astro-ph/9506136 28 Jun 1995 The Subject there thinner are in lation spread internal over larger based diametervelocity stellar data or in ters Infrared agreement distance V Infrared Using based is B is Excluding or scatter on derived p opulation The in and headings in no extinction dust distance the single on the signicant V improvement close photometric the with IR in content A infrared Diameter The channel the relative D fundamental to disp ersion due parameters outliers estimates from Coma optical the Institute  dierences age to than relation Lawrence infrared dust limit ComaVirgo the data in dierence cluster the distances indicates it in the depth relation for compared plane age implied is available other RMS L Velocity will infrared photometry Livermore in among Geophysics Livermore relation Michael greggigppllnlgov of the ABSTRACT metallicity b etween b e this scatter colors that for Galaxies the distance by optical more galaxies the to elliptical for result cluster is the there has D the East and National CA Disp ersion and Coma attributed Virgo at Virgo from accurate observational Gregg  of optical K promises and are using Avenue Planetary precludes galaxies for elliptical ellipticals the are and detectable times slop e Laboratory is other than literature limited to That Coma derived galaxies that of lower Physics in any a techniques errors those Relation the the decrease the the Since ellipticals signicant but to from scatter IMF Coma in a fundamental D derived just small provisional Distance Coma the the in  as and at indicating D relation for K sensitivity improvement well stellar from is K ob jects Virgo band  only than estimates relations Elliptical as plane Kband optical p opu has lower data clus in that the to B is a

Introduction Guzman Lucey By analogy with the

TF relation it is natural to susp ect that replac

There are two p opular metho ds for determin

ing Bband with infrared photometry might lead

ing indep endent distances to galaxies

to an improvement in the accuracy of distances

Both rely on a tight correlation b etween a sp ec

estimated by D and FP plane techniques

n

troscopically determined distanceindep endent mea

Guzman Lucey Gregg This pa

sure of the gravitational p otential and a photo

p er presents evidence that the D metho d and

metrically determined distancedep endent mea

by inference the FP has signicantly less scatter

sure of apparent size The TullyFisher TF re

in the IR than in the optical for ellipticals in the

lation for spirals Tully Fisher is based

Coma cluster

on the correlation b etween luminosity and rota

tional velocity The D technique for ellip

n

Derivation of Infrared Diameters

ticals Dressler et al D dep ends on the

Using IR data from Bower Lucey Ellis

correlation b etween a surface brightness dep en

a BLE it has b een shown elsewhere that

dent diameter and the central velocity disp ersion

the Kband magnitudevelocity disp ersion

relation for early type galaxies in the Coma

When rst introduced the TF metho d em

cluster has a scatter smaller by a factor of

ployed B band photometry necessitating rela

than the B band D relation Gregg

tively large and uncertain corrections for inter

Because the IR magnitudes are from single chan

nal extinction which vary with morphol

nel photometry in a ap erture the derived

ogy and formation rate Aaronson Huchra

IR relation is b etween velocity disp ersion and a

Mould AHM Diering current SFRs

metric size For a useful distance indicator it

probably also contribute to the spread in B mag

is necessary to dene a size based on structural

nitudes The accuracy of the TF metho d was

parameters of the galaxies individually the FP

improved markedly when AHM introduced the

or D relations accomplish this using the half

use of H band photometry where extinc

lightradius R or D D dene D as the diam

e n n

tion corrections are reduced to negligible levels

eter of a circular ap erture within which the mean

and the ux is mainly from the oldest p opula

B band surface brightness is magsq arc

tion of which is p erhaps more uniform from

sec and show that logD is well correlated with

n

galaxy to galaxy AHM

log reducing the scatter by a factor of two

There is increasing evidence from sp ectro

from the FaberJackson B vs log relation

T

scopic studies suggesting that the stellar p opu

Faber Jackson Typical ellipticals have

lation of ordinary elliptical galaxies can b e a mix

BK  so a K band diameter D which ap

K

of ages eg OConnell Rose Pickles

proximates D would enclose a mean K surface

n

Bower et al Gonzales Ex

brightness of magsq arcsec

treme cases such as merger remnants have exp e

The Virgo and Coma D are based on CCD

n

rienced strong bursts of star formation Carter

photometry D Burstein et al B

et al Schweizer et al Dust has

The ideal IR version of a D relation would use

also b een shown to exist in a large fraction of

K band imaging however with some simple as

ellipticals There is go o d evidence that the dis

tances derived from D and the closely related

n

Jorgensen Franx Kjaergaard have demon

fundamental plane FP technique Djorgovski

strated that the FP is an intrinsically more accurate dis

Davis for some ellipticals are inuenced by

tance indicator than D Using the ts detailed here

one or more of these factors Gregg

it is p ossible to derive an IR version of the FP Because

smaller than the error estimates for logD Burstein sumptions a provisional D relation can b e

n K

et al and comparable to those in logD derived for the Coma and Virgo clusters from the

