DETECTION OF ULTRAVIOLET HALOS AROUND HIGHLY INCLINED GALAXIES

GALEX is a 50 cm telescope that obtains near UV (NUV) and far UV (FUV) images simultaneously in a wide (12 diameter) field of view (Martin et al. 2005; Morrissey et al. 2007). The NUV filter is a wide-band filter covering 1700–3000 Å with a peak effective area at around 2200 Å and an angular resolution of 5.3 arcsec. The FUV filter covers 1400–1800 Å and has a peak effective area at 1500 Å, with an angular resolution of 4.3 arcsec. Additional properties are listed in Table 1.

The UVOT (Roming et al. 2005) is one of three instruments aboard the Swift observatory (Gehrels et al. 2004) and collects data simultaneously with the other instruments. The UVOT has a much smaller (17 × 17 arcmin²) field of view but a higher (∼1 arcsec) angular resolution and filters extending from 1600–8000 Å. In this paper, we use only the UV filters (uvw1, uvm2, and uvw2). A summary of their properties is given in Table 1.

The uvw1 and uvw2 filters have "red tails" in their effective area curves,¹ meaning that a portion of the measured flux comes from the optical band. Thus, the effective wavelengths in these filters are higher than their nominal wavelengths by an amount that depends on the source spectrum. This can be seen in Figure 1, where we show the effective area curves for the UVOT and GALEX filters in the top panel along with arbitrarily scaled UV spectra of template E/S0 and Sbc galaxies from Coleman et al. (1980). It is clear that the effective wavelength for early-type galaxies is higher than for late-type systems. Applying a correction to measure only the true UV fluxes requires knowledge of the intrinsic spectrum (in this case the galaxy halo), which has not previously been measured. The nature of this correction can be used to help determine the underlying spectrum in combination with the GALEX and uvm2 filters, which we discuss in Section 5.

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Although we do not know the underlying halo spectrum, the red tail is much smaller in the uvw2 than uvw1 filter, and the FUV and uvm2 fluxes bracket the uvw2 and provide a useful constraint on the real UV flux. There are two basic possibilities for the halo emission: a stellar halo or reflection nebula (discussed in detail in Section 5), but in either case the correction to the uvw2 flux, constrained by the other filters, is constrained enough to apply a correction to the reported fluxes. We do not correct the uvw1 fluxes, where the effective wavelength is a much stronger function of the underlying spectrum (but see Section 5).

To correct the uvw2 flux we use a template-based method similar to those in Brown et al. (2010) and Tzanavaris et al. (2010). We use the template galaxy spectra from Coleman et al. (1980) (as updated by Bolzonella et al. 2000) and Kinney et al. (1996) and the filter effective area curves, and measure the uvw2 flux below 2400 Å. The uvw2 flux density is

$$\begin{equation} F_{uvw2} = \frac{\int F_{\lambda } A_{{\rm eff}}(\lambda) d\lambda }{\int A_{{\rm eff}}(\lambda) d\lambda }, \end{equation} \tag{ 1 }$$

so the correction factor c_uvw2 is the ratio of F_uvw2 computed using a uvw2 response cut off at 2400 Å (rest-frame) and all wavelengths. The lower panel of Figure 1 shows the GALEX+UVOT SEDs for several templates with the corrected uvw2 fluxes shown as triangles. c_uvw2 ranges from 0.6–1.0 depending on the galaxy template. E/S0 galaxies have c_uvw2 = 0.55–0.65, whereas spirals of type Sb or later have c_uvw2 = 0.90–0.97. We adopt correction factors of c_uvw2 = 0.60 for elliptical galaxies, 0.65 for S0 galaxies, 0.80 for type Sa galaxies, and 0.93 for all late-type galaxies. We apply the same corrections to the halo fluxes.

We used the HyperLeda database² to define a sample of candidate galaxies that are within 50 Mpc, have an inclination of i ≳ 65°, and M_B < −19 mag. These criteria were guided by the need to spatially resolve the halo in galaxies with a large intrinsic UV brightness. The "inclination" of the early-type galaxies refers to the projected elongation.

The working sample consists of galaxies on this list with good Swift and GALEX data. For most galaxies, we require at least 1000 s of exposure time in each UV filter except uvw1. All of the data we use are archival, so there is a wide range in exposure times. We also included a few galaxies at larger distances with deep Swift data to determine the limits of our ability to detect halos.

The sample was further culled by excluding interacting galaxies with tidal tails and those that contain or are near very bright point sources (or bright starbursts) that might produce instrumental scattered-light rings (Section 3). We also excluded galaxies such as M82 with galactic winds that are clearly visible in the halo, galaxies that are too large (a major axis larger than ∼10 arcmin, such as for NGC 4945) to define meaningful background regions on the UVOT chip, and galaxies in regions of bright or visibly structured "cirrus" (scattered UV emission from dust in our Galaxy) on scales relevant to measuring a flat background. In a few cases, we are able to use emission from one side of a galaxy but not the other. Cirrus emission is all-sky, but for most of the galaxies in the working sample the surrounding region has approximately uniform foreground emission. Finally, we omit some galaxies for idiosyncratic reasons such as instrumental artifacts, proximity of the target to another extended object, or very crowded fields.

These criteria leave us with 30 galaxies with sufficient spectral coverage to measure a four-point SED, and we also include NGC 7090 because of its very deep uvm2 data, but do not use it for most of the analysis. There are many other galaxies with either Swift or GALEX data, but not both; as our major goal is to search for halo emission, we require both instruments to identify instrumental issues.

The basic properties of the sample are listed in Table 2, where we have used values from HyperLeda and the NASA/IPAC Extragalactic Database³ along with the mass-to-light ratio of Bell & de Jong (2001) and IR star-formation law of Kennicutt (1998) to estimate the stellar masses and star formation rate (SFR). The M_K values were obtained from the 2MASS archive,⁴ whereas the SFR was computed using IRAS fluxes.⁵ The inclinations for some galaxies are suspect, and inclinations reported for early-type galaxies may not be meaningful. The total good exposure times in each UV filter are given in Table 3.

Since we are using archival data from a variety of programs, the sample is not complete in any metric, and includes a variety of distances, inclinations, SFR, and galaxy morphologies. Still, most of the galaxies have M_K ∼ −24 mag and are roughly Milky Way (MW) sized. Many of the galaxies are in the GALEX Ultraviolet Atlas of Nearby Galaxies (Gil de Paz et al. 2007), but the authors did not examine the halo emission.

The archival GALEX data were retrieved⁶ as fully reduced data sets, and for most galaxies we did no further processing. The GALEX data reduction pipeline is described in (Morrissey et al. 2007). For our analysis, we use the reduced intensity maps but not the background-subtracted versions. The background files provided by the GALEX pipeline are not adequate for detecting diffuse emission (Sujatha et al. 2010).

Even in the intensity maps that include the background, the background is not flat because the images are flat fielded based on forcing observations of the standard white dwarf LDS 749B to be uniform everywhere on the chip. However, the main source of NUV background is the zodiacal light, which is redder than the standard star.⁷ It is difficult to correct this in post-processing because the GALEX field of view virtually always contains some Galactic cirrus with spatial variations on similar scales. Because the UVOT field of view is much smaller than the GALEX field, as long as the galaxy is within a region where the background varies slowly we do not need to correct the entire field.

The Swift data⁸ were reprocessed from the most basic data product (a list of events and telemetry information or raw images) so that we could combine exposures from within a single observation and between observations to achieve a high S/N. This is required for almost every Swift data set because in order to study the evolution of gamma-ray burst afterglow SEDs, a single Swift/UVOT observation typically consists of a large number of shorter exposures in several of the available filters.

To create the each analysis image, we first reduced and calibrated each exposure in the observations. We mostly followed the processing flowchart in the UVOT Software User's Guide,⁹ and applied the latest calibrations described in Breeveld et al. (2010, 2011).¹⁰ This includes the correction for large-scale sensitivity variations. Breeveld et al. (2010) note that for point source photometry, the large-scale sensitivity correction should not be applied directly to the image. However, for extended diffuse emission it is necessary to do so. We also added a few steps that are described in Section 3 to remove persistent scattered light artifacts. Finally, we summed and exposure corrected all the good data. It is important to note that because the background varies between exposures, exposure correction does not produce a uniform sensitivity where there is imperfect overlap, and we reject exposures with backgrounds much higher than the average. We used the USNO-B1.0 star catalog (Monet et al. 2003) to compute the astrometry for each exposure individually and to verify the final image.

We masked point sources outside the galaxies using the tool uvotdetect, which is based on the SExtractor code (Bertin & Arnouts 1996). Many point sources are bright at longer wavelengths but fade in the far UV, so we used a very conservative mask generated from the NUV to minimize contamination from undetected point sources in the FUV. We excised detected point sources out to 90% of encircled energy based on the latest point-spread function (PSF) calibration available¹¹ and used the nominal PSF FWHM in each filter to exclude undetected point sources seen in other filters. For very bright sources, we used a larger mask.

The detector background consists of foreground and background components. The foreground components include the instrumental dark current (which is negligible for both the UVOT and GALEX), instrumental scattered light (produced by off-axis light reflected from the detector housing and filter windows onto the chip), airglow, zodiacal light (which is much more important in the near UV bands), and the Galactic cirrus. Although the contribution of cirrus decreases with increasing Galactic latitude, it is important at all latitudes. Finally, there is the extragalactic UV background that likely originates in galaxies.

The airglow, zodiacal light and amount of instrumental scattered light vary with the orbital position of the satellite and pointing direction, so the total on-field background varies between observations of a given object. This is most relevant for Swift, where we combine multiple exposures to create a final image. In the rest of this paper, we use the term "background" to refer to the sum of the foreground and background components including residual instrumental scattered light unless otherwise specified.

Both GALEX and the UVOT have diffuse scattered light artifacts that can cover large portions of the chip. There are both persistent and transient artifacts, where persistent artifacts are those that are produced predictably under given circumstances.

