The Infrared Diameter Velocity Disp ersion Relation for Elliptical Galaxies Michael D Gregg Institute for Geophysics and Planetary Physics Lawrence Livermore National Laboratory L East Avenue Livermore CA greggigppllnlgov ABSTRACT Using single channel infrared photometry from the literature a provisional Kband diametervelocity disp ersion relation for elliptical galaxies in the Coma and Virgo clus ters is derived The Coma cluster relation has times lower scatter at K than in B or V Excluding outliers the RMS scatter at K for galaxies in Coma is only in distance close to the limit implied by the observational errors Distance estimates based on the IR D relation will b e more accurate than those derived from optical data The improvement in the infrared is attributed to a decrease in sensitivity to stellar p opulation parameters age metallicity and slop e of the IMF as well as lower internal extinction from dust compared to the optical That the D relation has a larger scatter in the optical indicates that there are detectable but small stellar p opu lation or dust content dierences among the Coma ellipticals Since the D relations are based on the fundamental plane this result promises that the fundamental plane is astro-ph/9506136 28 Jun 1995 thinner in the infrared than it is in the optical Infrared photometric data available for Virgo are limited to just ob jects the spread in distance due to the depth of the cluster precludes any signicant improvement over B and V A relative ComaVirgo distance of is derived from the K band data in agreement with estimates in other colors and using other techniques indicating that there is no signicant age dierence b etween Virgo and Coma ellipticals Subject headings galaxies distances galaxies elliptical Introduction Guzman Lucey By analogy with the TF relation it is natural to susp ect that replac There are two p opular metho ds for determin ing Bband with infrared photometry might lead ing redshiftindep endent distances to galaxies to an improvement in the accuracy of distances Both rely on a tight correlation b etween a sp ec estimated by D and FP plane techniques n troscopically determined distanceindep endent mea Guzman Lucey Gregg This pa sure of the gravitational p otential and a photo p er presents evidence that the D metho d and metrically determined distancedep endent mea by inference the FP has signicantly less scatter sure of apparent size The TullyFisher TF re in the IR than in the optical for ellipticals in the lation for spirals Tully Fisher is based Coma cluster on the correlation b etween luminosity and rota tional velocity The D technique for ellip n Derivation of Infrared Diameters ticals Dressler et al D dep ends on the Using IR data from Bower Lucey Ellis correlation b etween a surface brightness dep en a BLE it has b een shown elsewhere that dent diameter and the central velocity disp ersion the Kband magnitudevelocity disp ersion relation for early type galaxies in the Coma When rst introduced the TF metho d em cluster has a scatter smaller by a factor of ployed B band photometry necessitating rela than the B band D relation Gregg tively large and uncertain corrections for inter Because the IR magnitudes are from single chan nal extinction which vary with galaxy morphol nel photometry in a ap erture the derived ogy and star formation rate Aaronson Huchra IR relation is b etween velocity disp ersion and a Mould AHM Diering current SFRs metric size For a useful distance indicator it probably also contribute to the spread in B mag is necessary to dene a size based on structural nitudes The accuracy of the TF metho d was parameters of the galaxies individually the FP improved markedly when AHM introduced the or D relations accomplish this using the half use of H band photometry where extinc lightradius R or D D dene D as the diam e n n tion corrections are reduced to negligible levels eter of a circular ap erture within which the mean and the ux is mainly from the oldest p opula B band surface brightness is magsq arc tion of stars which is p erhaps more uniform from sec and show that logD is well correlated with n galaxy to galaxy AHM log reducing the scatter by a factor of two There is increasing evidence from sp ectro from the FaberJackson B vs log relation T scopic studies suggesting that the stellar p opu Faber Jackson Typical ellipticals have lation of ordinary elliptical galaxies can b e a mix BK so a K band diameter D which ap K of ages eg OConnell Rose Pickles proximates D would enclose a mean K surface n Bower et al Gonzales Ex brightness of magsq arcsec treme cases such as merger remnants have exp e The Virgo and Coma D are based on CCD n rienced strong bursts of star