The Infrared Diameter { Velocity Dispersion Relation for Elliptical Galaxies

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The Infrared Diameter { Velo city Disp ersion Relation for Elliptical

Galaxies

Michael D. Gregg

Institute for Geophysics and Planetary Physics

Lawrence Livermore National Laboratory

L-413, 7000 East Avenue

Livermore, CA 94550

[email protected] lnl.gov

ABSTRACT

Using single channel infrared photometry from the literature, a provisional K-band

diameter{velo city disp ersion relation for elliptical galaxies in the Coma and Virgo clus-

ters is derived. The Coma cluster relation has 1.5 times lower scatter at K than in B

or V. Excluding 4 outliers, the RMS scatter at K for 24 galaxies in Coma is only 4.8%

in distance, close to the limit implied by the observational errors. Distance estimates

based on the IR D relation will be more accurate than those derived from optical

data. The improvement in the infrared is attributed to a decrease in sensitivity to

stellar p opulation parameters (age, metallicity, and slop e of the IMF) as well as lower

internal extinction from dust compared to the optical. That the D relation has a

larger scatter in the optical indicates that there are detectable, but small, stellar p opu-

lation or dust content di erences among the Coma ellipticals. Since the D relations

are based on the fundamental plane, this result promises that the fundamental plane is

thinner in the infrared than it is in the optical.

Infrared photometric data available for Virgo are limited to just 13 ob jects; the

spread in distance due to the depth of the cluster precludes any signi cant improvement

over B and V. A relative Coma-Virgo distance of 5.56 is derived from the K band data,

in agreement with estimates in other colors and using other techniques, indicating that

there is no signi cant age di erence between Virgo and Coma ellipticals.

Subject headings: galaxies: distances | galaxies: elliptical 1

Guzman & Lucey 1993). By analogy with the 1. Intro duction

TF relation, it is natural to susp ect that replac-

There are two p opular metho ds for determin-

ing B-band with infrared photometry might lead

ing redshift-indep endent distances to galaxies.

to an improvement in the accuracy of distances

Both rely on a tight correlation between a sp ec-

estimated by D and FP plane techniques

troscopically determined distance-indep endent mea-

(Guzman & Lucey 1993; Gregg 1995). This pa-

sure of the gravitational p otential and a photo-

p er presents evidence that the D metho d, and

metrically determined distance-dep endent mea-

by inference the FP, has signi cantly less scatter

sure of apparent size. The Tully-Fisher (TF) re-

in the IR than in the optical for ellipticals in the

lation for spirals (Tully & Fisher 1977) is based

Coma cluster.

on the correlation between luminosity and rota-

tional velo city. The D technique for ellip-

2. Derivation of Infrared Diameters

ticals (Dressler et al. 1987; D87) dep ends on the

Using IR data from Bower, Lucey, & Ellis

correlation between a surface brightness dep en-

(1992a; BLE), it has b een shown elsewhere that

dent diameter and the central velo city disp ersion

the K-band (2:2) magnitude-velo city disp ersion

( ).

relation for 25 early typ e galaxies in the Coma

When rst intro duced, the TF metho d em-

cluster has a scatter smaller by a factor of 1.9

ployed B band photometry, necessitating rela-

than the B band D relation (Gregg 1995).

tively large and uncertain corrections for inter-

Because the IR magnitudes are from single chan-

nal extinction which vary with galaxy morphol-

nel photometry in a 17" ap erture, the derived

ogy and star formation rate (Aaronson, Huchra,

IR relation is between velo city disp ersion and a

& Mould 1979 AHM). Di ering current SFR's

metric size. For a useful distance indicator, it

probably also contribute to the spread in B mag-

is necessary to de ne 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 intro duced the

or D relations accomplish this using the half

use of H band (1:6) photometry where extinc-

light-radius R or D . D87 de ne 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 20.75 mag/sq arc-

tion of stars which is p erhaps more uniform from

sec and show that log(D )iswell correlated with

galaxy to galaxy (AHM).

