The Evolution of Cluster E and S0 Galaxies Measured from The

Home , Abell 2218

Mon. Not. R. Astron. So c. 000, 000{000 (0000) Printed 12 May1999 (MN L T Xstyle le v1.4)

The evolution of cluster E and S0 galaxies measured from

the Fundamental Plane

1;2 yzx 3;4;5 zx 6;7;8 x 3;5 x

Inger Jrgensen Marijn Franx , Jens Hjorth , Pieter G. van Dokkum

McDonald Observatory, The University of Texas at Austin, RLM 15.308, Austin, TX 78712, USA

Gemini Observatory, 670 N. A`ohoku Pl., Hilo, HI 96720, USA (Postal address for IJ)

Kapteyn Institute, P.O.Box 800, 9700 AVGroningen, The Netherlands

Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138, USA

Leiden Observatory, P.O.Box 9513, 2300 RA Leiden, The Netherlands (Postal address for MF and PvD)

Institute of Astronomy, Madingley Road, Cambridge CB3 0HA, UK

NORDITA, Blegdamsvej 17, DK-2100 Copenhagen , Denmark

Astronomical Observatory, University of Copenhagen, Juliane Maries Vej 30, DK-2100 Copenhagen , Denmark (Postal address for JH)

May 5, 1999, accepted for publication in Mon. Not. Royal Astron. Sco., Gemini Preprint #43

ABSTRACT

Photometry has b een obtained for magnitude limited samples of galaxies in the two

rich clusters Ab ell 665 (37 galaxies) and Ab ell 2218 (61 galaxies). Both clusters have

a redshift of 0.18. The limiting magnitude of the samples is 19 in the I-band. Sp ec-

troscopy has b een obtained for seven galaxies in A665 and nine galaxies in A2218,

all of whichalsohaveavailable photometry. Sp ectroscopy has b een obtained for two

additional galaxies in A2218, one of whichisabackground galaxy.

E ectiveradiir and mean surface brightnesses were derived from the pho-

e e

tometry. The typical uncertainties are 0:078 in log r and 0:12 in log . The

e e

combination log r +0:82 log that enters the Fundamental Plane (FP) has an un-

e e

certainty of only 0:018. The sp ectroscopywas used for measurements of the velo city

disp ersions, . The typical uncertaintyis 0:023 on log .

The data are used to establish the FP,logr = log + log + , for the

e e

clusters. The FP for these two clusters adds imp ortantknowledge ab out the prop erties

of E and S0 galaxies in the relatively unexplored redshift interval 0.05 to 0.3. Wehave

compared the FP for A665 and A2218 with the FP for the three clusters CL0024+16,

CL1358+62 and MS2053-04 with redshifts between 0.33 and 0.58, and with the FP

for the Coma cluster. The scatter around the FP is similar for all six clusters. We

nd that the FP for the intermediate redshift clusters has a smaller co ecient than

found for the Coma cluster and other nearby clusters. This mayeitherbecausedby

selection e ects for the intermediate redshift clusters or by di erences in the evolution

of low luminosity galaxies and high luminosity galaxies.

The mass-to-light (M/L) ratios, as measured from the FP,change with redshift.

At z =0.18 the M/L ratio for photometry in Gunn r in the rest frame of the clusters

is (11 7)% smaller than for the Coma cluster. Using the data for A665 and A2218

together with the previously published data for CL0024+16, CL1358+62 and MS2053-

04, we nd that the M/L ratios for photometry calibrated to Gunn r change with

redshift as log M=L =(0:26 0:06)z for q =0:5. This change in the M/L ratio

r o

is equivalent to the absolute magnitudes changing as M =(0:65 0:15)z .These

new results are consistent with the previously published analysis for CL0024+16,

CL1358+62 and MS2053-04.

For q =0:5 the results are consistent with passiveevolution of a stellar p opulation

which formed at a redshift larger than ve. For q =0:15 the formation redshift must

b e larger than 1.7. Our new data for A665 and A2218 con rm the gradual and slow

evolution of the bright E and S0 galaxies. However, p ossible star formation in E and S0

galaxies during the last 3-4 Gyr of the history of the Universe, as well as the selection

e ects complicate the interpretation of the data.

Key words: galaxies: clusters: individual: Ab ell 665, Ab ell 2218 { galaxies: elliptical

and lenticular, cD { galaxies: evolution { galaxies: stellar content.

0000 RAS

2 I. Jrgensen, M. Franx, J. Hjorth, P. G. van Dokkum

plies a relation b etween the M/L ratios and the masses of 1 INTRODUCTION

the galaxies.

Observational studies show that the formation and evolu-

The scatter of the FP is very low, equivalent to a scatter

tion of galaxies is a complex pro cess, whichmayinvolve in-

of 23% in the M/L ratio (e.g., JFK96). Thus, the FP o ers

teractions, star bursts and infall (e.g., Dressler et al. 1994ab;

the p ossibility of detecting even small di erences in the M/L

Lilly et al. 1996; Mo ore et al. 1996). It has also b een found

ratios by observing a handful of galaxies in a distant cluster.

that some nearby E and S0 galaxies mayhave exp erienced

The FP has been used to study the evolution of the

star formation in the last 3-4 Gyr. Caldwell et al. (1993)

M/L ratios of cluster galaxies as a function of redshift up

found some E and S0 galaxies in the Coma cluster to have

to a redshift of 0.83 (van Dokkum & Franx 1996; Kelson

p ost-starburst sp ectra, and Fab er et al. (1995) suggest that

et al. 1997; Bender et al. 1998; van Dokkum et al. 1998;

nearby eld E galaxies havea substantial variation in the

Pahre, Djorgovski & de Carvalho 1999). All of these studies

mean age of their stellar p opulations.

nd the M/L ratios of the galaxies to increase slowly with

In order to study the evolution of galaxies we need to

decreasing redshift. Only the study byPahre et al. contains

study b oth the morphological evolution as well as the evolu-

clusters with redshifts b etween 0.05 and 0.3. In this pap er

tion of the luminosities and the mass-to-light (M/L) ratios of

we establish the FP for the tworich clusters Ab ell 665 and

the galaxies. High-resolution imaging with the Hubble Space

Ab ell 2218. Both clusters have a redshift of 0.18, adding

Telescop e (HST) and from the ground, combined with sp ec-

data to a redshift interval not well-covered by the previous

troscopy from the ground make it p ossible to carry out this

studies.

kind of studies. Studies of the morphological evolution show

We use the data for A665 and A2218, data for the three

that the fraction of spiral galaxies and irregular galaxies in

clusters studied byvan Dokkum & Franx (1996) and Kelson

clusters was higher at larger redshifts (e.g., Dressler et al.

et al. (1997), and data for the Coma and the HydraI clusters

1994ab; Oemler et al. 1997; Dressler et al. 1997; Couchet

to study how the FP and the M/L ratios of the E and S0

al. 1998). A detailed investigation of how the luminosities

galaxies change with redshift. The full sample covers ab out

of disk galaxies change with redshift is p ossible using the

half the age of the Universe.

Tully-Fisher (1977) relation. Vogt et al. (1996) established

The available photometry and sp ectroscopy,aswell as

the Tully-Fisher relation for a sample of eld galaxies with

the derivation of the photometric and sp ectroscopic parame-

redshifts b etween 0.1 and 1 and found a luminosityevolution

ters is describ ed in Sections 2 and 3, resp ectively. The details

in the B-band of 0: 6between z = 1 and the present.

of the data reduction are provided in App endix A and B.

The Fundamental Plane (FP) (Dressler et al. 1987;

App endix A also contains photometric parameters (e ective

Djorgovski & Davis 1987) for elliptical galaxies makes it

radii, mean surface brightnesses and colors) of magnitude

p ossible to study how the luminosities and the M/L ra-

limited samples of galaxies in A665 and A2218. Section 4

tios of these galaxies change with redshift. Also, S0 galaxies

brie y describ es the data for the other clusters. The FP is

in nearby clusters follow the FP (e.g., Jrgensen, Franx &

analyzed in Section 5. In this section we also discuss the

Kjrgaard 1996, hereafter JFK96). The FP relates the ef-

evolution of the M/L ratios of the galaxies. The conclusions

fective radius, r , the mean surface brightness within this

are summarized in Section 6.

radius, , and the (central) velo city disp ersion, , in

a tight relation, which is linear in log-space. For 226 E

and S0 galaxies in nearby clusters JFK96 found log r =

2 THE PHOTOMETRY

1:24 log 0:82 log + cst, for photometry in Gunn r .

0:24 0:02

This relation may be interpreted as M=L / M r

The central parts of the two rich clusters Ab ell 665 and

(cf., Fab er et al. 1987). The change of the M/L ratio with

Ab ell 2218 were observed with the Nordic Optical Telescop e

the mass is partly caused bychanges in the stellar p opula-

(NOT), La Palma, in March 1994. Observations were done in

tions. Some of the apparentchange may also b e explained

the I-band and the V-band. The sizes of the observed elds

0 0 0 0

by non-homology of the galaxies (e.g., Hjorth & Madsen

are 3: 4 2: 7 for A665 and 2: 8 3: 5 for A2218. Table 1

1995). Throughout this pap er we assume that the FP im-

summarizes the instrumentation for the observations. The

I-band images were taken as individual 600 sec exp osures,

with a few shorter exp osures. The total exp osure time, the

Based in part on observations made with the NASA/ESA Hub-

seeing and the sky brightness of each of the nal co-added

ble Space Telescop e obtained at the Space Telescop e Science In-

images are given in Table 2. The V-band images were taken

stitute, which is op erated byAURA under NASA contract NAS5-

on another night than the I-band images, and have rather

26555; the Multiple Mirror Telescop e, a joint facility of the Smith-

p o or seeing.

sonian Institution and the University of Arizona; and the Nordic

Optical Telescop e, op erated on the island of La Palma jointly by

A665 was observed with the HST with the Wide-Field-

Denmark, Finland, Iceland, Norway and Sweden, in the Span-

Planetary-Camera 2 (WFPC2) in the lters F606W and

ish Observatorio del Ro que de los Muchachos of the Instituto de

F814W. Two elds were observed giving a total coverage

Astro sica de Canarias.

of approximately 9.4 square arc-minutes on the WF chips.

Hubble Fellow

For A2218 we use HST/WFPC2 archival data obtained in

Visiting Astronomer, Kitt Peak Observatory, a division of Na-

the F702W lter. One eld in Ab ell 2218 was observed with

tional Optical Astronomy Observatories, which is op erated by

the HST, covering approximately 4.7 square arc-minutes on

AURA under contract with the National Science Foundation.

the WF chips. The images were taken as individual exp o-

E-mail: [email protected], [email protected],

sures with exp osure times b etween 1600 sec and 2300 sec.

[email protected], [email protected]

The total exp osure times for the co-added images are given

in Table 3.

0000 RAS, MNRAS 000, 000{000

The Evolution of cluster E and S0 galaxies: The Fundamental Plane 3

Table 1. Instrumentation

Photometry Sp ectroscopy

Dates March 4-9, 1994 Sept.-Dec., 1994 Jan. 18-19, 1991 June 6-8, 1994

Telescop e NOT, LaPalma HST MMT KPNO 4m

Camera/Sp ec. Astromed WFPC2 Red Channel Sp ec. R&C Sp ec.

CCD EEV 1152770 Loral TI5 T2KB

r.o.n. 4.5 e 5.0 e 9.0 e 7.4 e

gain 0.9 e /ADU 7.5 e /ADU 2.0 e /ADU 2.6 e /ADU

00 00 a 00 00

Pixel scale 0.1635 /pixel 0.0996 /pixel 0.6 /pixel 0.69 /pixel

00 00

Slit width ...... 1.8 1.9

 

Sp ectral res., ...... 1.71A 1.38A

 

Wavelength range ...... 5780-6420A 4255-6970A

Cluster(s) A665, A2218 A665, A2218 A665 A2218

a b

Notes. All galaxies studied in this pap er are imaged on the WF chips of WFPC2. The unvignetted

range is 4550-6500A.

taking the point-spread-function (PSF) into account. The

Table 2. NOT images

output from the t is the center of the galaxy (x,y ), the

Image Filter t seeing m

exp

sky

e ective radius, r , the surface brightness at the e ective

00 m 2

[sec] [ ] [ =arcsec ]

radius, I , the ellipticity, , the p osition angle of the ma jor

axis and the level of the sky background. All galaxies pre-

A665 eld 1 I 9600 0.66 20.0

1=4

A665 eld 1 V 1200 1.86 21.8

sented here were tted with r pro les. The mean surface

A665 eld 2 I 5874 0.60 19.6

brightness <> was derived from the lo cal surface bright-

1=4

A665 eld 2 V 1200 2.03 21.8

ness at r under the assumption that the galaxies have r

A2218 eld 1 I 5400 0.70 19.3

pro les.

