussed by (e.g.) Steidel et al. (2000), care must be taken since spectroscopic and imaging measurements of  may not be measuring the same quantities. For measurements of  line emission from CB-NB color, the photometric aperture is often defined by the region within an isophote corresponding to a particular  surface brightness threshold, which of course depends on the depth of the  image. It also depends on the suitability of the continuum measurement for estimating the UV continuum flux density in the vicinity of the  line, which may require a color-term correction and/or correction for  line contamination. The 3  images used here are comparably deep to the deepest  surveys to date, with 1 surface brightness thresholds of 1.53, 0.86, and 0.63 ergs s cm arcsec for the HS1700, HS1549, and SSA22 fields, respectively444Isophotal apertures corresponding to above the local sky were used for NB-selected catalogs in all 3 cases.. Although these observed SB thresholds differ by a factor of more than 2, the deeper data at higher redshift result in rest-frame  surface brightness thresholds which differ by less than 10%. The last column of Table LABEL:tab:obstable shows the relative surface brightness thresholds when all 3 datasets are shifted to the mean redshift of .

Important to generating  line images for relatively continuum-bright galaxies (and for measuring line equivalent widths independently of spectroscopy) is a measure of their far-UV continuum (hereinafter CB, or ) near the wavelength of the  line. Ideally, the CB should have the same effective wavelength as the NB without including the  line itself. For the 3 fields presented here, deep CB images were created using linear combinations of two broad-band filters bracketing the NB passband; details of these procedures are described in the individual papers cited above. Briefly, in HS1700 we used very deep (3550/700) and (4730/1100) images obtained in 2001 May with the William Herschel 4.2m Telescope prime focus imager (see Shapley et al. 2005) to create a “UG” continuum image with an effective wavelength of 4010Å. For SSA22a, we used archival B and V images taken with the 8.2m Subaru telescope with Suprimecam to create a “BV” CB image with Å (see Nestor et al 2011). The HS1549 field was treated somewhat differently, since the deepest broad band image (10,800 s integration with Keck/LRIS) was obtained in the V band555Because the data were obtained using a dichroic with a transition wavelength of Å (d500), the V passband was shifted to slightly longer wavelength ( Å instead of 5464 Å. using the LRIS red channel contemporaneously with the March 2007 NB4670 images on the blue channel. A less-deep G-band image (2500 seconds with Keck/LRIS-B) was used to estimate the appropriate (object-dependent) color correction needed to adjust the deeper V-band images to an effective wavelength near 4670 Å. Since the observed range in continuum color among the sample galaxies at a given redshift is small (e.g., the mean and standard deviation in observed broad-band color for the 43 galaxies in the HS1700 field is , and where the standard deviation in both cases includes photometric scatter), and the passbands are separated by only Å in the galaxy rest frame, we believe that systematic errors associated with producing the CB image at the appropriate effective wavelength is likely very small ( mag.).

In brief, the CB and NB images were first scaled to have matching zeropoints based on photometry of spectrophotometric standard stars and by calculating the relative system throughput in each filter passband as a cross-check. The suitably scaled CB or NB images were smoothed using a Gaussian kernel to match the stellar point-spread functions (PSFs) in the two images; the final PSF size for each field is listed in Table LABEL:tab:obstable. Matched aperture photometry was performed using dual image mode in SExtractor (Bertin & Arnouts 1996), with CB-NB colors measured using photometric apertures defined in the NB image at an isophotal threshold equivalent to 1.5 per pixel above the estimated local sky background. The CB zero point was iteratively adjusted by a small amount ( mag in all cases) so that the median color of all objects in the image having (the principle range expected for the galaxies of interest) has CB-NB=0, corresponding to identical flux density measured in each band. The statistical error in the measurement of CB-NB can be conservatively estimated from the dispersion in color for all objects in the same range of apparent magnitude, which is quite small because of the intrinsically narrow range in color and the depth of both the CB and NB images [ mag.] A continuum-subtracted  line image (hereinafter “” image) was formed by subtracting the scaled continuum image from the NB image 666Among the 3 fields, only the SSA22a CB includes a small overlap (% of its full bandwidth) with the NB  passband; this would have the effect of a small (negligible for our purposes) over-subtraction of the continuum when producing the  line image..

We measured (in units of Å) from the CB-NB color using the simple relationship

(1)

where is the appropriate rest-frame bandwidth in Å of the NB filter (19.6 Å, 23.4 Å, and 27.3 Å for SSA22, HS1549, and HS1700, respectively). Note that with this definition, when , and positive (negative) values indicate net  emission (absorption). At an isophotal threshold of ergs s cm arcsec, the typical solid angle subtended by the detection isophote in the narrow-band (NB) image for the continuum-selected galaxies is arcsec, times larger than the spectroscopic aperture. If the spatial distribution of  emission is significantly different from that of the continuum light, then the measured colors [and hence the inferred ] could differ from the spectroscopic values. Figure 1 compares the measurements of from the spectra versus those based on the CB-NB colors for the same 92 galaxies in the current sample, while Figure 2 compares the two distributions. There is a modest tendency for the value of measured from the NB images to be larger in absolute value (whether in absorption or emission) near the extremes of the distribution, though they have very similar mean and median values (Figure 2) and agree well when is small. If significant  flux were distributed on still larger angular scales (with lower  surface brightness) while the same is not true of the UV continuum light, then even the larger NB-based would underestimate the true values.

TABLE 2: All 92 2.65 24.60  2.4 25.2  87.2 3.4  1.7  9.7 Ly Em 52 2.66 24.40  3.1 25.6 136.3 2.9  2.5 14.3 Ly Abs 40 2.63 24.72  1.5 20.8  52.5 4.5  0.7  4.0 All non-LAE 74 2.65 24.56  1.4 25.5 124.9 2.8  1.4  8.0 LAE only 18 2.64 24.68  3.9 28.4 110.3 2.9  4.0 22.8 Ly Blobs 11 2.59   15.7 27.6     11.5 65.7     \@ifx@empty\@ifx@empty a Galaxy sub-sample, drawn from the full sample (All) of 92 continuum-selected galaxies with Ly imaging. The details of the sub-samples are described in the text. b Average continuum apparent magnitude at Å, estimated from the CB photometry. c Best fit parameters assuming SB profile , where is in units of ergs s cm arcsec. The sub-scripts and refer to the Ly line and UV continuum profiles, respectively. d Average integrated flux, in units of ergs s cm. e Average integrated luminosity, in units of ergs s, assuming . f  rest equivalent width measured from spectrum (Figure 3). g  rest equivalent width of total Ly flux, in Å.

3 Inferences from Stacked Composites

3.1 Spectroscopic Stacks

  Fig. 3.—: Composite spectra formed from the average within the subsamples detailed in Table LABEL:table:tab2. Within each panel, the number of galaxies going into the stack is listed after the sub-sample name; the second line in the annotation lists the rest-frame equivalent width of the Ly line measured from the composite spectrum, with the convention that positive values indicate net emission.