V

LGCT The derived logD are listed in Table data of Persson Frogel Aaronson PFA

K

along with their A D from B and the V and BLE b oth present high quality single chan

e n

band equivalent D ap erture diameter enclos nel IR photometry for early type galaxies in the

V

ing magsq arcsec from BLE Note that Coma and Virgo clusters The BLE photometry

although V band A from LGCT have b een used has b een calibrated to b e on the same system as

e

in deriving D strict photometric indep endence that of PFA see BLE for discussion and their

K

b etween the V and K band results is maintained much larger b o dy of photometry sup ersedes the

by adopting D from BLE earlier PFA work As BLE present no new IR

V

photometry for Virgo the data of PFA are used

PFA present JHK photometry of Virgo

here

ellipticals through ap ertures and

=

which allows D to b e derived from an R law Table of BLE lists K magnitudes through an

K

t without recourse to any optical data For eective ap erture of for E or ES and

comparison D values were also derived for the S galaxies in the which also have

K

Virgo ellipticals using the same metho d as the log in Davies et al or Dressler

Coma ellipticals ie by adopting an optical A Corrections for background light red

e

and tting to a single ap erture It is testimony shift and Galactic reddening were applied as de

to the high quality of the data from PFA BLE tailed in BLE and PFA D can b e derived from

K

=

and B that the two metho ds give identical re these single ap erture data by assuming an R

sults within a few p ercent and that these are in law prole and adopting an eective diameter

turn extremely well correlated with the diame A from the V band photometry of Lucey et al

e

ters in B and V This test serves as a condence a LGCT for the ellipticals and the Third

check on the derived IR diameters for the Coma Reference Catalog de Vaucouleurs et al

galaxies Table includes the Virgo ellipti for the Ss In the absence of color gradients A

e

cals from PFA and their calculated D along is indep endent of wavelength and in most ellipti

K

with D B and D BLE One of the ob cals color gradients are negligible PFA Peletier