A2218 eld 1 V 1200 3.33 21.2

The PSF images for the NOT I-band images were con-

A2218 eld 2 I 5400 0.82 19.4

structed from 2-3 well-exp osed stars in each image. The PSF

A2218 eld 2 V 1200 4.23 21.2

00 00

images have a size of 10: 5 10: 5. It was tested that the PSFs

Notes. The seeing is measured as the full-width-half-maximum

did not vary over the eld. The PSF images for the HST ob-

(FWHM) of a Gaussian t to the core of images of stars. A665

servations were constructed using Tiny Tim (Krist & Ho ok

0 0

00 00

eld 1 is centered 0: 6 east and 0: 3 south of the BCG; eld 2 is

1997) and have a size of 3 3 .

0 0

o set 1: 7tothewest of eld 1. A2218 eld 1 is centered 0: 3to

All galaxies brighter than an apparent total magnitude

the south of the BCG; eld 2 is o set 1: 7 to the north of eld 1.

in the I-band of m 20 were tted. The brightest cluster

galaxies (BCG) in b oth clusters were tted within a radius

Table 3. HST images

of 1-2r . The fainter galaxies were tted within the radius

m 2

where the lo cal surface brightness reached 26 =arcsec in

Image Filter t [sec]

exp

the I-band. This radius is typically 5-7r .

A665 eld 1 F606W 4400

Before tting the fainter galaxies the BCGs were mo d-

A665 eld 1 F814W 4400

eled with the program Galphot (Franx, Illingworth &

A665 eld 2 F606W 5100

Heckman 1989a; Jrgensen, Franx & Kjrgaard 1992).

A665 eld 2 F814W 4800

This program ts a mo del of ellipses to the isophotes of

A2218 F702W 6500

the galaxy. The mo del was then subtracted. The use of

Notes. A665 eld 1 is centered 0: 3 south-east of the BCG. A665

Galphot ensures that gradients in the background due to

eld 2 is centered 1: 7west of the BCG. The observation of A2218

signal from the BCG are prop erly removed b efore tting

is centered 0: 9 east of the BCG.

the fainter galaxies. Further, the isophotes for the BCG in

A2218 are not co-centric, as also noticed by Kneib et al.

The basic reductions of the images are describ ed in Ap-

(1995). Galphot handles this prop erly while the tting

p endix A, which also covers the calibration of the photom-

technique describ ed ab ove uses a xed center and there-

etry to the standard passbands I and V . In the following

fore leaves large residuals, which in turn a ect the results

we describ e the determination of the global photometric pa-

for the fainter galaxies. The BCGs were also mo deled with

rameters (e ective radii and mean surface brightnesses) and

the 2-dimensional tting technique. The e ectiveradiide-

the calibration of the photometry to Gunn r and Johnson

rived from this agree within 0.02 in log r with the results

V in the rest frames of the clusters.

from ts to the growth curves pro duced by Galphot.Fit-

ting the growth curves pro duced by Galphot do es not give

the p ossibility of 2-dimensional mo deling the e ect of the

2.1 Global parameters

PSF. In the following, we therefore use results from the 2-

Determination of the e ective radius, r , and the mean sur-

dimensional tting technique.

face brightness inside this radius, <> ,was done following

Table 4 lists the derived e ective parameters. Only

the technique describ ed by van Dokkum & Franx (1996).

galaxies for whichwe also have sp ectroscopy are presented

This technique uses the full 2-dimensional information in

in this table. Tables A1 and A2 contain the derived e ec-

the image. Each galaxy is t with a 2-dimensional mo del,

tive parameters for all galaxies brighter than 19 and within

0000 RAS, MNRAS 000, 000{000

4 I. Jrgensen, M. Franx, J. Hjorth, P. G. van Dokkum

Table 4. Photometric parameters

NOT HST

2 2

Galaxy Field log r <> <> <> (V I ) log r <> <> <> (V I )

e c e c

e e e e e e

N N

pix pix

[arcsec] (I ) (r ) (V ) [arcsec] (I ) (r ) (V )

c z z c z z

A665-1150 1 1.012 21.82 2.9 22.67 22.96 1.54 1.056 21.97 5.2 22.82 23.11 1.53

A665-1168 1 0.333 19.78 2.1 20.63 20.92 1.54 0.376 19.93 1.3 20.78 21.06 1.52

A665-1196 1 -0.352 17.73 9.0 18.58 18.86 1.51 -0.149 18.58 7.9 19.43 19.68 1.47

A665-2105 2 0.876 22.09 29.7 22.92 23.07 1.20 1.003 22.42 18.5 23.23 23.41 1.24

A665-2108 2 -0.205 19.48 1.5 20.33 20.61 1.53 ......

A665-2111 2 -0.170 18.56 6.7 19.41 19.74 1.62 -0.011 19.17 4.1 20.02 20.29 1.51

A665-2144 2 -0.189 18.83 1.6 19.68 19.96 1.52 -0.096 19.22 1.6 20.06 20.29 1.41

A2218-L118 1 0.051 19.20 5.5 20.06 20.39 1.62 0.097 19.30 3.1 20.16 20.48 ...

A2218-L148 1 -0.075 18.53 3.1 19.39 19.70 1.59 0.067 19.03 6.4 19.89 20.20 ...

A2218-L198 1 -0.061 19.14 2.0 19.99 20.29 1.55 -0.143 18.81 1.9 19.67 19.96 ...

A2218-L244 1 0.934 22.01 2.0 22.87 23.15 1.53 0.930 22.02 1.4 22.88 23.16 ...

A2218-L341 1 -0.124 18.27 2.6 19.13 19.42 1.56 -0.116 18.26 4.1 19.11 19.41 ...

A2218-L391 1 1.403 23.07 3.6 23.92 24.18 1.48 1.412 23.25 21.0 24.10 24.37 ...

A2218-L430 2 -0.033 19.06 1.4 19.92 20.24 1.62 -0.061 18.95 1.0 19.81 20.13 ...

A2218-L482 2 0.036 18.77 2.2 19.63 19.95 1.62 ......

A2218-L535 2 0.238 19.63 1.9 20.49 20.82 1.63 ......

a b

Notes. Brightest cluster galaxy. E+A galaxy. Identi cations of galaxies in A2218 are from Le Borgne et al. (1992). Field { the NOT eld

that contains the galaxye, see Table 2 for seeing values. The observed magnitudes lab eled I and V and the colors (V I ) are standard

c c

calibrated to the Johnson-Kron-Cousins photometric system, and corrected for galactic extinction. The formal tting uncertainties are

typically as follows. log r : 0:006 for NOT data, 0:002 for HST data. <> : 0:02 for NOT data, 0:007 for HST data. The typical

(random) uncertainty on the (V I ) is 0.01. The go o dness-of- t is given as =N , where N is the numb er of pixels within the

pix pix

2 2 2

tting radius. = (n n ) = ,withthesumover all the pixels within the tting radius. n is the signal in pixel i, n

i i

i;mo del i;mo del

the noise (photon- and read-out-noise) in the pixel. is the mo del value in the pixel, and 

Magnitudes r are fully corrected Gunn r magnitudes in the rest frames of the clusters, see equations (2) and (3). Magnitudes V are

z z

fully corrected Johnson V magnitudes in the rest frames of the clusters, see equations (4) and (5).

ally of the order 0: 05 p er dex in the radius, for colors based the elds covered by the NOT images. The magnitudes were

on Johnson B and Gunn r (e.g., Jrgensen et al. 1995a). standard calibrated as describ ed in App endix A. The I

The color gradients in the ap erture magnitudes are smaller, magnitudes from the HST data have b een o set to consis-

typically less than 0: 04 per dex in the radius. Assuming tency with the ground-based magnitudes, see App endix A.

that the color gradients of the galaxies at redshift 0.18 are Table 4 gives typical values of the formal tting uncertain-

similar to those of nearby galaxies, the derived colors are ex- ties. However, a comparison of the NOT and the HST data

p ected to deviate less than 0:02 from global colors within results in more realistic estimates of the uncertainties, see

the e ective radii. This results in a negligible e ect of less App endix A. We nd the uncertainties of log r and <>

than 0: 002 on the calibrated magnitude in Gunn r in the to be 0:078 and 0:29, resp ectively. Because of the cor-

rest frame of the clusters, cf. Sect. 2.3. relation of the errors in log r and <> , the combination

For the galaxies in A665 colors were also derived from log r 0:328<> that enters the FP has an uncertainty

the HST images. We used ap ertures with radii of 1: 5. The of only 0:018. In the analysis of the FP for the clusters

ap erture size is smaller than those used for the NOT images (Section 5), weusetheaverage of the e ective parameters

in order to take advantage of the b etter spatial resolution determined from the HST observations and the NOT obser-

of the HST images and limit the amountofcontamination vations, whenever results from b oth telescop es are available.

from neighb oring ob jects. No correction for zero p oint o -

sets between the ground-based photometry and the HST

2.2 Colors

photometry were applied to the colors, since we have no

reliable wayofchecking the zero p oint for the HST V mag-

The colors of the galaxies were determined from the ground-

nitudes. Thus, we implicitly assume that the zero p ointdif-

based observations. First, the I-band images were convolved

ference b etween the ground-based photometry and the HST

to the seeing of the V-band images. This minimizes the er-

photometry is the same in the I-band and the V-band. The

rors in the derived colors due to mismatched seeing in the

colors derived from the HST observations are on average

two passbands. The colors were derived within ap ertures

00 00

0.04 mag bluer than the ground-based colors, cf. Table 4.

with radii 1: 64 (10 pixels) and 2: 94 (18 pixels) for A665

This maybecausedby errors in the HST colors due to the

and A2218, resp ectively. The larger ap erture for A2218 was

uncertainties in the magnitude zero points. Alternatively,

necessary due to the very p o or seeing of the V-band images.

uncertainties maybeintro duced by the p o or seeing of the

The colors within these ap ertures are in the following used

ground-based V images. The e ect on the magnitudes cali-

as global colors of the galaxies, see Table 4 for the sample

brated to Gunn r in the rest frame of the cluster will b e less

that also has sp ectroscopy and Tables A1 and A2 for all

than 0: 003, cf. Sect. 2.3.

galaxies brighter than 19 .For nearby E and S0 galaxies,

the color gradients in the lo cal surface brightnesses are usu-

0000 RAS, MNRAS 000, 000{000

The Evolution of cluster E and S0 galaxies: The Fundamental Plane 5

Table 5. Uncertainties a ecting the photometric calibration

Cluster Tel. Calibration/Parameter Random unc. Systematic unc.

A665 NOT Instrumental I 0.01

A2218 NOT Instrumental I 0.015

A665,A2218 NOT Standard I 0.021

A665,A2218 NOT Standard V 0.014

A665,A2218 NOT Standard (V I ) 0.025

A665 HST Holtzman et al. (1995) I 0.015

A665 HST Holtzman et al. (1995) (V I ) 0.028

A665 HST O set to ground-based I 0.009

A2218 HST Holtzman et al. (1995) I 0.017

A2218 HST O set to ground-based I 0.013

0.02 A665,A2218 NOT,HST (V I ) vs. (V I )

c meas c r

A665,A2218 NOT Total (V I ) 0.032

A665 HST Total (V I ) 0.034

A665,A2218 NOT,HST Gunn r in rest frame, transformation 0.02

A665,A2218 NOT,HST Johnson V in rest frame, transformation 0.02

A665 NOT Total r 0.028 0.01

A665 HST Total r 0.024 0.02

A665 NOT Total V 0.032 0.01

A665 HST Total V 0.029 0.02

A2218 NOT Total r 0.028 0.015

A2218 HST Total r 0.024 0.028

A2218 NOT Total V 0.032 0.015

A2218 HST Total V 0.029 0.028

Notes. Contributions from the transformation (V R ) = 0:52(V I ) and the transformation from

c c

Holtzman et al. (1995). Contribution from transformation, only.