In order to measure  emission with SB well below the detection threshold for individual objects, we constructed composite spectra and images after dividing the sample of 92 into several subsets, summarized in Table LABEL:table:tab2. We used the values of measured from the CB-NB colors for all galaxies, with apertures defined by the isophotal thresholds listed in column 9 of Table LABEL:tab:obstable. This method has generally smaller statistical uncertainties and aperture corrections compared to the spectroscopic measurements, and facilitates comparison with most deep  surveys, which are based primarily on equivalent widths and fluxes inferred from the NB photometry 777We have verified that none of the results of this paper depends significantly on whether the imaging or spectroscopic measures of  are used to define the subsets..

As illustrated in Figure 2, the median from both NB imaging and spectroscopic measurements is close to zero, in agreement with previous results for continuum-selected samples (Steidel et al. 2000; Shapley et al. 2003; Kornei et al. 2010). In forming subsets of the sample of 92, we used the NB  measurements to split the sample into “ Em”, those that have  in net emission (52), and “ Abs”, those having  in net absorption (40)–see the second and third rows of Table LABEL:table:tab2, respectively. Two other subsets were made consisting of galaxies satisfying the criteria commonly adopted for “Lyman Emitters” (LAEs), i.e., Å, of which there are 18 (20% of the total), with the remainder (74 of 92, or 80%) placed in a sub-sample called “non-LAEs”, i.e., all continuum-selected LBGs that would not be selected as LAEs.

For each sub-sample listed in Table LABEL:table:tab2, a composite far-UV spectrum was created by shifting the observed, flux-calibrated spectra into the galaxy rest-frame using the prescriptions given in S2010, re-sampling the rest-frame spectra to Å pix, and averaging. Each stacked composite spectrum was scaled so that the continuum level near  matched that obtained from the photometric stack of the same subset of galaxies, discussed below. The correction was typically a factor of , and was applied for the sole purpose of placing the continuum levels for the same subsets on the same flux scale. The resulting stacked spectra are shown in Figure 3; measured properties of the composite spectra are given in the figure and listed in Table LABEL:table:tab2.

3.2  and CB Stacks

A 25 x 25sub-image (“postage stamp”) centered on the position of the continuum centroid of each galaxy was extracted from the CB image and the (continuum-subtracted)  images after scaling them to a common zero point as discussed above. Masks were created by performing object detection on each continuum sub-image using SExtractor (Bertin & Arnouts 1996). These were used to exclude pixels lying within the detection isophotes of any object other than the central one, and were applied during the stacking to both the CB and  images. Two stacked images were formed for each subset listed in Table LABEL:table:tab2 (straight averages, with masking), one for the CB image and another for the  line image. Figure 4 compares the average CB image with the  image for the full sample of 92 galaxies, while Figure 5 compares the azimuthally-averaged surface brightness profiles of the same composite CB and  images. Figure 4 shows clearly that, on average,  emission is detected to radii of at least 10, or physical kpc at . Figure 5 shows that the average CB light profile for the same galaxies is much more compact and drops below the SB detection threshold for kpc (). Figure 5 also shows what the  line profile would look like if (i.e., Case B) and  and CB light had the same spatial distribution on average.

  Fig. 4.—: (Left:) Scaled far-UV continuum image produced (as described in the text) from the average of 92 continuum-selected LBGs, drawn from 3 independent fields. The regions shown are 20 ( kpc physical at ) on a side, with a grid spacing of 2. (Right:) The continuum-subtracted, stacked  image for the same sample of galaxies. In both panels, the contours are logarithmically spaced in surface brightness with the lowest contour shown at ergs s cm arcsec.

  Fig. 5.—: The observed average surface brightness profile for the 1220 Å continuum light (blue) and the  line (red) for the full sample of 92 continuum-selected galaxies, evaluated over the same rest-frame bandwidth sampled by the  image (24.3 Å). Note that these profiles are simply the azimuthal averages of the stacked images shown in Figure 4. The light-shaded region indicates the range of typical  surface brightness threshold reached by deep  surveys for the detection of individual objects. The dashed lines show the surface brightness profile assuming that with parameters given in Table LABEL:table:tab2. The corresponding angular scale at is given along the top axis. For the purpose of comparison, we also show the  profile expected for the same sources under the assumption of “Case B”  to CB ratio, no destruction of  by dust, and no spatial diffusion of  photons due to resonant scattering (i.e., the  and CB profiles would be identical in shape, and since Å, the  line image would be a factor of brighter than the continuum in the effective rest-frame bandwidth of 24.3 Å.)

The surface brightness profiles for both the continuum and the  line images are reasonably well-fit by an exponential of the form for projected radii beyond the central arcsec; the parameters of the best-fit values for the normalization and scale length are given in Table LABEL:table:tab2 for each sub-sample as well. In the full image stack, the effective surface brightness detection thresholds are a factor of lower than for individual galaxies; it is clear that the distribution of  emission is very different from that of the continuum for every sub-sample, with best-fit  scale lengths of kpc compared to the corresponding continuum emission which has kpc. It is important to note that the true difference in scale length is larger, since we have made no attempt to de-convolve the profiles from the seeing disk, which was FWHM 0.86, 1.20, and 0.80 for HS1549, HS1700, and SSA22a, respectively. The continuum profiles of the stacked composite CB images have , indicating average (seeing de-convolved) galaxy continuum sizes of FWHM (). These de-convolved angular sizes are also consistent with measurements of similar galaxies in deep HST/ACS images (e.g., Peter et al. 2007; Law et al. 2007.)

  Fig. 6.—: Same as Figure 5, comparing the average surface brightness profiles for the the sample divided according to whether the NB measurements indicate net  “Abs” or “Em”.

The stacked  and CB images as in Figures 5 and 6 represent unweighted averages of all galaxies in the sample (with masking as described above). This choice was motivated by the desire to preserve the photometric integrity of the stacks so that fluxes could be measured directly using aperture photometry, but also because any scaling or weighting would require deciding what the relevant figure of merit should be. Medians are often used to suppress outliers in stacked data sets, but they have the disadvantage for the present application of not preserving flux in two-dimensional images, of working best when scaling has been applied to individual images going into the stack, and of suppressing real signal as it approaches the noise level. Nevertheless, in Figure 7 we show a comparison of the surface brightness profiles for median-combined stacks as compared to mean-combined for both line and continuum.