n V

jects NGC with log is excluded Valentjin Jameson

=

from the analysis to follow

The R ts are uniquely determined by the

ap erture photometry and eective diameter Er

Velocity Disp ersions

rors have b een estimated by deriving D after

K

varying b oth quantities by their estimated stan

Velocity disp ersions from Davies et al

dard deviations  dex for l og A LGCT

e

have b een adopted b ecause these data pro duce

and  mag for the K ap erture magnitudes

tighter D correlations than other data sets

BLE These small errors have little eect on

eg Dressler or LGCT This can b e at

logD amounting to only  dex RMS

K

tributed to the careful treatment of systematic

eects as well as the averaging of several inde

of the use single channel IR data and A from V band

e

p endent measurements in many cases In cases

measurements this is not preferred here b ecause the V

however the velocity disp ersions of LGCT are

band photometry then plays a role in determining of

preferable The LGCT for RB is more

the dimensions of the FP A and and contributes

e e

to b oth sides the FP distance estimator itself A as well

than rms lower than that of Davies et al and

e

as log C  The results however of such an analysis

e

moves RB directly onto the D relation

are in agreement with the D relation discussed here

in all colors The Davies et al disp ersion for

Several groups are now working towards a full Kband FP

NGC is only kms well b elow other es

derivation eg Pahre et al

timates cf Whitmore McElroy Tonry at

kms The intermediate log of LGCT

km s again moves NGC onto the D

relation in all bands Finally the Davies et al

Table

value for NGC is the only one in the present

Data for Coma and Virgo Galaxies

sample based only on lower resolution Lick data

Name D A D D D

e n V K

Coma Cluster

the higher precision LGCT value is sup erior By

NGC

adopting the alternative velocity disp ersions for

NGC

these three ob jects the scatter in the D re

IC

lation is minimized in all three colors

IC

NGC

Additional supp ort for these three velocity dis

NGC

p ersions b eing sup erior comes from the funda

NGC

mental plane in planar ts to log and of

e

RB

the other galaxies in B and V the alternative dis

NGC

NGC

p ersions lower the residuals of the three ob jects

NGC

in question with the exception of RB in the

RB

B band by The eective radius of RB

IC

varies by a factor of more than in the liter

NGC

IC

ature ranging from to Seeing eects

NGC

may b e dominating the errors in R for this ob

e

IC

ject and its eective radius must b e considered

RB

uncertain

IC

IC

IC

Coma

IC

NGC

The IR and optical D relations for the

RB

Coma ob jects are compared in Figure upp er

NGC

panels ac The lled circles are ellipticals and

RB

NGC

the p ointed stars are Ss The op en circles

NGC A

are of the highest surface brightness galaxies in

Virgo Cluster

the sample RB NGC and NGC

NGC      

These clearly lie o the trend in K and tend to

NGC      

b e high in V and B as well They will b e dis

NGC      

NGC      

cussed further b elow and are not used in the ts

NGC      

The is IC which has a log just ab ove

NGC      

the cuto of applied by D it lies well b e

NGC      

low the relation in all colors and so will b e

NGC      

NGC      

excluded from further consideration The lines

NGC      

through the data in Figure are derived from

NGC      

a robust tting technique based on median val

NGC      

ues Emerson Hoaglin with log as

NGC      

the indep endent parameter to the remaining

galaxies Due to the nature of the robust tting

technique there is little dierence b etween ts

with and without the outliers The S galaxies

Fig Upp er panels comparison of the B V and K D relations for the Coma cluster Filled

circles are ellipticals p ointed stars are Ss op en circles are outliers identied in the K band data see

text The is IC Lines are robust ts to the lled circles and Ss Lower panels residuals

of the E and S ob jects used in the tting The RMS in K is times lower than in B times

lower than in V A representative error bar is plotted showing  in LogD The error estimates for

LogD and LogD are half this amount

K V

t well among the ellipticals as demonstrated The residuals in LogD at a given velocity dis

by Dressler The b est ts and Sp earman p ersion are plotted in the lower panels of Fig

correlation co ecients and probabilities are ure

Immediately apparent from Figure is that

LogD log

n

the D relation is tighter than either of its

K

S P 

S

optical counterparts The RMS scatter of the

galaxies is and in logD for

B V and K resp ectively The K band relation

LogD log

V

reduces the scatter by a factor of from B

S P 

S

and from V This corresp onds to a scatter

in distance of only roughly the predicted

and

limit from measurement errors Jorgensen et al

LogD log

K

The RMS for B and V are b oth less than

that found by Jorgensen et al from the Coma

S P 

S

FP for a similar sample this can b e attributed cance of the dierences A Students p oint t

to the use of the alternative velocity disp ersions test takes this into account Press et al and

and removal of the remaining outliers It can b e indicates that the average absolute value of the

demonstrated that removing the outliers and us residuals in D is signicantly lower than in D

K n

ing the b etter velocity disp ersions also improves or D at the and condence levels

