An extended dust disk in a spiral galaxy; An occulting galaxy pair in ANGST
B. W. Holwerda, W. C. Keel, B. Williams, J. J. Dalcanton, R. S. de Jong
aa r X i v : . [ a s t r o - ph ] O c t accepted by AJ An extended dust disk in a spiral galaxy;An occulting galaxy pair in ANGST
B. W. Holwerda , W. C. Keel , B. Williams , J. J. Dalcanton , R. S. de Jong [email protected] ABSTRACT
We present an analysis of an occulting galaxy pair, serendipitously discoveredin ACS Nearby Galaxy Survey Treasury (ANGST) observations of NGC 253taken with Hubble Space Telescope’s Advanced Camera for Survey in F W , F W and F W ( SDSS − g , broad V and I ). The foreground disk system (at z ≤ .
06) shows a dusty disk much more extended than the starlight, with spirallanes seen in extinction out to 1.5 R , approximately six half-light radii. Thispair is the first where extinction can be mapped reliably out to this distance fromthe center. The spiral arms of the extended dust disk show typical extinctionvalues of A F W ∼ . A F W ∼ .
25, and A F W ∼ .
15. The extinctionlaw inferred from these measures is similar to the local Milky Way one, and weshow that the smoothing effects of sampling at limited spatial resolution ( < Space Telescope Science Institute, Baltimore, MD 21218, USA Department of Physics & Astronomy, 206 Gallalee Hall, 514 University Blvd., University of Alabama,Tuscaloosa, AL 35487-0324, USA Physics-Astronomy Bldg., 3910 15th Ave NE, Room C319, Seattle WA 98195-0002 , USA
1. Introduction
Dust absorbs starlight and re-emits it in the infrared, producing profound effects onthe observed light of galaxies. The degree to which dust extinction affects observationsof their stellar disks was a source of contention in the early 1990’s (Disney et al. 1989;Valentijn 1990) but a consensus was soon reached; disks are semi-transparent within muchof the optical radius, but with more opaque spiral arms (Davies & Burstein 1995). However,the radial extent, distribution and evolution of the dust in spirals at large remain poorlyknown. While progress can be made using mid- and far-infrared emission from dust, suchmaps depends strongly on the availability of local dust heating sources, rather than solelythe total amount of dust. As an alternative, one can map the extinction caused by dustdirectly, provided one can identify a suitable background source. The challenge is thereforeto find a sufficiently smooth and known background light source with which to identify andcharacterize dust extinction in a foreground galaxy.With a method proposed by White & Keel (1992), one can estimate the extinction,using cases where a foreground spiral is observed partially in front of a background galaxy.The few suitable galaxy pairs known at the time were studied with ground-based imaging(Andredakis & van der Kruit 1992; Berlind et al. 1997; Domingue et al. 1999; White et al.2000), spectroscopy (Domingue et al. 2000), and subsequent Hubble Space Telescope (HST)observations (Keel & White 2001a,b; Elmegreen et al. 2001). The fact that spiral disks aresemi-transparent, with more opaque spiral arms, is in part based on these studies and con-firmed with distant galaxy counts through the disks of spirals (Holwerda et al. 2005a,b,c,e,d,2007a,d). The dust appears to be distributed in a fractal pattern and the extinction law innormal spirals is close to the Milky Way law, provided the extinction is measured on scalesof 60 pc or less (Keel & White 2001a).The occulting galaxy technique can be used to address outstanding questions aboutthe distribution of dust-rich interstellar medium in spiral galaxies. First, what is the ra-dial extent of dust in spirals? The interstellar matter (ISM) extends to large radii in theform of atomic hydrogen (HI) but thus far there is little direct evidence of dust beyondthe optical disk (de Vaucouleurs’ R ). Some indications have been found however, partlythrough studies of the thermal emission by dust. For example, Nelson et al. (1998) stackedInfraRed Astronomical