We have argued that our sample of galaxies with has emission line and continuum properties characteristic of those in the full LBG spectroscopic surveys at these redshifts. Figure 8 shows that the diffuse  emission is also consistent among the 3 survey fields taken individually. This is important, since each field samples galaxies at a different redshift with observations subject to a different set of conditions, using different telescope and instrument combinations. We also note that the bright QSO known to lie within the survey volume in the HS1549 field appears not to have had a significant effect on the  emission from the galaxies in our sample888The galaxy regions most likely to be affected by excess ionizing radiation from the QSO would lie in the outer parts; whether this radiation would increase or decrease the amount of  emission from galaxies would depend on the physical state of the gas. The galaxies in the HS1549 field are fainter by about 30% on average (in terms of apparent continuum magnitude) than in the other two fields; the differences in the  profiles on small scales may be a consequence of this selection issue..

  Fig. 7.—: Same as Figure 5, comparing the surface brightness profile measured from median-combined rather than mean-combined stacks of  and CB sub-images. Note that the line-to-continuum ratio is not necessarily preserved in the median stacks. The general effect of this alternative processing is to decrease the measured  scale lengths by %, though the  profiles remain much more extended than the continuum profiles.

Figure 6 shows the measured surface brightness profiles and best-fit exponential parameters for the sub-sample with net  emission (see the second row of Table LABEL:table:tab2). The profile of the Em composite is qualitatively similar to that of the full sample. The main difference is in the central  surface brightness —  Em objects have (on average)  surface brightness well above the threshold for individual detection (light shaded region in Figure. 5 and 6) to projected distances of kpc (2531), whereas even the peak  SB in the full sample (Figure 5) barely reaches the (individual) detectability threshold. Also illustrated in Figure 6 is the SB profile for the “ Abs” sub-sample. The  SB scale length for the Abs sample is still times larger than for the corresponding continuum light (third row of Table LABEL:table:tab2)– and has a comparable  scale length to that measured for the  Em sample (second row of Table LABEL:table:tab2), albeit with a times lower normalization for kpc. Clearly the difference is much larger for 1, where the Abs sample exhibits a large “hole” in which  absorption strongly dominates.

Figure 9 reproduces the SB profiles of the “ Em” and “ Abs” sub-samples together with the average profile of LAEs (green), and non-LAEs (cyan). The LAE sub-sample is very similar to that of the larger “ Em” subset, but has an average SB a factor of higher for kpc (and a factor higher for kpc.) Also plotted for comparison (Figure 9) is the average SB profile of 11 “ Blobs” (LABs; see e.g. Steidel et al. 2000; Matsuda et al. 2004), which for the present we define as  selected objects with detected isophotal diameters , discovered in the same 3 survey fields. None of the 11 Blobs is included in the main galaxy sample, since they do not have central continuum sources that satisfy the usual LBG color criteria. As indicated in Table LABEL:table:tab2, the Blobs have an average  luminosity times higher than an average galaxy in our sample. It appears that even the most extreme LABs do not have fundamentally different SB profiles compared to those of typical galaxies in the sample except that their surface brightness normalization exceeds the typical detection threshold to kpc (). In other words, if one were routinely sensitive to a surface brightness of ergs s cm arcsec, all continuum-selected LBGs would be “Blobs”999 Conversely, if the LABs were several times less luminous but had the same surface brightness profile, they would fail to be recognized as “blobs” at all.. We will return to a more detailed discussion of  demographics in §4.

If we assume for the moment that the extended  halos represent photons originating in the galaxies’ HII regions, we can use the composite  line and CB images to measure the integrated  line-to-continuum ratio, usually parametrized as , the  equivalent width. The total  fluxes have been measured directly from the calibrated stacked images (column 8 of Table LABEL:table:tab2); a comparison with the continuum flux density measured near the wavelength of  from the CB images (column 3 of Table LABEL:table:tab2) allows the calculation of (column 12). These numbers can be compared directly with the spectroscopic measurements (column 11) for the same galaxy sub-samples. The values that include the diffuse  extending to kpc radii around galaxies exceed the spectroscopically-inferred by an average factor of for the full galaxy sample. Figure 10 shows the cumulative fraction of the total  flux as a function of aperture radius (in arc seconds) for the galaxy samples in Table LABEL:table:tab2. It is interesting to note that including the spatially extended  emission brings the average galaxy into the range that would nominally qualify as a LAE ( Å)– even for the “No LAE” sub-sample that explicitly excludes the 18 conventional LAEs (row 4 of Table LABEL:table:tab2).

  Fig. 8.—: Average observed  surface brightness profiles for galaxy sub-samples separated by field, as indicated. The  profiles were scaled according to the relative continuum flux density in each field, for display purposes. The small differences in the mapping of angular scale to physical scale have also been removed to facilitate the comparison. The measured values of the average  rest equivalent width are Å  28.6 Å, and 42.0 Å for HS1549, HS1700, and SSA22, respectively.

One can also compare the measured large-aperture with expectations for the  to continuum ratio for Case-B recombination and no dust. As discussed above, an asymptotic value of Å is expected when star formation has been continuous for years101010The typical inferred age for galaxies similar to those in the present sample is Myr (e.g., Shapley et al. 2005; Reddy et al. 2008).. Note that approximately the same value of is expected as long as  photons do not suffer greater attenuation by dust than continuum photons just off the  resonance. Thus, the fact that most of the values of Å (Table LABEL:table:tab3) are significantly smaller than unity means that  photons suffer greater extinction than the continuum, by factors ranging from with an average for the full sample of 92 galaxies.

We note that the values in Table LABEL:table:tab3 for have been obtained using a method that appears to differ from that used in some recent work (e.g., Gronwall et al. 2007; Nilsson et al. 2009; Kornei et al. 2010). Most estimates of use stellar population synthesis models to estimate the level of extinction, which is then used to derive SFR to calculate the expected  luminosity based on the assumption of Case B recombination and the form of the stellar IMF. While we are using largely identical SED modeling to estimate , we use the observed as a direct observational estimate of . The present method relies on the same assumptions about the stellar IMF (i.e., based on a Salpeter-like IMF for high mass stars) to estimate the  photon production rate per unit star formation; the difference is that we rely on the ratio of  photon production to that of Å continuum photons from the same ensemble of stars. The advantage of using the equivalent width measurement is that it should be independent of extinction if  and Å continuum photons experience the same attenuation, and would directly reflect the relative attenuation of line and continuum if . Because both of these methods rely on measuring the integrated  line flux, an underestimate of  relative to the continuum will cause to be underestimated by the same factor. For the present purposes, we prefer using the method relying on since it depends on a largely independent measurement that may avoid propagating possibly large systematic errors in the estimates of E(B-V) from SED fitting [or from the assumed extinction curve, which relates E(B-V) to ] to the calculation of . In general, we expect that the under-counting of  photons due to the aperture effects discussed above are likely to dominate any differences in inferred .

