bulge-disk decomposition of 659 spiral and lenticular galaxy brightness profiles

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THE ASTRONOMICAL JOURNAL, 116:1626 È 1642, 1998 October1998. The American Astronomical Society. All rights reserved. Printed in U.S.A.(

BULGE-DISK DECOMPOSITION OF 659 SPIRAL AND LENTICULAR GALAXY BRIGHTNESS PROFILES

W. E. BAGGETT

Science Programs, Computer Sciences Corporation, 3700 San Martin Drive, Baltimore, MD 21218

S. M. BAGGETT

Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218AND

K. S. J. ANDERSON

Department of Astronomy, New Mexico State University, P.O. Box 30001, Department 4500, Las Cruces, NM 88003

Received 1996 October 21; revised 1998 June 29

ABSTRACT

We present one of the largest homogeneous sets of spiral and lenticular galaxy brightness proÐledecompositions completed to date. The 659 galaxies in our sample have been Ðtted with a de Vaucou-leurs law for the bulge component and an inner-truncated exponential for the disk component. Of the659 galaxies in the sample, 620 were successfully Ðtted with the chosen Ðtting functions. The Ðts aregenerally well deÐned, with more than 90% having rms deviations from the observed proÐle of less than0.35 mag. We Ðnd no correlations of Ðtting quality, as measured by these rms residuals, with either mor-phological type or inclination. Similarly, the estimated errors of the Ðtted coefficients show no signiÐcant

trends with type or inclination. These decompositions form a useful basis for the study of the light dis-tributions of spiral and lenticular galaxies. The object base is sufficiently large that well-deÐned samplesof galaxies can be selected from it.

Key words : galaxies: photometry È galaxies: spiral

1. INTRODUCTION

In order to compare the large-scale characteristics of gal-axies objectively, quantitative measures of the structuralcomponents are necessary. There are many schemes fordescribing the structure of galaxies, including Hubble classi-Ðcation isophotal radii(Sandage 1961), (Holmberg 1958),concentration parameters Okamura,(Kent 1985; Kodaira,& Ichikawa hereafter and the use of various1990, PANBG),

Ðtting functions Vaucouleurs(de 1953 ; Freeman 1970 ;All these techniques specify parametersKormendy 1977).that can provide insight into the formation and evolution of galaxies. The use of standardized Ðtting functions is argu-ably the most powerful method for measuring the large-scale structure of galaxies, as the functions yield a variety of parameters that can be easily compared with the results of theoretical models. They also provide a reasonably detaileddescription of the radial light distribution with a smallnumber of parameters.

Ideally, Ðtting functions would be based upon the physicsof the formation and evolutionary processes. Unfortunately,these processes are neither simple nor well understood, sothe most commonly used functions are derived empirically.

Traditional Ðtting functions for elliptical galaxies and spiralgalaxy bulges include the Hubble law the(Hubble 1930),King model and de Vaucouleurs law Vau-(King 1966), (decouleurs Recently, there has been some work that1953).suggests that a generalized version of the de VaucouleursproÐle (r1@n) provides for better bulge Ðts Pele-(Andredakis,tier, & Balcells and that late-type spirals often have1995),bulges that are best Ðtted by exponentials &(AndredakisSanders Exponentials and inner-1994). (Freeman 1970)truncated exponentials work well for the(Kormendy 1977)disk components of spiral galaxies. Overall, the de Vaucou-leurs law seems to be quite e†ective as a Ðtting function forbulges; it can be written as

IB

(r) \ Ie

10~3.33*(r@re)1@4~1+ , (1)

where is the surface intensity of the bulge at radius r,IB

(r)is a characteristic radius deÐned to be the radius withinr

ewhich half the total light is emitted, and the e†ectiveI

e,

intensity, is simply the surface intensity at (In this paper,re

.we will consistently use the term ““ surface intensity,ÏÏ I, tomean linear intensity units per square arcsecond, and““ surface brightness,ÏÏ k, to mean the same quantity in mag-nitude units.) Similarly, the inner-truncated exponential isdeÐned by asKormendy (1977)

ID

(r) \ I0

exp M[[r / r0

] (rh / r)n]N , (2)

where is the disk surface intensity at radius r, is theID

(r) I0

central intensity of the disk, is the disk scale length, andr0

rh

is the radius of the central cuto† of the disk (““ hole radius ÏÏ) ;the pure exponential disk is the same as withequation (2)

found that a value of nD 3 in therh \ 0. Kormendy (1977)

truncation term works well, and we have adopted n \ 3 forall of the Ðts presented here. illustrates the useful-Figure 1ness of including a truncation term in the Ðtting function,using NGC 3145 as an example.

Others have used these Ðtting functions to obtain therelevant structural parameters for spiral galaxies in orderto compare galaxies of di†erent types, luminosities, andenvironments. For example, Ðtted bright-Boroson (1981)ness proÐles for 26 nonbarred spiral galaxies in order todetermine how the bulge-to-disk ratios are related to theHubble types and to investigate the relationship betweenspiral and S0 (lenticular) galaxies. performed aKent (1985)similar analysis using 105 intrinsically luminous galaxies of all types. decomposed the brightness pro-Kormendy (1977)Ðles of seven compact S0 galaxies and one ““ normal ÏÏ galaxyto check hypothesis of a constant centralFreemanÏs (1970)disk surface brightness. More recently, Jong inves-de (1996)tigated the result of a constant centralFreeman (1970)surface brightness of disks, and some other relationshipsbetween the Ðtting parameters and the Hubble sequence,using B- and K-band brightness proÐles of 86 face-on disk

1626



BULGE-DISK DECOMPOSITION 1627

FIG. 1.ÈBrightness proÐle Ðts to the NGC 3145 data. Both plots show the bulge component, the disk component, and the sum of the two. The horizontalline at 25.3 V -mag arcsec~2 indicates the range of radius included in the Ðt. L eft : Fit without a truncation term in the disk component; the rms deviation of this Ðt is 0.28 mag. Right : Fit including the truncation term in the disk component; the rms deviation of this Ðt is 0.12 mag.

galaxies.A relatively recent innovation is to Ðt a surface to the

entire galaxy image & Freeman using the(Byun 1995)above Ðtting functions and also solving for the center andellipticity of the projected distributions. A general advan-tage of this approach is that the bulge and disk componentscan be allowed to have di†erent ellipticities, which alleviatesthe problem of projection e†ects for moderate- to high-inclination systems: because the rounder bulge is typicallysampled at a smaller galactocentric radius than the inclineddisk for a given position in the image, the derived bulgeparameters are systematically too large when estimatedfrom brightness proÐles obtained by azimuthal averagingtechniques. However, the proÐles used here are major-axiscuts (see below), so this difficulty should not a†ect our Ðttedparameters The cost of using major-axis(Burstein 1979).cuts is that of throwing away much of the information in theimages.

All of these programs except KormendyÏs (1977)employed a simple exponential to describe the disk lightdistribution. As part of a study of the origin of inner-truncated spiral galaxy disks, or type II brightness proÐles

we have used the de Vaucouleurs law and(Freeman 1970),the inner-truncated disk (ITD) Ðtting function from

for the bulge-disk decomposition of 659Kormendy (1977)spiral and lenticular galaxy brightness proÐles. Our prelimi-nary study Baggett, & Anderson indicated(Baggett, 1993)that a substantial fraction of all spiral galaxies exhibit aninner truncation, so the inclusion of such a term in theÐtting function seems justiÐed with this large set of bright-

ness proÐles. Furthermore, the data set used in this study isextremely homogeneous, all images having been obtained,reduced, and analyzed in the same way. Thus, the results of our Ðtting should be a useful resource for many studies of the large-scale properties of disk galaxies. The followingsections will describe the data and the bulge-disk decompo-sition procedures and will present the Ðtting results togetherwith a discussion of the associated errors.

2. DATA

The brightness proÐles used for this study were obtainedfrom the in a machine-readable form. The initialPANBG

sample of galaxies was selected on the basis of PANBGbeing included in the Revised Shapley-Ames Catalog of Bright Galaxies & Tammann hereafter(Sandage 1981,

and being north of declination [25¡. Of the 911 suchRSA)galaxies in the 791 are included in the andRSA, PANBG,659 of those have Hubble types (T -types) from the ThirdReference Catalogue of Bright Galaxies Vaucouleurs et(deal. hereafter in the range [3 to 9, which indi-1991, RC3)cates that they are spiral or lenticular galaxies. These 659galaxies form the basis of our study.