Satellite (IRAS) profiles of hundreds of galaxies and found dust emis-sion beyond R . Cuillandre et al. (2001) reported reddening in the outer parts of M31’s HIdisk. Gordon et al. (2003) find that there is a second ring structure just outside R in M31,Regan et al. (2004) finds a similar ring in NGC 7321 and Hinz et al. (2006) present the bestevidence to date in Spitzer data for a radially extended cold dust component in the dwarfUGC 10445. While the existing occulting-galaxy studies typically find dust scale lengths 3 –comparable to the optical starlight, the sample is too sparse to tell much about how the dustdistribution might vary within the disk-galaxy population.There is also indirect evidence of dust at large radii from observations of extended starformation in spiral disks. The existence of excess-ultraviolet (XUV) disks detected withGALEX (Gil de Paz et al. 2005; Thilker et al. 2005, 2007) suggests the presence of a coldmolecular-gas component at large radii, confined to spiral arms. This molecular componentis also likely to host dust –suggesting that there may well be extinction at these large radii–at least in spiral structures.The second question that can be addressed in occulting pairs is: How is the dust dis-tributed spatially? For the inner parts of spiral disks the distribution of the dust-rich ISMis well traced by the emission observed with
Spitzer (Dale et al. 2005, 2007; Draine et al.2007). However, studies of warm dust leaves the structure of the cold ISM traced by dustunexplored over much of the HI disk. In contrast, backlit dust can be detected independentof its temperature. In these regions, extinction studies that use occulting pairs, are the areliable probe of the dust distribution. The size distribution of dust extinction can then becompared to the sizes of giant molecular clouds (Rosolowsky 2005).The final outstanding question is how the opacity of spiral disks changes over time.There was more star formation at z ≈ ∼
1, provided a sufficient numberof pairs can be found. Local pairs such as the one presented here, serve as the local referenceframe to interpret the more distant pairs and as a test of different methods for analyzing theextinction.In this paper, we report on an occulting pair with nearly ideal geometry. The backgroundgalaxy ( z = 0 .
06) is a spiral with a prominent, regular and smooth bulge, which is partiallyocculted by a foreground spiral. The pair was serendipitously discovered in HST imagesfrom the ACS Nearby Galaxy Survey Treasury (ANGST) survey. We explore the radial andspatial distribution and the inferred extinction law of the dust in a smaller foreground spiral,which displays an extent of dust hitherto unseen in backlit galaxies. In § § §
4, the optical depth estimates. We 4 –discuss the results and approaches in § §
2. Data
The HST/ACS data were obtained for the ACS Nearby Galaxy Survey Treasury (ANGST,Dalcanton et al. 2007), as part of their observations of NGC 253 to characterize stellar pop-ulations as a function of radius (Figure 1). Data are in three filters: F W , F W and F W , corresponding approximately to SDSS − g , broad V and I . Exposure times are2256, 2283, and 2253 seconds respectively. Figures 1 and 2 show a grayscale and colorcomposite of the three filters. The image shows clear dust structures associated with theforeground spiral, extending to (and slightly beyond) the center of the bulge of the back-ground galaxy. Figure 5 shows the F W band grayscale image in which the dust lanes ofthe foreground galaxy are neatly visible against the background galaxy’s bulge.The background galaxy was catalogued as 2MASXJ00482185-2507365 by 2MASS. Ratcliffe et al.(1998) give its redshift as z = 0 .
06. At this distance a single ACS pixel (0 . ′′
05) correspondsto a physical scale of 57 pc., assuming h = 70 km/s/M pc. The redshift of the foregroundcompanion spiral is not known, so we take z = 0 .
06 as an upper limit when computingphysical scales within the foreground system.