The persistent artifacts include source-specific patterns that are most obvious around bright stars as well as filter-specific patterns in the UVOT that cover the entire chip. The most common source-specific patterns are out-of-focus ghost images that occur near the primary image and take the form of rings owing to the shape and geometry of the telescope mirrors (often called "smoke" or "halo" rings). These rings have a characteristic size and morphology based on the optics (in the UVOT, for example, the dimmer "halo rings" have an outer radius of 2 arcmin). The ghost images result from light that internally reflects in the detector window (Breeveld et al. 2010), so they actually occur around every source for which the ghost image falls onto the chip; whether a ring is visible depends on the source brightness. The filter patterns (Figure 2) affect every UVOT exposure and are produced by off-axis light that reflects onto the chip.

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Transient artifacts are most commonly large streaks of scattered light across the chip, but some exposures also have a scattered light gradient that covers most of the chip. The brightnesses and widths of the streaks vary, and other artifacts may appear if there is a very bright source nearby but outside the field of view.

With GALEX, both persistent and transient artifacts are an issue because there are typically just a few deep exposures of a given target. GALEX counts events and reconstructs images based on knowledge of the spacecraft attitude, so in principle it is possible to filter the event list by time. However, the transient artifacts are dim (so they cannot be easily identified in a light curve) and have an unknown time dependence, so we discard exposures where the target galaxy is affected by large-scale transient artifacts. Only a few galaxies in the sample are near bright stars that produce smoke rings, and in these cases we simply mask the artifact.

Swift observations consist of many short exposures with small pointing offsets, so the persistent artifacts are more important than in GALEX. Thus, we developed a way to subtract the filter patterns. These patterns consist of a large disk of scattered light (the large feature that fills most of each panel in Figure 2) whose brightness declines radially outward. The variation is significant, as is the absolute contribution to the background (up to 30%). In the uvw1 and uvw2 filters, these patterns include 2 arcmin halo rings that are fixed in position in chip coordinates. The uvm2 filter does not appear to have halo rings, possibly because it is a narrower filter (for a more in-depth discussion of these patterns, see Breeveld et al. 2010). The patterns are produced by the optics, so if only a portion of the chip is exposed (a "windowed" image), that section receives the same part of the pattern it would if the entire chip were exposed. However, the pattern does shift slightly (a few pixels) between exposures in detector coordinates because the optical axis is not always centered on the chip center.

There is presently no correction in the UVOT calibration software for this artifact, so we created templates in each filter that we scale and subtract to leave a flat background. This is possible because the scattered light is always "extra" light that is a linear function of the true sky background and the patterns are fixed in detector coordinates. Assuming the true sky background is flat across the field of view, the background in pixel i is

$$\begin{equation} B_i = B_{{\rm sky}} + m B_{{\rm sky}} f(x_i,y_i), \end{equation} \tag{ 2 }$$

where m is the scaling factor and f(x_i, y_i) is the fixed normalized distribution of the filter pattern. The appropriateness of adopting m can be seen in Figure 3, which shows the dependence of the background-subtracted "surface brightness" in the brighter halo ring that is part of the filter pattern in the uvw1 filter (Figure 2) on the sky background measured at the chip edges. The slopes are different in the other filters (probably because the feature we normalize to is different), but the relation remains linear.

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The filter pattern f(x, y) was generated in a similar way to the "blank sky" images in Figure 2. We used full-frame exposures of 1 ks or more in sparse fields with no bright sources, extended emission, or background gradients. The source exposures were chosen from the large number of gamma-ray burst follow-up observations in the archive. Each exposure was processed using the Swift pipeline up through flat-fielding, whereupon we masked all sources, subtracted the sky background measured at the mostly unaffected edges of the chip, and corrected for the large-scale sensitivity variations on the chip. The exposure-corrected images were stacked in detector coordinates, smoothed by a Gaussian kernel with σ = 3 pixels, and normalized.

We subtract the filter pattern after flat-fielding but before the transformation from detector to sky coordinates. The position of the template is first matched to the image binning and window, then we mask point sources and smooth a copy of the image. The "true" sky background is measured at the chip edges where the chip is fully exposed and the template surface brightness is less than 5% of its peak. Because of the scatter in the relationship between B_sky and m (e.g., Figure 3), we use least-squares fitting to minimize the residuals against what we assume to be a flat background. Since the background may not be perfectly flat, the flatness of the residuals is verified by binning the image by 16 pixels and measuring the variance and azimuthally averaged radial profile over the fully exposed portion of the chip. When the results are not flat or the variance is high, we inspect the images visually and adjust the scaling factor (in such cases, the pattern or its inverse is typically visible in a smoothed image).

This method is demonstrated in the uvw1 filter in Figure 4. The top two panels show the method as applied to a 1.4 ks exposure of NGC 6925 and the bottom two panels show a 1.6 ks exposure of a sparse field with no extended emission (GRB 10015a, ObsID 20126003). For both objects, we have clipped the maximum pixel values to show the background more clearly and lightly smoothed the field, but the scaling and color map are the same between the images. In the gamma-ray burst field one can see the filter pattern very clearly along with the telescope struts in the center halo ring.

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Subtraction typically accounts for more than 95% of the filter pattern light, making the residual smaller and more spatially uniform than other background sources. Figure 5 shows the azimuthally averaged radial profile for the two gamma-ray burst field images in Figure 4.

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After subtracting the filter pattern, we transform to sky coordinates and proceed with the remainder of the UVOT pipeline to produce reduced, calibrated exposures. However, we must insert one more step into the pipeline because the UVOT pixel scale is slightly non-uniform (Breeveld et al. 2010), but during the sky transformation (using the UVOT tool swiftxform) the plate scale is made uniform in a way that conserves flux. In other words, a truly uniform sky background would not appear perfectly uniform in the raw image, but our template subtraction assumes that it is. Thus, we apply a distortion correction to account for this assumption analogous to swiftxform. The result is a flat background in the sky image.

Halo rings produced by bright stars are not removed in the pipeline process. The scatter in the relationship between the source count rate and the ring "surface brightness" is too high to make automatic removal reliable, especially for short exposures and dimmer sources. It is possible to detect and subtract these rings because they are anchored to their progenitor star, so we can use a ring template even for faint rings. However, if the star is within the halo detection zone, the residuals can have a large variance and it is better to mask the region or discard the exposure.

The sensitivity in the Swift and GALEX data is limited by background spatial variation (photon counting noise can be reduced well below 1% of background by using deep exposures and averaging the flux over large bins).

Many Swift exposures have faint transient instrumental artifacts, such as broad, faint streaks parallel to a chip edge or background gradients. When these are bright enough to detect (which still requires smoothing and clipping the image), we discard the exposure, but often the artifacts are undetectable (when combining exposures, they are smoothed to some extent because of the different roll angles). Likewise, there are small variations in the astrophysical scattered light from the Galactic cirrus across many fields, so the "true" mean background light differs across the chip. These differences are generally larger than the standard deviation measured in a small region of uniform background and dominate the uncertainty in our flux measurements.

To characterize the uncertainty, we measure the variance in the background count rate measured in many regions across the fully exposed portion of the chip. For GALEX we restrict the region of interest to the Swift UVOT field of view for consistency. The background fields are then defined in the UVOT images using source-free regions more than 2 arcmin away from sources whose count rates might produce a bright halo ring (typically we use a cutoff of a total count rate less than 50 counts s⁻¹). The scattered light background count rate appears to follow a Poisson distribution when examining "event"-mode data and the number of background counts is quite high, so we adopt the standard deviation of the background σ_sky as our estimate for the uncertainty in background subtraction. For most of the galaxies in our sample, σ_sky ∼ 0.1%–4% of the mean sky background.

In both Swift and GALEX a small fraction of the incident photons from a given source are scattered by the optics into a region around the source, producing ghost images with an instrument-specific pattern as described above. For example, in the UVOT, which produces visible ghost images for fainter stars than GALEX, the characteristic outer radius of the larger ghost images (the "halo rings") is 2 arcmin. The rings are only visible for the brightest sources, but dimmer sources still scatter incident flux; they simply do not fill in the pattern. We denote this scattered light F_ring. This behavior can be generalized to extended sources such as galaxies, where the total instrumental scattered light F_scat is the sum of F_ring over all the sources in the galaxy.

Considering the angular sizes of galaxy halos, the contribution of F_scat to halo light may be important. However, the dependence of F_ring on the count rate of the associated star, F_star, is unknown. Because of the faintness of the rings it is also not clear whether F_ring is a continuous function of F_star or of there is a threshold F_star below which reflected light is not transmitted to the chip.

In this subsection, we examine the dependence of F_ring on F_star at low count rates to assess what F_scat we might expect from the galaxies in our sample. These galaxies have total count rates between 1 and 200 counts s⁻¹, but the compact clumps that characterize the emission typically have count rates of 1–10 × 10⁻⁴ counts s⁻¹. Clearly, F_ring must be less than this, but if it is not much less then F_scat will be a significant fraction of the background.

To address this issue we measured F_ring around a sample of stars from the Swift gamma-ray burst observations between 2008 and 2013, which randomly sample the sky. We only included exposures greater than 800 s for good background statistics and rejected exposures with strong background variation. The data were processed in an analogous way to the analysis sample.

For stars with visible halo rings we measured the background-subtracted count rate. Stars without immediately apparent halo rings may still have detectable halo rings, but there are two challenges. First, halo rings have large offsets from the primary images when the source has a large offset from the optical axis, so we restricted our sample to sources within 3–4 arcmin of the chip center where this is not a significant issue. Unfortunately, the uvw1 and uvw2 filter patterns have bright halo ring features near the chip center (Figure 2), so we restrict the analysis to the uvm2 filter. Second, if there is no visible halo ring we require the star to be by far the brightest in its vicinity so we do not measure competing halo rings. We then measure F_ring within the 2 arcmin around the star while also avoiding the primary image of the star and any other nearby sources to 95% of the encircled energy in the PSF. The values are scaled by the area in a complete ring. We measured F_ring for all stars above F_star = 10 counts s⁻¹ that meet these criteria. The sample was extended to F_star > 0.01 counts s⁻¹, but isolated stars are less common, and we limited the lower flux sample to fields with lower, more uniform backgrounds.

Halo rings are only detected above F_star = 10 counts s⁻¹. The detections are shown in the left panel of Figure 6. Nondetections are omitted for clarity, but are shown in the right panel. Above F_star ∼ 130 counts s⁻¹ the scatter increases markedly for unknown reasons. One possibility is that we see a secondary ring. Very bright stars sometimes produce multiple halo rings, where one is much brighter than the others. If a bright star's primary ring fell off the chip but its secondary did not, we might mistake the secondary ring for the primary. In any case, as a first step to determine the dependence of F_ring on F_star we fit the detected F_ring values below F_star = 130 counts s⁻¹ with simple models. The scatter precludes formally good fits for any model we tried (linear, log-linear, quadratic, and exponential), but the exponential model is the best fit. The best exponential and linear models are overlaid in Figure 6, where it is clear that the exponential model does a better job at reproducing the curvature in the data.