Galaxies in the were observed photographicallyPANBGover a period of almost two decades (late 1970s through1988) with the Kiso Observatory 1.05 m Schmidt telescope,using Kodak IIa-D plates and a Schott GG 495 glass Ðlterto deÐne the ““ photographic V band.ÏÏ Exposure timesranged from 30 to 60 minutes, with 50 minutes being stan-dard, and the plates were developed in Fuji Pandol orKodak D-19 developer. The plates were then digitized with



1628 BAGGETT, BAGGETT, & ANDERSON Vol. 116

the Kiso Observatory PDS microdensitometer utilizing a 1Asquare aperture, except for NGC 224 and NGC 598, whichwere measured with a 10A square aperture. Each plateincluded a step wedge image that was scanned in the samefashion as the galaxy images. Measured densities were con-verted into relative intensities via the wedge calibrator, andthe aperture photometry from & de VaucouleursLongo

was then used to transform the resulting magnitudes(1983)

to a standard photometric system. The stated internalphotometric accuracy in the is about 0.1 magPANBG(standard deviation) and is dominated by errors in theabsolute calibration.

The brightness proÐles in the were obtainedPANBGfrom the resulting calibrated images by taking a cut alongthe apparent major axis of each galaxy. The major axis wasdeÐned by Ðtting the 25 V -mag arcsec~2 isophote with anellipse whose center was Ðxed at the center of gravity of a21] 21 pixel region around the apparent nucleus of thegalaxy. The surface brightness was then sampled along thisaxis using a circular aperture that was stepped outwardfrom the galaxy center in 2 pixel steps (2A for all but NGC224 and NGC 598, which used 20A steps). The aperture usedwas 2 pixels in diameter at the galaxy center, and the diam-eter was varied in such a way as to be tangent to a sectorwith a 5¡ vertex angle centered on the major axis. Thisscheme of varying the aperture size was chosen to com-pensate for the decreased signal-to-noise ratio in the outerportions of the galaxies. As a result, there is some radialsmearing of the intensity information at large galactocentricradii, smoothing structure in the outer portions of eachproÐle. Further smoothing results from our averaging of thetwo halves of the major-axis cut to produce the Ðnal pro-Ðles. For full details of the data acquisition and reductionprocesses, the reader is referred to the PANBG.

3. FITTING

3.1. Procedure

The major-axis brightness proÐles were Ðtted using acombination of a Vaucouleurs law (eq. [1]) and ande (1953)inner-truncated exponential eq. [2]). The(Kormendy 1977 ;interactive STSDAS task NFIT1D was used for all of theÐtting; this task uses the downhill simplex algorithm forperforming a nonlinear least-squares Ðt of the data to aspeciÐed function and allows interactive control over theinclusion of the various parameters and the range of thedata to be Ðtted. It is a very Ñexible routine, and we foundthat it accurately returns the values of the Ðtting parametersin a number of test cases. Fitting is performed on the surfaceintensity data and is accomplished by minimizing the

weighted rms deviation of the data from the Ðt.The most appropriate weighting function, is one thatw

i,

uses the variance of the intensity measurement for eachpoint as its basis, with the weight of the ith point being

wi \

1

pi2

, (3)

where is the variance of the ith point 1969,pi2 (Bevington

p. We chose to use a weighting based on the Poisson184).distribution, where as this was consistent with thep

iP I1@2,

fashion in which the intensity measurements were obtained.An unfortunate side e†ect of this weighting function1/ I

iis that it destroys the usefulness of the weighted rms residualas a goodness-of-Ðt measure between galaxies. The value of

the weighted rms residual is highly dependent upon theÐtting range, with Ðts to lower surface intensities being vir-tually guaranteed a lower weighted rms value than Ðts stop-ping at higher surface intensities. As a result, the weightedrms residual is a useful diagnostic only during the Ðttingprocess for a given galaxy, and, as such, the weighted rmsvalues for each Ðt are not reported here.

However, one can compute the unweighted rms residuals,

after the fact, and we have tabulated([; (ki [kfit)2]/ N)1@2,these values, expressed in magnitude units, as a basis forassessing the relative quality of the Ðts. These residuals werecomputed from the portions of each brightness proÐle atradii larger than 3A and out to the point where the proÐleÐrst drops to a surface brightness fainter than 25 V -magarcsec~2. Hence, all of the calculations avoid the portion of the proÐle most a†ected by seeing and reach the same limit-ing surface brightness. Also, any structure present in theproÐle contributes to this measure, and thus galaxies withsigniÐcant structure will be recognizable by their corre-spondingly larger rms value. In this way, the unweightedrms residuals are directly comparable from galaxy to galaxyand reÑect more accurately the quality of the Ðts than dothe weighted rms residuals.

Aside from the weighting function, the only other con-trolled aspect of the Ðtting was the choice of components toinclude in each Ðt. In general, all Ðts were attempted withboth a bulge and a pure exponential disk, resulting in theestimation of four quantities and their uncertainties: I

e, r

e,

and ITDs, with the additional parameter, wereI0

, r0

; rh,

utilized only if the proÐle had the suggestion of a plateaunear the center. If any component (bulge, disk, ITD) wasÐtted with a negative value for a coefficient, that componentwas deemed nonphysical and was removed from the Ðttingfunction. In cases where the need for a speciÐc componentwas not obvious, Ðts with and without it were obtained, andthe component was included if the weighted rms value wassmaller by at least 10% than the Ðt without the component.

A sample of the results of the Ðtting are presented inwhich provides for each galaxy its NGC/IC design-Table 1,

ation, its revised Hubble type, T -type, and axis ratio fromthe and the Ðt parameters determined here. The ÐtRC3,parameters are given as the Ðtting range in arcseconds (inthe format minimum È maximum), the bulge e†ective surfacebrightness the bulge e†ective radius the disk central(k

e), (r

e),

surface brightness the disk scale length and the(k0

), (r0

),disk hole radius The table also includes the seeing as(r

h).

reported in the and the seeing-corrected values of PANBG,the Ðtted bulge parameters and see The(k

e0 r

e0 ; Appendix).

last two columns contain the unweighted rms deviation of the Ðt from the proÐle in V -mag arcsec~2 and a column of notes. All surface brightness quantities are in units of V -mag arcsec~2, and all radii are in units of arcseconds. Nocorrections for Galactic extinction, internal extinction, orinclination have been applied; the Ðts are for the observedmajor-axis proÐle. We have chosen to present the results forthe observed proÐles in order to allow the reader theopportunity to apply the corrections deemed most appro-priate ; we therefore avoid the necessity of uncorrecting ourÐts and subsequently applying a di†erent correction.

The Ðtting procedure did not include any allowance forthe e†ects of seeing on the brightness proÐle. In the Appen-

we describe an experiment that was designed to quan-dix,tify the impact on the Ðtted bulge parameters of excludingseeing from the Ðtting; the net result is that our Ðtted I

e



No. 4, 1998 BULGE-DISK DECOMPOSITION 1629

TABLE 1

SAMPLE GALAXY FIT PARAMETERS

Galaxya Typeb T c R25

d Rangee kef r

eg k

0h r

0i r

hj rmsk Seeingl k

e0 m r

e0 n Noteso

NGC 16 . . . . . . . .LX.-./ [3 0.27 3 È 70 20.83 13 22.41 18.8 . . . 0.07 1 20.67 12.37NGC 23 . . . . . . . .SBS1.. 1 0.19 3 È 58 7.18 0.1 19.83 11.5 . . . 0.21 1 . . . . . . DNGC 148.. . . . . .L..0*/ [2 0.4 3 È 68 12.3 0.4 19.24 12.5 . . . 0.11 5 13.64 0.5NGC 151 .. .. .. .SBR4.. 4 0.34 3 È 65 17.95 2.4 20.93 34.4 . . . 0.54 2 17.88 2.37 A, E