3. Analysis
To map the extinction in the foreground galaxy, we assume that the foreground andbackground galaxies are rotationally symmetric around their respective centers. This as-sumption holds well for ellipticals and generally well for grand-design spirals (with rotationalsymmetry rather than axisymmetry). Figure 3 shows a sketch of the method, where F and B indicate the unobscured flux due to the foreground and background galaxy, respectively.The flux in the overlap region comes from both galaxies, with the background galaxy dimmedby the opacity of the foreground disk with an optical depth τ : < F + Be − τ > . Assum-ing appropriate symmetry, we can estimate the local optical depth using the flux from theoverlap region and the corresponding point-symmetric sections in the foreground ( F ′ ) andbackground ( B ′ ) galaxy: e − τ ′ = < F + Be − τ > − F ′ B ′ . (1)When the contribution from the foreground galaxy becomes negligible compared with 5 –the background galaxy ( B >> F ), this can be approximated by (White et al. 2000): e − τ ′ = Be − τ B ′ . (2)The key step in this analysis is clearly estimating F and B at each location in the overlapregion. Using this formalism, we consider three approaches, whose applicability depends onthe geometry of the system and the data quality. The first approach (method A) is to rotateboth background and foreground galaxies 180 ◦ and then subtract both from the originalimage, minimizing the residual image. The optical depth is then obtained separately fromequation 1 (see also Holwerda et al. 2007c). The second approach (method B) assumes thecontribution of the foreground galaxy is negligible. The background galaxy is rotated by180 ◦ , and the optical depth is obtained from the ratio of the original and rotated image inequation 2. This method provides a lower limit to the opacity, because any foreground lightwill masquerade as background light, reducing the inferred extinction. The third option(method C) is to model the background galaxy with an appropriate isophotal model (e.g.,with a S´ersic profile, or via elliptical fits to a set of isophotes), and then to estimate thegalaxies’ contributions ( B ′ and F ′ ) from the model before estimating the optical depth fromequation 1 or 2.The appropriate approach to analyze the dust structure of the foreground galaxy de-pends on the geometry of the pair. In the pair considered in this paper, we can use anyof the three approaches because the background bulge completely dominates the flux in theouter overlap region of the foreground spiral, and there are large unobscured regions of bothgalaxies. Thus, we use these data to compare the performance of these three approaches.Using each of these, we will discuss the spatial extent, distribution of the extinction, andthe inferred extinction law. For this pair, we expect methods B and C to give more reliableresults, given that the assumption of axisymmetry is not as well justified for the outer regionsof the foreground galaxy. To construct the extinction map with the first approach, we applied the method de-scribed in Holwerda et al. (2007c). First, we ran Source Extractor (Bertin & Arnouts 1996;Holwerda 2005) on the image to segment it into different objects. Those sections assignedto either galaxy are copied to be used in the fit. The script uses the central positions of thebackground and foreground galaxy and their rotation angles (
P A B , P A F ) as fit parametersto minimize the flux in the residual image after both rotated galaxies are subtracted from the 6 –original. If both galaxies are perfectly symmetric and there is no dust extinction at all, theresidual image should have zero flux. Simply rotating copies of both galaxies and minimizingthe flux in the overlap region can be effectively automated, enabling its application to manypairs. We applied separate fits in all three HST filters and the resulting optical depth mapsare presented in Figure 5. The best-fit rotation angles were 180.67 and 180.74 degrees. For the second approach, we rotated the background galaxy 180 ◦ and constructed anoptical depth image of the overlap region from the ratio between the original and the flippedimage (Figure 5, second row). No fit was performed, and the center of the background galaxywas estimated visually. This approach is appropriate for a quick analysis, and can be donein cases where one has the luxury of a near-perfect geometry and a background galaxy thatis both bright and smooth. To estimate the underlying values of F and B , we used the stsdas ellipse and bmodel tasks to generate smooth models for both galaxies. First, the areas affected by the foregroundgalaxy were masked, and a set of elliptical isophotes were fit to the background galaxy. Wethen subtracted a noiseless realization of this mean profile, and modeled the foregroundgalaxy after masking off areas where absorption might be important, notably the overlapregion and dark lanes in the background galaxy. The masking