log ( ), reducing the scatter by a factor of two

There is increasing evidence from sp ectro-

from the Fab er-Jackson (B vs. log ( )) relation

scopic studies suggesting that the stellar p opu-

(Fab er & Jackson 1976). Typical ellipticals have

lation of ordinary elliptical galaxies can b e a mix

B-K 4.0, so a K band diameter (D ) which ap-

of ages (e.g., O'Connell 1980; Rose 1985; Pickles

proximates D would enclose a mean K surface

1985, Bower et al. 1990, Gonzales 1993). Ex-

brightness of 16.75 mag/sq arcsec.

treme cases such as merger remnants have exp e-

The Virgo and Coma D are based on CCD

rienced strong bursts of star formation (Carter

photometry (D87; Burstein et al. 1988, B88).

et al. 1988; Schweizer et al. 1990). 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 good evidence that the dis-

tances derived from D and the closely related

Jorgensen, Franx, & Kjaergaard (1993) have demon-

fundamental plane (FP) technique (Djorgovski &

strated that the FP is an intrinsically more accurate dis-

Davis 1987) for some ellipticals are in uenced by

tance indicator than D . Using the ts detailed here,

one or more of these factors (Gregg 1992, 1995;

it is p ossible to deriveanIRversion of the FP. Because 2

sumptions a provisional D relation can be smaller than the error estimates for log(D ) Burstein

K n

derived for the Coma and Virgo clusters from the et al. (1987) and comparable to those in log(D )

data of Persson, Frogel, & Aaronson (PFA 1979) (LGCT). The derived log(D ) are listed in Table

and BLE; b oth present high quality single chan- 1 along with their A , D from B88, and the V

e n

nel IR photometry for early typ e galaxies in the band equivalent, D (ap erture diameter enclos-

Coma and Virgo clusters. The BLE photometry ing 19.80 mag/sq arcsec) from BLE. Note that

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

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

much larger body of photometry sup ersedes the between the V and K band results is maintained

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

photometry for Virgo, the data of PFA are used

PFA present JHK photometry of 13 Virgo

here.

ellipticals through 2 ap ertures (29" and 56"),

1=4

Table 5 of BLE lists K magnitudes through an which allows D to b e derived from an R law

e ective ap erture of 17" for 25 E or E/S0 and 3 t without recourse to any optical data. For

S0 galaxies in the Coma cluster which also have comparison, D values were also derived for the

log ( ) > 2:0 in Davies et al. (1988) or Dressler Virgo ellipticals using the same metho d as the

(1987). Corrections for background light, red- Coma ellipticals, i.e., by adopting an optical A

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

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

1=4

these single ap erture data by assuming an R and B88 that the two metho ds give identical re-

law pro le and adopting an e ective diameter sults within a few p ercent and that these are in

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

(1991a LGCT) for the ellipticals and the Third ters in B and V. This test serves as a con dence

Reference Catalog (de Vaucouleurs et al. 1991) check on the derived IR diameters for the Coma

for the S0's. In the absence of color gradients, A galaxies. Table 1 includes the 13 Virgo ellipti-

is indep endentofwavelength and in most ellipticals from PFA and their calculated D , along

cals, color gradients are negligible (PFA; Peletier, with D (B88) and D (BLE). One of the ob-

n V

Valentjin, & Jameson 1990). jects, NGC 4387, with log ( ) < 2:0, is excluded

1=4

from the analysis to follow.