V = I +0:48(V I )+0:40 (4) 2.3 Calibration to the rest frame of the clusters

z c c

for A665 and

In order to compare the FP for A665 and A2218 with results

for nearbyclusterswe calibrate the photometry to Gunn r

V = I +0:49(V I )+0:39 (5)

z c c

in the rest frame of the clusters. Following Frei & Gunn

for A2218.

(1994), the magnitude in a broad passband can b e written as

Because the photometry for the b est comparison sample

m = c 2:5log F ( ), with c b 48:60. b are given

i i i i i i

(the Coma cluster) is available in Gunn r , and also b ecause

by Frei & Gunn. F ( ) is the ux densityat the e ective

of the uncertainty in the derived colors, cf. Section 2.2, we

wavelength of the passband. We assume the ux densityin

will primarily use the mean surface brightnesses calibrated

the redshifted Gunn r band is related to the observed V-

to Gunn r throughout the rest of this pap er.

band and I -band as F ( (z )) = F ( ) F ( ) ,cf.van

c r V I

Dokkum & Franx (1996). The magnitudes in Gunn r in the

rest frame of the clusters can then b e written

2.4 Summary of uncertainties

r = I + (V I ) c (c c )+c +2:5 log (1 + z )(1)

z c c I V I r

c c

Table 5 summarizes the di erent sources on uncertainty af-

where is derived from the sp ectral energy distribution.

fecting the photometric calibration. The entries noted as

The I magnitudes and the colors (V I ) are the observed

\Total" uncertaintygive the total uncertainty on the listed

c c

standard calibrated values, corrected for galactic extinction.

parameter, while all other entries give the contribution from

A665 has z=0.181 (Oegerle et al. 1991). From the sp ec-

the individual calibration step. The uncertainties on the in-

tral energy distributions for E and Sa galaxies given by Cole-

strumental I magnitudes for the NOT data refer to the

man, Wu&Weedman (1982) we nd =0:053. The

consistency of the magnitude zero points of the co-added

A665

resulting calibration to reach Gunn r in the rest frame is

images, cf. Sect. A1. The uncertainties on the standard cal-

ibrated magnitudes for the NOT data are the rms scatter

r = I +0:053(V I )+0:77 (2)

z c c

of the standard transformations, cf. Sect. A3. For the HST

data the uncertainties consist of random uncertainties due to

A2218 has z=0.176 (Le Borgne, Pello & Sanahuja 1992). We

the uncertainties in the transformations adopted from Holtz-

nd =0:062, and the resulting calibration is

A2218

man et al. (1995), cf. Sect. A3, and systematic uncertainties

r = I +0:062(V I )+0:76 (3)

z c c

in matching the HST photometry to the ground-based sys-

tem. The colors (V I ) are sub ject to an additional uncer-

The mean surface brightnesses, <> , calibrated to Gunn r

tainty b ecause we measure the colors within xed ap erture

in the rest frame of the clusters are given in Table 4.

sizes rather than within the e ective radii, cf. Sect. 2.2. Fi-

Table 4 also lists the mean surface brightnesses cali-

nally, the transformations used to calibrate the magnitudes

brated to Johnson V in the rest frame of the clusters. The

to Gunn r and Johnson V in the rest frames of the clus-

calibrations to reach Jonhson V are

ters contribute to the uncertainties. The last part of Table

0000 RAS, MNRAS 000, 000{000

6 I. Jrgensen, M. Franx, J. Hjorth, P. G. van Dokkum

5 summarizes the total uncertainties, random or systematic,

on the calibrated magnitudes r and V . The magnitudes

z z

havetypical random uncertainties of 0: 03, and typical sys-

tematic uncertainties of 0: 02.

3 THE SPECTROSCOPY

A665 galaxies were selected for the sp ectroscopic observa-

tions from a ground-based R-band image kindly provided

00 00

by M. Birkinshaw. The ux of the galaxies within a 1: 8 8

ap erture was used as selection criterion. Sp ectra of 7 galax-

ies in A665 were obtained with the MMT in January 1991,

cf. Table 1. The total integration time was 9 hours. For one

of the galaxies the signal-to-noise was to o low to derive a

reliable value of the velo city disp ersion.

For A2218 we used the catalog by Le Borgne, Pello&

Figure 1. The instrumental resolution for the A2218 sp ectra,

as derived from He-Ne-Ar calibration sp ectra. Triangles { central

Sanahuja (1992) as the main source for the selection of galax-

slit-let; b oxes and circles { the two slit-lets closest to the edges of

ies, supplemented with the catalog by Butcher, Oemler &

the CCD. The lled symb ols are based on sky lines. The resolution

Wells (1983). Galaxies were selected on magnitude and color.

derived from the sky lines agree with the resolution derived from

The (B R ) color was required to b e within 0.15 of the color-

the calibration sp ectra. The solid lines show the tted functions.

magnitude relation for the red cluster galaxies. One redder

The dot-dashed lines show the approximate wavelength interval,

galaxy,BOW97, was included. This galaxy turned out to b e

whichwas used for determination of the velo city disp ersions.

a background galaxy. Sp ectra of 10 galaxies in A2218 were

obtained with the KPNO 4m in June 1994, cf. Table 1. The

total integration time was 11.8 hours.

galaxy sp ectrum. The variation of the resolution with wave-

The basic reductions of the sp ectroscopy are describ ed

length was taken into account.

in App endix B, which also shows the nal sp ectra of the

galaxies. Here we describ e the determination of the velo city

3.2 Fourier Fitting

disp ersions (see also Franx 1993ab for the galaxies in A665).

The velo city disp ersions, ,were determined by tting the

galaxy sp ectra with the template sp ectra using the Fourier

3.1 Instrumental resolution and template stars

Fitting Metho d (Franx, Illingworth & Heckman 1989b). The

Determination of velo city disp ersions of galaxies is usually

Fourier transforms of the sp ectra were ltered to avoid the

done with sp ectra of template stars obtained with the same

low frequencies. We used a limit equivalentto (100A)

instrumentation as the galaxy sp ectra. Due to the large red-

in the rest frame of the clusters. This is the same limit used

shifts of A665 and A2218 this will not work for these clus-

by Jrgensen, Franx & Kjrgaard (1995b). In the case of

ters. A further complication is that the sp ectra of A665 and

A2218, the nal velo city disp ersion is the average of the de-

A2218 were obtained through multi-slit masks and the in-

terminations with the three di erent template stars. The for-

strumental resolution varies with wavelength and from slit-

mal tting uncertainty on log is typically 0.023. For A665

let to slit-let.

the mean sp ectra over the central 1: 8were tted. Thus, the

00 00

Following van Dokkum & Franx (1996), we mapp ed the

ap erture size is 1: 81: 8. The ap erture size used for A2218

00 00

instrumental resolution from He-Ne-Ar lamp exp osures. Fur-

was 1: 93: 45.

ther, the instrumental resolution was determined from the

For the A2218 galaxies we exp erimented with tting

sky lines in the nal average sp ectra of the galaxies. In all

the sp ectra in a limited wavelength range around the G-

cases Gaussian pro les were tted to the emission lines. Fig.

band region (rest frame 4080-4700A) and around the Mgb

1 shows the instrumental resolution versus wavelength for

region (rest frame 4800-5310A), as well as the full available

representative slit-lets for the A2218 sp ectra. The determi-

wavelength range (rest frame 4080-5310A). Fig. 2 shows the

nations from lamp exp osures and from sky lines agree. Low

comparison of the velo city disp ersions derived from the G-

order p olynomials were tted to the instrumental resolution

band region and from the Mgb region. The median o set in

versus wavelength for each slit-let.

log is 0:00 0:02. In the following the results from tting

We used a sp ectrum of HD192126 as the template star

the full wavelength range are used.

for the A665 sp ectra. The sp ectrum of the star was ob-

The velo city disp ersions were ap erture corrected to a

tained with the Canada-France-Hawaii Telescop e by K. Kui-

circular ap erture with diameter 1.19 h kp c, equivalentto

jken. The wavelength range for the sp ectrum is 4650-5650A,

3.4 arcsec at the distance of the Coma cluster. We adopt

with a resolution of = 0:56A. As template stars for

the technique for the ap erture correction established by

inst

the A2218 sp ectra we used sp ectra of HD56224, HD72324

Jrgensen et al. (1995b). The applied ap erture corrections

and HD102494 obtained with the Keck Telescop e in May

are 0.0215 and 0.028 in log for A665 and A2218, resp ec-

1996 by D. Kelson. The wavelength range of these sp ectra

tively.Table 6 gives the raw determinations of the velo city

 

is 4002-5314A, with a resolution of =0:9A.

disp ersions as well as the ap erture corrected values.

inst

For each galaxy sp ectrum the sp ectra of the template

The velo city disp ersion measurements for A665 and

stars were convolved to the instrumental resolution of the

A2218 are based on two indep endent observing runs. Fur-

0000 RAS, MNRAS 000, 000{000

The Evolution of cluster E and S0 galaxies: The Fundamental Plane 7

Table 6. Sp ectroscopic parameters

Galaxy log log z S/N

log 

(obs) (3: 4)

A665-1150 2.447 2.468 0.019 0.1831 54.5

A665-1168 2.356 2.378 0.019 0.1785 54.5

A665-1196 2.334 2.355 0.028 0.1691 32.6

A665-2105 2.127 2.149 0.035 0.1699 40.7

A665-2108 ...... 0.1939 16.5

A665-2111 2.369 2.391 0.025 0.1860 37.2

A665-2144 2.267 2.288 0.034 0.1729 29.4

A2218-L118 2.280 2.308 0.023 0.1748 32.2

A2218-L148 2.371 2.399 0.023 0.1833 27.6

A2218-L198 2.309 2.337 0.027 0.1737 22.4

A2218-L244 2.287 2.315 0.020 0.1772 32.2

A2218-L341 2.451 2.479 0.023 0.1630 25.2

A2218-L391 2.483 2.511 0.022 0.1731 38.1

Figure 2. The di erence between velo city disp ersions derived

A2218-L430 2.093 2.121 0.035 0.1810 21.7

from the Mgb region (rest frame 4800-5310A) and from the G-

A2218-L482 2.342 2.370 0.018 0.1788 35.2

band regon (rest frame 4080-4700A) versus the velo citydisper-

A2218-L535 2.270 2.298 0.021 0.1809 31.1

sions derived from the full wavelength range. Only data for galax-

A2218-BOW33 2.186 2.214 0.038 0.1734 18.2

ies in A2218 are shown. The median o set in log is 0:00 0:02.

A2218-BOW97 ...... 0.291 12.7

Notes. (obs) { raw measurements. (3: 4) { ap erture corrected to a

1 00

circular ap erture with diameter 1.19 h kp c, equivalentto3: 4at

ther, in the analysis (Sect. 5) we will use the data together

the distance of the Coma cluster. { formal uncertainty from

log 

the Fourier Fitting Metho d. S/N { signal-to-noise p er Angstrom

with measurements from other indep endent observing runs.

in the wavelength interval used for the Fourier tting. Identi ca-

Wehavenoway of testing the consistency of the velo city dis-

tions for A2218 are from Le Borgne et al. (1992) and Butcher et

p ersion measurements from the di erent runs, since there

al. (1983).

are no galaxies in common between the runs. For nearby

galaxies (redshifts less than 0.1) it is in general found that

the co ecients of the FP wehave also used data for galax-

velo city disp ersion measurements from di erent runs can de-

ies in the HydraI cluster. The main purp ose of including

viate with 0.01 to 0.025 in log (e.g., JFK1995b; Smith et

the HydraI cluster is to add more high luminosity galax-

al. 1997; Wegner et al. 1998). We adopt the mean o set of

ies to the nearby sample. We use the sample of E and S0

0.023 in log found byWegner et al. in their analysis of 33

galaxies byMilvang-Jensen & Jrgensen (1999). The sam-

observing runs to b e the typical systematic uncertaintyfor

0 0

ple covers the central 68 83 of the cluster. A total of 45

velo city disp ersion measurements from indep endent observ-

galaxies have photometry (in Gunn r ) and sp ectroscopy.The

ing runs. The uncertainty on the applied ap erture correction

sample is 80% complete to m =14: 5inGunnr (equiva-

is exp ected to b e signi cantly smaller than this systematic

m m

lenttoM = 20: 0, for a distance mo dulus of 34: 5). For

uncertainty.

the galaxies brighter than M = 20: 75, the FP for the

HydraI cluster is the same as for the Coma cluster.