typically left more than60% of each isophote. Subsequently, we subtracted the model of the foreground galaxyfrom the data, and refit the background galaxy. If some masked regions were missed inthis first iteration, these are masked in a second iteration. Original images, backgroundand foreground isophotal models and the residual image are shown in Figure 4 for all threeHST filters. We used the isophotal model galaxies to construct an optical depth map fromequation 1 using the model values for B ′ and F ′ . The resulting optical depth maps arepresented in Figure 5.The isophotal model fit gives an estimate of R for each galaxy (the radius at whichthe profile intercepts 25 mag/arcsec in F W ). The foreground galaxy’s R occurs at80 ± . ′′
4. Optical Depth Maps
To compare the different methods of deriving extinction, the optical depth maps forthe overlap section are shown in Figure 5 for method A, B, and C and filters F W , F W , and F W ). The full optical depth map from Method C is shown in Figure 6 forcomparison.The optical depth maps in Figures 5 have numerous features. Most noticeable is theclear presence of spiral arms. These features suggest that a cold, dense ISM does existat larger radii, and that it remains concentrated in the spiral arms. Figure 5 shows littleextinction in between the spiral features. These features are most prominent in F W due to the increase in dust absorption at shorter wavelengths. In addition, the effect ofsubstructure in the foreground disk is also the most profound in this filter. The F W and F W filters also show the dust structures, but at progressively smaller optical depths.From Figure 5 it is clear that the automated fit approach has a significant drawback forthis pair. Because of the many foreground stars associated with NGC 253 and the resolvedstructure in the foreground galaxy, using rotated images leads to artifacts in the resultingoptical depth map. The other two approaches suffer much less from this effect. Because thebulge of the background galaxy is largely axisymmetric, method B and C generally agreewell, and the dark extended structures can be identified in both. Notably, the nearly opaquespiral arm can be seen in all three types of optical depth map, independent of the methodused. To quantify the distribution of extinction seen in Figure 5, we plot in Figure 7 histogramsof the optical depth in each pixel for all three filters and all three methods. The distributionof optical depths shows the broadest distribution of optical depth values in the F W bandand the narrowest in the F W . It also shows that the median of the distributions shifts tolower values with redder filters. This effect is expected because the bluest band is the mostaffected by extinction. In each filter, the optical depth stays below one, which is consistentwith the paucity of molecular gas seen at large radii in nearby spirals.Method C shows no peak, and instead, the distribution of extinction rises smoothlytowards zero. In contrast, for methods A and B, the distribution of optical depths peaksat τ = 0.25 for F W and F W and τ = 0.15 for the F W band with Method Ahaving the most extreme extinction values due to the additional structure in the subtractedforeground galaxy. 8 –This shift to higher optical depths can be explained by the construction of the back-ground light model. Because methods A and B use the background galaxy itself, any duststructures in the background galaxy increase the inferred extinction distribution in the fore-ground galaxy. Method C is not affected by this contaminant due to the use of an isophotallight model. We can verify that Method C’s extinction values are unaffected by the contaminationof substructure by applying the same method to two apertures where we expect the meanextinction to be close to zero. Figure 8 shows the resulting distribution of optical depthvalues using Method C for three apertures, one in the overlap region, and two in the mostlyunobscured region (Figure 6). In both low-extinction apertures there is a clear and narrowpeak at τ = 0. Similar plots for Method A and B also show a peak at τ = 0, however with awider distribution of values around zero. This wider spread of optical depth values aroundthe zeropoint can be attributed to asymmetric structure in the background galaxy.Unlike for the unocculted regions, the distribution of extinctions for the occulted regionis clearly skewed to significantly higher values. Comparing to the unobscured regions suggeststhat these higher extinction values in the overlap region are likely to be physical rather thanan artifact of the background galaxy substructure. To obtain a simple estimate the uncertainty in the optical depth values in Method C, weshift the model background and foreground galaxy by a pixel in both x and y direction (x+1,y+1 and alternatively x-1 and y-1). Because asymmetry is one of the dominant sources ofuncertainty in the occulting galaxy extinction measure, a shift of the center of these models isa straightforward way to estimate the uncertainty in method C’s optical depth measurement.The fit of the center of these galaxies is unlikely to be off by more than a pixel. Figure 9shows the differences between the optical depth map values in the overlap region in Figure5. The change in optical depth as a result of a pixel shift is less than 0.05 magnitude. Theuncertainty is less than the difference with Method A or B Figure 8) and it is likely ofsimilar order as the uncertainty due to asymmetry in the general structure of both galaxies(see Figure 4). 9 –