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However, it is clear from the right panel of Figure 6 that the exponential model becomes unphysical for stars with F_star ≲ 0.2 counts s⁻¹ and is also disfavored by the upper limits we have measured. The constraints provided by individual stars are limited by the Swift background, so we averaged over the F_ring measurements below F_star = 10 counts s⁻¹, grouping stars in each decadal bin. After averaging there were still no detections, but the upper limits were reduced (diamonds in Figure 6).

Significantly tightening the constraints would require a much larger sample, but at low count rates another way of averaging is to use small asterisms. We measured F_ring in the region around isolated groups of dim stars, where the asterisms comprise 3–15 members contained within 1 arcmin in the inner portion of the chip. Since these stars should produce overlapping halo rings, we measured the average F_ring per star and the mean count rate F_star. Again, there are no detections, but the upper limits (shown as inverted triangles in Figure 6) improve the constraint on F_ring at low count rates.

The functional form of F_ring below F_star ∼ 10 counts s⁻¹ cannot be determined, but we can make some inferences from the limits and the requirement that F_ring < F_star (Figure 6). The linear fit to detected rings suggests a ratio of F_ring/F_star ≲ 0.01, while the cluster of detected rings at F_star ∼ 10 counts s⁻¹ is consistent with a ratio of 0.02–0.04. The averaged limit between F_star = 1–10 counts s⁻¹ rules out a significantly larger value. At lower count rates, the limits only constrain the ratio to be F_ring/F_star < 0.1.

The total instrumental scattered light we expect from the galaxy is between F_scat = 0.01–0.1F_gal. For F_gal = 200 counts s⁻¹ (at the high end of our sample), we would expect F_scat between 2 and 20 counts s⁻¹. However, galaxies with higher fluxes tend to be closer, and the angular size of the galaxy is important because a given clump in the galaxy only contaminates the surrounding 2 arcmin with instrumental scattered light. For a galaxy larger than 2 arcmin, only some of the scattered light contaminates the halo (the rest is coincident on the chip with the galaxy itself), and the exact contribution at any point in the halo depends on the region of the galaxy within 2 arcmin of that point on the chip. In our sample, we find that the galaxy count rates that could contribute to instrumental scattered light in the halo are 0.1–50 counts s⁻¹, with higher count rates nearer the galaxy. In the "worst case scenario" (bright galaxy, relatively compact, measurements near the disk), we expect F_scat ∼ 0.1B_sky, whereas at the low end we expect F_scat < 0.001B_sky. This is a wide range, but (based on count rates, angular sizes, and Figure 6), we suppose that F_scat is 1% or less of B_sky for most of our sample. The typical σ_sky is 0.1%–4% of B_sky.

Fluxes are computed from the background-subtracted count rates in the extraction boxes shown in the galaxy image panels. The total halo fluxes in each filter are given in Table 4.

We sum the count rate in each box and scale it to a uniform box size (accounting for point source masks and non-uniform box sizes). In most cases, the correction is small (1%–10%), but in some bins can exceed 50% because of bright stars or chip edges. The reported fluxes in such cases may be slightly too high or low, but for most galaxies this is not an issue. The location of the innermost box for each galaxy was chosen to be clearly above the disk for late-type galaxies and outside a few scale heights for E/S0 galaxies, but we do not use a uniform definition because of the different types and inclinations. Nonetheless, the boxes are defined conservatively to be at least a few kpc (projected) above the midplane, outside of several optical scale heights as seen around an edge-on system. We then subtract a mean background from the count rates and convert them to flux density using the conversion factors in Table 1, and correct for Galactic extinction using the Schlegel et al. (1998) dust map using the calibrations in Wyder et al. (2007) and Roming et al. (2009).

Finally, we apply the correction for the red leak in the uvw2 filter as described above. As the true correction depends on the true spectrum, we report both the corrected flux and the correction factor in Table 4. The uvw1 fluxes are not corrected and are not included in the SED plots (but we return to these in Section 7).

In Section 3 we argued that the contribution of instrumental scattered light from the galaxy to the measured light in the halo is typically a few percent of the background. Given the agreement between the GALEX and Swift flux profiles in the bright late-type galaxies (e.g., Figure 7) and the different systematic effects in each instrument, we posit that the contamination from instrumental scattered light is no worse than the error on the background σ_sky, which is dominated by spatial variation in the background.

From our flux measurements we can obtain three physical quantities: the luminosity, extent, and the SED of the halo emission. With the deeper data sets, we can map these quantities around the galaxy.

4.2.1. Luminosity

The luminosity L_ν = 4πd²F_ν is computed from the integrated halo fluxes (Table 4). As most of the flux comes from near the galaxy, the true halo UV luminosity is sensitive to the choice of the innermost bin height; our L_ν values are measured starting a few kpc from the midplane (well above the optical disk).

Figure 11 shows L_ν as a function of M_K (galaxies with M_K > −22 mag are not shown). The different symbols break the galaxies up by type: blue squares represent late-type (Sab through Sd) galaxies, black triangles are S0 galaxies, and red diamonds are elliptical galaxies.

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Most of the galaxies in the sample have M_K similar to the MW (M_K ∼ −24 mag) and are not cleanly separable in any of the bands. The largest differences are seen in the FUV band, where the elliptical and S0 galaxies tend to have lower FUV luminosities than the late-type galaxies; as we discuss below, this is even more apparent when comparing the fluxes as a function of height above the midplane. Since the galaxies have different sizes and the sample is not objectively defined, the overlap is not surprising.

In Figure 12 we show the specific integrated halo luminosities in the NUV (pink boxes), uvm2 (red triangles), uvw2 (blue diamonds), and FUV (green crosses) as a function of the specific SFR and the specific galactic luminosities, where "specific" is in reference to the stellar mass M_star (galaxies without the information to compute the SFR or M_star are omitted). We have separated the galaxies by type into spiral and early-type (E/S0) systems. To measure the correlation between these quantities (in each band), we use the Spearman ranked correlation coefficient ρ, which we prefer over the Pearson coefficient because of the small number of data points.

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With regard to the SFR, the only significant correlation at better than 99% is in the uvw2 band (ρ = 0.67, p = 0.004). The other bands do not even have marginally significant correlations (p = 0.16, 0.05, and 0.24 for the NUV, uvm2, and FUV respectively). If we consider only specific SFR >0.1 M_☉ yr⁻¹, there is no significant correlation in any band, so among galaxies with SFR similar to or greater than the MW the specific SFR does not predict the halo luminosity. For the early-type galaxies, there are not enough data to measure a significant correlation.

On the other hand, the specific halo luminosity in each band except the NUV is strongly and significantly correlated with the specific galaxy luminosity. For the NUV filter ρ = 0.57 and p = 0.02, for uvm2ρ = 0.69 and p = 0.002, for uvw2 ρ = 0.76 and p = 0.0004, and for FUV ρ = 0.80 and p = 0.0002. For the early-type galaxies, what looks like a significant correlation in Figure 12 is due to offsets between each band (which also appear in the SEDs; cf. Figure 10), and the only significant correlation is in the FUV (ρ = 0.86 and p = 0.007). The others have p > 0.05.

We also measured the correlation between the halo luminosity and M_K and find no significant dependence in any band for the late-type galaxies, whereas for the early-type galaxies there is a significant correlation in the FUV (ρ = 0.86, p = 0.0003) and a marginally significant correlation in the NUV (ρ = 0.59, p = 0.02).

The correlation between halo and galaxy UV luminosity hints at a physical connection in the late-type galaxies, but the connection is evidently not mediated by rapid (present-day) star formation. The actual correlations may be even stronger, as we have made no attempt to correct for the effects of inclination and extinction.

4.2.2. Scale Heights and Maximum Extent of the Halo Emission

Differences between galaxy types are more evident when considering the UV luminosity as a function of height above the midplane L_ν(z). We cannot reliably measure scale heights for the halo emission in most galaxies because of the coarseness of the flux measurement bins and the differences in the bin widths between galaxies. For many galaxies, there is a large artificial minimum on the measurable scale height.

It is possible to measure a scale height in the galaxies with the best data (where the S/N is high in narrow bins). These include the late-type galaxies NGC 5775, NGC 5907, and NGC 3079, and the early-type galaxies NGC 4594, NGC 5866, and NGC 3613. We fit profiles of the form I(z) = I₀e^−z/H in each band for these galaxies, where we averaged the flux on each side of the midplane at each height, and the results are given in Table 5. The early-type galaxies are fit well in each band except the FUV by the exponential fit (we also tried Gaussian fits, which were never better for any galaxy), with best-fit scale heights of H ∼ 2.75–3.5 kpc for NGC 4594, H ∼ 2–3 kpc for NGC 5866, and H ∼ 6–8 kpc for NGC 3613. The late-type galaxies also had generally good fits, although the exponential fit is too steep for most bands. We find H ∼ 2.5–3.5 kpc for NGC 5775, H ∼ 2–3 kpc for NGC 5907, and H ∼ 3–5 kpc in NGC 3079.

Table 5. UV Scale Heights

Galaxy	HNUV	χ2	HUVM2	χ2	HUVW2	χ2	HFUV	χ2	dof
	(kpc)		(kpc)		(kpc)		(kpc)
Late-type Galaxies
NGC 3079	2.9 ± 0.3	15.6	3.5 ± 0.5	0.56	5.1 ± 1.5	0.80	4.5 ± 0.1	17.8	3
NGC 5775	2.4 ± 0.3	3.5	3.0 ± 0.2	10.7	2.65 ± 0.08	4.6	3.4 ± 0.1	15.9	8
NGC 5907	2.7 ± 0.4	1.3	2.2 ± 0.3	1.45	3.0 ± 0.7	0.53	2.32 ± 0.03	22.5	8
Early-type Galaxies
NGC 3613	6.9 ± 0.1	5.8	7.8 ± 0.2	27.4	6.0 ± 0.2	16.2	6.1 ± 0.1	2.3	6
NGC 4594	3.5 ± 0.1	4.2	2.8 ± 0.3	2.2	3.1 ± 0.3	4.0	3.07 ± 0.05	3.7	8
NGC 5866	2.0 ± 0.1	1.5	2.5 ± 0.4	7.5	4.0 ± 1.5	0.11	2.0 ± 0.1	17	4

Notes. Scale heights are measured by fitting exponential profiles I₀e^−z/H to the data averaged over both sides of the midplane, where z is the projected distance above the midplane.