Column 10 of Table LABEL:table:tab2 compiles the average  luminosity implied by the measured value of assuming the sample mean redshift . If one naively converts these numbers to an equivalent star formation rate (i.e., divide by ergs s to yield SFR in units of yr) the results range from M yr for the various sub-samples, with an average of 3.1 M yr for the full sample. In Table LABEL:table:tab3 we have compiled the statistics of the far-UV inferred SFRs and continuum extinction for each of the sub-samples from Table LABEL:table:tab2. The extinction estimates are parametrized by and assume the Calzetti et al. (2000) starburst attenuation curve; E(B-V) was estimated from SED fits when available, and using the far-UV continuum slope for the 20% of galaxies lacking adequate near-IR photometric coverage for SED fitting. In the context of the assumed starburst attenuation relation, the extinction (in magnitudes) at 1500Å is (Meurer et al. 1999; Calzetti et al. 2000; Reddy et al. 2006, 2010). The UV continuum magnitudes near rest-frame 1500 Å were used to estimate (e.g., Madau et al. 1998; Steidel et al. 1999; Adelberger & Steidel 2000) with a median value of M yr. Applying the median E(B-V) to the median within each sub-sample implies that M yr, with an overall median of M yr— very close to the mean of the LBG sample observed in  by Erb et al. (2006b) and consistent with the mean bolometric luminosity of identically-selected LBGs estimated using multiple SFR indicators (Reddy et al. 2006, 2010). The median varies considerably among the sub-samples, so that the median attenuation of the UV continuum is inferred to range from for the LAEs to for the  Abs sub-sample. In Table LABEL:table:tab3 we list the inverse of this factor, which we have called . Our estimate of the fraction of all  photons produced by photoionization in the galaxy HII regions that have been detected is then given by . These values range from for the LAE sub-sample to for the “ Abs” sub-sample. The average for the entire sample is . We note that this fraction is close to the average value of estimated by Hayes et al. (2010) based on a very different approach involving a comparison of  and  luminosity density at .

  Fig. 9.—: As for Figure 5, where here the  radial SB profiles are shown for each of the sub-samples in Table LABEL:table:tab2, along with the exponential models for each. Also included for comparison is the average surface brightness profile of 11 giant  “Blobs” observed in the same 3 survey fields (red).

The last column of Table LABEL:table:tab3 shows the inferred ratio , where both quantities are expressed in magnitudes and is inferred from the stellar SED. The numeric value of this ratio is for all sub-samples except the LAEs, which have . Since the Calzetti et al. (2000) extinction curve predicts that the UV continuum near the  line has , it seems that  emission from the LAEs drawn from our LBG sample exhibit no evidence for selective extinction of  photons, while for other LBGs the attenuation is times higher than for continuum photons for the same value of . If the  escape fraction is controlled by processes confined to HII regions, the result suggests that with , on average. This can be compared with the relationship inferred for nearby star-forming galaxies, , based on measurements of the Balmer decrement (Calzetti et al. 2000). At present, there are few galaxies for which , and  have all been measured, though there are some indications that the same value of applies for both continuum starlight and  for galaxies similar to those in the current sample (Erb et al. 2006a; but see Förster Schreiber et al. 2009 for possibly conflicting evidence).

TABLE 3: All 0.17  6.3 34.3 0.17 0.36 0.061 17.9 Ly Em 0.11  6.0 18.6 0.32 0.45 0.144 19.1 Ly Abs 0.19  6.6 46.5 0.14 0.17 0.024 21.3 All non-LAE 0.18  6.7 42.6 0.16 0.29 0.046 18.5 LAE only 0.09  4.5 11.3 0.40 0.93 0.372 11.9 \@ifx@empty\@ifx@empty a Galaxy sub-sample, drawn from the full sample (All) of 92 continuum-selected galaxies with Ly imaging. The details of the sub-samples are described in the text. b Median and mean/standard deviation of continuum apparent magnitude at Å c Median inferred from SED fitting. d Median SFR, in M yr, from UV continuum with no dust correction. e Median SFR after correction based on E(B-V) and Calzetti (2000) reddening relation. f Fraction of 1500 Å photons escaping galaxy. g Relative escape fraction of  photons, Å. h Fraction of  photons escaping, . i Ratio of attenuation of  photons to when both are expressed in magnitudes.

4 Implications of Diffuse  Halos

Diffuse  emission from the outer parts of actively star forming galaxies is an unavoidable consequence of a gaseous CGM so long as some component of it is optically thick to  photons and some fraction of  photons initially produced in HII regions are not absorbed by dust at smaller galactocentric radii. Calculation of the emergent  emission is undoubtedly complex, since it will depend on the details of the gas-phase structure and kinematics as well as the relative distribution of the sources (e.g., HII regions) and the sinks (e.g., dust) of  photons. A fully successful model requires 3-D radiative transfer calculations and all of the relevant spatial and kinematic information as input. Such a treatment is far beyond the scope of this paper; however, it is interesting to ask whether the spatial profiles of  emission from the same star-forming galaxies can be understood in the context of a schematic model. In this section, we describe such a model that begins with inferences on the structure and kinematics of CGM gas from S2010, and then test for consistency with both the  emission observations and the absorption-based S2010 CGM model.

  Fig. 10.—: The cumulative fraction of the large-aperture  flux as a function of angular aperture radius for each galaxy sub-sample. The vertical dashed line drawn at indicates the typical effective aperture for the slit spectra of the same objects. The dark blue curve corresponds to the cumulative continuum flux (for the stack of the full sample) as a comparison.

4.1 A Model for  Scattering Halos

We first consider the probability that a  photon produced in a galaxy’s central few kpc will escape in the direction of a particular observer’s line of sight. The escape probability will depend on the kinematics and optical depth distribution of the CGM gas, and so one might expect it to be closely related to the characteristics of absorption lines observable both in the galaxy spectra themselves (-3 kpc) and in lines of sight to background objects with at larger impact parameter . The conditions necessary for a  line photon to escape in the direction of a particular observer are: 1) it must either be emitted at a frequency that is well off resonance for any HI in the foreground (i.e., between the point of emission and the observer), and/or 2) it must be scattered in a direction that happens to have low spatial covering fraction of HI111111In the limit of no HI gas outside of a galaxy’s HII regions, the emergent  line would have roughly the same spatial extent as that of the UV continuum..

For extended  produced by scattering in a gaseous halo, the observed surface brightness profile will then be related to the integral along the line of sight at impact parameter of the product of a) the  photon density, b) the probability that a  photon will be scattered in our (the observer’s) direction, and c) the probability that once scattered in our direction a photon will proceed to escape the nebula before being scattered once again. The situation is somewhat analogous to the galaxy outflow model used to match absorption line equivalent widths vs. impact parameter presented in S2010. Figure 11 shows the assumed geometry (cf. Figure 23 of S2010.) In the absorption case, a line of sight to a background object pierces the radial flow at projected distance , and the resulting absorption line strength is modulated by the integral along the line of sight of the quantity , where is the galactocentric radius and is the flow velocity at radius . As discussed by S2010, the velocity field in the absorbing gas can have a large effect on the strength of absorption lines in the spectra of background sources when the transition is saturated, even if the covering fraction is significantly smaller than unity. S2010 argued that consistency between the absorption line strength as a function of impact parameter on one hand, and the strength and profile shape of lines observed in the spectra of the galaxies themselves on the other, requires large velocities and velocity gradients in the gas. The absorption cross-section is dominated by outflowing material, and the flows are inferred to be clumpy (i.e., multi-phase), with both high- and low-ionization ionic species observed over similar ranges of velocity and galactocentric distance. In the context of the CGM model, most of the acceleration of cool gas to high velocity occurs in the inner several kpc. The covering fraction of gas giving rise to absorption in a particular transition decreases with increasing galactocentric distance , modeled as a power law of the form .