V

the FP ts resp ectively Either test applied b etween D and

V

D shows that they are not signicantly dierent

n

In K there are three ob jects which lie well

at the  condence level The conclusion is

ab ove the tight relation dened by the ma jor

that D is the b est relation at a signicantly

K

ity At V these ob jects are less clearly outliers

higher level

and at B only RB is clearly away from the

rest due to the increase in sample RMS The

Why is K b etter

trend with bandpass suggests stellar p opulation

eects but these three ob jects have typical VK

Jorgensen et al show that the observed

BLE These are among the highest surface

scatter in the Coma FP in B and r is ab out twice

brightness ob jects in the sample Jorgensen et

the exp ected from the measurement errors but

al have shown that the correlation of residuals in

could not identify a signicant additional param

the D relation with surface brightness Lucey

eter ruling out ellipticity Br colors or gradients

Bower Ellis results from the D rela

isophotal twists b oxiness and the presence of a

tion b eing a notquiteoptimum pro jection of the

disk The photometric errors in B V and K are

FP While this may account for these outliers it

magnitudes since the velocity disp er

is noted that RB and IC also have sur

sions in Figure are identical in B V and K the

face brightnesses in the same range yet lie close

increase in width of the D relation with de

to the D relations in all colors though not if

creasing wavelength is due to cosmic eects

log from Davies et al is adopted for RB

One p ossible source of this additional scatter

LGCT redetermined log for RB and it is

which explains the decrease with wavelength is

in go o d agreement with the Davies et al value

variations of stellar p opulation parameters age

Unusual central dynamics may b e resp onsible

IMF slop e or metallicity or the amount of dust

but further longslit observations are needed to

which may b e linked to the stellar p opulation at

resolve this Jorgensen et al An indep en

a given velocity disp ersion All of these will have

dent comprehensive sp ectroscopic study at high

a larger eect in the optical than in the IR Mo d

signaltonoise and high disp ersion is needed to

eling carried out by Tonry Ajhar Luppino

place the Coma velocity disp ersions on a truly

shows that the I band is less aected by

uniform system

these variables than V or R and it is reasonable

to exp ect that the sensitivity is further reduced

Statistical Signicance

at K Mo dels by Bruzual suggest that this

is the case Guzman Lucey The real

The Ftest indicates that the sample variance

situation may b e a go o d deal more complicated

of D is signicantly smaller than D at the

K n

however Early results from the surface bright

condence level while the improvement

ness uctuation distance indicator technique ap

over D is signicant at the level The

V

plied in the K band show a larger scatter galaxy

precision of the photometry is such that the ve

togalaxy than in the I band Luppino Tonry

lo city disp ersions are the limiting factor and con

Pahre Mould If further observa

tribute identically to the scatter in all three col

tions of nearby ellipticals continue to exhibit a

ors resulting in highly correlated residuals The

large range in IR prop erties the improvement in

Ftest therefore underestimates the real signi

the D relation demonstrated here for Coma ducted with narrow slits on relatively nearby ob

in the K band may not b e universal jects ap erture eects may also play a role If

the younger p opulations are conned to the in

The variations in age IMF slop e and metal

ner in galaxies Mp c distant they may

licity can b e quite small and still account for the

b e undetectable in Coma galaxies provided they

observed increase in scatter For instance the

have the same physical extent A comparison of

total scatter in the B band D relation can

H line strengths in the Coma and Virgo clus

b e accounted for by a corresp onding RMS in age

ters based on the same data as was used in the

of only Gyr for simple mo dels with mean

velocity disp ersion determinations by Gregg

age of Gyr typical IMF and solar or twice

Dressler shows that dierences do exist

solar metallicity Gregg Table Quite

and is consistent with an ap erture eect Bower

small changes in the metallicity or IMF can just

et al however argue against ap erture ef

as readily account for the scatter This is an

fects as an explanation for the sp ectroscopic dif

upp er limit since some p ortion of the scatter is

ferences they nd in a comparison of ellipticals

due to observational error rather than cosmic

from the Virgo and Coma clusters and other en

dierences taking the observational errors into

vironments A much more detailed sp ectroscopic

account lowers the age scatter by The

comparison of ellipticals in the Virgo and Coma

presence of dust would further reduce the allow

cluster is called for to shed more light on this

able scatter in the other stellar p opulation pa

issue

rameters From these data alone however it

is imp ossible to determine whether metallicity Since the scatter in the D relation is smaller

age the initial mass function or simply dust is at K then at a given luminosity or velocity dis

resp onsible for the additional scatter in the opti p ersion the residuals in the optical D rela