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The UV scale heights for the late-type galaxies are larger than the scale height of the thick disks, which range from 0.3–1.5 kpc (e.g., Yoachim & Dalcanton 2006). The scale height of the H i, where it has been measured (e.g., Fraternali et al. 2002; Oosterloo et al. 2007; Kamphuis 2008) is comparable but systematically lower (1–2 kpc) than UV values, probably because we start measuring at larger heights to avoid stars.

For the galaxies where H cannot be measured, the maximum extent of the emission z_max in each band is a useful proxy for the observable halo size. We define z_max as the mean height above the midplane for which we detect flux at 2σ on both sides of the galaxy. Because of real angular variation in the sky foreground (which dominates σ_sky, there is a natural limit to the halo flux that can be detected; additional exposure time may detect some emission beyond z_max, but not much. Within z_max, additional exposure time improves the S/N and allows smaller flux measurement box sizes.

The z_max values are tabulated in Table 6 for the non-uvw1 filters. The final column is the average z_max for the NUV, uvm2, and uvw2 filters, which gives a measure of the maximum detectable emission at or above 2000 Å. The left panel of Figure 13 shows z_{max, FUV} as a function of the average NUV z_{max, 2000}. Spiral galaxies are represented as blue squares, S0 as black triangles, and elliptical galaxies by red diamonds. The "error bars" show the width of the flux measurement bin for each galaxy, and the line shows where a galaxy would fall if the FUV z_max were equal to z_{max, 2000}.

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Table 6. Maximum Extent of UV Halo Emission

Galaxy	Binsize	NUV	uvm2	uvw2	FUV	zmax, 2000
	(kpc)	(kpc)	(kpc)	(kpc)	(kpc)	(kpc)
ESO 243−049	6.6	13.2	13.2	13.2	13.2	13.2
IC 5249	1.7	4.8	3.1	3.1	4.8	3.7
NGC 24	1.1	5.9	3.7	3.7	4.8	4.4
NGC 527	3.0	7.5	7.5	10.5	7.5	8.5
NGC 891	2.1	5.4	7.5	9.7	7.5	7.5
NGC 1426	1.3	16.2	9.8	5.7	3.2	10.6
NGC 2738	3.3	5.0	5.0	5.0	5.0	5.0
NGC 2765	1.8	10.9	12.7	10.9	7.2	11.5
NGC 2841	1.8	16.6	14.9	7.9	14.9	13.1
NGC 2974	3.5	17.5	10.5	14.0	7.0	14.0
NGC 3079	2.5	14.8	12.2	14.8	14.8	13.9
NGC 3384a	1.1	>4.0	>5.0	>4.0	2.8	>4.3
NGC 3613	2.2	14.1	20.7	20.7	12.0	18.5
NGC 3623b	0.88	7.4	7.4	6.6	7.4	7.1
NGC 3628	2.0	7.5	9.5	7.5	11.5	8.2
NGC 3818	2.0	12.0	10.0	8.0	4.0	10.0
NGC 4036	1.5	5.3	6.8	8.2	6.8	6.8
NGC 4088	2.2	12.4	12.4	10.1	12.4	11.6
NGC 4173b	1.1	3.1	3.1	6.5	3.1	4.2
NGC 4388	2.5	8.0	10.0	10.0	10.0	9.3
NGC 4594	1.0	12.5	8.5	7.5	10.5	9.5
NGC 5301	1.8	9.6	9.6	6.1	9.6	8.4
NGC 5775	1.8	13.4	15.2	15.2	17.0	14.6
NGC 5866	1.0	7.5	7.5	7.5	6.5	7.5
NGC 5907	1.5	6.8	5.2	6.8	15.8	6.3
NGC 6503b	0.5	3.3	2.3	5.8	3.8	3.8
NGC 6925	2.0	12.0	10.0	12.0	12.0	11.3
NGC 7090	⋅⋅⋅	⋅⋅⋅	6	6	⋅⋅⋅	6
NGC 7582	3.0	7.5	7.5	16.5	10.5	10.5
UGC 6697	⋅⋅⋅	17	⋅⋅⋅	17	23	17
UGC 11794b	4.0	14.0	14.0	10.0	14.0	11.3

Notes. We obtain a crude measurement of z_{max, i} of the halo emission in each filter i by finding the height above each galaxy z where there is at least a 2σ detection in both extraction bins at z. The final column is the mean z_max for the NUV, uvm2, and uvw2 filters. ^aThe galaxy was on the chip edge. ^bFlux was only measured on one side of the galaxy.

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All of the spiral galaxies except for NGC 4173 have z_{max, FUV} ⩾ z_{max, 2000}, whereas the ellipticals fall below this line. The S0 galaxies also tend to fall below or on the line. Since spiral and elliptical galaxies overlap in specific halo UV luminosity (see the right panels of Figure 12) and scale height (Table 5), the observation that the FUV flux falls less rapidly than the other bands among the spirals and more rapidly among the early-type galaxies hints at a different origin.

A difference can also be seen in the ratio of the FUV and NUV fluxes as a function of height above the midplane, normalized to z_max (the right panel of Figure 13). There is a clear separation between the spirals and E/S0 galaxies, but notably the S0 galaxies differ from the elliptical galaxies in that the FUV/NUV ratio is roughly constant with height, whereas in the ellipticals it drops (however, there are only four elliptical galaxies in our sample).

4.2.3. Spectral Energy Distributions

4.2.4. Variation along the Major Axis

Some of the data allow us to measure the flux as a function of displacement along the projected major axis as well as projected height above the galaxy. Figure 14 shows the flux profiles along the major axis at two different heights for three of the galaxies with the best data. The fluxes in each band are shown with an artificial offset for clarity. The bins closest to the galaxy follow a typical trend where a central enhancement is visible and the flux declines to larger displacements (except the FUV band in NGC 5775), but higher above the galaxy the profile is much flatter. In NGC 5907 and NGC 3079, we measure more flux on one side of the galactic center than the other. In the galaxies shown here (especially NGC 5907) most variations along the major axis are correlated between filters; this may be due to where star formation occurs in the disk or the structure of the halo or cirrus substructure.

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The SEDs at each height are shown in the right two panels of Figure 14 (with artificial offsets) and show that while there is general agreement on each side of the galactic center there are real variations. Again, it is not clear whether the source is halo structure, variation in the disk, or cirrus. Notably, the SED of NGC 5775 flattens out at large displacement. This may be due to the rapid, but "distributed" star formation in the galaxy (producing a bluer spectrum at larger offsets), or perhaps due to extinction within the halo itself modifying the observed spectrum. In the other two galaxies, the increased flux near the disk does not have a strong effect the SED as a function of displacement, except near R = 0 in NGC 3079.

Similar trends are seen in other galaxies in our sample which have deep data in fewer than three filters. At any given height, differences as a function of displacement are usually visible in more than one band, so the background is low enough to permit searches for halo substructure.

Cirrus around NGC 891, NGC 3623, and NGC 6925. Galactic cirrus is in virtually every field, but for most of the sample the contribution is small and the variation across the field is slight. The cirrus is faint and can only be seen in heavily smoothed, stretched images (it cannot be seen in the galaxy images presented in this work), but it can be brighter than the halo light. Some galaxies cannot be used at all because of the cirrus (e.g., NGC 7331), but there are several borderline cases. NGC 891 has more cirrus emission on the west side of the galaxy (but the surface brightness is still very low relative to the galaxy). This was partially corrected by using different background regions on each side of the galaxy. NGC 3623 has spatially variable cirrus emission on the east side of the galaxy, but no visible cirrus on the west side, so we measure fluxes only on this side. NGC 6925 is in a region of patchy cirrus with stronger emission on the east side, which may explain the irregular appearance of the halo flux profile (Figure 8).

NGC 2974. NGC 2974 is classified as an E4 galaxy, but the GALEX data (described in detail in Jeong et al. 2007) reveal a blue star-forming ring in the galaxy. However, this ring does not seem to differentiate the halo emission from NGC 2974 from the other elliptical galaxies (Figure 10) except in the innermost bin, where the relative FUV flux is higher.

IC 5249, NGC 24, NGC 6503, and NGC 4173. These galaxies are significantly smaller than the other spiral galaxies in our sample, and were included because they met our cutoff criteria and had good Swift data. Their inclusion in the sample is useful since they demonstrate that UV emission around smaller galaxies has the same general character as that from the large ones.

NGC 24 and NGC 6503 have large UV halos for their specific SFR relative to the other galaxies in the sample (on absolute scales, they are smaller than the halos of the more massive galaxies). NGC 4173 also has a relatively large halo, assuming it is indeed at 8 Mpc, where its M_K = −18 mag indicates a stellar mass of M_star ∼ 3 × 10⁸ M_☉. We are only able to measure the halo emission to one side of NGC 4173 because of the members of HCG 061 to the south; NGC 4173 was originally classified as a member of HCG 061 (HCG 061b), but it is known to be a foreground object. IC 5249 has a smaller halo.

Since z_max does not scale with the angular size of the galaxy for these or other galaxies in our sample, it seems likely that this is a real effect, but the reason for the large UV halos is not clear, since the small galaxies do not have unusually high specific L_ν. One possibility is that the galaxies have less extinction in the disk. Another is that the galaxies have large dusty halos despite their smaller stellar mass relative to the rest of the sample. Data for more small galaxies are required to determine how z_max is related to galaxy mass and other parameters.

NGC 24 is remarkable in that it has very high quality Swift data. Its flux height profile and SED (Figure 7) look very similar to other spiral galaxies with very deep data, suggesting that all star-forming late-type galaxies have similar UV halos.

UGC 6697, UGC 11794, NGC 527, and ESO 243-049. Most of our sample is restricted to d < 50 Mpc because the angular sizes of the halos become too small to use multiple flux measurement boxes. However, for galaxies with sufficiently deep data it may be possible to measure a halo size.