4 DATAFOR OTHER CLUSTERS

4.2 Intermediate redshift clusters

4.1 The Coma cluster and the HydraI cluster

In the following analysis we also use data for the three inter-

The Coma cluster is in the following used as the low redshift

mediate redshift clusters CL0024+16 (van Dokkum & Franx

reference for our study of changes in the FP as a function of

1996), CL1358+62 and MS2053-04 (Kelson et al. 1997). Van

the redshift. We use the sample of E and S0 galaxies, which

Dokkum & Franx and Kelson et al., who previously stud-

has photometry in Gunn r from Jrgensen et al. (1995a), see

ied these clusters, give e ective radii, magnitudes V cal-

also Jrgensen & Franx (1994). The sample covers the cen-

0 0

ibrated to the V-band in the rest frame of the clusters,

tral 64 70 of the cluster. Velo city disp ersions published by

colors, and velo city disp ersions. We establish the transfor-

Davies et al. (1987), Dressler (1987), and Lucey et al. (1991)

mations from the observed I magnitudes and (R I )to

c c c

have been calibrated to a consistent system and ap erture

Gunn g in the rest frames of the clusters, using the tech-

corrected to a circular ap erture with diameter 1.19 h kp c,

nique describ ed in Section 2.3. We then use the relation

equivalentto3.4 arcsec at the distance of the Coma clus-

(V g )= 0:517(g r ) 0:027 (Jrgensen 1994), based on

ter, see Jrgensen et al. (1995b). Further, we use new ve-

standard stars, to transform (V g )to(g r ), where

z z z z

lo city disp ersion measurements from Jrgensen (1999). A

g and r are Gunn g and Gunn r , resp ectively, in the rest

z z

total of 116 galaxies have available photometry and sp ec-

frames of the clusters. This results in calibrations that allow

troscopy. The sample is 93% complete to a magnitude limit

m m

us to transform from the published magnitudes V and the

of m = 15: 05 in Gunn r , equivalentto M = 20: 75

T r

m 1 1

color (R I )toGunnr in the rest frames of the clusters.

c c

(for a distance mo dulus of 35: 8, H =50kms Mp c and

For CL0024+16 at a redshift of 0.39 we nd

q =0:5).

For the purp ose of testing for possible di erences in

V r =0:58(R I ) 0:21 (6)

z z c c

0000 RAS, MNRAS 000, 000{000

8 I. Jrgensen, M. Franx, J. Hjorth, P. G. van Dokkum

Figure 3. The FP edge-on for Coma, A2218, A665, CL1358+62, CL0024+16, and MS2053-04. The sources of the data are given on the

panels. The skeletal symb ols on panel (c) and (d) are the E+A galaxies. The photometry is calibrated to Gunn r in the rest frames of

the clusters. The mean surface brightness log = 0:4(<> 26:4) is in units of L =pc . The photometry is not corrected for the

1 1

dimming due to the expansion of the Universe. The e ective radii are in kp c (H =50kms Mp c and q =0:5). The solid lines are

the FPs with co ecients adopted from JFK96 and zero p oints derived from the data presented in the gure. Typical error bars are given

on the panels; the thin and thick error bars show the random and systematic uncertainties, resp ectively.

(1995) who used passbands shifted to match the redshift of For CL1358+62 at z =0:33 we nd

the studied clusters.

V r =0:50(R I ) 0:19 (7)

z z c c

The data for CL1358+62 include two E+A galaxies (Kelson

et al.). For MS2053-04 at z =0:58 we nd

5 THE FUNDAMENTAL PLANE

V r =0:30(R I ) 0:15 (8)

Fig. 3 shows the FP edge-on for A665 and A2218 as log z z c c

versus log r +0:82 log . The mean surface brightness

e e

The uncertainties on r derived using these transforma-

log = 0:4(<> 26:4) is in units of L =pc .The

tions consist of the uncertaintydueto the transformation

gure also shows the FP for the Coma cluster and for the

between (V g )and(g r ) (0.015) and the uncertainty due

three intermediate redshift clusters CL1358+62 (z =0:33),

m m

to the transformation to g (0: 02), a total of 0: 025. Wedo

CL0024+16 (z = 0:39) and MS2053-04 (z = 0:58). The

not include additional uncertaintyfrom the authors' orig-

E+A galaxies in A665 and CL1358+62 are excluded from

inal transformation to V since that uncertainty is closely

the following analysis, but are shown on the gures.

correlated with the uncertainty on the transformation to g .

We adopt the co ecients for the FP from JFK96,

The uncertaintyof0: 025 do es not include the uncertainties

( , )=(1:24 0:07,0:82 0:02). The co ecients were de-

in the standard calibrations to I and R established byvan

c c

rived for a sample of 226 galaxies in 10 nearby clusters.

Dokkum & Franx and Kelson et al.

Photometry in Gunn r was used. The relations shown on

The typical values of V r derived from equations (6)

z z

Fig. 3 are FPs with these co ecients.

to (8) are 0.2. This is comparable to the average (V r ) color

The error bars on Fig. 3 showing the systematic errors

of nearbyE and S0 galaxies (e.g, Jrgensen et al. 1995a).

include the systematic uncertainties in the photometry (cf.

Others found similar small color evolution for E galaxies in

0:82

Table 5) and a 2% systematic uncertaintyinr due

e e

clusters with redshifts less than 0.6, e.g., Rakos & Schombert

1=4

to any deviations from r pro les and p ossible di erences

0000 RAS, MNRAS 000, 000{000

The Evolution of cluster E and S0 galaxies: The Fundamental Plane 9

Figure 4. The FP for Coma, HydraI and the veintermediate redshift clusters. Small triangles { galaxies in HydraI; other symb ols as

on Fig. 3. The photometry is calibrated to Gunn r in the rest frames of the clusters and corrected for the dimming due to the expansion

1 1

of the Universe. The e ective radii are in kp c. H =50kms Mp c and q =0:5were used. (a) The FP face-on. The dashed line

marks the luminosity limit for the completeness of the Coma cluster sample, M = 20: 75. The dotted line is the so-called exclusion

zone for nearby galaxies, y 0:54x +4:2, rst noted by Bender et al. (1992). (b) and (c) The FP edge-on. The solid line is the FP for

the Coma cluster with co ecients adopted from JFK96. The small error bars on panels (a) and (b) refer to Coma and HydraI, while

the larger error bars refer to the intermediate redshift clusters. The error bars on panel (c) refer to Coma and HydraI. The error bars

for the intermediate redshift clusters cannot b e summarized in a simple fashion, and we refer to Fig. 3 for their sizes.

originating from di erences in the tting metho ds for the smaller samples (e.g., Jrgensen et al. 1993, 1996; Lucey et

nearby and intermediate redshift galaxies (cf. Kelson et al. al. 1991).

1997). The systematic uncertainties on log is shown as

0.023 for the intermediate redshift clusters and zero for the

5.1 The co ecients of the FP

Coma cluster, since the relevant uncertainty is the possi-

ble inconsistency b etween the velo city disp ersions for Coma

The sample of intermediate redshift galaxies is heavily bi-

galaxies and the intermediate redshift galaxies.

ased towards intrinsically bright galaxies. The faintest galax-

Fig. 4 shows the FP face-on and in two edge-on views.

ies observed in the intermediate reshift clusters typically

The HydraI sample is included on this gure. The mean

have M = 21: 65. The selection e ect is clearly visible

surface brightnesses have been corrected for the dimming

in the face-on view of the FP, Fig. 4a. Further, the edge-on

due to the expansion of the Universe. The e ective radii are

view on Fig. 4c shows that the samples are limited in b oth

1 1

in kp c (H =50kms Mp c and q =0:5).

0 o

the velo city disp ersions and in log r +0:82 log . The

e e

The scatter around the FP is similar for A665 and

selection e ects make it dicult to test for p ossible di er-

A2218 (0.060 and 0.112 in log r ) and for the Coma clus-

ences b etween the co ecients of the FP for Coma and the

ter (0.092 in log r ). Using the photometry calibrated to

FP for the intermediate redshift clusters.

Gunn r , we nd the scatter for CL1358+62, CL0024+16

Fig. 5a shows the FP as the relation b etween the M/L

and MS2053-04 to be 0.066, 0.064 and 0.076, resp ectively

ratio and the mass. The masses were derived as M =

(see also van Dokkum & Franx 1996; Kelson et al. 1997).

5r =G (cf., Bender, Burstein & Fab er 1992). This g-

This is not signi cantly di erent from the scatter for Coma,

ure and Fig. 4c indicate that the co ecient for the log 

A665 and A2218. The scatter for the Coma cluster rep orted

term in the FP is di erent for the intermediate redshift clus-

here is somewhat larger than previous estimates based on

ters and for the Coma cluster. This was also noted byvan

0000 RAS, MNRAS 000, 000{000

10 I. Jrgensen, M. Franx, J. Hjorth, P. G. van Dokkum

Dokkum & Franx (1996) in their analysis of the CL0024+16

observations.

We tried to t the FP to the intermediate redshift clus-

ters individually, in order to test if the co ecients of the FP

for the intermediate redshift clusters are di erent from those

for nearby clusters. A total of 35 galaxies were included in

the ts.The E+A galaxies in A665 and CL1358+62 were

omitted, since we aim at tting the FP for the E and S0

galaxies, only. The ts were determined by minimization

of the sum of the absolute residuals p erp endicular to the

relation. The uncertainties were derived using a b o otstrap

metho d (cf., JFK96). All the ts gave values in the inter-

val 0:75 to 0:81. The values are in the interval 0.54{

1.74 and, due to the small sample sizes, the uncertainties

are large. We therefore rep eated the ts with = 0:79

for all the clusters. This gives in the interval 0.45{1.42,

with uncertainties of 0.14{0.70. No signi cantchange of

with redshift was detected. It must await larger samples of

galaxies to map the p ossible change of the co ecients as a

function of the redshift.

Next, we t the FP to the ve clusters as parallel

planes, under the assumption that the FPs for these clusters

have the same co ecients. For the photometry calibrated to

Gunn r , this gives ( , )=(0:89 0:17,0:79 0:04). In John-

son V we nd( , )=(0:92 0:13,0:79 0:04). A t to the

Coma cluster galaxies alone gives ( , )=(1:27 0:08,0:81 

0:03), for photometry in Gunn r . The di erence b etween

for the Coma cluster sample and for the intermediate red-

shift sample is 0.38. Of the 1000 b o otstrap ts derived for

the FP for the intermediate redshift sample, 3.8 p ercenthave

values that deviate from =0:89 with more than 0.38.

Hence, the di erence in is signi cant at the 96 percent

level.

Figure 5. (a) The M/L ratio as function of the mass. The dashed

In order to explore the e ect of the di erent selection

line marks the luminosity limit for the completeness of the Coma

criteria we rep eated the t to the Coma cluster galaxies rst

cluster sample, M = 20: 75. (b) The M/L ratio as function

enforcing a magnitude limit of M = 21: 65, and next

of the velo city disp ersion. Solid line { relation tted to the Coma

enforcing limits of log 2:12 and log r +0:82 log 

e e

cluster; dotted-dashed line { relation tted to the intermediate

2:80. Applying the magnitude limit, do es not give a result

redshift clusters. Symb ols as in Fig. 3. The small and large error

bars refer to the random uncertainties a ecting the Coma cluster

signi cantly di erent from the t for the full sample, we nd

and the intermediate redshift clusters, resp ectively.