cal tion should correlate with galaxy color Galaxies

which have to o small a diameter in the optical

Similarly tight constraints on the ages have

at a given velocity disp ersion must b e brighter

b een reached by Bower Lucey Ellis b

in the IR and hence redder for their total lumi

using these same data in the form of color

nosity galaxies which are to o large in the opti

magnitude relations Although they detect a

cal will b e bluer Thus the diameter residuals

scatter in their Coma VK colormagnitude re

from the D relation should anticorrelate with

lations larger than their estimated errors they

the residuals from the colormagnitude relation

are reluctant to attribute it to a real variation in

Figure plots the residuals D of Figure

n

the Coma galaxies The dierences seen in the

against the residuals from the V VK rela

T

D relations of Figure strongly argue that

tion of Bower et al b based on a sample

the larger scatter in the optical is due to intrinsic

of ES Coma galaxies The Sp earman rank

variations among the Coma early type galaxies at

correlation co ecient for the residuals is

the tiny levels discussed ab ove

probability  The residuals in this plot

Such tight constraints on the spread in the

are completely indep endent of each other and the

stellar p opulation parameters stands in stark

evident anticorrelation strongly supp orts the re

contrast to the often large range in ages at

sults of Figure that the D relation is tighter

tributed to ellipticals in the sp ectroscopic stud

in the IR and is consistent with the interpreta

ies cited in the Introduction The disagreement

tion that the additional scatter in the optical is

can b e resolved as already suggested ab ove if

from stellar p opulation variations or dust

the Coma cluster ellipticals contain a highly uni

Jorgensen et al rep ort no correlation

form stellar p opulation Because most of the

of residuals from a FP t with Br color resid

sp ectroscopic p opulation studies have b een con

the IR Such work is already b eing carried out by

several groups eg Pahre et al

Virgo

Figure compares the D and D rela

n V

tions for Virgo ellipticals with the D re

K

lation derived here based on the PFA data The

lines are linear least squares ts forcing the same

slop e as derived from the Coma relations exclud

ing NGC sign b ecause of its low ve

lo city disp ersion There is little dierence among

the colors and the RMS residuals are times

those for the Coma cluster Within the uncer

tainties due to the large scatter and small num

b er of ob jects the Virgo relations are compatible

with those for Coma The larger scatter of the

Virgo ellipticals and the lack of improvement go

ing from B to K can b e attributed primarily to

Fig Residuals D from the B band relation

n

the sizable depth of the Virgo cluster eg Tonry

of Figure plotted against residuals VK from

et al The computed intercepts for B V

the V band color magnitude relation of Bower

and K are and resp ectively

et al b The anticorrelation is exp ected if

From these the relative ComaVirgo distance in

either stellar p opulations or dust are resp onsible

each color can b e derived in B in V

for the increase in scatter of the B band D

n

and in K essentially identical given the scat

relation Symbols as in Figure

ter of  in LogD These relative distances

are in go o d agreement with other estimates D

uals at a given velocity disp ersion for the Coma

Sandage Tammann Bower et al b

galaxies The p ositive result shown in Figure

Bower et al present evidence for a

can b e attributed primarily to greater sensitivity

rather large age dierence b etween the ellipti

provided by the longer wavelength baseline of V

cal p opulations of the clusters based on Roses

K as well as complete indep endence of the two

sp ectral indices applied to comp osite sp ec

residual quantities Correlated errors in residu

tra The indicated age dierence is approxi

als b oth involving log will tend to wash out

mately a factor of two which in turn predicts

any real eects from other causes

that the derived distance ratio should b e a rather

Even if the use of optical eective diameters to

strong function of wavelength b eing smal ler at

derive D for the Coma sample is inappropriate

K

longer wavelengths Gregg No such trend

and the results of Figure are completely fortu

is found arguing for no signicant dierence in

itous Figure is an indep endent prediction that

the mean ages of the Coma and Virgo el lipticals

IR imaging data will show that the fundamental

A similar conclusion regarding the relative ages

plane is thinner at K than in the optical An

has b een reached by Bower et al b based

IR imaging study of ellipticals in Coma Virgo

on broad band colors of ellipticals in the clus

and other clusters is needed for an indep endent

ters

assessment of the total improvement available at

K and a complete characterization of the FP in

Fig Upp er panels comparison of the B V and K D relations for the Virgo cluster The

is the low ob ject NGC The lines are linear least squares ts excluding NGC forcing the

same slop es as in Figure for the Coma cluster Lower panels residuals of the E galaxies The large

scatter and high degree of similarity is attributed to the depth of the Virgo cluster A representative

error bar is plotted showing  in LogD The error estimates for LogD and LogD are half this

K V

amount

Summary and Conclusions servational errors alone Jorgensen et al

The improvement is attributed to lower sensi

Using published single channel K band pho

tivity at K to variations in stellar p opulation pa

tometry combined with optical eective diame

rameters age metallicity and slop e of the IMF

=

ters and the assumption of an R law a provi

as well as negligible inuence from any dust Dis

sional IR version of the diametervelocity dis

tance estimates based on K band photometry will

p ersion relation has b een derived for early type

b e of sup erior accuracy to those in the optical

galaxies in the Coma and Virgo clusters The K

The improvement in the IR also indicates that

band relation has times less scatter

there are small but detectable dierences in ei

than the B V band D relation for galax

ther the stellar p opulations or the amount of dust

ies in the Coma cluster excluding a few outlying

in the Coma ellipticals Because the D re

galaxies The RMS scatter in distance is only

lation dep ends on the FP a further implication

p er galaxy for the Coma cluster K band

is that the FP is thinner in the IR than in the

D relation close to the limit from current ob

optical

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