NGC 157 . . . . . . .SXT4.. 4 0.19 3 È 11, 92 È 148 20.85 7.2 20.56 35.8 . . . 0.51 2 20.74 7.01 ANGC 224 . . . . . . .SAS3.. 3 0.49 100 È 5600 19.89 282.2 20.58 1781.2 . . . 0.13 4 . .. . . .NGC 237 .. . . . . .SXT6.. 6 0.24 3 È 8, 27 È 50 . . . . . . 19.99 10.4 . . . 0.17 2 . . . . . . ANGC 245 .. . . . . .SAT3P$ 3 0.06 3 È 46 20.11 3.9 19.24 8.8 10.1 0.12 2 20.02 3.82NGC 253 . . . . . . .SXS5.. 5 0.61 3 È 276, 725 È 936 21.19 18.7 19.51 192.3 . . . 0.4 5 21.3 19.73 ANGC 254 . . . . . . RLXR]*. [1 0.21 3 È 82 15.94 1.4 20.09 18.5 . . . 0.12 5 16.93 1.75NGC 255 .. .. .. .SXT4.. 4 0.08 3 È 70 21.98 12 19.97 14.7 12.5 0.12 2 21.87 11.61NGC 268 .. .. .. .SBS4*. 4 0.14 3 È 52 . . . . . . 19.86 11.2 . . . 0.25 3 . . . . . . DNGC 274.. . . . . .LXR-P. [3 0.01 4 È 40 16.67 2 16.79 5 17.5 0.22 3 16.87 2.11 INGC 278 .. .. .. .SXT3.. 3 0.02 3 È 102 20.36 17.1 . . . . . . . . . 0.19 3 20.32 16.95NGC 289 .. .. .. .SBT4.. 4 0.15 3 È 60 . . . . . . 18.81 14 . . . 1.12 5 . . . . . . A, DNGC 309 .. .. .. .SXR5.. 5 0.08 3 È 74 11.88 0.2 20.9 21.4 . . . 0.25 3 . . . . . .NGC 357 . . . . . . .SBR0*. 0 0.14 3 È 19, 57 È 80 18.5 3.5 22.35 31.5 . . . 0.38 3 18.6 3.62 A, ENGC 404.. . . . . .LAS-*. [3 0 3 È 288 22.15 63.8 23.02 129.5 . . . 0.09 2 22.05 60.86NGC 428 . . . . . . .SXS9.. 9 0.12 4 È 92 . . . . . . 20.19 20.7 . . . 0.12 5 . . . . . .NGC 473 . . . . . . .SXR0*. 0 0.2 3 È 58 19.22 4.2 20.44 13.8 . . . 0.1 5 19.69 4.85NGC 514 . . . . . . .SXT5.. 5 0.1 3 È 94 24.17 38.5 20.97 24.4 13.2 0.12 5 24.21 39.51

NGC 521 .. .. .. .SBR4.. 4 0.04 3 È 94 21.26 10.9 20.9 26.6 20.8 0.1 5 21.46 11.82 FNGC 524 . . . . . . .LAT].. [1 0 4 È 136 21.47 33.6 . . . . . . . . . 0.11 3 21.41 32.92NGC 598 . . . . . . .SAS6.. 6 0.23 3 È 2256 22.71 109.6 20.3 533.3 . . . 0.12 2 . . . . . .

NOTES.ÈA, Prominent arm/bar/ring/dust lane removed from Ðt; B, much structure in proÐle; C, truncated disk Ðt to a bright arm or lens; D, bar nearmajor axis; E, bar near minor axis; F, bar between axes; G, edge-on ; H, box/peanut bulge evident in published image; I, interacting; J, NGC 4891 is notincluded in the but it appears to be listed as NGC 4897. The data listed are those for NGC 4897. Table 1 is presented in its entirety in theRC3, RC3electronic edition of the Astronomical Journal. A portion is shown here for guidance regarding its form and content.

a Galaxy ID.b Revised Hubble type from RC3.c T -type from RC3.

[\log(a / b)] fromd R25

RC3.e Fitting range(s), in units of arcseconds.f Bulge e†ective surface brightness in V -mag arcsec~2.g Bulge e†ective radius in units of arcseconds.h Disk central surface brightness in V -mag arcsec~2.i Disk scale length in units of arcseconds.j Disk truncation radius in units of arcseconds.k Unweighted rms deviation of the Ðt in V -mag arcsec~2.l Seeing in arcseconds from the PANBG.m Fully corrected bulge e†ective surface brightness in V -mag arcsec~2.n Fully corrected bulge e†ective radius in units of arcseconds.o Notes about individual galaxies.

tends to be too large by up to an order of magnitude whenthe seeing is much larger than the input e†ective radius, andour Ðtted tends to be slightly too small in the same cases.r

eThis is what is intuitively expected, of course.

Although the proÐle deÐnition procedure introduces asigniÐcant level of radial smearing, structure is still appar-ent in many of the proÐles. The Ðtting process nominallymade no allowance for the presence of structure, Ðttingacross arms and bars as if they were simply noise in thedata, except in some speciÐc instances. These instancesoccur when a very strong, isolated feature is present; thenthe radial range occupied by the feature was excluded fromthe Ðt. If a strong feature is present at the end of the Ðttingrange, the Ðtting range was suitably shortened. The exis-tence of such a condition was manually determined, and isindicated in by the presence of multiple ranges inTable 1the Ðtting range column and/or by a note (e.g., ““ A ÏÏ) in thelast column of the table.

presents the proÐles and Ðts for the galaxiesFigure 2from Each plot shows the observed proÐle from theTable 1.

as crosses, and the Ðtted bulge and disk com-PANBGponents and their sum as solid lines. In addition, the rangeof radius included in the Ðt is indicated by the horizontal

line(s) at the 25.3 V -mag arcsec~2 level, and the Ðt param-eters are provided near the top of each plot. This selectionof objects includes some very good Ðts as measured by therms deviations (NGC 16, NGC 404), some typical-qualityÐts (NGC 224, NGC 237), some Ðts that avoid strong struc-ture in the proÐle (NGC 151, 157, 253), and one of the worstÐts in the entire sample (NGC 289).

There were 39 galaxies in the sample for which no Ðtswere obtained; these objects are listed in with theirTable 2,revised types and axis ratios from the These galaxiesRC3.are particularly ill-suited for Ðtting by the selected Ðttingfunctions, as many of them have pronounced concavitiestoward low surface brightness or multiple exponential com-ponents in their brightness proÐlesÈthe chosen functionssimply do not represent their light distributions in anymeaningful way.

Finally, there are also several Ðts (e.g., NGC 16, 628, 890,and 5033) where the disk component is everywhere fainterthan the bulge, and other Ðts where the disk becomesbrighter than the bulge only at intermediate radii (e.g.,NGC 670, 955, 1090, and 1187). In both of these situations,the bulge Ðt might have beneÐted from an alternative func-tional form, perhaps the generalized de Vaucouleurs law as



FIG. 2.ÈBrightness proÐle Ðts to the galaxies presented in Each plot shows the observed proÐle (crosses), the bulge and disk components andTable 1.their sum (solid lines), and the range of radius included in the Ðt (horizontal line(s) at bottom). Also shown are the Ðtted parameters, where the surfacebrightness parameters are in units of V -mag arcsec~2 and the size parameters are in arcseconds.

1630



FIG. 2.È Continued

1631




TABLE 2

NONFITTED GALAXIES

Galaxy Type R25

Comments

NGC 150 . . . . . . . .SBT3*. 0.32 Very bright arms at rD 50ANGC 275 . . . . . . . .SBT6P. 0.14 Concave to low k (ITD with no bulge?)NGC 337 . . . . . . . .SBS7.. 0.20 Concave to low kNGC 908 . . . . . . . .SAS5.. 0.36 Exponential disk truncated at D150A

NGC 941 . . . . . . . .SXT5.. 0.13 Strong structure in outer proÐleNGC 1035 . . . . . . .SAS5$. 0.48 Concave to low kNGC 1358. .. .. . .SXR0.. 0.10 Large, bright plateau with sharp outer cuto† NGC 1667 . . . . . . .SXR5.. 0.11 Three exponentials ?NGC 2146. . . . . . .SBS2P. 0.25 Very disturbed galaxyNGC 2633. .. .. . .SBS3.. 0.20 Strong structure throughout proÐleNGC 2793. . . . . . .SBS9P. 0.07 Very asymmetric proÐleNGC 2976 . . . . . . .SA.5P. 0.34 Concave to low kNGC 2990 . . . . . . .S..5*. 0.27 Concave to low kNGC 3003. . . . . . .S..4$. 0.63 Strong structure throughout proÐleNGC 3021 . . . . . . .SAT4*. 0.25 Concave to low kNGC 3043 . . . . . . .S..3*/ 0.48 Concave to low kNGC 3067 . . . . . . .SXS2$. 0.42 Concave to low kNGC 3312. .. .. . .SAS3P$ 0.42 Large, bright plateau with sharp outer cuto† NGC 3432. .. .. . .SBS9./ 0.66 Strong structure throughout proÐleNGC 3455 . . . . . . PSXT3.. 0.21 Concave to low k, faint outer extensionNGC 3556. .. .. . .SBS6./ 0.59 Strong structure throughout proÐle