( , )=(1:30 0:17,0:82 0:06). The limits in log and

log r +0:82 log result in ( , )=(1:09 0:27,0:85 

e e

0:05). Though this is formally not di erent from the t to the

simulations b ecause the Coma cluster sample has only six

full sample, the smaller value of the co ecient indicates

galaxies brighter than M = 23 . Our sample of galax-

that part of the di erence in between the Coma cluster

ies in the intermediate redshift clusters include 13 galaxies

sample and the sample in the intermediate redshift clusters

brighter than M = 23 .Thus, using only the Coma clus-

may b e due to selection e ects.

ter sample for the test could p otentially bias the result, since

To further test if the di erence in may b e due to selec-

the bright galaxies would app ear several times in each sub-

tion e ects, wehave p erformed two simulations that are b oth

sample. The combined Coma and HydraI sample contains

based on tting the FP to random sub-samples of galaxies

10 galaxies brighter than M = 23 . While this maynot

selected from the Coma cluster sample plus the HydraI clus-

b e enough to eliminate all bias due to some of the bright

ter sample. The sub-samples eachcontain 35 galaxies in or-

galaxies b eing included more than once in each sub-sample,

der to match the size of the intermediate redshift sample. In

we exp ect the bias to b e fairly small.

the rst simulation, the sub-samples were selected such that

Figs. 6a and c show the distribution of values for 1000

their luminosity distributions match the luminosity distri-

random sub-samples for each of the two simulations. The

bution for intermediate redshift cluster sample. In the sec-

values for the full Coma cluster sample and for the inter-

ond simulation, the sub-samples were selected to match the

mediate redshift sample are overplotted. Eight (0.8 p ercent)

distribution of log r +0:82 log . The mean luminosity

e e

of the sub-samples selected to match the luminosity distri-

evolution of the galaxies in the intermediate redshift clusters

bution result in values of within the one sigma error bar

(see Section 5.2) was taken into accountinbothsimulations.

of the co ecient found for the intermediate redshift sample.

However, the results do not dep end on whether this correc-

For the sub-samples selected to match the distribution in

tion is applied.

We have included the HydraI cluster sample in these

0000 RAS, MNRAS 000, 000{000

The Evolution of cluster E and S0 galaxies: The Fundamental Plane 11

Figure 6. (a) Histogram of the values of the co ecient of the FP for 1000 random sub-samples of galaxies selected from the Coma

cluster and HydraI cluster sample. The sub-samples are selected so their luminosity distributions match the luminosity distribution for

the intermediate redshift sample. The values found for the intermediate redshift sample and for the full Coma cluster sample are also

shown. (b) Histogram of the di erence b etween the values derived by b o otstrapping the full Coma sample and the values derived from

the random sub-samples selected to match the luminosity distribution. The absolute di erence j j is larger than 0.38 for 1.8 p ercent

of the cases. (c) Histogram of the values of the co ecient of the FP for 1000 random sub-samples of galaxies selected from the Coma

cluster and HydraI cluster sample. The sub-samples are selected so their distribution in log r +0:82 log match the distribution for

e e

the intermediate redshift sample. The values found for the intermediate redshift sample and for the full Coma cluster sample are also

shown. (b) Histogram of the di erence b etween the values derived by b o otstrapping the full Coma sample and the values derived

from the random sub-samples selected to match the distribution in log r +0:82 log . The absolute di erence j j is larger than

e e

0.38 for 3.8 p ercent of the cases.

log r +0:82 log , 20.3 p ercentgive values within the 6b and d show the distributions of the di erence for the

e e

one sigma error bar. two comparisons. For the sub-samples selected to matchthe

The distributions of the values for the sub-samples en- luminosity distribution, 18 of the 1000 cases, or 1.8 p ercent,

compass for b oth simulations the value for the Coma cluster have an absolute di erence j j larger than 0.38. For the

sample as wellasthevalue for the intermediate redshift sam- sub-samples selected to matchthe distribution in log r +

ple, which in turn are not signi cantly di erent from each 0:82 log , 3.8 p ercentofthecaseshave j j > 0:38.

other. Based on these simulations, we conclude that the di er-

In order to construct two-sided tests, we compare the ence in the co ecient of the FP is not likely to b e due to

values derived from the two simulations of the sub-samples the di erence in the luminosity distributions of the two sam-

to those derived by b o otstrapping the full Coma sample. ples. It is p ossible that part of the di erence in the co e-

The comparison with the rst simulation gives a measure cient is due to the distribution of log r +0:82 log being

e e

of how often we can exp ect two samples with luminosity di erent for the two samples. The di erent app earances of

distributions similar to the intermediate redshift sample and the distributions shown on Figs. 6a and c add to the evidence

the Coma cluster sample, resp ectively, and drawn from the that the selection e ect presentinlogr +0:82 log may

e e

same underlying distribution, to give a di erence in larger a ect the derived value of .

than the measured di erence of 0.38. The comparison with The co ecients we nd for the FP for the intermediate

the second simulation gives the same measure for samples redshift clusters imply that

selected on the distribution in log r +0:82 log . Fig.

e e

0:17 0:27 0:87 0:44

(9) / M r M=L / r

e e

0000 RAS, MNRAS 000, 000{000

12 I. Jrgensen, M. Franx, J. Hjorth, P. G. van Dokkum

Table 7. Uncertainties on the FP zero p oint

Clusters

Source Coma A665 A2218 random/systematic

Photometric zero p oint (<> ) 0.015 0.02 0.02 systematic

Velo city disp ersion 0.000 0.023 0.023 systematic

Coma p eculiar velo city, 300km/s, (log r ) 0.018 ...... systematic

Total systematic uncertainty, (log r ) 0.023 0.035 0.035 systematic

Uncertainty on the FP zero p oint , (log r ) 0.009 0.027 0.037 random

1=2

Note. The uncertainty on the FP zero p ointis =N where is the rms scatter of the FP and

t t

N is the numb er of observed galaxies.

0:22 0:49

 / This should be compared with M=L / r

0:24 0:02

M r found for nearby clusters (JFK96). The di er-

ence may indicate that the low mass galaxies show a stronger

luminosity evolution than the more massive galaxies. The

driving factor mayhowever b e the velo city disp ersion rather

than the mass of the galaxies. A direct t to the M/L ratio

as a function of the velo city disp ersion gave for the nearby

0:86

clusters M=L / (JFK96). Fig. 5b shows the M/L ra-

tio versus the velo city disp ersion for the Coma cluster and

the intermediate redshift clusters. The di erent slop es for

the two samples is clearly seen. For the Coma cluster alone

0:660:13

we nd M=L / , while the sample of galaxies in

1:490:29

the intermediate redshift clusters gives M=L / .

The relations for the Coma cluster and for the intermediate

redshift clusters are overplotted on Fig. 5b.

If real, the di erence in the slop es of the FP (and the

Figure 7. The o sets in the surface brightnesses derived from

slop es of the M/L- relation) may b e due to bursts of star

the FP versus the redshift of the clusters. q = 0:5 was used.

formation in the low mass galaxies in the intermediate red-

The small and large error bars show the random and system-

shift clusters leading to a lower M/L ratio for these galaxies.

atic uncertainties, resp ectively. These were derived as (<> )=

Alternatively, the samples in the intermediate redshift clus-

 (log r ) 2:5=0:82. See Table 7 for values of (log r ). The solid

e e

ters may contain some early-typ e spirals.

line is the exp ected relation for an expanding Universe and no

evolution of the galaxies. The data are in agreement with an ex-

panding Universe and a slow luminosityevolution. A smaller q

5.2 The evolution of the M/L ratio

results in smaller values of <>, and therefore a larger lumi-

nosityevolution.

The zero p oint of the FP dep ends on the cosmological e ects

(surface brightness dimming, the value of q ,andthevalue

of the cosmological constant), and the evolution of the galax-

Fig. 7 shows the o sets in the surface brightnesses,

ies. We assume a cosmological constant of zero. We adopt

<>, based on the zero points of the FPs. We used

the co ecients for the FP for nearby clusters (JFK96) for

q = 0:5. No correction for the expansion of the Universe

all the clusters. Because of the p ossible di erence in the co-

has b een applied and the solid line on the gure shows the

ecients of the FP (cf. Section 5.1) the following discussion

exp ected relation for an expanding Universe. A smaller q

of the evolution of the M/L ratios should b e understo o d as

results in smaller values of <> . The data are consistent

the average evolution of the available samples of galaxies.

with an expanding Universe and a slow luminosityevolution

Sp eci cally, the results refer to galaxies with masses ab ove

of the galaxies. In the following we correct the data for the

10 1 1

6:5 10 M (H =50kms Mp c and q =0:5).

0 o

expansion of the Universe, and then use the FP to study the

Table 7 summarizes the sources of uncertainty a ecting

mean evolution of the galaxies in the clusters.

the zero p oints of the FP for Coma, A665 and A2218. The

The FP zero p oint di erences b etween the intermediate

total systematic uncertainty on the FP zero p ointisthesum

redshift clusters and the Coma cluster can b e interpreted as

of the systematic uncertainties and is given as (log r ). The

di erences in the M/L ratios. With the FP co ecients from

random uncertainties intro duced by the random photomet-

JFK96 the M/L ratios can b e expressed as

ric uncertainties and tting uncertainties are included in the

log M=L =0:49 log +0:22 log r =0:82 + cst

uncertainty on the FP zero p oint since this is based on the

=0:24(2 log +logr ) 0:02 log r

(10)

measured rms scatter of the FP.

e e

=0:82 + cst

On the following gures the error bars re ect the uncer-

tainties listed in Table 7. The uncertainties for the other in-

(cf., JFK96), where is the FP zero p oint. Under the as-

termediate redshift clusters were adopted from van Dokkum

sumption that no merging or accretion takes place, the mass

&Franx (1996) and Kelson et al. (1997), and where neces-

and therefore (2 log + log r ) is constant. We can then de-

sary the total uncertainties were derived in the same wayas

rive the di erences in the M/L ratios from the di erences in

for A665 and A2218.

the FP zero p oints, ignoring the small term 0:02 log r .Fig.

0000 RAS, MNRAS 000, 000{000

The Evolution of cluster E and S0 galaxies: The Fundamental Plane 13

is the slop e of the IMF. A Salp eter (1955) IMF has x =1:35

(equivalent to 0:6). For photometry in Johnson V,

the exp ected evolution is nearly the same. The mo dels from

Vazdekis et al. give 0:95 0:2x.

Equation (11) can b e used to relate the changeinthe

M/L ratio with redshift to the formation redshift, z , and

form

the value of q . The dashed lines on Fig. 8 show the ex-

p ected relations for =0:6 and z = 1; 5 and 1. Mo dels

form

with shallower IMFs make the slop e of the exp ected relation

steep er, while a mo del with steep er IMFs make the slop e of

the relation shallower.

For q = 0:5, the mo dels with a Salp eter IMF and

z > 5 are consistent with the data within 2 . A for-

form

mation redshift of z = 2:4 represents a 3 deviation.

form

Mo dels with z smaller than 2.4 deviate more than 3

form

from the t to the data. If we assume q =0:15 more mo d-

els are consistentwith the data. A mo del with a Salp eter

IMF then implies z 2:5. Mo dels with z in the in-

form form

terval 1.7{6.5 are consistent with the data within 2 . Mo dels

with z < 1:4 deviate more than 3 from the t to the

form

data.

Because of the larger numb er of clusters analyzed here

we are able to put stronger formal limits on the formation

redshift, z , than done in previous studies (van Dokkum

form

& Franx 1996; Kelson et al. 1997). However, the derived

mo del constraints should only b e taken as rough guidelines.

The correct interpretation of the data is most likely rather

Figure 8. The evolution of the M/L ratio as function of the

more complicated than indicated here. The correct value of

redshift of the clusters. The photometry has b een calibrated to

 is not known. Further, the evolution of E and S0 galax-

Gunn r in the rest frame of the clusters. The small and large error

ies cannot b e viewed as a single burst event. The presence

bars show the random and systematic uncertainties, resp ectively.

of younger stellar p opulations in the galaxies would imply

These were derived as (log M=L)= (log r )=0:82. See Table 7

stricter lower limits on z . The most fundamental assump-

form

for values of (log r ). (a) q =0:5; (b) q =0:15. The top axis

e o o

tion for the interpretation of the data is that the observed

on each panel shows the time of emission in units of the present

E and S0 galaxies in the intermediate redshift clusters in

age of the Universe. Solid lines { least squares ts to the data.

fact evolveinto galaxies similar to the presentday E and S0

Dashed lines { passiveevolution with z = 1; 5and1(topto

form

b ottom).

galaxies. It is p ossible that our selection of E and S0 galax-

ies in the intermediate redshift clusters is biased to select

already aged galaxies (see also Franx & van Dokkum 1996).