formation Carter photometry D Burstein et al B et al Schweizer et al Dust has The ideal IR version of a D relation would use also b een shown to exist in a large fraction of K band imaging however with some simple as ellipticals There is go o d evidence that the dis tances derived from D and the closely related n Jorgensen Franx Kjaergaard have demon fundamental plane FP technique Djorgovski strated that the FP is an intrinsically more accurate dis Davis for some ellipticals are inuenced by tance indicator than D Using the ts detailed here one or more of these factors Gregg it is p ossible to derive an IR version of the FP Because smaller than the error estimates for logD Burstein sumptions a provisional D relation can b e n K et al and comparable to those in logD derived for the Coma and Virgo clusters from the V LGCT The derived logD are listed in Table data of Persson Frogel Aaronson PFA K along with their A D from B and the V and BLE b oth present high quality single chan e n band equivalent D ap erture diameter enclos nel IR photometry for early type galaxies in the V ing magsq arcsec from BLE Note that Coma and Virgo clusters The BLE photometry although V band A from LGCT have b een used has b een calibrated to b e on the same system as e in deriving D strict photometric indep endence that of PFA see BLE for discussion and their K b etween the V and K band results is maintained much larger b o dy of photometry sup ersedes the by adopting D from BLE earlier PFA work As BLE present no new IR V photometry for Virgo the data of PFA are used PFA present JHK photometry of Virgo here ellipticals through ap ertures and = which allows D to b e derived from an R law Table of BLE lists K magnitudes through an K t without recourse to any optical data For eective ap erture of for E or ES and comparison D values were also derived for the S galaxies in the Coma cluster which also have K Virgo ellipticals using the same metho d as the log in Davies et al or Dressler Coma ellipticals ie by adopting an optical A Corrections for background light red e and tting to a single ap erture It is testimony shift and Galactic reddening were applied as de to the high quality of the data from PFA BLE tailed in BLE and PFA D can b e derived from K = and B that the two metho ds give identical re these single ap erture data by assuming an R sults within a few p ercent and that these are in law prole and adopting an eective diameter turn extremely well correlated with the diame A from the V band photometry of Lucey et al e ters in B and V This test serves as a condence a LGCT for the ellipticals and the Third check on the derived IR diameters for the Coma Reference Catalog de Vaucouleurs et al galaxies Table includes the Virgo ellipti for the Ss In the absence of color gradients A e cals from PFA and their calculated D along is indep endent of wavelength and in most ellipti K with D B and D BLE One of the ob cals color gradients are negligible PFA Peletier n V jects NGC with log is excluded Valentjin Jameson = from the analysis to follow The R ts are uniquely determined by the ap erture photometry and eective diameter Er Velocity Disp ersions rors have b een estimated by deriving D after K varying b oth quantities by their estimated stan Velocity disp ersions from Davies et al dard deviations dex for l og A LGCT e have b een adopted b ecause these data pro duce and mag for the K ap erture magnitudes tighter D correlations than other data sets BLE These small errors have little eect on eg Dressler or LGCT This can b e at logD amounting to only dex RMS K tributed to the careful treatment of systematic eects as well as the averaging of several inde of the use single channel IR data and A from V band e p endent measurements in many cases In cases measurements this is not preferred here b ecause the V however the velocity disp ersions of LGCT are band photometry then plays a role in determining of preferable The LGCT for RB is more the dimensions of the FP A and and contributes e e to b oth sides the FP distance estimator itself A as well than rms lower than that of Davies et al and e as log C The results however of such an analysis e moves RB directly onto the D relation are in agreement with the D relation discussed here in all colors The Davies et al disp ersion for Several groups are now working towards a full Kband FP NGC is only kms well b elow other es derivation eg Pahre et al timates cf Whitmore McElroy Tonry at kms The intermediate log of LGCT km s again moves NGC onto the D relation in all bands Finally the Davies et al Table value for NGC is the only one in the present Data for Coma and Virgo Galaxies sample based only on lower resolution Lick data