NGC 3628. . . . . . .S..3P/ 0.70 Disturbed edge-on systemNGC 3664. .. .. . .SBS9P. 0.03 Strong structure throughout proÐleNGC 3717. . . . . . .SA.3*/ 0.73 Double exponential, edge-onNGC 3810. .. .. . .SAT5.. 0.15 Strong structure in outer proÐleNGC 4013 . . . . . . .S..3./ 0.71 Concave to low k, edge-onNGC 4085 . . . . . . .SXS5*$ 0.55 Concave to low kNGC 4302 . . . . . . .S..5*/ 0.74 Extremely edge-onNGC 4487 . . . . . . .SXT6.. 0.17 Double exponentialNGC 4517 . . . . . . .SAS6*/ 0.83 Extremely edge-onNGC 4618. . . . . . .SBT9.. 0.09 Strong structure in outer proÐleNGC 5112. . . . . . .SBT6.. 0.15 Strong structure in outer proÐleNGC 5170 . . . . . . .SAS5*/ 0.91 Concave to low k, edge-onNGC 5301. .. .. . .SAS4*/ 0.69 Strong structure in outer proÐleNGC 5474. . . . . . .SAS6P. 0.05 Very asymmetric proÐleNGC 5746 . . . . . . .SXT3$/ 0.75 Concave to low k, edge-onNGC 5775 . . . . . . .SB.5$/ 0.62 Concave to low k, edge-onNGC 5949 . . . . . . .SAR4$. 0.33 Concave to low kIC 764 .. .. . . . . . . .SAS5$. 0.47 Strong structure throughout proÐle

discussed by et al. although no attemptAndredakis (1995),has been made to investigate this in the present study.

3.2. Fitting Errors

We have chosen three methods of estimating the Ðttingerrors: (1) unweighted rms residuals, (2) error estimates pro-vided by the Ðtting software, and (3) comparison with theresults of other workers.

The unweighted rms residuals for each Ðt are tabulated inBecause we have computed them in a uniformTable 1.

fashion for all objects, including all structure in the proÐles,these values provide an unbiased and consistent measure-ment of how well the Ðtting functions and the determinedparameters describe the observed brightness distribution.From these values we Ðnd that the median rms deviation of the Ðts is only 0.15 mag and that more than 90% of the Ðtsare better than 0.35 mag; shows the distribution of Figure 3the rms deviations using bins of width 0.05 mag. The overallability of the Ðts to describe the brightness distributions isquite good, given that the unweighted rms residuals includeall of the structure present in the proÐle.

In an e†ort to quantify the value of the unweightedresiduals as a measure of the goodness of Ðt, we have exam-ined plots of the proÐles and selected the best examples of proÐles that are without signiÐcant structure and appear tobe well represented by the chosen Ðtting functions. Note

that this selection did not involve consideration of the com-puted unweighted rms residuals. There were 16 objectsincluded in this selection, and they have a mean unweightedrms deviation of 0.05 mag and a range of 0.03 È 0.10 mag;this suggests that Ðts with unweighted rms residuals greaterthan about 0.10 mag are a†ected to some degree by signiÐ-cant structure and/or poor Ðtting quality. The full samplecontains 161 galaxies with rms residuals of 0.10 mag or less.

At the other end of the distribution, the worst-Ðt galaxieshave been investigated to attempt to Ðnd out why they wereso poorly Ðtted. We have inspected the 18 galaxies that haveunweighted rms residuals greater than 0.5 mag to search forcommon characteristics such as morphology and inclina-tion. The T -type distribution of these 18 galaxies is essen-tially the same as for the sample as a whole, so there appearsto be no correlation between poor Ðt and T -type. There alsoappears to be no serious trend with inclination: the meaninclination of the group is 57¡, consistent with a randomdistribution of tilts. The most common characteristic is alow surface brightness extension to the brightness proÐle,such that the Ðt falls below the measurements in the outerportion. The extension is sometimes featureless, and some-times it contains a distinct bump (as if an outer ring or arm);sometimes it is nearly constant brightness, and other timesit is more or less parallel with the inner proÐle. There is onlyone case (NGC 157) where the problem region is in the




FIG. 3.ÈDistribution of rms deviations of the Ðts from the data. Therms deviations were computed for all data points in each proÐle between 3Aand the Ðrst point at which the surface brightness drops below 25 V [ magarcsec~2. The median value of the distribution is at 0.15 mag. There are sixobjects with rms deviations greater than 1.0 mag that are not included inthe Ðgure.

main portion of the disk, and this galaxy looks disturbed,almost as if undergoing a collision. The apparent overridingreason for the poor Ðts is simply that the chosen Ðttingfunctions do not work well for some galaxies. This sameconclusion holds for the 39 galaxies that were not Ðtted inthis e†ort: common characteristics of these objects areextremely strong, large-scale structures, concavity of thebrightness proÐle toward faint surface brightness, andapparent multiple components of the proÐle, usually withmore than one exponential. This occasional inappropriate-ness of the Ðtting functions suggests that careful consider-ation of the Ðtted parameters and their error estimatesshould be exercised before judging whether a speciÐc Ðt istruly meaningful for a detailed study of any individualgalaxy.

The second method of judging the Ðtting errors was theuse of estimated coefficient errors as produced by the Ðttingsoftware. The NFIT1D task estimates the errors in eachparameter by a process of bootstrap resampling, with achoice of distribution functions for use in the procedure. Weused the Poisson distribution as the distribution functionfor the parameter error estimation since this reÑects thephoton statistics expected to a†ect the measured relativeintensities in the brightness proÐles. In order to minimizethe e†ects of comparing parameters that vary wildly invalue from galaxy to galaxy, we have computed the frac-tional error in each Ðtted parameter. lists theseTable 3fractional error estimates for a sample of the galaxies:column (1) gives the galaxy identiÐcation and columns (2) È (6) the fractional error of each of the parameters. Note thatsince the Ðtting was performed in the surface intensity scale(not surface brightness), the relative errors are computed inlinear units, not magnitude units.

The fractional errors for the full set of galaxies are sum-marized in which gives for each parameter theTable 4,

TABLE 3

PARAMETER FRACTIONAL ERRORS

Galaxy *Ie

*re

*I0

*r0

*rh

(1) (2) (3) (4) (5) (6)

NGC 16 . . . . . . . 0.212 0.125 0.447 0.087 . . .NGC 23 . . . . . . . 0.365 0.094 0.023 0.008 . . .NGC 148 . . . . . . 0.520 0.157 0.031 0.012 . . .

NGC 151 . . . . . . 0.255 0.099 0.044 0.035 . . .NGC 157 . . . . . . 0.601 0.380 0.117 0.035 . . .NGC 224 . . . . . . 0.078 0.047 0.018 0.010 . . .NGC 237 .. . . . . . . . . . . 0.023 0.010 . ..NGC 245 . . . . . . 0.337 0.165 0.053 0.018 0.019NGC 253 . . . . . . 0.671 0.350 0.010 0.007 . . .NGC 254 . . . . . . 0.258 0.110 0.038 0.014 . . .NGC 255 . . . . . . 0.250 0.174 0.035 0.018 0.021NGC 268 .. . . . . . . . . . . 0.012 0.008 . ..NGC 274 . . . . . . 0.117 0.053 0.154 0.028 0.015NGC 278 .. . . . . 0.026 0.014 . . . . . . . . .NGC 289 .. . . . . . . . . . . 0.007 0.004 . ..NGC 309 . . . . . . 4.950 0.620 0.021 0.014 . . .NGC 357 . . . . . . 0.257 0.121 0.230 0.115 . . .NGC 404 . . . . . . 0.057 0.052 0.158 0.080 . . .NGC 428 .. . . . . . . . . . . 0.010 0.007 . ..NGC 473 . . . . . . 0.365 0.307 0.114 0.014 . . .