The R ts are uniquely determined by the

ap erture photometry and e ective diameter. Er-

2.1. Velo city Disp ersions

rors have b een estimated by deriving D after

varying b oth quantities by their estimated stan-

Velo city disp ersions from Davies et al. (1987)

dard deviations, 0:028 dex for log (A ) (LGCT)

have b een adopted b ecause these data pro duce

and 0:026 mag for the K ap erture magnitudes

tighter D correlations than other data sets

(BLE). These small errors have little e ect on

(e.g., Dressler 1984 or LGCT). This can be at-

log(D ), amounting to only 0:01 dex RMS,

tributed to the careful treatment of systematic

e ects as well as the averaging of several inde-

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

p endent measurements in many cases. In 3 cases,

measurements, this is not preferred here b ecause the V

however, the velo city disp ersions of LGCT are

band photometry then plays a role in determining 2 of

preferable. The LGCT for RB 257 is more

the 3 dimensions of the FP (A and ), and contributes

e e

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

than 4 rms lower than that of Davies et al. and

as log ( )+C . The results, however, of such an analysis

moves RB 257 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 nowworking towards a full K-band FP

NGC 4874 is only 245 km/s, well b elow other es-

derivation (e.g.,Pahre et al. 1995). 3

timates (c.f. Whitmore, McElroy,&Tonry at 304

km/s). The intermediate log ( ) of LGCT (279

km s ) again moves NGC 4874 onto the D

relation in all bands. Finally, the Davies et al.

Table 1

value for NGC 4923 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 4839 31 2.413 1.725 1.238 1.278 1.306

adopting the alternative velo city disp ersions for

NGC 4926 49 2.431 1.281 1.248 1.269 1.293

these three ob jects, the scatter in the D re-

IC 3959 69 2.301 1.060 1.048 1.064 1.093

lation is minimized in all three colors.

IC 3957 70 2.176 0.921 0.938 0.948 0.932

NGC 4923 78 2.318 1.147 1.128 1.144 1.137

Additional supp ort for these three velo city dis-

NGC 4906 118 2.225 1.149 1.058 1.029 1.030

p ersions b eing sup erior comes from the funda-

NGC 4876 124 2.260 0.990 1.008 1.030 1.028

mental plane: in planar ts to log ( ) and of

RB 43 125 2.221 0.515 0.860 0.874 0.825

the other galaxies in B and V, the alternative dis-

NGC 4874 129 2.446 2.040 1.288 1.287 1.324

NGC 4872 130 2.326 0.768 1.058 1.048 1.054

p ersions lower the residuals of the three ob jects

NGC 4867 133 2.346 0.852 1.058 1.060 1.070

in question, with the exception of RB 257 in the

RB 257 136 2.130 0.446 0.868 0.877 0.865

B band, by 2-5 . The e ective radius of RB 257

IC 4051 143 2.348 1.572 1.078 1.107 1.134

varies by a factor of more than 1.5 in the liter-

NGC 4889 148 2.581 1.775 1.468 1.481 1.544

IC 4011 150 2.025 0.976 0.868 0.868 0.854

ature, ranging from 1.4" to 2.2". Seeing e ects

NGC 4886 151 2.215 1.173 1.048 1.036 1.006

maybe dominating the errors in R for this ob-

IC 3998 152 2.192 1.18 0.895 0.903 0.934

ject and its e ective radius must be considered

RB 45 153 2.130 0.813 0.858 0.842 0.863

uncertain.

IC 4045 168 2.324 0.960 1.098 1.123 1.148

IC 4026 170 2.146 1.16 0.917 0.921 0.874

IC 4021 172 2.199 0.777 0.958 0.956 0.955

3. Coma

IC 4012 174 2.253 0.577 0.978 0.999 1.032

NGC 4883 175 2.234 1.00 1.026 1.027 1.050

The IR and optical D relations for the

RB 155 193 2.079 0.858 0.818 0.828 0.808

Coma ob jects are compared in Figure 1 (upp er

NGC 4860 194 2.391 1.185 1.168 1.192 1.228

panels, a-c). The lled circles are ellipticals and

RB 167 207 2.167 0.885 0.898 0.894 0.894

NGC 4881 217 2.340 1.293 1.108 1.134 1.146

the 4-p ointed stars are S0's. The op en circles

NGC 4841A 240 2.422 1.459 1.248 1.299 1.302

are 3 of the highest surface brightness galaxies in

Virgo Cluster

the sample (RB 43, NGC 4867, and NGC 4872).