8shows the di erences in the M/L ratios as a function of

In this case we are likely to underestimate the mean evo-

the redshifts.

lution measured from the FP when comparing to complete

The galaxies in A665 and A2218 haveonaverage M/L

samples of galaxies in nearby clusters. Larger and more com-

ratios (11 7)% smaller than the M/L ratios of the galaxies

plete samples in intermediate redshift clusters are needed in

in the Coma cluster. Together with the previous data from

order to address this problem in detail.

van Dokkum & Franx (1996) and Kelson et al. (1997), this

shows the gradual and slow evolution of the M/L ratio of

the galaxies as a function of the redshift. A least squares t

6 CONCLUSIONS

to the all data shown on Fig. 8 gives log M=L =(0:26 

0:06)z for q =0:5 and log M=L =(0:34 0:06)z

o r

We have established the Fundamental Plane (FP) for the

for q =0:15. For the photometry calibrated to Johnson V

two rich clusters Ab ell 665 and Ab ell 2218, b oth at a red-

we nd log M=L =(0:29 0:08)z and log M=L =

V V

shift of 0.18. The photometric parameters were derived from

(0:37 0:08)z for q =0:5 and 0.15, resp ectively. Our

ground-based observations obtained with the Nordic Opti-

results in Johnson V are in agreement with the results by

cal Telescop e, La Palma, and from HST observations. The

van Dokkum & Franx and Kelson et al.

photometry was calibrated to Gunn r in the rest frame of

The M/L ratio of a stellar p opulation can b e mo deled

the clusters. Central velo city disp ersions were measured for

six galaxies in A665 and ten galaxies in A2218. The FPs for

the two clusters were compared to the FP for nearby clus-

M=L / t (11)

ters derived by JFK96, and to the FP for the Coma cluster.

where t is the age of the stellar p opulation (Tinsley 1980).

The scatter around the FP for A665 and A2218 is similar to

The co ecient dep ends on the initial mass function (IMF)

the scatter found for nearby clusters.

of the stars and on the passband. Based on the single burst

We have used the data for A665 and A2218 together

stellar p opulation mo dels from Vazdekis et al. (1996), we

with other recently available data for intermediate redshift

nd for photometry in Gunn r that 0:9 0:2x where x

clusters (van Dokkum & Franx 1996; Kelson et al. 1997) to

0000 RAS, MNRAS 000, 000{000

14 I. Jrgensen, M. Franx, J. Hjorth, P. G. van Dokkum

grantnumb er HF-01073.01.94A to IJ, b oth grants from the test if the slop e of the FP changes with redshift. The data

Space Telescop e Science Institute, which is op erated bythe for the clusters CL0024+16 (z=0.39), CL1358+62 (z=0.33)

Asso ciation of Universities for Research in Astronomy, Inc., and MS2053-04 (z=0.58) were calibrated to Gunn r in the

under NASA contract NAS5-26555. JH was supp orted in rest frame of the clusters. We nd that the co ecient for

part by the Danish Natural Science Research Council. the log term in the FP is signi cantly smaller for the in-

termediate redshift clusters than for the Coma cluster. The

di erence cannot b e explained by the di erence in the lu-

minosity distribution of the Coma cluster sample and the

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A2 Basic reduction of HST images

APPENDIX A: THE PHOTOMETRY

The HST/WFPC2 images were corrected for bias, dark-

A1 Basic reductions of ground-based images

current and at eld corrected using the pip eline reduction

supplied by Space Telescop e Science Institute. The images

The bias level and pattern turned out to dep end on the CCD

were co-added and cleaned for cosmic-ray-events using the

temp erature, which in turn varied with 1:0K. Therefore,

iterative metho d implemented in the Space Telescop e Sci-

the bias was subtracted row-by-row based on the overscan

ence Data Analysis Software (STSDAS) task \crrej". Where

region of the images. After this pro cessing a few of the im-

necessary, the individual images were rst registered byap-

ages showed row-to-rowvariations in the background of 1-

plying small integer pixel shifts.

1.5%. The level of these variations were determined directly

from the images, and subtracted out with appropriate lter-

ing to ensure the levels were not a ected by signal from the

A3 Calibration to standard passbands

ob jects. No correction for the dark currentwas p erformed.

A3.1 Ground-based photometry

The dark current is less than 2e p er hour.

The o set b etween the set exp osure time and the ac-

The NOT photometry was standard calibrated based on ob-

tual exp osure time for the iris shutter of the camera was

servations of stars in M67, M92, and the eld SA101 taken

determined from dome ats. The average shutter correction

during the nights of the galaxy observations. All nights dur-

is = 0:0826 0:0008 sec.

ing which galaxy observations were obtained were photomet-

The linearity of the CCD was tested from dome ats. No

ric. Ap erture photometry was derived for 188 observations

signs of non-linearity can b e detected within the detection

of a total of 35 stars. The observations have large variations

accuracy of 1.5%, for levels up to the software saturation

in the seeing, and some of the exp osures were taken with

limit.

the telescop e slightly defo cused due to the brightness of the

Flat elds were constructed from twilight at elds.

stars. The ap erture radii for the photometry were typically

0000 RAS, MNRAS 000, 000{000

16 I. Jrgensen, M. Franx, J. Hjorth, P. G. van Dokkum

The photometry for galaxies in A665 was calibrated using 4: 9. Based on growth curves of bright stars in the elds the

the transformations for I and V and colors based on HST ap erture magnitudes were corrected for the nite sizes of the

data. We use the following transformations ap ertures. The growth curves typically extended to 9: 5, and

the typical size of the correction is 0: 04. This correction

I = m 0:062(V I )+0:025(V I )

c 814 c c

(A4)

ensures consistency b etween the defo cused and fo cused ob-

V = m +0:254(V I )+0:012(V I )

606 c c

servations, and b etween observations with large di erences

The I transformation is for the in- ight system based on

c in the seeing. All observations in the I-band were obtained

stars bluer than the typical colors of the observed galaxies,

during night 1 and night 5. All observations in the V-band

(V I )= 1:5. However, for (V I )=1:5 the transforma-

c c

were obtained during night 2. The typical seeing for the stan-

00 00 00 00

tion agrees within 0: 005 with the synthetic transformation.

dard star observations was FWHM=0: 6 0: 7, 1: 5 2: 5 and

00 00

A2218 was observed in the F702W lter, only.Wehave

0: 7 1: 0 for the nights 1, 2 and 5, resp ectively.

calibrated this photometry to I using the transformation

The 9-15 stars in M67 were used for determination of

for R given by Holtzman et al. (1995b) and the relation

c the atmospheric extinction. We nd k (night1)=0:063 

(V R )=0:52(V I ), whichwe derived from standard

c c 0:001, k (night5) = 0:124 0:001, and k (night2 ) = 0:165 

I V

star magnitudes for stars with (V I )intheinterval 1{2

0:004. Further, observations from night5 were o set to con-

(Landolt 1992). The co ecient is in agreement with colors

sistency with night1 by subtraction of 0: 011.

of E and S0 galaxies at z =0:2 (e.g., Fukugita, Shimasaku

Wehave used standard magnitudes from Landolt (1992)

&Ichikawa 1995; Frei & Gunn 1994). This gives the trans-

(SA101) and Davis (1994) (M92). The magnitudes from

formation

Davis are consistent with Christian et al. (1985) and Stet-

son & Harris (1988) for the stars in common. The standard

I = m 0:227(V I ) 0:021(V I ) (A5)

c 702 c c

magnitudes from M67 are from Montgomery et al. (1993),

We used colors from the ground-based photometry in order

Joner & Taylor (1990) and Jrgensen (1994), in this prior-

to calibrate the HST observations of A2218. Finally, the

ity.The magnitudes from the three sources are consistent

photometry was corrected for the galactic extinction.

for the stars in common. We derived the following standard

transformations

I = I +cst rms = 0:021

c inst

A4 Photometric parameters

(A1)

V = V +0:0596(V I ) +cst rms = 0:014

inst inst

Tables A1 and A2 give the e ective parameters and colors

The I magnitudes were calibrated to Cousins I . The trans-

of all galaxies in the two clusters brighter than m =19 in

formation for I has no signi cant color term; if we include

I and within the elds covered by the NOT observations.

a(V I ) term in the transformation we nd a co ecientfor

Five of the galaxies in A665 were also observed by Oegerle

this term of 0:001 0:007. The photometry for the galax-

et al. (1991). The cross-references are as follows, with our

ies was corrected for the galactic extinction. For A665, the

galaxy number given rst. 1032 = 218, 1150 = 201, 1168 =

galactic extinction is A =0:15 equivalentto A =0:07 and

B I

224, 2105 = 225 and 2122 = 227.

A =0:11. A2218 has a galactic extinction in the B-band

of A =0:10, equivalenttoA =0:05 and A =0:08. The

B I V

A5 Comparison of ground-based and HST

galactic extinctions were derived from the reddening maps

photometry

published bySchlegel, Finkb einer & Davis (1998).

The ground-based photometry and the HST photometry

were compared by means of ap erture magnitudes. In or-

A3.2 Photometry from HST observations

der to limit the e ect of the di erent spatial resolution and

The photometry from the HST images was calibrated using

the choice of the ap erture size we convolved the HST im-

the transformations given by Holtzman et al. (1995b). For

ages to approximately the same resolution as the ground-

F814W we use the transformation based on observations,

based images. Ap erture magnitudes for the galaxies were

while for F606W and F702W we use the synthetic transfor-

then derived within ap ertures of with radii of 3 arcsec. The

mations. We de ne instrumental magnitudes as

magnitudes were standard calibrated as describ ed in Sec-

tions A3.1 and A3.2. Fig. A1 show the comparison of the

m = 2:5 log (DN=t )+ZP+2:5 log GR +m+0:05(A2)

inst exp i

ap erture magnitudes. We nd the mean di erences to be

\DN" is the number of counts, \ZP" are the zero points

I (NOT) I (HST) = 0:066 0:007 and 0:017 0:010 for

c c

given by Holtzman et al. (1995b) for the relevant transfor-

A665 and A2218, resp ectively. Galaxies with ap erture mag-

mation (see equations [A4] and [A5]). We use GR =2:003,

nitude fainter than 19 were excluded from this comparison

GR =2:006 and GR =1:955. The term 0.05 is added as

in order to limit the errors intro duced by uncertaintyinthe

3 4

a correction for the di erence b etween \short" and \long"

sky subtraction.