NGC 514 . . . . . . 0.227 0.248 0.032 0.028 0.036NGC 521 . . . . . . 0.070 0.042 0.038 0.017 0.021NGC 524 .. . . . . 0.024 0.014 . . . . . . . . .NGC 598 . . . . . . 0.202 0.162 0.011 0.006 . . .

NOTES.ÈCol. (1), galaxy ID; col. (2), fractional error in col.Ie

;(3), fractional error in col. (4), fractional error in col. (5),r

e; I

0;

fractional error in col. (6), fractional error in Table 3 isr0

; rh.

presented in its entirety in the electronic edition of the Astronomi-cal Journal. A portion is shown here for guidance regarding itsform and content.

number of error estimates, the mean fractional error, thestandard deviation of the fractional errors, the median frac-tional error, and the minimum and maximum fractionalerrors. As can be seen in every parameter exceptTable 4, I

0is signiÐcantly a†ected by outliers; histograms of the frac-tional error of each parameter are shown in whichFigure 4,demonstrate this problem. Removing the most discrepantoutlier from the statistical calculations (second part of

improves the results considerably. Unfortunately,Table 4)there is not just one ““ badÏÏ Ðt in the sample causing all of these outlying points: the bulge parameter errors are bothdominated by the Ðt for NGC 2441, while the disk centralsurface intensity error is a†ected by the Ðt for NGC 2541,the disk scale length error by NGC 5033, and the holeradius error by NGC 2997.

The bulge component of NGC 2441 dominates the diskonly at radii smaller than about 6A, so there are very fewdata points deÐning the bulge, and the coefficient uncer-tainties reÑect this fact. The proÐle for NGC 2541 is Ðttedwith a faint ITD (the peak disk brightness is only about 24V -mag arcsec~2), and the hole radius is more than six diskscale lengths from the galaxy center. The southern half of the brightness proÐle contains a relatively bright spiral arm(about 23 V -mag arcsec~2 at its brightest), and this asym-metry results in a bump in the averaged proÐle, which hasbeen Ðtted with the inner truncation. NGC 5033 was Ðttedwith a very faint V -mag arcsec~2), very Ñat disk(k

0 \ 25.1

that was never comparable in brightness to the(r0

\ 732A)bulge. As a result, the disk parameters for this galaxy arenot well constrained by the data, and the estimated errors inthe coefficients are correspondingly large. Finally, NGC2997 has been Ðtted with a hole radius just smaller than the




TABLE 4

FRACTIONAL ERROR SUMMARY

StandardParameter Number Mean Deviation Median Min Max

All Fitted Galaxies

Ie

. . . . . . . . . 507 43.2 912.3 0.126 0.014 20508re

. . . . . . . . . . 507 0.194 0.910 0.082 0.010 19.4I

0 . . . . . . . . . 559 0.075 0.110 0.040 0.000 1.03

r0

. . . . . . . . . 559 1.67 38.8 0.016 0.003 917.9rh

. . . . . . . . . . 156 0.022 0.015 0.019 0.005 0.160

Most Discrepant Galaxy Removed

Ie

. . . . . . . . . 506 2.79 55.2 0.125 0.014 1241.3re

. . . . . . . . . . 506 0.156 0.317 0.082 0.010 5.0I

0 . . . . . . . . . 558 0.073 0.102 0.040 0.000 0.767

r0

. . . . . . . . . 558 0.027 0.064 0.016 0.003 1.304rh

. . . . . . . . . . 155 0.021 0.010 0.019 0.005 0.068

radius of the innermost data point, so the value of the holeradius is, again, not really constrained by the data.

Because of the presence of these extreme outliers, themedian fractional errors are much more useful than themean for examining the Ðtting errors of the sample as awhole. The summary in shows that the medianTable 4coefficient fractional errors range from a low of 1.6% for thedisk scale length to more than 12% for the bulge e†ectiveintensity. From these data, it is clear that the bulge param-eters are the least well determined quantities in the Ðts,while the disk parameters are generally well determined.This is not unexpected: since the bulge coefficients areusually dominated by a relatively small number of datapoints, the constraints on them are not very strong.

Finally, a few of the galaxies included in this study havebeen previously Ðtted by others with the same Ðtting func-tions, providing a completely independent check of the

results of our Ðtting procedure. There are Ðve galaxies in thecurrent study that are also included in andBoroson (1981),12 are in common with making a total of 17Kent (1985),measurements available for use in this comparison. Prior tomaking any comparisons between the various works, the

surface brightness parameters reported in Boroson (1981)and have been “ “uncorrected ÏÏ for the e†ects of Kent (1985)inclination and galactic absorption as applied in each study,and the length parameters have been converted from kilo-parsecs to arcseconds using the distances adopted by thoseauthors. Furthermore, lists values for theBoroson (1981)disk B[V color, which have been used to convert his diskcentral surface brightnesses from the B bandpass to the V .Finally, there are two galaxies in common between Boroson

and and the same analysis has been(1981) Kent (1985),applied to them. The percentage di†erences between theÐtting parameters from these works and the present studyhave been computed and tabulated in In this table,Table 5.we list for each galaxy the percentage di†erence between theparameters in the referenced work and this study, and alsobetween the two reference works; the last column identiÐesthe reference work. The di†erences were computed in the

sense reference work minus this study, and Boroson minusKent. These data are also presented in whichFigure 5,shows the Ðtting parameters from andBoroson (1981) Kent

plotted against the values obtained in the present(1985)study.

TABLE 5

FITTING COMPARISONS

P.D.(Ie) P.D.(r

e) P.D.(I

0) P.D.(r

0)

Galaxy (%) (%) (%) (%) Reference

NGC 16 . . . . . . . . . . . 80 [56 159 [14 1NGC 628 . . . . . . . . . . 146 [169 [8 42 2NGC 670 . .. . . . . . . . 35 [11 [12 18 1NGC 2268 . . . . . . . . 88 [108 25 5 2

NGC 2639 . . . . . . . . [

114 73 11 [

4 1NGC 2683 . . . . . . . . [125 105 30 [13 1NGC 2776 . . . . . . . . 87 [89 55 5 1NGC 2782 . . . . . . . . 8 [13 171 [120 1NGC 2880 . . . . . . . . [180 142 [135 27 1NGC 3627 . . . . . . . . 41 [46 118 [42 1NGC 3898 . . . . . . . . [168 76 [65 50 2NGC 5380 . . . . . . . . [154 69 82 [23 1NGC 5533 . . . . . . . . 0 17 34 [9 1NGC 5676 . . . . . . . . [200 167 43 [2 1NGC 5970 . . . . . . . . [142 69 [2 21 1NGC 6340 . . . . . . . . [193 154 [53 24 2NGC 7331 . . . . . . . . [23 [49 [30 16 2Comparison:

NGC 488 . . . . . . . 112 [127 [12 [7 2NGC 2967 . . . . .. 195 [180 [37 11 1

R EFERENCES.È(1) (2)Kent 1985; Boroson 1981.




FIG. 4a FIG. 4b

FIG. 4c FIG. 4d

FIG. 4e

FIG. 4.ÈHistograms of the fractional errors. The distributions of the estimated fractional errors of each Ðtted parameter are shown to illustrate theproblem with outliers: (a) (b) (c) (d ) and (e) Note the smaller bin size for andI

e, r

e, I

0, r

0, r

h. r

0 r

h.

In general, the Ðts from the various studies do not agreevery well, although the disk Ðts are typically more similarthan the bulge Ðts. The mean of the absolute values of thepercentage di†erences are 105% for 83% for 61% forI

e, r

e,

and 26% for with 17 objects for all parameters. OurI0

, r0

,bulge Ðts agree somewhat better with those of Kent (1985),while our disk central surface brightnesses are closer to

resultsÈthis reÑects the conversion of BorosonÏs (1981)BorosonÏs surface brightnesses to the V band. Interestingly,

our values of agree equally well, on average, with bothr0

reference works, leading us to believe that a 25% scatter inthe disk scale length is to be expected under the circum-stances of this comparison (di†ering bandpasses).