  Fig. 11.—: Coordinate system for the schematic model of scattered  emission from galaxies, where is the line of sight impact parameter, is the galactocentric distance, and is the assumed physical size of the scattering medium. In the model,  photons are produced near , after which they diffuse outward until they are either destroyed or they escape the scattering medium. The covering fraction of gas at galactocentric radius is assumed to be of the form (see also S2010).

In general, the larger the range of gas-phase bulk velocity sampled along the observer’s line of sight at impact parameter , the greater the chance that a scattered  photon will reach the observer without further scattering. For simplicity, in our model we assume that all scattering events are isotropic, and that the gas-phase velocity field is axisymmetric and is a monotonic function of galactocentric distance (see S2010 for a justification of this assumption). If the bulk velocity field in the outflow has a range and amplitude much larger than that of the local velocity dispersion in the HI gas121212In the models discussed here, this is assumed to be the case based on the results presented in S2010. While velocity is not used explicitly as a model parameter, large velocity gradients along the line of sight directly affect the probability that a scattered  photon will ultimately escape. In other words, the effective covering fraction of optically thick HI as seen by a  photon emitted from a particular position in the CGM implicitly includes an integral over velocity even if it is not explicitly used as a model parameter. See Steidel et al. 2010 for a more detailed discussion of this issue., or when when , the problem can be reduced to a geometric one in which the covering fraction depends only on galactocentric radius , . Clearly it would be interesting to measure the velocity field of extended  emission in order to gauge the role kinematics play in the transfer of  photons. Unfortunately, beyond the central, high surface brightness regions there are few constraints on the line shapes, and at present we have only (projected) spatial information integrated over the full range of velocity.

When considering emission (rather than absorption in the spectra of background objects) one needs to account for the  “source function” which varies with spatial position, as well as variations in opacity parametrized by . The  photon density available to contribute to the observed will depend on the fraction of  photons that have been able to diffuse outward to , which may be only a small fraction of the  photons initially produced by recombination in HII regions. When the covering fraction is high at small radii, one would expect the emergent  emission from that region to be suppressed – photons are either destroyed or radiatively trapped until they make their way to locations from which escape is more probable. The flux of  photons (assumed to be produced at small at a constant rate related to the SFR) at galactocentric radius will be reduced by an overall geometric factor , and by the destruction of  via absorption by dust grains131313Under the assumption of spherical symmetry,  photons scattered at smaller radii are returned to the “pool” of  photons potentially available for scattering at larger radii. .

This diminished  radiation field would produce no  halo at if , since photons would appear to be released from a  “photosphere” that would approximately extend to the edge of the gas distribution. The apparent outer edge of the  scattering halo should correspond to the radius at which becomes negligible and the scattered component of  falls below the observational threshold. At small radii, where and the optical depth encountered in any direction is substantial, (e.g., for galaxies having absorption-dominated continuum spectra),  photons will be resonantly trapped for a large number of scattering events before diffusing spatially outward. Most of the dust absorption, if present, would be expected to occur in such regions. Once falls below unity at larger radii,  photons which have not been destroyed may be scattered in the observer’s direction. Thus, the relative rate of  scattering events at radius will be where is the HI covering fraction. The chance that a scattered  photon will be emitted in the observer’s direction (without any further interactions prior to escape) increases with decreasing characteristic , with probability roughly for . The  surface brightness as seen by an observer in a particular direction will then be proportional to the product of these two terms, integrated along the line of sight through the galaxy at impact parameter :

(2)

where is the coordinate distance along the observer’s line of sight at impact parameter , , is a normalization for the surface brightness distribution, and is the effective size of the scattering halo (see Figure 11) . Note that the integrand tends toward zero when , qualitatively accounting for the suppression of  emission in regions with high . Clearly, when the purely geometric model is no longer valid, since the  emission intensity associated with an optically thick region can be “negative”, i.e., there is a net removal of  photons at that spatial position that will reduce the net surface brightness along that particular line of sight.

In the S2010 CGM model, the radial dependence of the covering fraction of gas was found to be consistent with a power law of the form , where depending on the ionization state of the tracer ion; becomes consistent with zero for kpc for most of the observed ions. If we take the power law form for (with index ) characteristic of the highest HI optical depth material, equation 2 can be used to predict given an overall normalization , a characteristic radius at which first falls below unity [i.e. ], and the the effective size of the scattering medium, . We account qualitatively for the variation of the spatial profile of  emission in the central regions of a galaxy by (artificially) allowing at , using an extrapolation of the same power law form for . Since the integrand becomes negative when , this leads to suppression of the  surface brightness for any line of sight that intercepts such a region. In practice, the central  emission must be substantially suppressed to match the observed profiles of any of the galaxy subsets, including the LAEs (cf. Figure 5).

Figures 12 and 13 show example models based on equation 2 compared with the observed composite  surface brightness profiles; the corresponding model parameters are given in Table LABEL:tab:models. The overall shape of the predicted SB profile is sensitive to the value of parametrizing the radial dependence of the covering fraction of HI; produces  profiles that are flatter than observed, while predicts  emission which falls too rapidly with increasing (Figure 13). As discussed above, the shape of the central portion of is modulated by adjusting the galactocentric radius where (i.e., serves as a normalization of the maximum covering fraction). The presence of a central “hole” in (as observed for the  Abs sub-sample in Figure 12) can be reproduced by increasing so that the transition from net  absorption to net  emission moves to larger galactocentric radius. Once  has a finite probability of escape (i.e., where in the context of our simple model), the residual  photons at become available for re-direction toward an external observer who then perceives the photon being “emitted” from a position at impact parameter in projection.

  Fig. 12.—: Same as Figure 9, but where models described by equation 2 have replaced the exponential profile used in Figure 9. Parameters for the 4 models shown are summarized in Table LABEL:tab:models. All 4 model curves have kpc and with . The “ Abs” model produces a central hole in the  emission by adjusting the normalization of with the parameter ; the larger value of indicates that the CGM remains optically thick to  photons to larger galactocentric radii than for the other sub-samples.