We detect halos out to about the same distances from the midplane, but as a result of the larger physical sizes of the bins, we only see the halo emission in the two innermost bins. If these galaxies are representative of galaxies at 50 Mpc < d < 100 Mpc, halo detection should be straightforward but the maximum extent, SED, and total flux will depend strongly on the bin sizes used and are more sensitive to undetected point sources or background variations. Indeed, the profiles and SEDs for UGC 11794 and NGC 527 look more confused than the other galaxies in the sample, and for UGC 11794 it is questionable whether we see any halo emission.

If the UV light is consistent with a single-population stellar halo, we expect it to have a UV−optical color comparable to an early-type galaxy (perhaps bluer if the halo consists of metal-poor stars, but not as blue as a late-type galaxy).

We measured the UV−r colors using the uvm2, uvw2, and Sloan Digital Sky Survey (SDSS) DR7 (Abazajian et al. 2009) r bands for the diffuse emission. We use the UVOT rather than GALEX filters because of the better spatial resolution and the difficulty of removing the large-scale artifacts from the GALEX images (Section 3). We use the uncorrected uvw2 fluxes to eliminate potential bias, but note that this means the filter has an effectively longer central wavelength. The r-band flux was measured from source-free regions above the galaxy corresponding to the UV flux extraction boxes, and both the UV and r-band fluxes are converted to surface brightnesses (mag arcsec⁻²).

Figure 15 shows the UV−r colors for the two bands as a function of height above the midplane along the x-axis and as a function of increasing morphological type along the y-axis. Only galaxies with suitable SDSS data are included. The UV−r color (in magnitudes) is encoded as an RGB color based on the UV−r color–magnitude diagram (CMD) from Wyder et al. (2007), i.e., a blue color corresponds to a galaxy on the blue sequence and a red color to a galaxy on the red sequence in their CMD. Wyder et al. (2007) based their CMD on GALEX data, so we computed a small magnitude shift due to the difference in filters. Figure 15 is not itself a CMD, but one can see a clear dichotomy among the early- and late-type galaxies. The blueness of the emission in the late-type galaxies indicates that the UV emission from late-type galaxy halos is not consistent with an older stellar population. In contrast, the redness of the emission above the early-type galaxies and the small extent of the FUV emission relative to the spirals (Figure 13) suggests that we are seeing the outskirts of the galaxy.

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Figure 15 is imprecise. The coloring is based on the Wyder et al. (2007) CMDs, which are measured for galaxies rather than halos. There are also issues with measuring diffuse emission in the SDSS that add uncertainty to the r-band magnitudes, and the colors in the outer bins are unreliable. Still, the difference between early- and late-type galaxies is larger than the expected magnitude uncertainties (in total, less than 0.3 mag near the galaxy).

If the halo light is a reflection nebula, then its spectrum will be the emergent galaxy spectrum modified by the dust in the halo. Here we test this scenario by fitting reflection nebula models (based on galaxy template spectra and Local Group dust models from WD01) to the measured halo SEDs (from fluxes in Table 4).

Even if the UV halos are reflection nebulas, we do not know the dust type or the galaxy spectrum as seen by the halo (the galaxies are highly inclined), so we do not expect our models to produce formally good fits in many or most cases. To provide context, we fit each halo SED with a suite of reflection nebula models produced for several galaxy types and dust models. A good or marginal fit for a model constructed from the "right" galaxy template and dust model that is significantly better than fits with other models would support the reflection nebula hypothesis (but not rule out other, non-reflection nebula models).

5.2.1. Model SEDs

For an optically thin halo with a single type of dust, the scattered spectrum is

$$\begin{equation} L_{{\rm halo}}(\lambda) = L_{{\rm gal}}(\lambda)(1-e^{-\tau (\lambda)\varpi (\lambda)}), \end{equation} \tag{ 3 }$$

where τ(λ) = N_Hδ_DGRσ_ex(λ) is the optical depth and ϖ(λ) = σ_scat(λ)/σ_ex(λ) is the scattering albedo. N_H is the column density of hydrogen, δ_DGR is the dust-to-gas ratio, and σ_ex(λ) is the extinction cross-section for a given dust mixture. σ_ex(λ) and ϖ(λ) come from a dust model. L_halo and L_gal are measured quantities, so if one knows two of the constituents of τ(λ), the UV measurements yield the third. In our case, we know neither N_H nor δ_DGR, but these do not affect the spectrum (assuming an optically thin halo). Thus, we can fit each model SED to the halo SED with the dust column N_d = N_Hδ_DGR as a free parameter.

If τ ≪ 1, then L_halo ≈ L_galτϖ. This depends on N_H and δ_DGR, since σ_exδ_DGR ∼ 10⁻²¹ cm² and ϖ ≲ 0.5 between 1500 and 3000 Å for dust models based on Local Group dust. It is difficult to separate the truly extraplanar gas from the disk gas, which has a finite height, without a fully three-dimensional view of the galaxy, but here we loosely define the halo as a region above several optical scale heights (as seen around edge-on systems), which is where we measure the UV light. In practice, this means a few kpc. At this height, N_H ∼ 0.1–1 × 10²⁰ cm⁻² around many MW-sized edge-on galaxies (e.g., Sancisi et al. 2008, and references therein). Since the extraplanar H i at a few kpc from the midplane or above is typically consistent with an exponential atmosphere, the mean column from the "bottom" of the halo to infinity is perhaps 10²⁰ cm⁻² (L_gal must then also be defined as the emergent galactic light at this height). For the δ_DGR ∼ 1/100 in the MW (and galaxy halos; Ménard & Fukugita 2012), this means τ ≲ 0.1 and the optically thin approximation is valid.

This implies a L_halo/L_gal ratio of a few percent for ϖ ≲ 0.5. We discuss this in detail in Section 6, but here the relevant point is that the attenuation of the reflection nebula spectrum by dust in the halo is less than 10%, and often much less because by the time a typical photon has scattered it will have passed through the densest region of the halo and scattering is highly forward-throwing (Draine 2003). In other words, the scattered light we see at any point in the halo was largely traveling outward and thus sees a smaller τ on the way out of the halo. A self-consistent Monte Carlo radiative transfer scheme is required to rigorously compute the reflection nebula spectrum (including a disk emission model, halo model, and dust model), and this will be the subject of a future paper. However, we expect the extinction of the reflection nebula spectrum in the halo is between 1% and 5%, which is smaller than the error on the measured fluxes. Thus, the effect will not be discernable in our fitting.

Our model spectra consist of galaxy templates and Local Group dust models from WD01. We used galaxy templates for the input spectra because the sample galaxies are highly inclined and a detailed model is required to de-redden them. For the spiral galaxies we used six templates, including Bolzonella et al. (2000) templates for the Sbc and Scd galaxies (denoted as BMP Sbc and BMP Scd respectively) and the Kinney et al. (1996) templates (starburst2, Sc, Sb, and Sa), which we denote as KC SB2, KC Sc, KC Sb, and KC Sa respectively. The different starburst templates are based on different levels of internal extinction, and for our sample a low level is appropriate (the starbursts in the sample are not luminous infrared galaxies). For the early-type galaxies we used the Kinney et al. (1996) and Bolzonella et al. (2000) templates (denoted KC E and BMP E).

Figure 16 shows model SEDs for four galaxy templates with the MW (R_V = 3.1), Large Magellanic Cloud (LMC) average, and Small Magellanic Cloud (SMC) bar dust models from WD01. In each panel, we show the models and a raw template spectrum normalized to their maxima in order to show the differences. The LMC and SMC models have offsets for visual clarity. While models with MW and LMC dust appear redder than the input spectrum in this wavelength range, the SMC dust model is bluer. The region of the spectrum near the 2175 Å UV bump is unreliable. The bump is thought to be purely absorptive (Andriesse et al. 1977; Calzetti et al. 1995; also A. Witt 2014, private communication) because of the size of the grains that produce it. Although the WD01 model does show the bump is primarily absorptive (cf. Draine 2003), ϖ is a derived quantity in their models and there is a small residual bump that may indicate a small inaccuracy. Thus, the peak seen in the uvm2 filter for the MW model (and, to a lesser extent, the LMC model) in the Scd and Sbc models may be inaccurate. However, the LMC and SMC dust are adequate representations of a scattered spectrum for testing whether the halo light is consistent with a reflection nebula. Thus, in the reflection nebula scenario we expect the best fits with LMC- or SMC-type dust and a galaxy template that matches the galaxy type.

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5.2.2. Fitting Results

We fit the measured halo SED using least-squares fitting with the χ² goodness-of-fit statistic. The measured SEDs come from the fluxes in Table 4, and the uvw1 filter is not used because of the red leak (we return to this later). It is also formally inappropriate to use the uvw2 correction factor, which depends on the true underlying spectrum, but for these fits the difference in correction factor between galaxy templates is only a few percent after the dust model has been folded in because extinction is much more efficient in the UV.

Figure 17 shows χ²/ν for the best-fit scaling factor in each model for the spiral galaxies. The left-hand panel shows the Sa–Sbc galaxies, and the right-hand panel the Sc–Scd galaxies. In each row, we show the χ²/ν values for the best fit for each model, where there are three circles per template representing (from left to right) the χ²/ν value for MW-, LMC-, and SMC-type (dark red, orange, and light orange) dust models respectively. The best fit overall for each galaxy is marked by a box, and the values are encoded as circles whose sizes correspond to χ²/ν, which is clipped at 25. Smaller circles are better fits. We omit the early-type templates, but these are never preferred.

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The best 2–3 fits typically occur for a galaxy template close to the host galaxy type (Figure 17, note that an asterisk after the galaxy type denotes a starburst), and the best-fit model uses the SMC or LMC dust in 18/20 cases. If we consider only those cases where χ²/ν ⩽ 3, 9/11 use the SMC model, which we think has the most accurate ϖ of the WD01 models. For most galaxies the fit gets significantly worse as the template becomes a worse match to the galaxy type if we use the MW dust model. An obvious exception is NGC 3628 (Figure 17), whose halo SED is closer to an Sa type galaxy (Figure 8).

Only a few of the early-type galaxies in the sample have "halo" emission that is fit well by any of the reflection nebula models (not shown). In most cases, the observed SED rises continuously toward longer wavelengths and the FUV emission is too weak to obtain χ²/ν ≲ 25.