The bulge Ðt di†erences are dominated by the e†ects of the proÐle acquisition procedures used in the di†erentstudies : this work used a wedge-shaped major-axis cut,while and used two variationsBoroson (1981) Kent (1985)on azimuthal averaging. In particular, it has been pointed




FIG. 5.ÈComparison of Ðtted parameters. The Ðt parameters for the galaxies in common with ( plus signs) and (asterisks) areBoroson (1981) Kent (1985)shown along with the line. The surface brightness parameters are expressed in units of mag arcsec~2, and the length parameters are given in arcseconds.45¡.There is a reasonable correlation for all of the parameters, although the disk parameters have tighter correlations than those for the bulge.

out by that azimuthally averaged proÐlesBoroson (1981)will be systematically too bright in the bulge-dominatedregions owing to sampling the rounder bulge at a smallergalactocentric radius than the disk, at a given position inthe image. Inspection of reveals that every instanceTable 5

of a large departure in shows a large departure in of theIe reopposite sign. That our bulge parameters agree better with

than with probably reÑects theKent (1985) Boroson (1981)use of Ðxed ellipticities and position angles by Boroson,while Kent allowed those quantities to vary with radius. Asa result, the mean surface brightness around ellipses inbulge-dominated regions are more representative of themajor axis with KentÏs proÐle acquisition procedure thanwith BorosonÏs, hence the slightly better agreement with ourmajor-axis cuts.

4. FITTING CHARACTERISTICS

The basic result of the proÐle decomposition process isthat 620 of the 659 proÐles were successfully Ðtted with the

chosen Ðtting functions. In this section, we will discuss someof the characteristics of the proÐle decomposition and theerrors as they appear with this sample of galaxies. Ourintent is to provide information regarding the character-istics of the Ðtting; we will present our analysis regarding

the structure of disk galaxies elsewhere.

4.1. Fitting Parameters and Morphology

All galaxies included in this sample have lenticular orspiral types; however, 61 of the Ðts have beenRC3 Hubblemade with no disk component, indicating a lack of anyappreciable exponential component to their brightness pro-Ðles. Visual inspection of these galaxies in the PANBGshows many of them to have what appear to be disks eventhough the proÐle shows none (e.g., NGC 1784, 1961, and3370) ; others are possibly misclassiÐed elliptical galaxies(e.g., NGC 2655, 3998, and 5485). The galaxies with no diskcomponent span a range in T -type from [3 to 9, the entirerange of T -type included in this sample. Early-type galaxies




TABLE 6

M EDIAN FRACTIONAL ERROR MORPHOLOGY D EPENDENCE

T -Type Range *Ie

*re

*I0

*r0

*rh

[3.5¹T \ [0.5 . . . . . . 0.09 (131) 0.05 (131) 0.06 (119) 0.03 (119) 0.02 (41)[0.5¹T \ 2.5 . . . . . . . . 0.12 (114) 0.07 (114) 0.05 (100) 0.02 (100) 0.02 (27)

2.5¹T \ 5.5 . . . . . . . . 0.14 (204) 0.10 (204) 0.03 (246) 0.01 (246) 0.02 (71)5.5¹T \ 9.5 . . . . . . . . 0.24 (58) 0.17 (58) 0.02 (94) 0.01 (94) 0.02 (17)

NOTE.ÈThe numbers in parentheses are the number of galaxies contributing to the medianfractional error.

are somewhat more likely to be Ðtted without a disk thanare late types, but the trend is not very strong. There is nosigniÐcant di†erence in the Ðt quality (as measured by thetabulated rms deviation) between the galaxies without diskÐts and the sample as a whole.

A total of 113 galaxies were Ðtted without a bulge com-ponent, and although these galaxies range in T -type from[2 to 9, they are mostly late-type galaxies. This, of course,is consistent with the basic behavior of the Hubble classi-Ðcation scheme, where bulges are less prominent in latertypes. Again, the basic Ðtting quality is the same for galaxieswithout bulge Ðts as with the sample in general.

An investigation of the variation of the median fractionalerrors with T -type is summarized in This tableTable 6.gives for each range of T -type the median fractional error of each Ðtting parameter, as well as the number of galaxiesincluded in each median determination. The errors in I

e, r

e,

and show some slight trends that are in the expectedI0

senses but which are small enough to be of questionablesigniÐcance. The two bulge parameters seem to have some-what larger median errors for later types, as would beexpected as the bulge contribution to the light distributiondecreases. We should also note the work of &AndredakisSanders who show that the inner regions of late-type(1994),spirals are perhaps better represented by an exponentiallight distribution than a de Vaucouleurs law. Similarly, thedisk central intensity error has larger values at earlier types,when the disk contribution is generally lower.

We also looked at the possibility of a Ðtting qualitydependence on the presence or lack of a bar, and we havefound nothing signiÐcant. The median rms residual of theÐts on nonbarred galaxies (Hubble type in the containsRC3an ““ A ÏÏ explicitly) is about 0.14 mag, for barred galaxies(““ B ÏÏ) it is 0.15 mag, for mixed types (““ X ÏÏ) 0.16 mag, and forobjects with no bar classiÐcation given in the we Ðnd aRC3value of 0.14 mag. All of these values are sensibly the sameas the median value of 0.15 mag found for the full sample,and there is clearly no trend apparent. lists theTable 7median fractional error of the individual Ðtting parametersfor each bar class; there are no signiÐcant trends in theseresults. We conclude that bars have no discernible e†ect onthe quality of the Ðts.

Objects that have been Ðtted with an inner truncationmake up about 25% (156/620) of the sample. Rememberingthat inner truncations were included only if they improvedthe weighted rms by at least 10%, this serves to justify ourinitial decision to use that function with this large data set.Some of these inner truncations are probably caused byarms or rings at large galactocentric radii (e.g., NGC 2859,3368, and 5701)Èthe arm/ring is bright relative to the localdisk and thus mimics an inner truncation. In these cases, thearm/ring is typically faint (peaks near 24 V mag arcsec~2)and has a short disk scale length. These galaxies are alsogenerally classiÐed as having an outer ring. These objectsare identiÐed in with a ““ C ÏÏ in the commentTable 1column. A more detailed analysis of the presence of an innertruncation is left for a later study.

4.2. Fitting Parameters and Inclination

An analysis of the unweighted rms residuals shows littleor no trend in the mean value with inclination. We dividedthe sample into three inclination ranges based solely on the

value listed in the assuming that this isophoteR25

RC3,corresponds to a Ñat, circular disk: i ¹ 30¡ (R

25 ¹ 0.0625),

30¡\ i¹ 60¡ and i[ 60¡(0.0625\R25 ¹ 0.301), (R

25[

0.301). Note that no T -type dependence was included in thisinclination estimate. The resulting mean rms residuals forthe low-, medium-, and high-inclination samples are 0.16,0.19, and 0.21 mag, respectively. These three values are allmuch less than 1 p from each other, so the trend is sta-tistically meaningless. The median rms residuals for eachinclination sample are 0.15, 0.14, and 0.17 mag for the low,medium, and high inclinations, respectively. We concludethat the sample has no signiÐcant inclination dependenceon the unweighted rms residuals of the Ðts.

The quality of the individual Ðtting components is inves-tigated by computing the median fractional errors withineach inclination range; the mean fractional errors are notuseful because of the outliers discussed previously. Table 8provides the results of this investigation, which shows thatthere are no indications of any inclination dependencies. In

the Ðrst column lists the parameters, and the nextTable 8,three columns give the median relative errors in each incli-nation range.

TABLE 7

M EDIAN FRACTIONAL ERROR BAR CLASS D EPENDENCE

Bar Class *Ie

*re

*I0

*r0

*rh

SA . . . . . . . . . . . . . . 0.11 (173) 0.08 (173) 0.04 (173) 0.02 (173) 0.02 (42)SB . . . . . . . . . . . . . . 0.12 (154) 0.08 (154) 0.05 (176) 0.02 (176) 0.02 (61)SX . . . . . . . . . . . . . . 0.16 (148) 0.09 (148) 0.04 (170) 0.01 (170) 0.02 (44)Not typed . . . . . . 0.16 (32) 0.07 (32) 0.03 (40) 0.01 (40) 0.02 (9)

NOTE.ÈThe numbers in parentheses are the number of galaxies contributing to themedian fractional error.




