Scale Length of Disk Galaxies
Kambiz Fathi, Mark Allen, Eduardo Gonzalez-Solares, Evanthia Hatziminaoglou, Reynier Peletier
11 SCALE LENGTH OF DISK GALAXIESKambiz Fathi , Mark Allen , Eduardo Gonzalez-Solares , Evanthia Hatziminaoglou , and Reynier Peletier Department of Astronomy, Stockholm University, 106 91 Stockholm, Sweden Observatoire de Strasbourg, UMR 7550 Strasbourg 67000, France Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UK European Southern Observatory, Karl-Schwarzschild-Str. 2, 85748 Garching bei M¨unchen, Germany Kapteyn Astronomical Institute, Postbus 800, 9700 AV Groningen, The Netherlands
ABSTRACT
As a part of a Euro-VO research initiative, we have un-dertaken a programme aimed at studying the scale lengthof 54909 Sa-Sd spiral galaxies from the SDSS DR6 cat-alogue. We have retrieved u, g, r, i, z -band images forall galaxies in order to derive the light profiles. We alsocalculate asymmetry parameters to select non-disturbeddisks for which we will derive exponential disk scalelengths. As images in different bands probe differentoptical depths and stellar populations, it is likely that aderived scale length value should depend on waveband,and our goal is to use the scale length variations withband pass, inclination, galaxy type, redshift, and surfacebrightness, in order to better understand the nature of spi-ral galaxies.Key words: Virtual Observatory, Galaxies: Structure.
1. INTRODUCTION
The exponential scale length of a galaxy disk is one ofthe most fundamental parameters to determine its mor-phological structure, as well as to model its dynamics,and the fact that the light distributions are exponentialmakes it possible to contrain the formation mechanisms(Freeman 1970). The scale length determines how thestars are distributed throughout a disk, and can be usedto derive its mass distribution, assuming a specific M/Lratio. Ultimately, this mass distribution is the primaryconstraint for determining the formation scenario (e.g.,Dutton 2008, and references therein), which dictates thegalaxy’s evolution. As the galaxy evolves substructuressuch as bulges, pseudo-bulges, bars, rings, and spiralarms may build up, which in turn considerably change themorphology of the host disks (e.g., Combes & Elmegreen1993). Analytic disk formation scenarios (e.g., Lin &Pringle 1987) predict that in cases where angular momen-tum is conserved, the disk scale length is determined by the the angular momentum profile of the initial cloud, andthe scale length in a viscous disk is set by the interplaybetween star formation and dynamical friction (e.g., Silk2001). These processes form the basis of a galaxy’s grav-itational potential and the strength of gravitational pertur-bations, the location of resonances in the disk, the forma-tion and evolution of spiral arms and bars, and the dy-namical feeding of circumnuclear starbursts and nuclearactivity (e.g., Elmegreen et al. 1996; Fathi et al. 2008).Photometrically, the scale length is derived by az-imuthally averaging profiles of the surface brightnesswhich is in turn decomposed into a central bulge and anexponential disk, accounting for other components suchas bars and rings.As images in different bands probe different opticaldepths and stellar populations, it is likely that a derivedscale length value should depend on waveband. Dustydisks are more opaque and often deliver larger scalelength values in bluer bands when compared with redand/or infrared images. Similar effects can also be causedby the stellar populations. These observational effectsthus not only give us insights about the disks that weare studying, but also need to be quantified for a bettercomparison between different data sets and galaxy types.Both the effects of stellar populations and dist extinctionhave been subject to much discussion over the years (e.g.,Simien & de Vaucouleurs 1983; Valentijn 1990; van Drielet al. 1995; Peletier et al. 1995; Beckman et al. 1996;Prieto et al 2001; Graham & de Blok 2001; MacArthur2003; Cunow 1998, 2001, 2004). A detailed and exten-sive analysis of the dust effects has also been presentedfor a few tens of galaxies in Holwerda (2005) and subse-quent papers, however, as noted by Peletier et al. (1994)and van Driel et al. (1995), the scale length alone indifferent band passes in small sample cannot be used tobreak the age/metallicity and dust effects. Investigatingthe scale length variation as a function of inclination forlarge numbers of galaxies is necessary to distinguish be-tween the dust and population effects. a r X i v : . [ a s t r o - ph . C O ] J u l Table 1. Sample sizes for the work mentioned in the text(in alphabetic order).