The distribution of extinction values is an essential prior to the Bayesian fits of SN1alightcurve fits (see discussions in Wood-Vasey et al. 2007; Jha et al. 2007, their AppendixA). The Bayesian approach with an extinction prior was first used by Riess et al. (1996) andin much subsequent work. However, the well-known danger of using the extinction prior isthat it may be in error and, thus, propagate systematic errors into the final distance estimate.The models by Hatano et al. (1998), Commins (2004), and Riello & Patat (2005) show thatfor late-type galaxies, the likelihood distribution for extinguished lines of sight follows anexponential function with a maximum at zero extinction: n = n e − τ/τ . (3)The common exponential scale used is τ = 0.5 in Johnson V . Jha et al. (2007) use a seriesof Monte-Carlo simulations to characterize the effect of a wrong prior and conclude it canresult in a significant bias in the distance scale.In Figure 10, we show the distribution of extinction values for Method C, along withexponential fits to the positive values. The τ values decrease with wavelength as expected: τ is 0.28, 0.15, and 0.09 for F W , F W , and F W , respectively. These decay ratesare much smaller than the value of 0.5 commonly used as the SNIa prior. Moreover, thedistributions do not continue to rise as an exponential all the way to no extinction. Thepeak in distribution at zero extinction is smeared somewhat by measurement uncertainties.However, assuming that equation 3 holds for all values of τ would lead one to overestimatethe fraction of the disk that has low extinction values.The caveats are that the distribution we measure, is not necessarily the same thatthe one SNIa experience. Our distribution is for the outskirts of a smaller late-type spiraland includes extinction by dust through the entirety of the disk’s height, rather than forwhat one might expect for an embedded source. On the other hand, our area weightedmeasurement may be representative for a smooth distribution of sources, such as one mightexpect for an old population of SNIa precursors. An additional issue is the z -distributionsof dust and the target objects. The three-dimensional distribution of SN Ia then factorsinto how the extinction statistics should be used to form a prior. We hope to obtain a largesample of optical depth distributions in occulting pairs with HST data to further specifythese distributions and their variance among spirals. 10 – The most remarkable feature of this overlapping pair is the extraordinary radial extentof dust in the foreground spiral. Using the extinction maps in Figure 5, we examine thedistribution of extinction values as a function of the projected radius from the center of theforeground galaxy. Figure 11 shows dust opacity vs. radius for the overlap region shown inFigure 5, and for the larger range in radii both derived with Method C (Figure 6). Startingat ∼ ∼ R = 4 R ) in all three filters can be attributed tothe spiral arm visible in the optical depth maps as a single dark feature in Figure 5, whichcrosses the azimuth of the brightest background light and is thus detected with high S/N.The signal of two secondary spiral arms can be seen at 2.5 and 5.5 R . At small radii,the extinction appears to decline. However, at these radii, we have few pixels and the mostsignificant contribution from light emitted by the foreground spiral and the least flux by thebackground galaxy.Figure 11 shows the radial plot that can reliably be derived over the entire backgroundbulge using Method C (Figure 6). Because we use a model light distribution for the back-ground galaxy flux estimate rather than rotating the galaxy, the extinction profile can beextended to the far side of the center of the background galaxy. Figure 11 averages overa large section, and thus the mean value (dashed white line) emphasizes the R ∼ R extinction feature but averages out any smaller dust structures. The radial profile is similarto other radial extinction plots, for example those derived from the UV/FIR flux ratio byBoissier et al. (2004) or counts of distant galaxies in Holwerda et al. (2005b). However, thisis the first on to be derived for a single galaxy using this technique.Figure 12 shows the average radial profiles for overlap region in Figure 5 derived usingall three methods. The differences in opacity at smaller radii between the