TABLE 8

M EDIAN FRACTIONAL ERROR INCLINATION D EPENDENCE

Error i¹ 30¡ 30¡\ i¹60¡ i[60¡

*(Ie) . . . . . . 0.12 (68) 0.12 (291) 0.14 (148)

*(re) . . . . . . 0.09 (68) 0.08 (291) 0.09 (148)

*(I0

) . . . . . . 0.05 (76) 0.05 (283) 0.02 (200)*(r

0) . . . . . . 0.02 (76) 0.02 (283) 0.01 (200)

*(rh) . . . . . . 0.02 (24) 0.02 (92) 0.02 (40)NOTE.ÈThe numbers in parentheses are the number of

galaxies contributing to the median fractional error.

Finally, we check if the rate of occurrence of the innertruncation has any inclination dependence by computingthe rate in each inclination range. The rates are28% ^ 6.5% for the low-inclination group, 28% ^ 3.3% forthe medium inclinations, and 19% ^ 3.3% for the high-inclination sample. Thus, there is no trend signiÐcant at the2 p level.

5. CONCLUSIONS

We have presented one of the largest, if not the largest,collections of spiral and lenticular galaxy brightness proÐlebulge-disk decompositions yet completed. Of the 659brightness proÐles in our sample, 620 were Ðtted with the deVaucouleurs law plus inner-truncated exponential diskfunction, while the remaining 39 proÐles could not be soÐtted. The general quality of the Ðts is quite high, withabout 50% having an unweighted rms deviation from thedata (including real structures) of less than 0.15 mag andmore than 90% having unweighted rms residuals of lessthan 0.35 mag. We Ðnd no systematic trends in the Ðttingquality with either galaxy morphology or inclination. Com-parison of our Ðts with those of andBoroson (1981) Kent

show discrepancies attributable to a number of (1985)observational and data reduction factors.

Probably the most interesting result from this process of Ðtting is simply that we achieved a ““ success ÏÏ rate of 620/659 (94%) in our Ðts, compared to success rates of 75/94(80%) for Kent spiral and S0 galaxies only) and 16/26(1985;(62%) for While these success rates are sta-Boroson (1981).tistically similar, we wonder if the small number statisticsare the only di†erences. An analysis of the 19 nonÐttabledisk galaxy proÐles from shows that we foundKent (1985)Ðts for all 10 of those galaxies that were also in our sample.

For these 10 objects, the mean inclination is 41¡ ^ 18¡, themedian is 42¡, and only one galaxy (NGC 5566) has aninclination greater than 60¡. Thus, KentÏs nonÐttable gal-axies do not tend to be high-inclination objects. Further-more, the rms deviations of our Ðts for these same galaxiesare generally small, with a median value of 0.15 mag, thesame as for our full sample. The principal di†erence seemsto be that we included the ITD factor in our Ðts: seven of

these 10 galaxies have ITDs in our Ðts, often with large rh / r0

ratios. It is also possible that KentÏs simultaneous Ðtting of the minor-axis proÐles made his results more sensitive todeviations from the standard Ðtting functions. A similaranalysis of the 10 nonÐttable proÐles in BorosonÏs (1981)sample shows us having Ðts for the nine that are included inour sample. These nine galaxies are also of relatively lowinclination (the largest is about 58¡) and have small rmsdeviations in our Ðts (median value of 0.13 mag). However,our Ðtted parameters show three objects with bulge only,three with a bulge plus exponential disk, and three with abulge plus ITD; the case for the inclusion of the ITD is notas strong with this set of proÐles. We conclude, however,that the inclusion of the ITD term in our Ðtting functionshas allowed us to Ðt 10% È 15% more galaxies than wewould have Ðt without the inner-truncation term.

It is also interesting that about 25% of the proÐles in oursample are Ðtted better by an ITD function than with aplain exponential. Some of these Ðts are certainly due to theITD being Ðtted to outer rings (as indicated by a ““ C ÏÏ in thelast column of and others may be marginalTable 1),improvements (remember the requirement for a 10%improvement of the weighted rms to include the inner-truncation term), but clearly a signiÐcant fraction of theproÐles support the physical reality of the inner truncationin the light distribution. A quantiÐcation of the strength of the inner truncation and the search for the origin of thisfeature is the subject of a future paper.

W. E. B. has been supported by STScI under contractNAS 5-26555 for this work. The authors would like tothank M. Hamabe for making the brightness pro-PANBGÐles available to us for this project. We also wish to thankthe anonymous referee for some useful suggestions. Part of the data analysis for this paper used STSDAS, which wasdeveloped by the Space Telescope Science Institute underUS government contract NAS 5-26555.

APPENDIX

EFFECTS OF SEEING ON THE FITTING RESULTSThe Ðtting procedure described in makes no allowance for the e†ects of seeing other than to start the Ðtting at a radius° 3.1

larger than 3A to avoid the most a†ected portion of the brightness proÐle. We describe in this appendix a set of experimentsthat were used to derive estimates of the correction factors for the Ðtted parameters to measure more accurately the trueparameters of the bulge light distributions.

There are four factors in the proÐle acquisition process that can inÑuence the Ðtting results, all of which occur at distinctstages of the process and which can be assumed to be separable. Seeing smears the galaxy light as it travels through theatmosphere, while Poisson noise occurs during the photographic exposure physics and chemistry. Pixelation broadens sharpfeatures during the digitalization of the plate, as well as adding some additional Poisson noise, and smearing by the aperturephotometry happens as a result of the proÐle acquisition from the digitized data. Our experiments were designed toinvestigate only those processes that broaden sharp features of the galaxy light distribution: seeing, pixelation, and aperturephotometry.

The provides seeing estimates for all plates in their Table 4.1; we assume that ““ seeing ÏÏ in this case refers to thePANBGFWHM of stellar proÐles. The tabulated seeing in the ranges from 1

Ato 7

Aand is included in ourPANBG Table 1.




We attempted to replicate the proÐle deÐnition process as accurately as possible utilizing computer-generated images.These images consist of a perfectly circular de Vaucouleurs light distribution with input values of in arbitraryI

e \ 1000

intensity units and 1A, 2A, 4A, 8A, 16A, and 32A. Poisson noise was included in the images. No disk component wasre \ 0A.5,

included in these images because the most pronounced e†ects of seeing will be on the bulge component, owing to its very steepslope at small radii. We generated 512] 512 pixel images with these characteristics, assuming a pixel scale of 3 pixelsarcsec~1 (to simulate the photographic resolution), then smeared them with Gaussians of FWHM \ 1A, 2A, 3A, 4A, 5A, 6A, and7A to simulate the e†ect of the atmosphere during a long exposure. The resulting images were then block-averaged with a3]3 pixel (1A square) block to replicate the plate scanning utilized for most of the galaxies in the Finally, thePANBG.

brightness proÐles from the simulated images were extracted using a set of variable-diameter circular apertures along a singleradius of the ““ galaxies.ÏÏ These proÐles were then Ðtted in the same fashion as the real proÐles in order to estimate thefunctional parameters, using a Ðxed Ðtting range of 3A È 48A. A second set of images was generated using the same inputparameters, but these were not smeared by the Gaussians; these images were used to determine the correction factors due tothe pixelation and proÐle acquisition aperture photometry prior to estimating the e†ects of smearing with a Gaussian.

The results of this procedure are presented in which includes for each simulation the seeing size in arcseconds, theTable 9,input and the Ðtted and and the ratio of each Ðtted parameter to its input value, all based on the fully degradedI

e r

e, I

e r

e,

brightness proÐles. The are all in arbitrary intensity units, and the are all in simulated arcseconds. shows theIe

re

Figure 6relationship between the ratio of the Ðtted to the input as a function of the ratio of the Ðtted to the input the twoI

e r

e;

quantities are highly anticorrelated, suggesting that the Ðtted parameters are not truly independent of one another.As can be seen from there are some cases where the Ðtted parameters are very di†erent from the input values: theTable 9,

worst cases, as would be expected, are where the seeing disk is large compared to the input For the percentage errorsre. r

e,

range from less than 1% to almost 40% (seeing \ 7A, while for the range is from almost 0% (seeing \ 4A,re \ 1A), I

e r

e \ 32A)

to more than 1000% (seeing \ 7A, We have every reason to suspect that similar Ðtting errors exist in the Ðts,re \ 1A). PANBG

and a means of correcting these errors is highly desirable.The correction procedure has been separated into two stages: Ðrst correct the Ðtted parameters for the combined e†ects of

pixelation and aperture photometry, then correct these modiÐed parameters for the e†ects of the Gaussian smearing. Thepixelation/aperture photometry correction for the e†ective radius, based on the simulations without Gaussian smearing, hasbeen found to be well represented by a power law of the form

log (re@ / r

e) \ 0.005 log (b / r

e) [ 0.018 , (4)

or

re@ \ 0.959r

e(b / r

e)0.005 , (5)

where is the Ðtted e†ective radius, b is the digitization aperture size (1A), and is the e†ective radius corrected for the e†ectsre

re@

of pixelation and aperture photometry; the units of all quantities are in arcseconds. This function has a correlation coefficientof 0.989, and a maximum percentage error of 0.2% within the parameter space studied.