Reference Number of galaxiesCunow (1998, 2001, 2004) 14, 60, 39Graham & de Blok (2001) 120MacArthur et al. (2003) 121Peletier et al. (1995) 37Prieto et al. (1996) 15Simien & de Vaucouleurs (1983) 98van Driel et al. (1995) 55The common denominator in all the previous studies isthe roughly comparable sample sizes. Most studies haveso far analysed individual galaxies, or samples contain-ing a few tens of galaxies (see table 1). This is not tobe mistaken with the number of great results from theSloan Digital Sky Survey (SDSS) studies in the last years,but these works have not studied the astrophysical effectsmentioned here. We have undertaken a programme thataims at quantifying how the disk scale length varies withband pass, inclination, galaxy type, redshift, and surfacebrightness. We have searched the entire SDSS Data Re-lease 6 (DR6) data set and have selected 54909 spiralgalaxies suitable for our analysis. Here, we present adescription of our study along with some preliminary re-sults.
2. SAMPLE SELECTION
The sample was selected by searching the SDSS DR6catalogue and cross matching with the LEDA catalogue(Paturel et al. 2003) to retrieve Hubble classifications. Asthe SDSS provides a number of morphological as wellas kinematic parameters, which we use to constrain oursample against biases. Our first requirements ensure thatfor each galaxy we have reliable redshift measurement,low extinction, and number of pixels sufficient to derivea light profile with a good coverage of the disk region.Moreover, we decided to ensure that our galaxies do notcontain edge-on or face-on galaxies to avoid selection ef-fect problems. We first retrieved tabular data for all SDSSgalaxies for which excellent image quality is delivered,are larger than 30 pixels, spectroscopic redshifts are avail-able, have extinction A V ≤ . mag, have inclination ◦ < i < ◦ . We retrieved a total of 475408 galax-ies, and first investigated the smallest numbers of pixelsneeded to resolve the disk. We found that a minimum of70 pixels are needed, thus removed all galaxies with ma-jor axis (in r -band) smaller than 70 pixels (28 arcsec) toensure that the images cover the disk region.We made use of LEDA by first retrieving the entire cat- http://leda.univ-lyon1.fr/ Figure 1. Top: Right ascension and declination distribu-tion of the SDSS sample fulfilling the first sorting criteria(i.e., galaxies with spectroscopic redshift, larger than 10pixels, extinction smaller than A V = 1 . , and with incli-nation between ◦ and ◦ ), Middle: The total LEDAcatalogue for which the LEDA services provide a hubbleclassification number (0=S0a, 1=Sa, 2=Sab, etc.), andBottom: Our final sample fulfilling all our selection cri-teria described in the text. Figure 2. Distribution of some key parameters (magnitude, Galactic extinction, major axis, redshift, velocity dispersion,and morphological type) retrieved from the SDSS and LEDA database. alogue. As this service provides a numeric Hubble clas-sification parameter, we could easily select all the spiralgalaxies, which we later cross-correlated with the SDSScatalogue. We found a total of 54909 Sa-Sd spiral galax-ies (see Fig. 1), for which all the morphological and spec-troscopic parameters from SDSS and LEDA were stored,and u, g, r, i, z -band images were to be downloaded. Itshould be noted that at this stage, we are unable to de-termine whether the galaxies in our sample are isolatedor disturbed systems, as this information is not providedby any of the catalogues we have used. We make thisdistinction using the asymmetry parameter described inConselice (2003).The first question that rises at this point is the fact thatSDSS delivers the disk scale length as well as de Vau-coulers effective radius for each galaxy (in all bands), andthat these values could be used to carry out or analysis.In Fig. 2, we show that the values provided by the SDSSteam show anomalies that are beyond our satisfaction forcarrying out our analysis. The plot shows a strange ”clus-tering” of the effective radii and scale lengths aroundsome numbers, the source for which we cannot find. Wethus decide to re-calculate the scale lengths.Various Virtual Observatory (VO) methods were investi-gated to perform the download of the SDSS images. TheSkyView was chosen for this task. This service has theadvantage of being able to create fits files centred at agiven sky coordinate and with a pre-specified size. Theimage size is an important parameter for achieving a re-liable an accurate sky subtraction, thus we require that http://skyview.gsfc.nasa.gov/ Figure 3. De Vaucouleurs effective radius ( y -axis) versusdisk scale length ( x -axis) provided by the SDSS team forall 54909 galaxies in our final sample. Although thesenumbers are good first guesses, the odd clustering of thedata points lead us the to conclusion that we re-derive thescale lengths. The insets illustrate the strange clusteringof the points (coloured data points) provided by the SDSS. Figure 4. Illustrating the fits to the different regions of the light profile. Fitting different regions results in different scalelength values, and as shown in the bottom right panel, fitting over the entire galaxy reproduces the value provided bythe SDSS, which is illustrated by the ”blue” line (arbitrarily shifted (in y -axis). Printed at the top of each panel, is thecorresponding scale length value. the images are × pixels for the sky region to besampled for all galaxies. Moreover, SkyView is able tore-scale the image backgrounds to the same level, hencecorrecting for differences between the SDSS plates. Wehave experienced that a linear image download could bea tedious process. With an image size of 3.2 MB/image,and at a constant rate of 0.2 MB/s, the download wouldrequire at the very best and with a continuous connection ≈ days. We have therefore carried out the downloadusing multiple parallel data requests to the SkyView ser-vice using the python scripting language, and utilising 3individual computers. This allowed us to download thefull sample over approximately 13 days.