The values of required to produce model profiles in reasonable agreement with their observed counterparts (Table LABEL:tab:models and Figure 12) are near the high end of the range inferred from the behavior of absorption line strength versus impact parameter (S2010). One possible explanation for slightly steeper profiles is that the emission models assume no  photons are destroyed once they propagate beyond ; if  has a finite chance of being absorbed by dust at , the additional attenuation of  would manifest itself as a steepening of the profile with respect to the pure scattering model. That the  Abs model exhibits both the steepest decline in  surface brightness ( compared to for the other sub-samples) and the largest global extinction correction (§3 and Table LABEL:table:tab3) suggests dust may not be confined solely to the central regions in such galaxies.

The model of the CGM proposed by S2010 almost certainly does not provide a unique explanation for the IS absorption line strength and kinematics as observed in the spectra of background galaxies; however, we have shown, with a simple extension of the model, that scattering of  photons from the same CGM gas can can also account for  emission with radial surface brightness profiles and physical extent consistent with the observations. Regardless of the model details (which admittedly could be incorrect), the very similar physical scales involved ( kpc) suggest a close causal connection between the cool gas observed to produce strong HI and low-ionization metallic absorption lines in the spectra of background continuum sources, and spatially extended  emission from the same host galaxies.

TABLE 4: All 11.5 2.2 0.6 90 Ly Em 17.0 2.0 0.6 90 Ly Abs  4.5 5.9 0.8 90 All non-LAE  7.0 2.0 0.6 90 LAE only 25.0 1.9 0.6 90 \@ifx@empty\@ifx@empty a Galaxy sub-sample, drawn from the full sample (All) of 92 continuum-selected galaxies with Ly imaging. b Intensity normalization for model (see Eq. 2), in units of ergs s cm Hz. c Galactocentric radius at which d Power law index in the radial behavior of the covering fraction, . e Effective size of CGM region producing detectable  emission, in kpc.

  Fig. 13.—: Same as Figure 5, where the preferred model is drawn with the solid black curve, corresponding to ergs s cm arcsec, kpc, kpc, and , for covering fraction parametrized as (see also S2010). The dashed curve shows a model with the same parameters, except kpc, while the dotted curve assumes , with all other parameters as for the preferred model.

4.2 Comparison with  Emission in Simulations

A scenario in which extended  emission around galaxies is dominated by scattering of  photons initially produced inside the galaxies, rather than by external processes, has been the focus of a number of recent galaxy models including treatment of  radiative transfer (e.g., Verhamme et al. 2008; Laursen et al. 2009a, b; Zheng et al. 2010a, b; Barnes et al. 2011). Each of these studies places emphasis on different aspects of the model galaxies, and cursory examination suggests a qualitative similarity to the observations presented here, since  scattering leads to the spatial re-distribution of the  emission as seen by an observer. Gas-phase kinematics play a large role in determining how much  emission escapes the galaxies, and in all of the models except those of Verhamme et al. 2008 (which do not explicitly consider the spatial distribution of  emission) the dominant velocity field is associated with infall/accretion. The predicted  line profiles tend to be asymmetric and sometimes double-peaked, usually dominated by photons that are blue-shifted with respect to the galaxy systemic velocity– a configuration that is very rarely observed in galaxy spectra (e.g., Pettini et al. 2000; Shapley et al. 2003; Steidel et al. 2010). Also, while the 3-D models all produce  emission that is significantly more extended than the UV continuum, the predicted surface brightness profiles of scattered emission generally declines much more rapidly than for the observed LBG  halos (i.e., most would fall well below the current surface brightness limit). Barnes et al. (2011) have pointed out that higher outflow velocities tend to produce more extended  emission in the context of their models, which include both inflows and outflows of gas, so that perhaps the missing ingredient is the presence of higher-velocity outflows than have generally been modeled.

Most of the simulations work on  emission from galaxies has not highlighted the potential utility of using  emission observations as a means of revealing gas-phase structure in the surrounding CGM and IGM. One exception is a a series of recent papers exploring how very sensitive NB observations of  emission can be used along with cosmological simulations (including detailed radiative transfer) to trace the underlying large scale structure at high redshifts (Zheng et al. 2010a, b). In Zheng et al. (2010b), the authors explicitly calculate the expected properties of diffuse  emission around star-forming galaxies, with principal focus on LAEs at . Like the scenario we have described above, the models assume that the ultimate source of the  photons seen in emission is the galaxy HII regions, with extended emission resulting from the details of the  radiative transfer. Zheng et al. (2010b) predict that the surface brightness profile surrounding individual galaxies will have two distinct components related closely to 1) the “halo exclusion scale” within comoving distances of Mpc ( physical kpc at ), and a larger-scale component arising from galaxy clustering, extending to Mpc (comoving), or physical kpc at . The smaller scale is similar to the virial radius of the characteristic dark matter halos being considered in the simulation. 141414Note that our procedure of masking out all identified continuum sources other than the central one when producing the  and continuum stacks (§3) would suppress what Zheng et al. (2010b) call the “two-halo term” due to clustering, so our observed  profiles should be compared only with the “one-halo”, central component. It is not completely straightforward to move the predictions to for comparison with our observations, but (as discussed in S2010) the CGM scattering medium observed around galaxies (which we have argued is responsible for absorption against background sources as well as for the extent of scattered  emission) also has a size similar to the virial radius kpc. However, it is not clear that the observations are consistent with the predictions when it comes to the dependence of the  emission halo on other properties of the galaxies. In the Zheng et al. (2010b) models, the primary driver of the surface brightness profile is the gas-phase kinematics of the CGM gas; the characteristic scale of the inner component of  emission relates to the “infall” region for the halo, within which gas is accreting onto the central galaxy (the simulations do not have outflowing material, and it is the kinematics of infalling material that modulate the escape of  photons). On the other hand, in our picture the characteristic scale is related to the radial dependence of the covering fraction of neutral material and the gas-phase kinematics (assumed to be dominated by outflows). Within our sample of LBGs, the stacked  images of various subsets indicate a rather consistent exponential scale length of kpc with at most a weak dependence on  or UV luminosity or on the fraction of  photons that escape the galaxy ISM. If there is a trend, it is in the direction opposite to that expected in the models.

Interestingly, many recent theoretical investigations focusing primarily on diffuse and extended  from the outer parts of galaxies or LAEs have deliberately neglected the scattering of  from the inside out (Dijkstra et al. 2006; Dijkstra & Loeb 2009; Kereš et al. 2009; Faucher-Giguere et al. 2010; Goerdt et al. 2009). Instead, attention has been drawn to  emission associated with gas cooling as it accretes onto galaxies (“ Cooling”), or on  fluorescence as a means of measuring the intensity of sources of ionizing photons at high redshifts. Both of these processes are discussed in §5 below.

In any case, there is no doubt that radiative transfer calculations will be key to a full understanding of diffuse  emission from galaxies. However, it is essential that the CGM gas distribution and kinematics in the simulations match real galaxies. Without the correct gas-phase model, even the most sophisticated treatment of radiative transfer cannot yield a realistic result. The observations suggest that possibly important ingredients include a CGM that is clumpy on small scales and which has very large (non-gravitational) velocity gradients dominated by galaxy-scale outflows.