The pixelation/aperture correction function for the e†ective intensity is similarly found to beIe@ \ [0.068 log (b / r

e) ] 1.246]I

e , (6)

where is the Ðtted e†ective intensity, is the Ðtted e†ective radius, b is the digitization aperture size, and is the e†ectiveIe

re

Ie@

intensity corrected for pixelation and aperture photometry. This function has a correlation coefficient of 0.995 and amaximum percentage error of 0.6% within the parameter space studied. shows the Ðts of the pixelation/apertureFigure 7photometry correction functions for both andr

e I

e.

FIG. 6.ÈRelationship between Ðtting accuracy and Ðtting accuracy. The apparent anticorrelation suggests some dependence of the Ðtting parametersIe

reon each other.



TABLE 9

MODEL PROFILE FITTING R ESULTS (INPUT Ie \ 1000)

Input re

Fitted re(arcsec) (arcsec) Fitted r

e /Input r

e Fitted I

e Fitted I

e /Input I

e

Seeing \ 1A

0.5 . . . . . . . 0.51 1.02 856.7 0.861.0 . . . . . . . 1.03 1.03 843.6 0.842.0 . . . . . . . 2.08 1.04 842.3 0.84

4.0 . . . . . . . 4.18 1.04 848.4 0.858.0 . . . . . . . 8.39 1.05 858.7 0.8616.0 . . . . . . 16.85 1.05 871.1 0.8732.0 . . . . . . 33.81 1.06 884.2 0.88

Seeing \ 2A

0.5 . . . . . . . 0.49 0.97 1139.2 1.141.0 . . . . . . . 0.99 0.99 1009.4 1.012.0 . . . . . . . 2.01 1.01 947.8 0.954.0 . . . . . . . 4.08 1.02 917.9 0.928.0 . . . . . . . 8.23 1.03 905.2 0.9116.0 . . . . . . 16.60 1.04 902.4 0.9032.0 . . . . . . 33.41 1.04 905.2 0.91

Seeing \ 3A

0.5 . . . . . . . 0.46 0.92 1571.1 1.57

1.0 . . . . . . . 0.92 0.92 1437.7 1.442.0 . . . . . . . 1.89 0.94 1223.8 1.224.0 . . . . . . . 3.88 0.97 1080.4 1.088.0 . . . . . . . 7.93 0.99 1004.0 1.0016.0 . . . . . . 16.13 1.01 964.7 0.9632.0 . . . . . . 32.69 1.02 945.2 0.95

Seeing \ 4A

0.5 . . . . . . . 0.43 0.86 2260.0 2.261.0 . . . . . . . 0.85 0.85 2071.9 2.072.0 . . . . . . . 1.75 0.87 1665.8 1.674.0 . . . . . . . 3.64 0.91 1340.2 1.348.0 . . . . . . . 7.55 0.94 1153.8 1.1516.0 . . . . . . 15.54 0.97 1053.2 1.0532.0 . . . . . . 31.79 0.99 998.8 1.00

Seeing \ 5A

0.5 . . . . . . . 0.40 0.81 3440.4 3.441.0 . . . . . . . 0.78 0.78 3254.8 3.252.0 . . . . . . . 1.60 0.80 2396.8 2.404.0 . . . . . . . 3.40 0.85 1700.3 1.708.0 . . . . . . . 7.18 0.90 1336.4 1.3416.0 . . . . . . 14.99 0.94 1150.6 1.1532.0 . . . . . . 30.99 0.97 1052.4 1.05

Seeing \ 6A

0.5 . . . . . . . 0.37 0.74 5767.5 5.771.0 . . . . . . . 0.70 0.70 5709.5 5.712.0 . . . . . . . 1.45 0.73 3641.8 3.644.0 . . . . . . . 3.17 0.79 2176.4 2.188.0 . . . . . . . 6.85 0.86 1534.6 1.5316.0 . . . . . . 14.54 0.91 1241.8 1.24

32.0 . . . . . . 30.37 0.95 1100.2 1.10

Seeing \ 7A

0.5 . . . . . . . 0.34 0.67 10658.8 10.661.0 . . . . . . . 0.61 0.61 11727.6 11.732.0 . . . . . . . 1.31 0.66 5652.2 5.654.0 . . . . . . . 2.98 0.75 2726.0 2.738.0 . . . . . . . 6.61 0.83 1716.7 1.7216.0 . . . . . . 14.27 0.89 1308.3 1.3132.0 . . . . . . 30.19 0.94 1117.8 1.12



BULGE-DISK DECOMPOSITION 1641

FIG. 7a FIG. 7b

FIG. 7.ÈPixelation/aperture photometry correction functions. (a) The data and Ðt for the correction function for shown in a log-log plot. There isre

clearly a systematic residual function, but it is of insigniÐcant amplitude. ( b) The data and Ðt for the correction function; again there is an insigniÐcantIesystematic residual, particularly at large values of b / r

e.

The seeing correction is applied by the linear interpolation of the galaxy parameters on the model parameters for the samevalue of seeing. In we list the model data used in the interpolation; column (1) lists the seeing in arcseconds (S),Table 10column (2) the ratio of the seeing to the pixelation-corrected e†ective radius column (3) the ratio of the input e†ective(S / r

e@ ),

intensity to the pixelation-corrected e†ective intensity and column (4) the ratio of the input e†ective radius to the(Ie0 / I

e@ ),

pixelation-corrected e†ective radius The interpolation procedure is performed by computing the ratio for a Ðt and(re0 / r

e@ ). S / r

e@

interpolating the and ratios for the tabulated seeing-disk size to derive the fully corrected and from theIe0 / I

e@ r

e0 / r

e@ I

e0 r

e0

previously computed values of and (eqs. andIe@ r

e@ [5] [6]).

We include in the corrected bulge parameters resulting from the described correction procedure. Corrections forTable 1objects whose Ðtted parameters lie outside of the interpolation parameter space are not provided in Table 1.

TABLE 10INTERPOLATION DATA FOR S EEING CORRECTION

S S(arcsec) S / r

e@ I

e0 / I

e@ r

e0 / r

e@ (arcsec) S / r

e@ I

e0 / I

e@ r

e0 / r

e@

1 . . .. . . . 2.03 0.922 1.015 5 . . .. . . . 12.857 0.228 1.2861.011 0.952 1.011 6.675 0.245 1.3350.504 0.969 1.008 3.263 0.339 1.3050.251 0.979 1.006 1.544 0.486 1.2350.126 0.984 1.005 0.734 0.63 1.1740.063 0.987 1.005 0.353 0.745 1.1290.031 0.99 1.005 0.171 0.83 1.096

2 . . . . . . . 4.274 0.692 1.068 6 . . . . . . . 16.764 0.136 1.3972.101 0.795 1.05 8.938 0.139 1.491.038 0.861 1.038 4.319 0.222 1.440.515 0.904 1.03 1.986 0.379 1.324

0.256 0.933 1.024 0.922 0.548 1.230.128 0.953 1.02 0.436 0.69 1.1640.064 0.967 1.017 0.21 0.793 1.119

3 . . . . . . . 6.777 0.501 1.129 7 . . . . . . . 21.527 0.073 1.5383.396 0.557 1.132 11.954 0.068 1.7081.662 0.666 1.108 5.567 0.143 1.5910.811 0.767 1.082 2.461 0.302 1.4070.399 0.84 1.063 1.115 0.489 1.2740.197 0.89 1.049 0.519 0.654 1.1860.097 0.925 1.04 0.246 0.781 1.125

4 . . . . . . . 9.606 0.348 1.2014.879 0.386 1.222.391 0.488 1.1961.153 0.618 1.1530.558 0.73 1.1160.272 0.815 1.0890.134 0.875 1.069



1642 BAGGETT, BAGGETT, & ANDERSON

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