exp osures (Hill et al. 1998). The ap erture corrections m

The e ective parameters derived from the NOT images

were estimated from data for the encircled energy given

and the HST images were compared, see Fig. A2 and Table

by Holtzman et al. (1995a). We use m = 0:0983,

A3. Only the galaxies with total magnitudes brighter than

814

m = 0:1087, and m = 0:1138. The instrumental

19 in the I-band were included in this comparison, a total

702 606

magnitudes in the three lters are then given by

of 56 galaxies. For the fainter galaxies the individual param-

eters (log r , <> and m ) b ecome highly uncertain due to

e T

m = 2:5 log (DN=t )+ 20:987 + 2:5logGR

814 exp i

the small size of the galaxies compared to the FWHM of the

(A3) m = 2:5 log (DN=t )+ 21:670 + 2:5logGR

702 exp i

PSF for the ground-based data, and due to rather low signal-

m = 2:5 log (DN=t )+ 22:257 + 2:5logGR

606 exp i

to-noise for these faint galaxies in the HST observations of

0000 RAS, MNRAS 000, 000{000

The Evolution of cluster E and S0 galaxies: The Fundamental Plane 17 ) c I 1.46 1.52 1.50 1.49 1.53 1.49 1.45 1.47 1.48 1.52 1.47 1.48 1.47 1.54 1.52 1.37 1.45 1.47 1.51 1.49 1.24 1.12 1.49 1.47 0.87 1.49 1.46 1.41 V ( 02 for NOT : 0 tal magnitudes pix 1.9 3.5 1.4 1.6 5.2 2.1 1.6 1.3 2.2 2.2 1.2 1.4 2.1 3.3 1.3 2.1 1.2 7.9 4.1 4.6 8.0 1.4 2.3 1.9 0.9 1.6 18.5 12.3 N : = e 2 > (F814W) the noise (photon- and < 2 i ) e c ) for b oth the NOT and the > I c ( I 19.59 19.32 19.67 19.88 21.97 20.10 21.43 19.82 21.21 19.39 19.33 20.27 18.92 19.47 19.93 21.85 21.21 18.58 19.17 19.96 22.42 21.80 18.67 20.27 22.73 19.66 19.24 19.22 < V e > b er of pixels within the tting radius. 19.63 19.36 19.71 19.92 22.01 20.14 21.47 19.86 21.25 19.43 19.37 20.32 18.96 19.51 19.97 21.90 21.25 18.62 19.21 20.00 22.46 21.85 18.71 20.32 22.77 19.70 19.28 19.26 < um (F606W) are the instrumen )and( 002 for HST data. e (F814W) V : ( > 0 e > < e is the n alue in the pixel, and r < HST pix 0.037 0.088 0.027 1.056 0.144 0.209 0.111 0.072 0.376 0.358 0.159 1.003 0.594 0.150 0.597 log ), -0.172 -0.190 -0.170 -0.034 -0.223 -0.112 -0.149 -0.011 -0.107 -0.191 -0.195 -0.339 -0.096 N c [arcsec] I ( e > pix 2.3 4.4 1.6 1.9 4.4 1.8 1.8 1.8 2.6 2.9 1.5 1.5 3.6 4.1 2.0 3.5 1.8 4.0 3.3 8.6 2.1 3.5 2.3 1.1 2.2 < 10.5 29.3 22.9 , where (F814W) and N = is the mo del v e 2 pix > N (F606W) 006 for NOT data, = : < alues. 2 0 mo del i; ) e n V > : ( e , i r 21.01 20.88 21.24 21.33 23.47 21.62 22.86 21.24 22.55 20.88 20.46 21.74 19.98 20.94 21.40 23.09 22.60 20.07 20.44 21.34 23.96 22.69 20.14 21.55 23.41 21.05 20.22 20.20 < en as log e > Abell 665 ws. 20.71 20.56 20.93 21.03 23.15 21.32 22.56 20.94 22.25 20.56 20.15 21.44 19.68 20.62 21.09 22.82 22.31 19.77 20.13 21.04 23.73 22.48 19.83 21.25 23.28 20.74 19.92 19.92 < able 3 for seeing v (F606W) e r , see T is the signal in pixel 0.063 0.121 0.035 1.070 0.170 0.221 0.092 0.081 0.382 0.334 0.157 1.130 0.543 0.112 0.560 log -0.172 -0.188 -0.166 -0.109 -0.317 -0.117 -0.125 -0.058 -0.118 -0.182 -0.209 -0.449 -0.192 i [arcsec] ypically as follo n arameters, ABLE A1 The go o dness-of- t is giv T ) c I 1.49 1.55 1.53 1.54 1.54 1.52 1.44 1.47 1.53 1.53 1.45 1.54 1.53 1.51 1.54 1.38 1.56 1.56 1.54 1.34 1.44 1.51 1.62 1.52 1.20 1.11 1.57 1.53 1.51 0.96 1.20 1.52 1.53 1.52 1.56 1.52 1.39 ties are t tains the galaxy V ( ) is 0.01. c I pix 1.8 3.4 2.0 1.5 2.9 1.2 1.7 1.8 1.6 2.1 3.7 1.7 1.5 3.1 3.0 3.9 2.1 4.3 1.3 9.0 6.7 1.5 1.9 1.5 5.2 2.8 5.6 1.3 1.7 1.6 1.6 2.2 2.7 mo dels. 15.7 14.9 29.7 20.1 V N = 4 2 = Photometric p 1 r ) e c y on the ( > I NOT t ( 19.30 19.15 19.54 19.47 21.82 19.92 21.55 19.59 18.84 20.22 20.37 18.40 18.86 20.41 18.75 19.01 18.24 18.44 19.78 20.87 20.77 17.73 18.56 19.43 22.09 21.71 18.70 19.48 20.68 22.32 21.79 19.47 18.97 18.83 18.61 18.94 19.29 < e r The formal tting uncertain 0.049 1.012 0.091 0.243 0.289 0.109 0.333 0.070 0.015 0.876 0.566 0.264 0.475 0.494 log -0.248 -0.010 -0.080 -0.249 -0.257 -0.122 -0.422 -0.154 -0.262 -0.302 -0.226 -0.399 -0.352 -0.170 -0.256 -0.187 -0.205 -0.252 -0.404 -0.189 -0.344 -0.194 -0.049 Field { the NOT eld that con e b een tted with [arcsec] v er all the pixels within the tting radius. v 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 Field , see Eq. (A3). ypical (random) uncertain ely Dec. , with the sum o The t (J2000) 2 i 65:49:00.2 65:49:17.3 65:49:12.4 65:49:28.5 65:50:30.4 65:49:20.2 65:49:36.4 65:50:44.1 65:49:25.0 65:50:23.7 65:49:39.2 65:50:43.5 65:50:06.7 65:49:37.4 65:50:41.5 65:50:21.6 65:49:47.4 65:50:43.3 65:50:48.1 65:50:58.0 65:50:58.5 65:51:04.6 65:50:43.5 65:51:03.2 65:50:35.7 65:50:44.8 65:49:01.8 65:50:36.1 65:50:01.3 65:50:47.1 65:50:26.3 65:49:24.9 65:50:23.6 65:51:07.5 65:49:26.6 65:50:25.6 65:51:23.7 = ti cations { this pap er. 2 ) R.A. mo del i; (J2000) n 8:31:00.34 8:31:10.37 8:30:55.99 8:31:11.34 8:30:57.36 8:31:06.97 8:31:07.73 8:31:05.41 8:31:07.66 8:30:58.71 8:31:06.35 8:31:00.86 8:30:55.20 8:31:02.03 8:30:55.32 8:30:59.22 8:30:55.96 8:30:58.68 8:31:03.25 8:30:59.37 8:30:56.51 8:31:05.16 8:30:53.35 8:30:55.79 8:30:42.21 8:30:43.39 8:30:55.59 8:30:39.23 8:30:48.79 8:30:41.37 8:30:40.03 8:30:54.48 8:30:54.45 8:30:50.19 8:30:52.46 8:30:43.11 8:30:53.69 i n 007 for HST data. ( : .| Galaxy iden 0 P OTE = Galaxy 1022 1032 1035 1046 1150 1040 1060 1161 1044 1138 1067 1164 1114 1069 1166 1134 1084 1167 1168 1191 1193 1196 2111 1202 2105 2122 2007 2108 2063 2127 2096 2023 2081 2144 2029 2092 2159 N 2

in F814W and F606W, resp ectiv HST data are standard calibrated to the Johnson-Kron-Cousins photometric system and corrected for galactic extinction. data, read-out-noise) in the pixel. All the galaxies ha

0000 RAS, MNRAS 000, 000{000

18 I. Jrgensen, M. Franx, J. Hjorth, P. G. van Dokkum

TABLE A2

Photometric parameters, Abell 2218

NOT HST

2 2

Galaxy R.A. Dec. Field log r <> =N (V I ) log r <> <> =N

e pix c e pix

e e e

(J2000) (J2000) [arcsec] (I ) [arcsec] (F702W) (I )

c c

L106 16:36:04.77 66:13:41.1 2 -0.381 18.48 1.3

L112 16:36:04.31 66:13:27.4 2 -0.163 19.52 2.8 1.47 -0.169 19.99 19.57 7.7

L113 16:36:04.17 66:13:23.9 2 -0.148 18.27 2.8 1.61 -0.017 19.24 18.77 7.4

L114 16:36:04.13 66:12:10.8 1 -0.159 19.49 1.7 1.50

L118 16:36:03.95 66:11:39.2 1 0.051 19.20 5.5 1.62 0.097 19.76 19.30 3.1

L119 16:36:03.67 66:13:32.5 2 0.010 19.74 4.9 1.46

L143 16:36:02.54 66:13:30.8 2 0.007 20.58 2.1 1.41 0.009 21.07 20.66 1.0

L148 16:36:02.23 66:11:51.7 1 -0.075 18.53 3.1 1.59 0.067 19.49 19.03 6.4

L149 16:36:02.15 66:12:33.3 1 0.190 19.55 2.3 1.55

L181 16:36:00.49 66:12:05.9 1 -0.155 20.02 1.8 1.38 -0.292 19.91 19.52 2.3

L185 16:36:00.35 66:12:19.5 1 0.095 21.46 1.3 1.29

L187 16:36:00.26 66:12:42.9 1 -0.353 18.24 1.7 1.55

L196 16:35:59.33 66:12:05.4 1 0.339 20.43 1.8 1.55 0.380 21.00 20.55 1.2

L198 16:35:59.31 66:12:52.3 1 -0.061 19.14 2.0 1.55 -0.143 19.25 18.81 1.9

L221 16:35:58.29 66:13:20.1 2 -0.123 19.73 1.5 1.61 -0.101 20.30 19.83 0.7

L232 16:35:57.35 66:12:14.5 1 -0.274 18.46 2.0 1.53 -0.322 18.70 18.26 4.6

L244 16:35:56.74 66:11:54.4 1 0.934 22.01 2.0 1.53 0.930 22.46 22.02 1.4

L246 16:35:56.66 66:12:39.9 1 -0.062 19.71 1.8 1.41

L259 16:35:56.25 66:11:49.9 1 -0.156 18.81 2.8 1.49 -0.170 19.18 18.75 3.1

L268 16:35:56.07 66:12:23.4 1 -0.072 20.62 1.4 1.24 0.121 21.66 21.30 3.9

L291 16:35:54.84 66:12:16.9 1 -0.033 20.42 1.7 1.35 0.150 21.45 21.07 2.7

L302 16:35:54.38 66:13:03.9 1 -0.403 18.80 1.8 1.52 -0.347 19.43 19.00 0.7

L319 16:35:53.33 66:12:31.3 1 0.405 22.27 2.1 1.47

L320 16:35:53.31 66:12:37.3 1 0.196 20.80 2.8 1.42 0.218 21.25 20.84 3.5

L341 16:35:51.80 66:12:33.1 1 -0.124 18.27 2.6 1.56 -0.116 18.71 18.26 4.1

L348 16:35:51.42 66:13:10.9 1 0.002 19.53 1.8 1.56 0.006 20.00 19.55 5.1

L360 16:35:50.73 66:12:19.2 1 -0.067 19.21 4.5 1.49 -0.065 19.65 19.22 8.5

L364 16:35:50.56 66:12:00.7 1 -0.221 19.63 1.5 1.49 -0.117 20.41 19.98 1.8

L371 16:35:50.18 66:12:18.3 1 -0.115 20.00 4.6 1.47

L373 16:35:49.94 66:12:22.6 1 0.153 19.44 4.9 1.54 0.008 19.35 18.91 10.8

L378 16:35:49.80 66:11:43.7 1 0.138 20.61 1.4 1.50 0.054 20.73 20.30 1.0

L385 16:35:49.41 66:12:35.0 1 -0.049 19.13 3.3 1.46 -0.215 18.93 18.51 6.5

L391 16:35:49.20 66:12:43.5 1 1.403 23.07 3.6 1.48 1.412 23.68 23.25 21.0

L395 16:35:49.00 66:12:59.7 1 -0.104 19.22 2.4 1.29

L404 16:35:48.75 66:12:08.5 1 0.008 20.75 1.3 1.43 -0.194 20.46 20.05 1.7

L421 16:35:47.55 66:12:41.4 1 -0.134 18.84 3.4 1.51 0.020 19.86 19.42 7.8

L430 16:35:47.22 66:13:14.8 2 -0.033 19.06 1.4 1.62 -0.061 19.42 18.95 1.0

L436 16:35:46.79 66:12:21.7 1 -0.086 19.26 1.9 1.50 -0.210 19.23 18.80 3.6

L442 16:35:47.53 66:12:31.2 1 -0.215 18.88 2.2 1.53 -0.275 19.07 18.63 5.5

L446 16:35:46.30 66:12:50.6 1 -0.025 19.57 1.7 1.49 -0.212 19.30 18.87 5.7

L448 16:35:45.95 66:12:31.7 1 -0.377 18.88 1.4 1.49 -0.527 18.74 18.32 2.6

L457 16:35:45.56 66:11:46.8 1 -0.444 18.56 1.6 1.52

L482 16:35:44.10 66:13:19.0 2 0.036 18.77 2.2 1.62

L484 16:35:43.89 66:11:54.6 1 0.236 21.33 2.4 1.39

L535 16:35:41.23 66:13:45.7 2 0.238 19.63 1.9 1.63

L542 16:35:40.84 66:12:35.5 1 -0.219 19.85 1.5 1.50

L553 16:35:40.05 66:12:55.1 1 -0.313 18.87 2.5 1.58

L554 16:35:39.99 66:11:39.9 1 -0.408 18.52 2.3 1.38

L589 16:35:37.13 66:12:57.3 1 -0.069 19.30 2.3 1.63

J1191 16:35:40.25 66:13:53.5 2 -0.255 18.86 1.8 1.56

BOW06 16:35:47.31 66:14:43.1 2 0.138 19.03 2.3 1.59

BOW25 16:35:54.64 66:13:59.0 2 0.294 20.18 2.0 1.54

BOW44 16:35:57.23 66:14:20.1 2 -0.195 18.52 1.7 1.67

BOW67 16:35:55.24 66:14:11.8 2 -0.051 19.39 1.9 1.64

BOW75 16:35:37.75 66:13:59.8 2 -0.027 19.72 2.7 1.61

BOW81 16:36:01.57 66:14:56.0 2 -0.137 19.27 1.4 1.60

BOW83 16:35:39.09 66:14:16.9 2 -0.085 19.94 4.6 0.95

BOW91 16:35:48.91 66:14:27.7 2 0.123 20.55 1.7 1.80

BOW97 16:35:39.97 66:14:46.9 2 0.046 20.29 1.8 1.88

BOW107 16:35:44.60 66:14:23.0 2 0.037 20.62 1.8 1.51

BOW116 16:35:42.35 66:14:12.2 2 -0.136 19.72 1.7 1.60

NOTE.| Galaxy identi cations - Le Borgne et al. (1992) (L numb ers), Butcher et al. (1983) (BOWnumb ers), this pap er (J number).