5 Discussion

We have shown above that, on average, LBGs with far-UV luminosities at exhibit spatially extended  emission to physical radii of at least 80 kpc (10), even when  appears only in absorption for regions coincident with the UV continuum starlight. Figures 5, 6, and 12 show that the profiles of the  emission are quite similar in shape independent of the spectral morphology, with the main difference being the overall intensity normalization and the presence or absence of emission spatially coincident with the continuum light (i.e., the inner kpc). The observations suggest that the -scattering CGM may be statistically universal, with the main variable being the fraction of  photons able to emerge from the inner few kpc region without being destroyed. For example, the difference between the  Em and  Abs (see Table LABEL:table:tab2) spectrally classified subsets is an overall factor of in the  surface brightness at the full continuum extent (Figure 6), beyond which the ratio of for the two sub-samples remains essentially constant. The scale lengths for  emission ( kpc) are consistent among the statistically distinct galaxy sub-samples in spite of the fact that the integrated line-to-continuum ratio varies by large factors among the same sub-samples.

5.1 Previous Results on Statistical  Detections

 emission with physical extent larger than that of a galaxy’s continuum starlight is not a surprising result from a theoretical perspective (e.g., Barnes & Haehnelt 2009, 2010; Laursen et al. 2009a, b), and has been observed and noted in many individual cases both in the nearby (e.g. Mas-Hesse et al. 2003; Hayes et al. 2007; Östlin et al. 2009) and high redshift (e.g.,Franx et al. 1997; Moller & Warren 1998; Steidel et al. 2000; Fynbo et al. 2003; Matsuda et al. 2004; Adelberger et al. 2006; Ouchi et al. 2008) universe. However, relatively few surveys at high redshift have reached adequate  surface brightness limits to allow the detection of the very low surface brightness levels discussed above. An exception is the extremely deep spectroscopic survey for  emission conducted by Rauch et al. (2008) [R08]. Using a  –selected sample distributed over the redshift range , these authors noted that extended  emission was a common feature of the LAEs discovered in their survey. A spatial stack of all of the  emitting sources exhibited significant emission (with threshold ergs s cm arcsec) to an angular scale of , or kpc projected physical radius. The R08 sample, as the authors themselves point out, covers a different range of UV luminosity compared to most continuum-selected LBG spectroscopic surveys– only one of 27 objects has , while 80% our sample (which has a median ) has , although there is is a tendency for the faintest objects to be among those with the strongest  emission lines (see Tables LABEL:table:tab2 and  LABEL:table:tab3). 151515Moving our continuum-selected sample to the somewhat higher median redshift of R08 would result in % of our sample having . Nevertheless, the average surface brightness profile for the R08 -selected sample is remarkably similar to that of our continuum-selected sample (e.g., compare Figure 6 to Figure 20 of R08). For objects in our “ Em” sub-sample (Table LABEL:table:tab2), the peak  SBs are somewhat higher than for the R08 sample, while the angular extent (at the same limiting SB of ergs s cm arcsec) is times larger in the present LBG sample. Within our sample there is a significant dependence of on apparent UV continuum luminosity, but the average  profiles are similar, as shown in Figure 14.

  Fig. 14.—: A comparison of the continuum and  surface brightness profiles of the full sample divided into two at the median continuum apparent magnitude. The “UV bright” sample is a factor of times brighter in the continuum than that of the “UV faint” sample (CB(Bright) versus CB(Faint)), but the average  flux for the UV bright sub-sample is 10% smaller than that of the UV-faint sub-sample, i.e. Å, while Å).

In any case, it is worth pointing out that, under the hypothesis that  scattering, and not fluorescence, is the dominant process producing the observed  halos, the scattering medium need not be optically thick in the HI Lyman continuum. This means that it is not necessarily correct to associate the observed physical extent of  emission with regions having cm as R08 have suggested – in principle, could be 1000 times lower and still remain optically thick to  photons.

Perhaps more directly analogous to the results of the present sample is the narrow-band  survey of Hayashino et al. (2004). These authors used deep NB  images in the SSA22 field, and stacked the  images of 22 continuum-selected LBGs from the survey of Steidel et al. (2003), of which 19 are in common with our current SSA22 sample161616 The new NB image used in the present sample includes both archival Subaru data as well as an additional 10 hours’ integration using LRIS on the Keck 1 telescope, and so is substantially deeper ( factor of 2-3), but covers a much smaller area, than that of Hayashino et al. (2004). . Indeed, Hayashino et al showed that significant emission extends to angular scales of at least 4  and that the “ring” in the range 2-4 often contains as much or more  flux than the inner  region. They also stated (but did not show) that a stack of the 13 galaxies which did not individually exhibit extended  emission results in a significant detection on the same 2-4 scales. Although the authors did not discuss what physical mechanism might have been responsible for their observation, these results clearly provided an early indication of the nature of  emission in L* galaxies, borne out by our larger and more sensitive sample.

5.2 Has the Whole Iceberg Been Detected?

The level of sensitivity to low-SB  emission at high redshifts is unlikely to improve by large factors using the current generation of ground-based telescopes, and so a natural question would be: How much more is there at still lower SB? Many  surveys (e.g., Rauch et al. 2008; Bunker et al. 1998) have been designed to detect  fluorescence induced by the metagalactic radiation field at redshifts . The radiation field intensity is usually expressed as ergs s cm Hz sr, where the quoted range indicates the dispersion among published observational or theoretical estimates (e.g., Shapley et al. 2006; Bolton et al. 2005; Scott et al. 2000; Faucher-Giguère et al. 2008). The expected maximum fluorescent signal at is in the range ergs s cm arcsec if the only source of ionizing photons is the general UV background (see e.g. Cantalupo et al. 2005; Kollmeier et al. 2010; Faucher-Giguere et al. 2010). These expectations clearly lie at or below the current SB thresholds of any survey completed to date. The difficulty of detecting the fluorescent signal from the metagalactic UV field has instead inspired several searches for fluorescence near bright sources of ionizing photons, such as QSOs (Francis & Bland-Hawthorn 2004; Cantalupo et al. 2005; Adelberger et al. 2006; Hennawi et al. 2009). The results from such studies have been mixed.

A different argument can be used to suggest that fluorescence from the UV background will always be overwhelmed by  scattering from the CGM of star-forming galaxies, at least at . This assertion follows from the fact that S2010 found that the total absorption cross-section contributed by the CGM of LBGs (using kpc for the detection of low-ionization absorption species) can account for a large fraction of all gas with N(HI) cm (i.e., in the Lyman continuum, also known as “Lyman Limit Systems”). In other words, any gas of sufficiently high to produce a detectable signal from fluorescence also lies within kpc of a star-forming galaxy with properties similar to those in our sample. We have shown that these galaxies generically exhibit diffuse  emission on the same physical scales when a surface brightness threshold of ergs s cm arcsec is reached. Unless the fluorescent  signal lies at the very top of the allowed range, it will have much lower SB than the signal we have attributed to scattering from the inside of the galaxy out.