Some halo SEDs get bluer farther from the galaxy, and a few galaxies have data of sufficient quality to measure a change in the SED slope. Figure 18 shows the SED measured near and farther from the galaxy for NGC 5907 and NGC 5775, where the sign of the slope reverses from closer to the disk (though still several kpc above the midplane) to farther out. We have also plotted the best-fit models for each dust model using the BMP Scd template. The SEDs closer to the disk cannot be fit well with a reflection nebula model, whereas the SEDs higher up are fit very well by the SMC model. Thus, near the disk there may be an additional component or the reflection nebula model is invalid. Extinction of a reflection nebula by dust in the halo cannot explain the change in slope, as the required N_H is several× 10²² cm⁻² (for δ_DGR ∼ 1/100). A similar transition is also seen in NGC 891 and NGC 5301, but not in NGC 3079 (or NGC 24 and NGC 4088, which are less inclined, so the halo extraction boxes slice through multiple heights).

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We note that the SMC δ_DGR is 5–10 times smaller than in the MW (depending on the region; Gordon et al. 2003; Leroy et al. 2007), so for SMC dust the implied N_H to produce a given L_halo is likewise higher. However, Ménard & Fukugita (2012) found δ_DGR = 1/108 for the halo dust with an SMC-like extinction curve (i.e., a similar dust composition to the SMC but a different δ_DGR). Using their value, we find a mean N_H ∼ 5 × 10¹⁹–3 × 10²⁰ cm⁻² based on Equation (3). For truly SMC dust, the value is commensurately higher. The column density through the halo is discussed in more detail in Section 6.

The UVOT red leak means that the uvw1 and uvw2 filters have redder central wavelengths than the nominal values. The effect is stronger in the uvw1, which we excluded from our SED fitting. The best-fit models for the four-point SEDs all underpredict the measured uvw1 flux for the spiral galaxies, so the proportion of excess flux tells us about the luminosity of another component. If the second component is a (classical) stellar halo and the reflection nebula hypothesis is correct, we expect the model to fit well when the stellar component has about the same luminosity (and perhaps color) as observed halos.

We attempted to determine the stellar halo luminosity in this way for NGC 5907 and NGC 5775, which have some of the best data. For the reflection nebula component, we used the best-fit models from above, and for the stellar halo we tried the elliptical galaxy templates from above as well as GALEV (a population synthesis and evolution code; Kotulla et al. 2009) E/S0 and Sa models with metal-poor populations, which may better represent the stellar halo. We fit the halo model to measured SEDs including the uvw1 flux, where the free parameter is the proportional flux in the stellar halo.

The best fits are shown in the top panels of Figure 19. The measured SEDs are shown as black boxes, and the best-fit model SED is shown as red diamonds connected by a red line. We have also overplotted the model λF_λ and its components (the dotted blue and red lines represent the reflection nebula and stellar halo respectively). The uvw1 point is shown at an effective wavelength computed from the model and filter response. This wavelength is strongly model dependent. In both galaxies, the best stellar halo model is an early-type template rather than a metal-poor template, but the χ² values are not much different. For NGC 5775, χ²/ν = 1.7, whereas for NGC 5907 χ²/ν = 1.1 (NGC 5775 also has a worse χ² for the best fit in the prior subsection).

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For NGC 5907, the model predicts a bolometric stellar halo luminosity of 2 × 10⁹L_☉, and for NGC 5775 about 5 × 10⁹ L_☉. This is consistent with stellar halo measurements for these galaxies and with the MW (Carney et al. 1989), and stellar halos typically tend to have luminosities of a few percent of the host galaxy. We also computed the model B − V colors by folding the spectrum through the B and V filters and adding a constant factor for comparison with observations, following Fukugita et al. (1995). The model B − V color is 0.91 mag for NGC 5907 and 0.93 for NGC 5775. Lequeux et al. (1996) measured B − V = 0.90 for NGC 5907 (which is remarkable for being a "red" halo; Sackett et al. 1994), so for this galaxy the model is consistent with the observations.

We also tried fitting a dual stellar halo model, where the first component is simply a late-type galaxy template instead of the reflection nebula spectrum. This is motivated by the possibility that the UV light comes from halo stars of a separate population. Stars might form in some of the gaseous material expelled into the halo. Molecular gas has been seen up to a few kpc around some edge-on galaxies (e.g., Garcia-Burillo et al. 1992; Lee et al. 2002), and only a small amount of halo star formation is needed to explain the UV fluxes. For example, in NGC 891, the GALEX FUV halo flux integrated above 1 kpc requires a halo SFR of ∼0.028 M_☉ yr⁻¹ (using the formulae in Kennicutt 1998; Parnovsky et al. 2013). We would expect some associated Hα emission, but NGC 891 has a bright Hα halo; using the scale height of 520 pc and total L_Hα ∼ 9 × 10⁴⁰ erg s⁻¹ from Howk & Savage (2000), the diffuse Hα above 1 kpc is over seven times higher than that expected from halo star formation.

The dual halo model provides equally good fits (bottom panels of Figure 19), but the luminosity of the redder halo is several times smaller than for the reflection nebula (plus halo) model, and the B − V colors are bluer. The reflection nebula and stellar halo model predicts more realistic stellar halos.

There are several other galaxies where we can do similar fits: NGC 24, NGC 891, NGC 2841, and NGC 5301. In each case, 80%–85% of the flux in the best-fit models comes from the reflection nebula component in that model, with B − V ∼ 0.84–0.93. The early-type galaxies, by comparison, have uvw1 fluxes consistent with the outskirts of the galaxy.

In Section 4, we noted that around spiral galaxies the FUV emission is visible at least as far or farther than emission in the other bands, whereas in elliptical galaxies the FUV emission drops below 2σ before the other bands (Figure 13). This is probably not due to a difference in scale height between bands (e.g., Table 5) but rather a difference in SED and emission mechanism.

The extent of the FUV emission is simply explained in the reflection nebula scenario by the relatively large FUV flux emerging from star-forming galaxies as well as the higher scattering cross-section at shorter wavelengths. A traditional stellar halo (even a metal-poor one) is not likely to be more detectable in the FUV than other bands. If the light is from younger stars, the scale heights of 3–5 kpc for NGC 3079, NGC 5775, and NGC 5907 indicate that there are some young stars over 10 kpc from the disk.

In late-type galaxies, the reflection nebula model is a better explanation than a stellar halo for the UV halo SED. We have considered the UV−r colors in the halo and the halo SEDs. The early-type galaxies, on the other hand, have UV−r colors and SEDs in their "halos" that are consistent with being the faint galactic outskirts rather than a reflection nebula. The S0 galaxies have some distinct halo emission (the halo SEDs differ from the galaxy and the FUV emission extends far from the galaxy), but additional data are required to separate the light from the stellar halo/galaxy outskirts.

We caution that we have not tried models other than the reflection nebula, classical stellar halo, and two-component stellar halo, so our results do not prove a reflection nebula origin. Even if the UV halo is a reflection nebula, the dust model we used may not be accurate. A better dust model (perhaps patterned after Nozawa & Fukugita 2013), including Monte Carlo radiative transfer, is required to make stronger statements about the dust content, and will be the subject of a future paper.

MSFR10 fit a curve to the mean optical extinction in the V band, A_V(r_p), toward background sources with r_p = 15–1000 kpc (Equation (30) in their paper). A_V(r_p), depends on the projected column density N_{H, proj}(r_p) through the halo and the dust model:

$$\begin{eqnarray} A_V(r_p) &=& 0.23\pm 0.06 \left (\frac{r_p}{1\ {\rm kpc}}\right)^{-0.86\pm 0.19} \nonumber\\ &=& 1.086\sigma _{{\rm ex}}(V) \delta _{{\rm DGR}} N_{{\rm H},{\rm proj}}(r_p), \end{eqnarray} \tag{ 4 }$$

where σ_ex(V) is the extinction cross-section in the V band.

If the halo of dust-bearing gas is spherically symmetric, we can use N_{H, proj}(r_p) to obtain the volume density as a function of galactocentric radius r (Figure 20). From n(r), we can then find the column density between the center of the halo and a point within, N_H(r) = ∫n(r)dr. N_{H, proj}(r_p) is integrated through the halo on a path perpendicular to r_p (see Figure 20), i.e., N_{H, proj}(r_p) = ∫n(s)ds. The integral is effectively over all volume densities n(r > r_p) and the path length from r_p to some higher r along the path is $s = \sqrt{r^2 - r_p^2}$. Thus,

$$\begin{eqnarray} N_{{\rm H}}(r_p) &=& \int n(s) ds = 2\int _{r_p}^{\infty } n(r)\frac{r}{\sqrt{r^2 - r_p^2}} dr \nonumber\\ &=& \frac{A_V(r_p)}{1.086\sigma _{{\rm ex}} \delta _{{\rm DGR}}}. \end{eqnarray} \tag{ 5 }$$

It is possible that n(r) does not have an easily integrable form, but based on the MSFR10 fit a reasonable choice is $n(r) = n_0 r_{{\rm kpc}}^{-x}$, where x is determined by choosing a value, evaluating the integral, and comparing the resulting N_{H, proj}(r_p) to the MSFR10 curve. The best-fit exponent is x = 1.96 ± 0.06, which is consistent with x = 2 within the MSFR10 error bars (Figure 20). Thus, we adopt $n(r) = n_0 r_{{\rm kpc}}^{-2}$. Since n(r) diverges at n = 0, N_H(r) is effectively normalized by some minimum radius,

$$\begin{equation} N_{{\rm H}}(r) = n_0{\rm (1\, kpc)}\left (\frac{1}{r_{{\rm min}}} - \frac{1}{r}\right), \end{equation} \tag{ 6 }$$

where the radii are in kpc. We do not know r_min, and in real galaxies the disk–halo interface is nebulous. Considering that thick (stellar) disks in disk galaxies have scale heights of 0.2–1.5 kpc (Yoachim & Dalcanton 2006), a reasonable choice of r_min is 2 kpc for MW-sized disk galaxies, which is consistent with where we measure UV fluxes. Of course, a spherical halo model breaks down near the disk (extraplanar gas tends to look like an exponential atmosphere near the disk; e.g., Sancisi et al. 2008), so r_min could be thought of as a normalization. For r_min = 2 kpc and δ_DGR = 1/100, the total N_H through the halo is a few× 10²⁰ cm⁻². As N_H depends on δ_DGR but τ depends only on the dust column, we defer a discussion of N_H and gas mass to the end of this section.