NGC 4365 2.394 1.88 1.88 1.96

These clearly lie o the trend in K and tend to

NGC 4374 2.458 2.03 2.01 2.07

be high in V and B as well. They will be dis-

NGC 4387 1.924 1.48 1.47 1.47

NGC 4406 2.398 2.02 1.94 2.02

cussed further b elow and are not used in the ts.

NGC 4458 2.025 1.39 1.39 1.37

The \+" is IC 4011 which has a log ( ) just ab ove

NGC 4472 2.458 2.14 2.14 2.23

the cuto of 2.0 applied by D87; it lies well be-

NGC 4473 2.250 1.87 1.86 1.88

low the relation in all 3 colors and so will be

NGC 4478 2.174 1.70 1.67 1.69

NGC 4486 2.558 2.08 2.09 2.21

excluded from further consideration. The lines

NGC 4552 2.417 1.93 1.90 1.97

through the data in Figure 1 are derived from

NGC 4621 2.381 1.91 1.90 1.94

a robust tting technique based on median val-

NGC 4636 2.281 1.86 1.87 1.92

ues (Emerson & Hoaglin 1983), with log ( ) as

NGC 4660 2.296 1.69 1.71 1.73

the indep endent parameter, to the 24 remaining

galaxies. Due to the nature of the robust tting

technique, there is little di erence between ts

with and without the outliers. The S0 galaxies 4

Fig. 1.| Upp er panels: comparison of the B, V, and K D relations for the Coma cluster. Filled

circles are ellipticals, 4-p ointed stars are S0's, op en circles are outliers identi ed in the K band data (see

text). The \+" is IC 4011. Lines are robust ts to the lled circles and 3 S0's. Lower panels: residuals

of the 24 E and S0 ob jects used in the tting. The RMS in K is 1.68 times lower than in B, 1.42 times

lower than in V. A representative error bar is plotted showing 0:02 in Log(D). The error estimates for

Log(D ) and Log(D ) are half this amount.

K V

t well among the ellipticals, as demonstrated The residuals in Log(D) at a given velo city dis-

by Dressler (1987). The b est ts and Sp earman p ersion are plotted in the lower panels of Fig-

correlation co ecients and probabilities are ure 1.

Immediately apparent from Figure 1 is that

Log(D )=1:279 log ( ) 1:855; (1)

the D relation is tighter than either of its

S=0:96; P =7:110

optical counterparts. The RMS scatter of the 24

galaxies is 0.0345, 0.029, and 0.0205 in log(D) for

B, V, and K, resp ectively. The K band relation

Log(D )=1:319 log ( ) 1:938; (2)

reduces the scatter by a factor of 1.68 from B

S=0:97; P =4:93 10

and 1.42 from V. This corresp onds to a scatter

in distance of only 4.8%, roughly the predicted

and

limit from measurement errors (Jorgensen et al.

Log(D )=1:458 log ( ) 2:243; (3)

1993). The RMS for B and V are b oth less than

that found by Jorgensen et al. from the Coma

S=0:98; P =9:26 10 :

S 5

cance of the di erences. A Student's 2 p oint t- FP for a similar sample; this can be attributed

test takes this into account (Press et al. 1984) and to the use of the alternative velo city disp ersions

indicates that the average absolute value of the and removal of the 3 remaining outliers. It can b e

residuals in D is signi cantly lower than in D demonstrated that removing the outliers and us-

K n

or D at the 99.2% and 98.9% con dence levels, ing the b etter velo city disp ersions also improves

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

D shows that they are not signi cantly di erent

In K, there are three ob jects which lie well

at the 45% con dence level. The conclusion is

ab ove the tight relation de ned by the ma jor-

that D is the b est relation at a signi cantly

ity. At V, these ob jects are less clearly outliers

higher level.