three methods isdue to the small coverage of the overlap region at ∼ R and the dominance of foregroundgalaxy structure at these radii in the case of method A. Method B and C are generally in goodagreement because the background bulge is reasonably symmetric. Structures such as thethe extinction in the foreground galaxy’s spiral arms show up well with either method. Nearthe center of the foreground galaxy, Method B is likely less accurate because the assumptionthat the flux from the background galaxy dominates (B >> F) and the use of equation 2 is lessvalid. From Figure 12 we can conclude that all three methods agree well at the intermediateradii, but that closer to the center of the foreground galaxy, method A suffers from samplingeffects and foreground structure and Method B from the less dominant background flux.Hence, Method C has the widest range of places it is applicable in the foreground disk. 11 –
The extinction law can be characterized by its slope R as a function of wavelength. Fora given reddening E(B-V) and extinction A V (= 1.086 × τ V ), R is expressed as: R ≡ A V A B − A V = A V E ( B − V ) . (4)This relation can be generalized to other wavelengths and bandpasses, such as those onHST. We derive the values of R from the model given in Cardelli et al. (1989) for reference inTable 2. Figure 13 plots the values of A F W and A F W vs. A F W for the overlap regionin Figure 5 for Method C. There is a clear relation between the extinction values in thethree filters, similar to the Milky Way extinction relation from Cardelli et al. (1989). Thebootstrap mean and standard deviation of the A F W /A F W and A F W /A F W valuesfor all three methods are in Table 2. The inferred R values are also listed.One expects the observed relation to be grayer than the intrinsic grain properties wouldgive, due to sampling effects at greater distance. If the typical pixel size covers large phys-ical scales, lines of sight with different extinction values are combined into a single mea-surement. The lines of sight with lower extinction dominate the emerging light, biasing thecolor measurement towards less reddened values. This effect is increasingly effective at shortwavelengths, and thus the observed extinction law turns gray. For the system studied here,each pixel covers an area of less than 57 ×
57 pc, assuming the foreground galaxy is at theredshift of the background galaxy. Keel & White (2001a) report that the extinction law isgrayer when sampled over physical scales greater than approximately 60 pc. Our consistencywith the Milky Way extinction law in this pair is consistent with this conclusion.In Figure 13, we use Method C extinction map to explore the relation between thereddening-extinction relation and sampling, given that Method C retrieves a reasonablywell-defined extinction law. We average the model and data over 2 × × . ′′ . ′′ R values for the averaged images are also listed in Table2. There is a trend towards a grayer extinction law, as expected. From the inferred relationbetween extinction and filter, we can conclude that one is likely to see deviations from theMilky Way extinction law in external galaxies due solely to the effects of sampling. Thecritical point is when the extinction and color are measured averaged over a physical scalegreater than 60 pc. 12 –
5. Discussion
This serendipitously discovered pair of occulting galaxies is in a nearly perfect geometryfor the analysis of dust extinction. The other advantages are high-quality HST observationsin three filters with long integration times. This particular pair is therefore ideal for con-straining dust properties at larger radii as well as for testing three different approaches foranalyzing occulting pairs.The radial extent of the dust in the foreground disk is the most striking feature of thepair. In a part of the disk where there is barely any light from the foreground galaxy, thereis significant structured extinction evident in the spiral arms, readily visible in the colorimage (Figure 2). At the corresponding radius on the other side of the disk, even theselong exposures do not detect starlight, indicating that the cold dense ISM extends well pastthe optical limit of the disk. The presence of significant amounts of dust at these radiialso suggests that substantial quantities of metals have been transported well outside thestarforming regions, either through radial mixing or a galactic fountain.If this is the typical size of a spiral’s dusty ISM, it has implications for studies involvinglines-of-sight to the distant universe (e.g., Trenti & Stiavelli 2006; Robaina & Cepa 2007) orcomputed SN1a rates (e.g., Hatano et al. 1998; Cappellaro et al. 1999; Goobar et al. 2002;Riello & Patat 2005; Mannucci et al. 2007). The typical optical depth at R is also criticalfor the Tully-Fisher relation in diameter-limited samples. From the inclination effects onlarge samples, it is commonly inferred that spiral disks are optically thin ( τ << .