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The spherical halo described here (hereafter the MSFR10 halo) will be used through the rest of this section to estimate L_halo in the MSFR10 model, its light profile, and the total mass. We also assume that the halo is optically thin and that a scattered photon scatters only once before escaping, based on the N_H and δ_DGR ∼ 1/100. While the spherical approximation must break down near the disk, we will see below that it is useful.

L_halo/L_gal can be derived in the MSFR10 halo from a dust model and a source/halo geometry. In this subsection, we determine the total luminosity and ignore the directional dependence in the scattering cross-section (which affects how much of the light is seen at a given viewing angle).

A ray traveling from the origin a distance r is attenuated by e^−τ, where τ(r, λ) = N_H(r)σ_ex(λ)δ_DGR (Equation (3)). If τ ≪ 1 and we integrate over all rays to r = ∞, Equation (3) becomes

$$\begin{equation} L_{{\rm halo}}/L_{{\rm gal}} \sim \tau (\lambda) = \overline{N_{{\rm H}}} \sigma _{{\rm ex}}(\lambda)\varpi (\lambda)\delta _{{\rm DGR}}, \end{equation} \tag{ 7 }$$

where $\overline{N_{{\rm H}}}$ is the mean N_H over rays in all directions (and thus contains all geometric considerations).

We now consider two limiting cases to bracket the plausible range of L_halo/L_gal for the MSFR10 halo: a "point source" galaxy and a thin galaxy disk in a completely spherical halo. In the case of the point source, $N_{{\rm H}} = \overline{N_{{\rm H}}} = n_0/r_{{\rm min}}$, so

$$\begin{equation} (L_{{\rm halo}}/L_{{\rm gal}})_{{\rm ps}} \sim 0.2/r_{{\rm min,kpc}} \sim 0.1 \end{equation} \tag{ 8 }$$

for r_min = 2 kpc. In a real galaxy, L_gal is distributed over a disk much larger than r_min. Even if the halo becomes like an exponential atmosphere near the disk, the average N_H seen by light emitted from farther out in the disk will be smaller than near the center, so (L_halo/L_gal)_ps is higher than we expect in a real galaxy.

On the other hand, if L_gal is distributed over a thin, uniformly bright disk in the MSFR10 halo (i.e., extraplanar gas does not look like an exponential atmosphere near the disk), the $\overline{N_{{\rm H}}}$ farther out in the disk will be lower than we expect from a real galaxy, so this situation provides a lower bound on L_halo/L_gal. To obtain L_halo/L_gal, we first find the $\overline{N_{{\rm H}}}$ as a function of radius for a source emitting in the disk. We then integrate over the disk.

Consider a point source at a radius r in a disk of radius R (Figure 21). The total column density through the halo for each ray then depends on the angle θ, but one can see that the sum of N_H(θ) and N_H(π + θ) is equal to the projected column density N_{H, proj}(r_p) at r_p = rsin θ. The mean N_{H, proj}(r_p) occurs at r_p = 2r/π, since the mean of sin θ = 2/π between 0 and π, so for n(r) = n₀r⁻²,

$$\begin{equation} \overline{N_{{\rm H}}}(r) = \frac{n_0}{2} \int _{r_p}^{\infty } dr \frac{1}{r^2} \frac{r}{\sqrt{r^2-r_p^2}} = \frac{n_0 \pi ^2}{8}\frac{1}{r}. \end{equation} \tag{ 9 }$$

For a uniformly bright, thin disk of total luminosity L_gal and inner and outer radii r_min (for consistency) and R, the total area is $\pi (R^2-r_{{\rm min}}^2)$ and the area element is dA = 2πrdr. Thus,

$$\begin{eqnarray} \left (\frac{L_{{\rm halo}}}{L_{{\rm gal}}}\right)_{{\rm disk}} &=& \frac{\sigma _{{\rm ex}}\delta _{{\rm DGR}}\varpi }{\pi (R^2-r_{{\rm min}}^2)} \int _{r_{{\rm min}}}^{R} 2 \pi r \left (\frac{\pi ^2}{8}\frac{n_0}{r}\right) dr \nonumber\\ &=& r_{{\rm min}}\frac{\pi ^2}{4}\frac{(R-r_{{\rm min}})}{(R^2-r_{{\rm min}}^2)} \left (\frac{L_{{\rm halo}}}{L_{{\rm gal}}}\right)_{{\rm ps}}. \end{eqnarray} \tag{ 10 }$$

The MW-sized disk galaxies in our sample have UV luminous disks with projected semimajor axes between 10 and 20 kpc. Taking this range for R, the scattered halo luminosity from our idealized disk is between 1/3 and 2/11 of that from a point source of the same L_gal at the center of the halo, or

$$\begin{equation} (L_{{\rm halo}}/L_{{\rm gal}})_{{\rm disk}} \sim 0.02\hbox{--}0.03. \end{equation} \tag{ 11 }$$

The value can be scaled up or down if the disk is not uniformly bright, based on the concentration of light at each radius.

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For the parameters above, we expect 0.02 ≲ L_halo/L_gal ≲ 0.1. Considering differences in N_H, morphological type, disk size between galaxies of a similar absolute magnitude, and differences between σ_ex model curves, we expect the late-type galaxies to have

$$\begin{equation} L_{{\rm halo}}/L_{{\rm gal}} \sim 0.04\hbox{--}0.1. \end{equation} \tag{ 12 }$$

This ratio does not depend on the galaxy color.

The total L_halo/L_gal is not directly comparable to the measured values. First, we must determine the fraction of L_halo that we would see from a region of interest around a galaxy of a given inclination and disk thickness. This is important because scattering is forward-throwing (Draine 2003) and extinction in galaxy disks makes L_gal anisotropic. Second, we must correct the measured L_gal for extinction within the disk, as the galaxies in our sample are highly inclined.

6.3.1. Observable Fraction of L_halo

If we compute an isotropic luminosity from the measured UV fluxes (4πd²F_halo), it will underestimate the true L_halo for several reasons. The most obvious is that the flux measurement boxes (e.g., Figure 7) are smaller than the halo, but as most of the scattering occurs near the disk, inclination effects are more important. Due to extinction in the disk, more light emerges along the minor axis than near the major axis. A scattered photon is most likely to have a new trajectory at a small angle from the incident path (Draine 2003), so more of the total L_halo is visible from above the disk than from the side (if it could be separated from the non-scattered light).

For the MSFR10 halo we can estimate the amount of light that would be scattered into the line of sight for a given inclination, measurement region, and disk emission model. The "isotropic" halo luminosity derived from the visible light we call L_{halo, vis}. L_{halo, vis} underestimates the true L_halo for an edge-on galaxy and overestimates it for a face-on galaxy. For the remainder of this subsection, we consider a perfectly edge-on galaxy for the two limiting cases of a point source and a uniformly bright disk of radius R described above (Figure 21). L_{halo, vis} is derived for a given flux measurement region by finding $\overline{N_{{\rm H}}}$ for rays passing through that region and integrating over dσ_scat/dΩ from Draine (2003).

The boxes where we measure fluxes have finite width and height, but measure light from an infinite depth. For the MSFR10 halo, we can define a box and integrate numerically to evaluate N_H and dσ_scat/dΩ, but with a few geometric simplifications we can make an instructive estimate. The box width is chosen to match the projected major axis of each galaxy, which corresponds to a radius R. The maximum height of the boxes in our sample is typically less than R, but as the halo fluxes drop below our sensitivity at lower heights, we make only a small error by assuming the distance from the top of the measurement boxes to the midplane of the galaxy is R. Since most scattering occurs at small radii, we can likewise truncate the depth and consider a cube with each side having a length 2R (the extension and truncation cause small errors in opposite directions). This geometry is shown in the left panel of Figure 22.

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We can then identify a sphere that is similar enough to the cube that the $\overline{N_{{\rm H}}}$ is approximately correct. This has the advantage of making N_H independent of angle and simplifying the integral over dσ_scat/dΩ. The radius of the sphere can be obtained from the largest sphere that fits within the cube and the smallest one that bounds it (Figure 22). In the former case, the radius is R and in the latter it is $\sqrt{2}R$, so we take the mean N_H from the galactic center to the cube edge to be N_H ≈ n₀(1/r_min − 1/1.2R).

In this framework, the anisotropy in flux scattered into a given line of sight can be described in terms of an effective minimum polar angle θ_min for light emitted from the galaxy to escape its disk (Figure 22). For a chosen viewing angle, the amount of scattered light can be obtained by integrating dσ_scat/dΩ between θ_min and π − θ_min and multiplying by N_H (the integral over ϕ gives a factor of 2π). If the disk is uniformly thick at all radii and a gaseous disk extends beyond the UV-emitting region, θ_min is essentially constant, but one could also imagine a tapered disk (left and right halves of the circle shown on the right side of Figure 22). Based on typical N_H values in galaxy disks, θ_min in our sample is near θ_min ∼ π/9 (20°), but the extent of the range is not known. A real disk model is required and will be presented in a future work.

Using the WD01 SMC bar model and the Draine (2003) curve for the uvm2 wavelength, R = 10 kpc and r_min = 2 kpc, and θ_min = π/9, we find L_{halo, vis}/L_gal ∼ 0.001 and 0.03 for the uniform disk and point source cases respectively. The lower bound is small because the flux measurement boxes are truncated at the disk width.

Considering the range in disk radii and uncertainty in θ_min, the geometric simplifications we made, and the different dust models, a plausible range for L_{halo, vis}/L_gal for edge-on galaxies in the MSFR10 halo is

$$\begin{equation} L_{{\rm halo,vis}}/L_{{\rm gal}} \sim 0.01 - 0.05. \end{equation} \tag{ 13 }$$

When we numerically evaluate L_{halo, vis} for extraction boxes of width 2R in the two limiting cases, we find values that fall within this range. The integral over dσ/dΩ increases for galaxies at lower inclination, but we actually expect a lower L_{halo, vis}/L_gal for these systems because most scattering occurs at small radii, and the lower regions of the halo are seen in projection against the galaxy (where we do not measure halo flux).