and at B, only RB 43 is clearly away from the

rest, due to the increase in sample RMS. The

3.2. Why is K b etter?

trend with bandpass suggests stellar p opulation

e ects, but these three ob jects havetypical V-K

Jorgensen et al. (1993) show that the observed

(BLE). These 3 are among the 5 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 signi cant additional param-

the D relation with surface brightness (Lucey,

eter, ruling out ellipticity, B-r colors or gradients,

Bower, & Ellis 1991) results from the D rela-

isophotal twists, boxiness, and the presence of a

tion b eing a not-quite-optimum pro jection of the

disk. The photometric errors in B, V, and K are

FP. While this may account for these outliers, it

0.02-0.03 magnitudes; since the velo city disp er-

is noted that RB 257 and IC 4012 also have sur-

sions in Figure 1 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" e ects.

log ( ) from Davies et al. is adopted for RB 257).

One p ossible source of this additional scatter,

LGCT redetermined log ( ) for RB 43 and it is

which explains the decrease with wavelength, is

in good agreement with the Davies et al. value.

variations of stellar p opulation parameters (age,

Unusual central dynamics may be resp onsible,

IMF slop e, or metallicity) or the amount of dust

but further longslit observations are needed to

(whichmay b e linked to the stellar p opulation) at

resolve this (Jorgensen et al. 1993). An indep en-

a given velo city disp ersion. All of these will have

dent, comprehensive sp ectroscopic study at high

a larger e ect in the optical than in the IR. Mo d-

signal-to-noise and high disp ersion is needed to

eling carried out by Tonry, Ajhar, & Luppino

place the Coma velo city disp ersions on a truly

(1990) shows that the I band is less a ected by

uniform system.

these variables than V or R, and it is reasonable

to exp ect that the sensitivity is further reduced

3.1. Statistical Signi cance

at K. Mo dels by Bruzual (1983) suggest that this

is the case (Guzman & Lucey 1993). The real

The F-test indicates that the sample variance

situation may b e a go o d deal more complicated,

of D is signi cantly smaller than D at the

K n

however. Early results from the surface bright-

98.5% con dence level, while the improvement

ness uctuation distance indicator technique ap-

over D is signi cant at the 91.0% level. The

plied in the K band showa larger scatter galaxy-

precision of the photometry is such that the ve-

to-galaxy than in the I band (Luppino & Tonry

lo city disp ersions are the limiting factor and con-

1993; Pahre & Mould 1994). 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 improvementin

F-test therefore underestimates the real signi - 6

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

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

the younger p opulations are con ned to the in-

The variations in age, IMF slop e, and metal-

ner 1-2" in galaxies 5-20 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 0.6-0.9 Gyr for simple mo dels with mean

velo city disp ersion determinations) by Gregg &

age of 15 Gyr, typical IMF, and solar or twice

Dressler (1986) shows that di erences do exist

solar metallicity (Gregg 1995, Table 1). Quite

and is consistent with an ap erture e ect. Bower

small changes in the metallicity or IMF can just

et al. (1990), 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-

di erences; taking the observational errors into

vironments. Amuch more detailed sp ectroscopic

account lowers the age scatter by 20-30%. 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

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

at K, then at a given luminosityorvelo city dis- age, the initial mass function, or simply dust is

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

tion should correlate with galaxy color. Galaxies cal.

which have to o small a diameter in the optical

Similarly tight constraints on the ages have

at a given velo city disp ersion must be brighter

b een reached by Bower, Lucey, & Ellis (1992b)

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 be bluer. Thus the diameter residuals

scatter in their Coma V-K color-magnitude re-

from the D relation should anticorrelate with

lations larger than their estimated errors, they

the residuals from the color-magnitude relation.

are reluctant to attribute it to a real variation in

Figure 2 plots the 24 residuals D of Figure 1

the Coma galaxies. The di erences seen in the

against the residuals from the V |(V-K) rela-

D relations of Figure 1 strongly argue that

tion of Bower et al. (1992b), based on a sample

the larger scatter in the optical is due to intrinsic

of 40 E+S0 Coma galaxies. The Sp earman rank

variations among the Coma early typ e galaxies at

correlation co ecient for the residuals is -0.63,

the tiny levels discussed ab ove.

probability1:010 . 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

evidentanticorrelation strongly supp orts the re-

contrast to the often large range in ages at-

sults of Figure 1 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 Intro duction. The disagreement

tion that the additional scatter in the optical is

can be 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. (1993) rep ort no correlation

form stellar p opulation. Because most of the

of residuals from a FP t with B-r color resid-

sp ectroscopic p opulation studies have b een con- 7

the IR. Suchwork is already b eing carried out by

several groups (e.g.,Pahre et al. 1995).