1) atthis radius, but it depends greatly whether a spiral arm intersects R , as it does in ourforeground galaxy.Spiral arms are easily identifiable in the optical depth maps in Figure 5 and in the radialprofiles in Figure 11 and 11. The width of the arms in the optical depth maps appears tobe of the order of 0.5 R (0.6 kpc), with three arms showing in the radial plots between2 × and 6 × R . The typical value of opacity in the disk depends on the filter; the bluestfilters, F W and F W , have a typical optical depths of 0.25, while in F W it is 0.15(Figure 7). The range in optical depth values becomes much larger in the spiral arms.The extinction distribution in a spiral disk has wide implications for other observationsof spiral galaxies, both nearby and at higher redshift. We find different distributions for ourdifferent methods, but Method C seems the best constrained, and the extinction distributionrises smoothly to τ = 0 for Method C. In the case of Method C, the distribution can bewell modeled with an exponential. Compared with the distribution of values commonly usedfor SNIa light curve fits, these fall off more steeply with increasing τ . More occulting pairswould be needed to accurately describe the distribution in just the spiral arms and over a 13 –range of Hubble types and redshifts. This distribution could then be used to form priors forthe SNIa lightcurve fits. The best approach for analyzing an occulting pair depends very much on the type ofpair and the quality of the data. For poorly resolved data, Methods A and B are moreattractive because their drawbacks –the effects of substructure– are less pronounced. Themain attractions of Methods A and B are the speed at which they can be applied. In thecase of higher resolution data, such as these HST images, Methods B and C make moresense because there is enough information in the image to derive results. Method B doesrely on the assumption that there is little flux from the foreground galaxy, which in this caseonly holds true at larger projected radii away from the foreground galaxy center. MethodC allows us to estimate optical depth to higher radii and estimate the contribution by theforeground galaxy closer to the foreground’s center. When the data quality permits, thistechnique is preferred.None of the approaches we tested can be completely automated at present. All ap-proaches require the position of an aperture in which to measure the optical depth in apoorly resolved pair. Method B’s assumption needs to be validated and Method C requirersvisual masking of sections affected by extinction or structure. We mostly automated MethodA for Holwerda et al. (2007c), and an new automated version of Method C could be appliedto occulting pairs of various galaxy types found by the GalaxyZOO project or at higher red-shift HST surveys such as DEEP2 and COSMOS. In this case, a S´ersic model or isophotalprofile of both galaxies would be part of the fit solution to the image of the pair.