6.3.2. Correcting for Extinction in the Measured L_gal

L_gal must be corrected because the observed flux is measured at a viewing angle with maximal extinction in the disk, whereas light escaping to the halo sees much less extinction. We correct for this by estimating the intrinsic UV luminosity and then estimating the extinction along the minor axis.

The UV flux absorbed by dust in the disk is reprocessed into the FIR, so one can use the FIR-to-UV flux ratio to estimate the UV extinction. As in Buat & Xu (1996), we use the sum of the IRAS 60 μm and 100 μm fluxes for the FIR flux. We adopt the fit in Buat et al. (1999) to star-forming galaxies (measured at 2000 Å),

$$\begin{eqnarray} A_{{\rm UV}} &= & 0.466(\pm 0.024) \nonumber\\ && +1.00(\pm 0.06)\log (F_{{\rm FIR}}/F_{{\rm UV}}) \nonumber\\ && +0.433(\pm 0.051)\log (F_{{\rm FIR}}/F_{{\rm UV}})^2 \end{eqnarray} \tag{ 14 }$$

and apply the extinction to the uvm2 fluxes to obtain the intrinsic UV luminosity.

The light is attenuated as it exits the galaxy along the minor axis. We can estimate this factor from extinction corrections toward face-on galaxies (which also include any halo extinction, and are thus slightly too large). The extinction toward face-on disks depends on the galaxy type, luminosity, and the radius where it is measured. Based on Calzetti (2001) and references therein, the effective B-band extinction along the minor axis for late-type galaxies is perhaps A_B = 0.4–0.6 mag for an Sc or Sd galaxy and A_B = 0.3–0.4 mag for Sa and Sb galaxies. For MW-type dust with R_V = 3.1, A_UV/A_B = 2.4, so L_gal as seen by the halo is about 0.7–1.7 mag smaller than the intrinsic UV luminosity obtained from the Buat et al. (1999) correction. For SMC-type dust, A_UV/A_B = 2.8. Even within galaxies, it is not clear what dust model to use, as some have SMC-type dust (Calzetti et al. 1994) and others MW-type dust. The location of the dust relative to star forming regions may also play a role (Panuzzo et al. 2007), and starbursts tend to have higher A_B. As the difference is rather small, we adopt the MW-type dust value for the dust within the disk.

Thus,

$$\begin{equation} L_{{\rm gal,corr}} = 4\pi d^2 F_{{\rm gal}} 10^{(A_{{\rm UV,maj}}-A_{{\rm UV,min}})/2.5}, \end{equation} \tag{ 15 }$$

where the "maj" and "min" subscripts refer to extinction through the disk along the major and minor axes respectively. Considering the scatter in the Buat et al. (1999) FIR-to-UV relation, reported differences in the extinction toward face-on galaxies, and the dependence of the extinction on the galaxy model (Calzetti 2001; Marcum et al. 2001), we suppose that L_{gal, corr} is accurate to within 50% in most systems.

We can now compare the MSFR10 L_{halo, vis}/L_gal to that derived from the UV data. Since we rely on the FIR data, we quote values for the 15 highly inclined Sa–Sc galaxies with FIR and uvm2 data in Table 7. The other quantities in the table go into computing L_gal. For these galaxies, we find

$$\begin{equation} (L_{{\rm halo,vis}}/L_{{\rm gal,corr}})_{({\rm obs})} = 0.002-0.06. \end{equation} \tag{ 16 }$$

This is remarkably similar to the range predicted by our MSFR10 extrapolation,

$$\begin{equation} (L_{{\rm halo,vis}}/L_{{\rm gal}})_{{\rm MSFR10}} = 0.01-0.05. \end{equation} \tag{ 17 }$$

Galaxies with smaller inclination angles tend to have smaller values, as expected.

There are several comments worth making at this point. First, we expect L_{halo, vis}/L_gal values of a few percent for a range of geometries and parameters because the MSFR10 A_V curve has a maximum column density of a few× 10²⁰ cm⁻² for a realistic r_min, and integrating the Draine (2003) expression gives a cross-section of a few× 10⁻²² cm². The errors we make through the various simplifying assumptions are smaller than the range from our upper/lower bound analysis.

Second, the observed L_{halo, i}/L_gal values are consistent with the MSFR10 fit, but also any halo model that produces N_H ∼ 10²⁰ cm⁻². The ratio by itself does not prove the MSFR10 model.

Third, there is intrinsic variation in the sample and L_halo/L_gal does not necessarily follow H i halo mass (for example, NGC 891 has an unusually massive H i halo but a relatively low L_halo/L_gal). This could be due to variation in extinction through the disk, the location of star formation in the disk, and the difference in "real" r_min for each galaxy. A larger sample is also required to rigorously determine whether the MSFR10 halo is valid within 15 kpc of the disk.

Finally, the results are shown for the uvm2 data only, but we can also use the GALEX NUV and FUV with appropriate corrections and using the WD01 and Draine (2003) data for the right wavelengths. For example, for the FUV the Draine (2003) model and MSFR10 curve predict L_{halo, vis}/L_gal ∼ 0.02–0.09. The Buat et al. (1999) correction is measured at longer wavelengths and so may not be valid, but blindly applying an extrapolation to the FUV band, we find L_{halo, vis}/L_gal ∼ 0.01–0.04 for several galaxies where the FUV fluxes are well constrained.

We can also compare the expected light profile from MSFR10 to the observed fluxes. In Figure 23 we show the observed flux profiles for several of the galaxies in our sample with excellent data (boxes), where the fluxes have been normalized so that the y-axis shows the percentage of the total observed halo light seen in each bin. We have also overplotted a model based on the MSFR10 n(r) using the same heights and projected bin sizes (albeit making a spherical approximation as for L_{halo, vis} above). There is excellent agreement between the late-type galaxies in Figure 23, consistent with n(r) = n₀r⁻² even at small radii.

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It is worth noting that the profiles in Figure 23 do not depend on the galaxy luminosity, and the corresponding curves do not depend on the dust model (which affects total extinction). The profiles are thus a clean measure of how the density varies with radius, assuming a single type of dust and δ_DGR. A few of the early-type galaxies also show good agreement in Figure 23. The reason is unclear (most of the early-type galaxies in the sample prefer a shallower radial dependence), but in these galaxies the observed L_halo/L_gal ∼ 0.3–1.5 before any correction for galactic extinction (the Buat et al. 1999, fit is calibrated to star-forming galaxies), which is badly inconsistent with a scattered light origin.

The flux profiles and L_{halo, vis}/L_gal derived from extrapolating the MSFR10 fit inward are consistent with the observations.

If the MSFR10 halo extends to small radii, we can estimate the mass of dust-bearing gas within 20 kpc.

The N_H and mass implied by the MSFR10 curve depend on δ_DGR, which varies by location in the galaxies of the Local Group. For the MW, δ_DGR ∼ 1/100, whereas in the SMC it is 5–10 times smaller (Gordon et al. 2003; Leroy et al. 2007). MSFR10 prefer SMC-type dust for the (outer) halo, but Ménard & Fukugita (2012) find that δ_DGR = 1/108 for the halo dust outside 20 kpc. Thus, it seems likely that the true δ_DGR between 5 and 20 kpc is also about 1/100. This gives a maximum N_H(r) ∼ 3 × 10²⁰/r_{min, kpc}. For r_min = 2 kpc, this is similar to typical sight lines out of the MW at high latitudes, but these include disk material. It is about three times higher than N_H viewed out of the Lockman hole.

Column densities measured in projection toward edge-on extraplanar galaxies (e.g., Sancisi et al. 2008, and references therein) indicate maximum extraplanar N_{H, proj}(r_p) of a few× 10²⁰ cm⁻² (NGC 891 has a particularly massive halo with a maximum N_H(r_p) about 10 times higher). In the spherical halo model, at r_p = 2 kpc, N_H(r_p) ≈ 2.4 × 10²⁰ cm⁻², which is in agreement with these galaxies.

From the density profile we can measure the enclosed mass within a given radius (one could also integrate the projected column density implied by the MSFR10 extinction curve over a visible area),

$$\begin{eqnarray} M(<r) &=& 4\pi \mu m_p \int r^2 n(r) dr \nonumber\\ &\sim & 3.1\times 10^{7} (r_{{\rm kpc}}-r_{{\rm min,kpc}}), \end{eqnarray} \tag{ 18 }$$

where μ is the mean atomic weight per particle and $n \sim 0.1 r_{{\rm kpc}}^{-2}$ cm⁻³. Within 20 kpc, this yields 5 × 10⁸ M_☉ of gas, or several percent of the gas in the disk for a typical late-type galaxy.

This section started from the proposition that if the extraplanar UV emission is a reflection nebula, we can use the fluxes to determine whether the UV emission is consistent with the same dust seen in extinction at larger radii. We found that the halo luminosities and flux profiles are indeed consistent with the MSFR10 fit within 20 kpc down to the edge of the thick disk, with a total dust-bearing gas mass of around 5 × 10⁸ M_☉ in this volume.

There are several potential weaknesses in this analysis. First, the results depend on the WD01 models and the Ménard & Fukugita (2012) δ_DGR for their halo dust, which determines n₀ (and thus N_H). N_H also depends on $r_{{\rm min}}^{-1}$, so both L_halo and M_gas(< r) in the halo depend on this value. Our choice of r_min = 2 kpc is based on physical considerations (albeit in an unphysical halo approximation), and perhaps validated by the extraplanar N_H measured in other galaxies. Still, a real halo model where the halo connects smoothly to the disk gas is required to explore this issue. Third, the L_gal that emerges from the disk depends on the disk thickness and density. We incorporated this as a θ_min above which light escapes into the halo, but a disk model is required to do a more careful computation. Finally, our corrections to the observed L_gal are based on the Buat et al. (1999) work and measurements of A_B through galaxy disks. There is a large scatter in both between galaxies, so our range of "measured" L_halo/L_gal may not be conservative (i.e., wide) enough.

It is worth noting that most of the geometric simplifications we make introduce errors in N_H that are small compared to the range between the limiting cases we considered. A real model is required to go beyond this simple analysis. Likewise, the choice of SMC- or MW-type dust from the WD01 models does not make a large difference if we adopt the Ménard & Fukugita (2012) δ_DGR for SMC-type halo dust.