4. Virgo

Figure 3 compares the D and D rela-

n V

tions for 13 Virgo ellipticals with the D re-

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 4387 (\+" sign) b ecause of its low ve-

lo city disp ersion. There is little di erence among

the colors and the RMS residuals are 2-3 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 be attributed primarily to

Fig. 2.| Residuals D from the B band relation

the sizable depth of the Virgo cluster (e.g. Tonry

of Figure 1 plotted against residuals (V-K) from

et al. 1990). The computed intercepts for B, V,

the V band color - magnitude relation of Bower

and K are -1.121, -1.224, and -1.498, resp ectively.

et al. (1992b). The anti-correlation is exp ected if

From these, the relative Coma-Virgo distance in

either stellar p opulations or dust are resp onsible

each color can be derived: 5.42 in B, 5.18 in V,

for the increase in scatter of the B band D

and 5.56 in K, essentially identical given the scat-

relation. Symb ols as in Figure 1.

ter of 0.07 in Log(D). These relative distances

are in go o d agreement with other estimates (D87;

uals at a given velo city disp ersion for the Coma

Sandage & Tammann 1990; Bower et al. 1992b).

galaxies. The p ositive result shown in Figure 2

Bower et al. (1990) present evidence for a

can b e attributed primarily to greater sensitivity

rather large age di erence between the ellipti-

provided by the longer wavelength baseline of V-

cal p opulations of the 2 clusters, based on Rose's

K, as well as complete indep endence of the two

(1985) sp ectral indices applied to comp osite sp ec-

residual quantities. Correlated errors in residu-

tra. The indicated age di erence is approxi-

als b oth involving log ( ) will tend to wash out

mately a factor of two which in turn predicts

any real e ects from other causes.

that the derived distance ratio should b e a rather

Even if the use of optical e ective diameters to

strong function of wavelength, b eing smal ler at

deriveD for the Coma sample is inappropriate

longer wavelengths (Gregg 1995). No such trend

and the results of Figure 1 are completely fortu-

is found, arguing for no signi cant di erence in

itous, Figure 2 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. (1992b) based

IR imaging study of ellipticals in Coma, Virgo,

on broad band colors of ellipticals in the 2 clus-

and other clusters is needed for an indep endent

ters.

assessment of the total improvementavailable at

K and a complete characterization of the FP in 8

Fig. 3.| Upp er panels: comparison of the B, V, and K D relations for the Virgo cluster. The \+"

is the low ob ject NGC 4387. The lines are linear least squares ts (excluding NGC 4387), forcing the

same slop es as in Figure 1 for the Coma cluster. Lower panels: residuals of the 12 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 0:02 in Log(D). The error estimates for Log(D ) and Log(D ) are half this

K V

amount.

5. Summary and Conclusions servational errors alone (Jorgensen et al. 1993).

The improvement is attributed to lower sensi-

Using published single channel K band pho-

tivityatKtovariations in stellar p opulation pa-

tometry combined with optical e ective diame-

rameters (age, metallicity, and slop e of the IMF)

1=4

ters and the assumption of an R law, a provi-

as well as negligible in uence from any dust. Dis-

sional IR version of the diameter|velo city dis-

tance estimates based on K band photometry will

p ersion relation has b een derived for early typ e

be 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 1.68 (1.42) times less scatter

there are small but detectable di erences in ei-

than the B (V) band D relation for 24 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

4.8% per 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. 9

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