It is more difficult to assess what fraction of observed  emission may be due to cooling processes such as those described by a number of recent authors (e.g., Dijkstra & Loeb 2009; Kollmeier et al. 2010; Faucher-Giguere et al. 2010; Goerdt et al. 2009.) In particular, the predictions of the emergent  emission from cooling gas accreting onto galaxies are extremely sensitive to gas temperature (Kollmeier et al. 2010; Faucher-Giguere et al. 2010) and to the small-scale structure in the gas. As a result, the range in  flux and SB, as well as the galaxy mass dependence and spatial distribution of cooling emission, must be regarded as uncertain by a factor of , with an upper bound (based on energetic arguments) that can be as large as ergs s, but which under different assumptions could be as small as ergs s for a galaxy with M (Faucher-Giguere et al. 2010), approximately the mean halo mass of the galaxies in the present sample (see Adelberger et al. 2005; Conroy et al. 2008; Steidel et al. 2010).

The observations appear to argue against a significant contribution of cooling radiation to the detected  halos, at least on average. We have shown that the shape of the observed radial surface brightness distribution among the LBGs in the sample is remarkably consistent beyond the inner kpc, within which the  intensity for a given continuum luminosity varies by orders of magnitude. Moreover, the overall intensity scaling for the  emission at large radii is strongly correlated with the behavior of  emission in the inner 5-10 kpc region — at the same continuum luminosity,  absorption-dominated galaxies (on average) exhibit diffuse  emission with a factor of 3-4 lower normalization than galaxies with spectroscopically detected  emission. In the context of  cooling radiation, one might expect the extended  emission to be strongly correlated with galaxy mass and/or SFR since it is believed by some (e.g., Goerdt et al. 2009) that the baryonic accretion rate ultimately controls the SFR. In this scenario, the central region of  emission might be suppressed by higher HI column densities mixed with dust, but the outer regions would have no obvious way to “know about” the number of  photons being produced at smaller radii. Instead, one might expect that the brightest  halos would be associated with the “ Abs” sub-sample, since these have a median SFR nearly 3 (4.5) times larger than the “ Em” (LAE) sub-samples. Clearly, the observations are inconsistent with this expectation. If on the other hand most or all of the  emission at all radii originates in the central regions and is subsequently scattered by the CGM gas, the density of photons available for scattering at (for example) kpc will be very tightly linked to the number of  photons that successfully diffuse past kpc, beyond which the  halos appear “self-similar”. The emergent  luminosities are entirely consistent with the observed level of star formation in the galaxies, and are more attenuated than the UV continuum, for all sub-samples except the LAEs. It is not necessary to invoke sources of  emission other than scattering (from the inside outward) to account for both the  luminosity and its spatial distribution.

Under the scattering hypothesis, and further assuming that the scattering medium is self-similar for all galaxies, then sub-samples with more luminous  halos should provide information on the degree to which even the current SB threshold might lead to an underestimate of the total  flux emergent from a galaxy. To increase the dynamic range for detecting diffuse  emission, one might use the observed properties of giant LABs (which are well-detected in the stack to ) to estimate how much additional  flux may lie beyond the SB detection threshold near  for more typical galaxies. Under the assumption that diffuse emission from LABs and LBGs has a similar origin and differs only in total  luminosity, the curve-of-growth for LABs (Figure 10) suggests that an aperture of radius  would underestimate the total  flux by only %. Thus, further aperture corrections to the integrated  would probably leave the values of (Table LABEL:table:tab2) and (Table LABEL:table:tab3) more or less unchanged. At least at , the current SB limit appears to be sufficient to detect most of the “iceberg”.

Finally, we note that the differences in the intensity of the large-scale diffuse emission among sub-samples divided according to their spectral morphology suggest that galaxy viewing angle is relatively unimportant (on average) for  emission; that is, most galaxies are not LAEs in some directions but strong  Abs systems in others, consistent with the inference of generally axisymmetric CGM gas distributions inferred from the absorption line studies (S2010).

5.3 IS Absorption,  Emission, and the CGM

Perhaps the strongest correlation (first explored in detail by Shapley et al. 2003 for galaxies at ) among the observed spectral properties of LBGs is between the strength of low-ionization IS absorption lines and the spectral morphology and equivalent width of . Galaxies with the strongest  emission (among the continuum-selected samples) invariably have much weaker than average low-ionization IS absorption lines (see Erb et al. 2010 for a well-observed example), while those with the  appearing strongly in absorption have correspondingly strong IS absorption features, often reaching zero intensity over some or most of the line profile (see e.g. Pettini et al. 2002) indicating unity covering fraction. These trends are easy to understand in the context of the CGM model discussed by S2010 and extended in this paper to cover the expectations for  scattering and its effects on the observability of  emission: both the IS absorption lines and  line strengths and morphologies are controlled by the kinematics and geometry of the same interstellar and circum-galactic gas.

Dust certainly plays a role in determining the fraction of both  and continuum photons that will end up reaching an observer. However, the gas-phase geometry and kinematics are more directly responsible for the observed line strength (and line-to-continuum ratios) in the spectra. If a galaxy has strong  emission emerging from the same region as the UV continuum, it must have shallow IS absorption lines; if it did not, then at least the spatial distribution of  (if not also its integrated flux) would be substantially modified– it would become more spatially diffuse. When a slit spectrum (generally a small-aperture measurement) shows very strong and deep low-ionization IS absorption lines, including , it must be the case that any  seen in emission will have escaped either from a region spatially distinct from the continuum (the subject of this paper), or by way of scattering from very high velocity material (see S2010).  emission seen in spectra which also show strong IS absorption will be primarily in the latter category, hence the nearly universal systemic redshift of  emission in LBG spectra. We have emphasized above that any  photons that are not destroyed by dust will eventually find their way out of their host galaxy– but will be much harder to detect by the time they do.

The point is that IS absorption and  emission are causally intertwined through their mutual dependence on the structure and kinematics of the CGM on scales from a few kpc to kpc.

6 Summary

We have presented observations of a sample of 92 continuum-selected LBGs at having both rest-UV spectra and very deep narrow-band  images. The sample, which is representative of LBGs at , was used to examine the nature of diffuse  emission from star-forming galaxies as function of their spectral morphologies and NB-inferred  fluxes. By stacking both UV continuum and  line images for subsets of the galaxy sample, we are able to study the spatial distribution of  and continuum emission to much lower surface brightness thresholds ( ergs s cm arcsec) than would be possible for individual galaxies. We find:

1. Relatively luminous star-forming galaxies generically exhibit low-surface brightness