6. Conclusions and Future Work
From this occulting pair with a nearly ideal geometry, serendipitously imaged by HST,we can learn the following:1. Most of the disk is optically thin ( τ <
1) in F W , F W and F W , from 3 R to 10 R (Figures 7 and 11).2. The distribution of optical depth values follows an exponential with scales of 0.28, 0.15,and 0.09 for F W , F W , and F W respectively (Figure 10). At lower opticalvalues close to zero, the exponential distribution overpredicts this distribution some. 14 –3. Measurable extinction extends to six half-light radii or well beyond the optical disk(1.5 R ) of the foreground spiral (Figure 11 and 11).4. Spiral structure is visible as regions of high extinction beyond R (Figures 5 and 11),confirming that there is a dense cold ISM confined to spiral arms, even at large radii.5. The slope of the observed extinction law is similar to the Milky Way extinction law(Figure 13 and Table 2).6. Averaged over physical scales greater than 60 pc., the observed extinction law is grayer,because the observed light is biased towards the low-extinction lines-of-sight (Figure13 and Table 2).7. All three approaches for measuring optical depth have their specific uses, and eitherMethod A or C could be used effectively for future automated analysis of large samplesof occulting pairs.8. If the data is of high enough quality, Method C is to be preferred, because it introducesless noise. Asymmetry and substructure are the dominant sources of uncertainty inthe other two methods (section 5.1)9. Due to the likely 30 ◦ inclination of the foreground spiral, the optical depths we mea-sured are likely to be 15% higher than for a perfectly face-on geometry.For future studies, one would need a very large sample, such as the 800 occulting pairsidentified by the Galaxy Zoo project (Raddick et al. 2007; Lintott & the GalaxyZOO team2008) in the Sloan Digital Sky Survey, or the many occulting pairs in high-redshift HSTimaging surveys, such the Extended Groth Strip and COSMOS (Koekemoer et al. 2007).With such a large sample, the effect of inclination of the foreground disk on the observedoptical depth and the evolution of optical depth since a redshift of one can be determined(Holwerda et al. 2007b, 2008).The authors would like to thank Ron Allen for useful discussions and Kristen Keener forher comments and edits. The authors would like to thank Zolt Levay for Figure 2. W. C. Keelacknowledges support from a College Leadership Board faculty fellowship. J.J. Dalcantonand B. Williams were partially supported by a grant from NASA (GO-10915), throughthe Space Telescope Science Institute, which is operated by the Association of Universitiesfor Research in Astronomy, Inc., under NASA contract NAS 5-26555. J.J. Dalcanton waspartially supported by a Wyckoff Faculty Fellowship. Based on observations made with theNASA/ESA Hubble Space Telescope as part of program GO-10915, P.I. J.J. Dalcanton. 15 – REFERENCES
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Table 1: Basic data on the foreground and background galaxies in Vgalaxy RA Dec m V PA Incl. R deg. deg. mag deg. deg. pixelforeground 12.088910 -25.126517 18.15 66.7 29.2 21.1background 12.090799 -25.126916 16.5 -48.9 30.9 32.7Table 2: The ratio of A F W and A F W over A F W and the corresponding R values: R F W − F W = A F W / ( A F W − A F W ) and R F W − F W = A F W / ( A F W − A F W ). The equivalent values for Cardelli et al. (1989) are given and those for the re-sampled Method C (Bin 2 and 4). The bootstrap mean and uncertainty are determined forthe optically thin ( A > , A <
1) values.Origin A F W /A F W A F W /A F W R F W − F W R F W − F W CCM 1.297641999 1.671395795 3.36 2.49Method A 1.2 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± This preprint was prepared with the AAS L A TEX macros v5.2.
20 –Fig. 1.— The position of our occulting pair with respect to NGC 253. The Digitized SkySurvey image of NGC 253 retrieved from NED. The blow-up is a grayscale version of thecolor image, Figure 2. 21 –Fig. 2.— The RGB color composite of the pair with F W for blue, F W for green,and F W for red. The RGB stars of the halo and disk of NGC 253 contaminate theforeground. The effect of the foreground galaxy’s dust can be seen extending to the centerof the central background galaxy. Image thanks to Zolt Levay of the Hubble Heritage Team. 22 – F’