3. DERIVING THE LIGHT PROFILE
We derive the disk scale length using standard IDL rou-tines and make use some important parameters includedin the SDSS information in order to constrain galaxy ge-ometry as well as the location of the sky region. Theseare iso B , iso A , iso P hi , and for consistency, we use thesequantities in r -band. The procedure carries out the fol-lowing steps: • Reading the image, and calculating the asymmetryparameter A = (cid:80) ( I − I ) / (cid:80) I , where I is thegalaxy image and I is the image rotated by 180degrees around the galaxy centre. • Selecting the sky region as the ellipse encompass-ing the region between . ∗ iso A and . ∗ iso A .The mean value of this region, using Tukey’s bi-weight mean formalism described in Mosteller &Tukey (1977), is used for the sky subtraction as wellas setting the background level. • To remove nuisance stars and point sources fromthe image, we extract point sources with SExtractor(Bertin & Arnauts 1996), but storing pixels belong-ing to all point sources that are larger than 4 pixelsand more than 3 σ above the background level. Allpixels belonging to these sources are then maskedout. • Using the iso B , iso A , iso P hi parameters fromSDSS, we then section each galaxy into 2-pixelswide ellipses oriented at iso
P hi and with minor-to-major axis ratio b/a = iso B /iso A . The mean sur-face brightness value within each ellipse is calcu-lated, to compile the galactocentric light profile foreach galaxy image. • As experience has shown that light profile decompo-sition in a disk together with any other component(e.g., Fathi et al. 2003) introduces complicationsthat are not necessary for the nature of our analy-sis. We thus derive the disk scale length simply byfitting an exponential profile to the disk region ofeach galaxy. We determine the region of interest byempirically fitting eight different regions covering
Figure 5. Scale lengths for a sub sample of 1315 ran-domly selected galaxies in u , r , i , and z -band. Here, fitsto three different disk regions are plotted to show that fit-ting some outer region is not necessarily the best strategy.The relatively large scatter in the top and bottom panelsalso demonstrate that the images are not very deep in u and z bands. At the bottom right corner of panel, thefitted regions are printed, where 0-120% means that thelight profile between galactocentric radius of r = 0 ∗ iso A and r = 1 . ∗ iso A was fitted by one single exponentialprofile, etc. . the range between 15%-30% and 85%-115% of the iso A parameter. This procedure means that we aresimply cutting out the central regions of the galaxieswhere bulges and strong bars are expected. Fig. 4shows the result of such a test where we find that(in many cases) we are able to derive a scale lengthcomparable to the value from the SDSS catalogue. Itshould be noted that this plot is only for one galaxy,and for regions outside what is noted here, and wehave tested more regions than the eight regions de-tailed above here.Assuming that the r and i -band images probe similar stel-lar populations and dust content, we are able to use thecorrelation of the scale length values between these bandsto find the optimal region for deriving the scale lengths.Fig. 5, illustrates for a preliminary and randomly selectedsub-sample of 1315 galaxies, that using a small outer re-gion is not the best way to derive the scale length, but forthis sub-sample is seems that fitting the galaxy light pro-file over . ∗ iso A gives the best result. We plan to carryout this test for the entire sample.
4. CURRENT STATUS
We have currently downloaded the u, g, r, i, z images forall 54909 galaxies, and we are in the process of calcu-lating the scale length using different regions from eachimage. With the data at hand, we will be able to firstremove highly asymmetric galaxies to minimise the useof disturbed disks. We will then derive the disk scalelengths for all the ”isolated” disk galaxies, and statisti-cally explore how this parameter changes as a functionof inclination, band, redshift, etc. Moreover, we plan tocross-correlate our sample with the Two Micron All SkySurvey to further explore the scale lengths also in
J, H, K bands and to further explore the dust and stellar popula-tion effects.
ACKNOWLEDGMENTS