Field { the NOT eld that contains the galaxy, see Table 3 for seeing values. <> (I )and(V I ) for b oth the NOT and the HST

c c

data are standard calibrated to the Johnson-Kron-Cousins photometric system and corrected for galactic extinction. <> (F702W) is

the instrumental magnitude in F702W, see Eq. (A3). The formal tting uncertainties are typically as follows. log r : 0:006 for NOT

data, 0:002 for HST data. <> : 0:02 for NOT data, 0:004 for HST data. The typical (random) uncertaintyonthe(V I )is

2 2 2 2

0.01. The go o dness-of- t is given as =N , where N is the numb er of pixels within the tting radius. = (n n ) = ,

pix pix i

i;mo del

with the sum over all the pixels within the tting radius. n is the signal in pixel i, n is the mo del value in the pixel, and the

i;mo del

noise (photon- and read-out-noise) in the pixel. The galaxies L114, L395, BOW83 and BOW97 have b een tted with exp onential disk

1=4

mo dels, all other galaxies have b een tted with r mo dels.

0000 RAS, MNRAS 000, 000{000

The Evolution of cluster E and S0 galaxies: The Fundamental Plane 19

Figure A1. Comparison of ap erture magnitudes. An ap erture

with radius 3 arcsec was used.

Table A3. Comparison of e ective parameters

Parameter mean di erence rms

log r 0:033 0:015 0.11

<> 0:119 0:053 0.41

m 0:044 0:021 0.16

FP 0:006 0:003 0.026

Figure A2. Comparison of e ective parameters in the I-band.

Notes. the combination log r 0:328<> . The di erences are

Boxes { A665; triangles { A2218. Solid symb ols { galaxies for

calculated as \NOT"{\HST". Only galaxies with total magni-

which we have sp ectroscopy. The di erences are calculated as

tudes brighter than 19 were included in the comparisons. The

\NOT"{\HST". The formal errors derived from the tting are of

two clusters are combined in this table, and the HST photometry

the size of the p oints. \FP" is the combination log r 0:328<>

has b een o set to consistency with the ground-based photometry,

whichenters the FP. Only galaxies with total magnitudes brighter

see text.

than 19 are shown. The HST photometry shown on the gure

has not b een o set to consistency with the ground-based photom-

A665. The combination \FP"=log r 0:328<> , which

etry.

enters the FP,was also compared. This combination is well

determined even for the fainter galaxies, but since none of

another check of the magnitude zero p oints of the HST pho-

the galaxies for whichwehave sp ectroscopyarefainter than

tometry. Fig. A3 shows the di erence in log r versus the dif-

19 we restrict the comparisons to galaxies brighter than

ference in <> . The di erences were calculated as \NOT"-

this limit. The rms scatter for the comparison of the combi-

\HST". The dashed lines on the panels show least squares

nation \FP" is similar to typical values for comparisons of

ts to the data. If the zero p oint for the HST photometry

data for nearby clusters (e.g., Jrgensen et al. 1995a). If the

was in p erfect agreement with the ground-based zero p oint,

uncertainty is equally distributed on two data sets, the typi-

then the dashed lines would go through (0,0). The o set in

cal uncertainty on the combination \FP" is 0.018. The small

<> is equal to the di erence in the zero p oints. We nd

mean di erence in the combination \FP" b etween the NOT

I (NOT) I (HST) = 0:063 0:011 and 0:015 0:008 for

data and the HST data is equivalent to a di erence in the

c c

A665 and A2218, resp ectively. This is in agreement with the

FP zero p oint of only 1.4%. The comparisons of the param-

determinations of the zero p oint di erences based on ap er-

eters log r , <> and m have slightly larger scatter than

e T

ture magnitudes.

usually found for comparisons b etween e ective parameters

O sets of a few hundredths of a magnitude are com-

for nearby galaxies derived by di erent authors.

mon b etween HST photometry and ground-based photome-

The errors on log r and <> are highly correlated

try (e.g., Ellis et al. 1997; Hill et al. 1998). The o set we

(e.g., Jrgensen et al. 1995a). Weuse this fact to provide

0000 RAS, MNRAS 000, 000{000

20 I. Jrgensen, M. Franx, J. Hjorth, P. G. van Dokkum

Figure A3. The di erence in log r versus the di erence in <> .

The di erences are calculated as \NOT"-\HST". Only galaxies

with total magnitudes brighter than 19 are shown. Solid symb ols

{ galaxies for whichwehave sp ectroscopy. The dashed lines show

least squares ts to the data. The o set in <> can b e used to

derive the o set b etween the HST photometry and the ground-

based photometry, see text.

nd for the A665 photometry is slightly larger than ex-

p ected. However, in order to ensure the consistency of the

data for A665 and A2218 we havechosen to calibrate the

HST photometry to the ground-based I .Wehave applied

Figure B1. Sp ectra of the observed galaxies in A665. The sp ectra

the following o sets: I = I (HST) + 0:065 for A665 and are not ux calibrated.

c c

I = I (HST) + 0:016 for A2218.

c c

We have no reliable way of checking the zero point

The at elds show strong variations in the fringing

for the V magnitudes based on the HST data, b ecause of

dep ending on the zenith distance of the telescop e due to the

the poor seeing of our ground-based V-images. We have

exure of the instrument Therefore, at elds obtained in

therefore not applied any zero p oint correction to the colors

day time did not give suciently go o d at eld correction.

(V I ) derived from the HST data.

Instead we use at elds obtained during the night. These

at elds were obtained with the internal quartz lamp in the

instrument. Two at elds bracket each science exp osure.

APPENDIX B: SPECTROSCOPY

The at elds obtained in daytimewere combined in the sets

they were taken cleaned for cosmic-ray-events (CR). Then

The sp ectroscopic observations were made through multi-

all the at elds were normalized by tting a high order

slit masks. One eld was observed in each cluster. The nal

spline in the direction of the disp ersion. In order to clean the

sp ectra are shown in Figs. B1 and B2. The reductions of the

night time at elds for CRs they were each compared to

A2218 sp ectra are describ ed in the following. The metho ds

the the day time at eld, which b est resembled night time

for the reductions of the A665 sp ectra were very similar. We

at eld. The nal at elds were derived as the average of

refer to Franx (1993ab) for additional information regarding

the two at elds, which bracket the science exp osure. The

the A665 sp ectra.

typical pixel-to-pixel noise in the nal at elds was 0.6%.

Areas of the at elds that had a pixel-to-pixel noise larger

B1 A2218

than 1.5% were set to one, and no at eld correction was

p erformed. This also ensures that no arti cial variations are

The sp ectra were corrected for the bias and the dark by

intro duced at the edges of the slit-lets.

standard metho ds. The bias subtraction was based on the

The individual exp osures of A2218 were cleaned for CRs

level in the overscan region as well as individual bias frames.

0000 RAS, MNRAS 000, 000{000

The Evolution of cluster E and S0 galaxies: The Fundamental Plane 21

as follows. First, the median image was derived. Then di er- on exp osures of the ux standard star HD192281. The ux

ence b etween each individual image and the median image calibrated sp ectra are in this pap er used for display purp oses

was calculated. This image naturally has strong residuals only. The determination of the velo city disp ersions do es not

from the sky lines and the galaxies. The residuals from the dep end on the ux calibration.

galaxies were tted with a smo oth function in the direction

of the disp ersion, and the t was subtracted. The residuals

from the sky lines were tted with a constant across each

slit-let, and the t was subtracted. The resulting di erence

image contains noise and signal from CRs, plus some resid-

uals from the strongest sky lines. Pixels for which the devia-

tions were b elow 7 times the lo cal noise or which had resid-

uals from the sky lines were set to zero. This resulted in a

mask image for each of the science exp osures. The mask im-

age was subtracted from its corresp onding science exp osure.

The net-e ect is that pixels a ected by the CRs get substi-

tuted with the median value, variations due to the shifts of

the galaxy sp ectra and the sky lines taken into account.

The sp ectra were corrected for the slit function based

on sky at elds. The derived slit function was shifted up to

0.4 pixel in the spatial direction in order to takeinto account

the shifts in the slit-lets due to the exure.

The wavelength calibration was done for each slit-let in-

dividually. The main wavelength calibration was established

from high signal-to-noise He-Ne-Ar lamp sp ectra taken in

day time. The disp ersion solution was then shifted slightly

based on He-Ne-Ar lamp sp ectra taken immediately b efore

and after each science exp osure. The typical rms of the wave-

length calibration is 0.18A.

The sp ectra were corrected for the S-distortion by trac-

ing the p osition of the sp ectrum of the BCG. Because the

signal in the individual exp osures is to o low to establish the

S-distortion for the fainter galaxies the same S-distortion

was used to correct all the galaxies. After the correction was

applied, we veri ed that the same correction could b e use

for all the galaxies by deriving the di erences b etween the

mean center of the the sp ectra in the wavelength intervals

 

5295{5445A and 6040{6130A. The BCG has a di erence of

0.02 pixels, while the rest of the galaxies show di erences

of less than 0.2 pixels. The ap erture used for the velo city

disp ersion measurements is 5 pixels. We therefore conclude

that the adopted correction for the S-distortion do es not

a ect the velo city disp ersion measurements.

The wavelength calibration and the correction for the

S-distortion were applied simultaneously resulting in indi-

vidual science exp osures that are all on the same wavelength

scale and with the galaxies centered on the same pixels. The

sp ectra were sampled on a logarithmic wavelength scale. The

individual images were then averaged with scaling according

to their exp osure time. The individual expsure times were

11 1h and one exp osure of 48 minutes. The average im-

age was at this stage cut into sub-images, each sub-image

contains the sp ectrum from one slit-let. The sub-images are

then treated as individual long-slit sp ectra.

The sky background was subtracted from each sub-

00 00

image based on the outer 3: 5-10: 35. When p ossible the sky

sp ectra were extracted from b oth sides of the galaxy sp ectra.

In some cases residuals were left from the stronger sky lines.

The sky subtraction of these lines was improved by ttinga

linear function to the residuals in the spatial direction, and

then subtracting the t. The residuals from the sky line at

5577Awere interp olated across.

The sp ectra were calibrated to a relative ux scale based

0000 RAS, MNRAS 000, 000{000

22 I. Jrgensen, M. Franx, J. Hjorth, P. G. van Dokkum

Figure B2. Sp ectra of the observed galaxies in A2218. The sp ectra are calibrated to a relative ux scale. The panels are lab eled with

galaxy numb ers from Le Borgne et al. (1992) or Butcher et al. (1983). BOW97 is a background galaxy at z=0.291.

0000 RAS, MNRAS 000, 000{000