The Infrared Tully-Fisher Relation in the Ursa Major Cluster R. F. Peletier Kapteyn Laboratorium, Postbus 800, 9700 AV Groningen, The Netherlands and European Southern Observatory, K. Schwarzschildstr. 2, D-8046 Garching bei M¨unchen, Germany and S. P. Willner Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138 USA Accepted for publication in The Astrophysical Journal, 1993 December 1. Abstract We present new magnitudes derived from 1.65 µm images for 23 galax- ies in the Ursa Major cluster. Magnitudes now exist for all but one spiral meeting our criteria for cluster membership and having H i velocity width arXiv:astro-ph/9307021v1 13 Jul 1993 greater than 187km s−1 and inclination greater than 45◦. These spirals fit a Tully-Fisher relation with dispersion in intrinsic magnitudes (after known ob- servational uncertainties and the effect of cluster depth are removed) of 0.36 and a slope of 10.2 ± 0.6. The magnitude dispersion is smaller than found in the Virgo cluster but still significantly larger than claimed by some authors. We find a hint that the Tully-Fisher relation may turn over at the bright end. Adding the central surface brightness of the disk as a third parameter flattens the slope of the Tully-Fisher relation and may give a distance esti- mate with slightly less dispersion, but the significance of the decrease must be tested on an independent sample. Page 2 Peletier and Willner 1. Introduction 2. Sample Selection The Tully-Fisher relation (Tully & Selection of the sample to be studied Fisher 1977) is one of the most useful is crucial both to avoid biases in the mag- ways to measure distances to spiral gal- nitudes, which could lead to bias in derived axies (e.g., Jacoby et al. 1992). However, distances (Teerikorpi 1984, 1987; Kraan- the amount of scatter in the Tully-Fisher Korteweg, Cameron, & Tammann 1988; relation is still a key issue, one of impor- Bottinelli et al. 1988), and to calculate the tance not only for estimating the distance correct dispersion in the derived magni- uncertainties but also because the amount tudes (Paper 1). An ideal sample would of scatter is crucial in estimating the bias in be selected without any reference whatever the distances themselves (Teerikorpi 1984, to galaxy magnitudes. Although the ideal 1987, Bottinelli et al. 1987). Several au- is impossible, for such nearby clusters as thors have found remarkably small disper- Ursa Major a close approximation to the sions (e.g., Freedman 1990, review by Ja- ideal can be achieved. coby et al. 1992), but Fouqu´eet al. (1990) There are two methods commonly and Peletier and Willner (1991, hereinafter used to define cluster membership. The Paper 1) have found intrinsic dispersions first is based on a nearest-neighbor anal- among Virgo cluster spirals near 0.5 mag- ysis (e.g., Huchra and Geller 1982), while nitudes in the blue and 0.4 magnitudes in the second is simply to establish posi- the infrared. tion and velocity limits. In the nearest- The natural question is whether the neighbor or “tree” analysis, a list of gal- large dispersions are a property of just the axies with positions, velocities, and magni- Virgo cluster or are inherent in the Tully- tudes is somehow sorted according to the Fisher relation itself. An ideal test case is presumed “closeness” of the various galax- the Ursa Major cluster. It lies at nearly the ies. A density threshold is then established, same redshift as Virgo, has plenty of spi- and any section of the list having density ral galaxies, and earlier studies (Pierce & above the threshold is taken to be a group. Tully 1988, hereinafter PT) have indicated This method assumes no a priori knowl- a smaller Tully-Fisher dispersion than in edge of cluster locations, but practical im- Virgo. plementations (e.g., Tully 1987) often have an explicit dependence on galaxy magni- This paper presents magnitudes de- tudes. rived from infrared images for a nearly com- plete sample of Ursa Major spirals. The The second method is necessarily primary aim is to investigate the disper- somewhat empirical. The position limits sion, but we also examine how best to de- are usually expressed as a cluster center rive magnitudes and inclinations for Tully- and radius, and minimum and maximum Fisher purposes. Sample selection is given velocity limits are established. The ad- considerable attention. vantage of this method is that there is no explicit dependence on galaxy magnitudes, Ursa Major Tully-Fisher Page 3 though a dependence could arise if the orig- explicit magnitude dependence in selecting inal list is seriously incomplete at fainter this sample, or indeed any requirement that magnitudes. Incompleteness is not a prob- magnitudes be known, but galaxies must lem for this study, however, because cata- have been cataloged and had redshifts mea- logs contain galaxies fainter than 15th mag- sured. This will introduce some incom- nitude (though they are not complete at pleteness, but this probably becomes seri- this limit, of course) while most of the spi- ous only below magnitude 14. rals in the Ursa Major cluster are brighter From the initial list, we have excluded than 12th in B. 15 galaxies that are not spirals (keeping For this study, we examined data com- only galaxies with T > 0 according to the piled for the CfA Redshift Survey (Huchra RC3—de Vaucouleurs et al. 1991). Only et al. 1983 and unpublished). An initial ex- reasonably edge-on galaxies can give use- amination in Right Ascension-Declination- ful velocity widths, so we have excluded Redshift space found distinct groupings at 13 galaxies with axis ratio less than 1.40 −1 −1 ◦ Vh < 400 km s , 625 < Vh < 825 km s , corresponding to inclination less than 45 −1 825 <Vh < 1025km s , and 1100 <Vh < (Paper 1). Finally, we have excluded 1300km s−1. The last group seems to be 17 galaxies that lack H i observations or separated from the others in position, while have inclination-corrected velocity widths c −1 the first three are separated mainly in ve- ∆V20 < 187.5 km s , an arbitrary limit re- locity. The position centroid of those gal- flecting the completeness of our photomet- −1 axies in the range 600 <Vh < 1050km s ric observations. Many of the excluded gal- is approximately 11H 54M , 48◦ 53′, which axies are faint, but it is possible that better we have adopted as the cluster center.1 The H i observations would allow some of them surface density of galaxies falls off beyond to be used for Tully-Fisher purposes. Ta- 7◦ from this position, so we have adop- ble 2 lists all the excluded galaxies. ted this as the cluster radius even though The remaining cluster sample contains there are undoubtedly cluster galaxies be- 29 galaxies listed in Table 1. In prac- yond this radius. Finally, we have slightly tice, an almost identical sample would have extended the velocity limits to 550 <Vh < −1 been obtained from nearest-neighbor anal- 1150km s in order to make our definition ysis simply by adopting group “12-1” from correspond more closely to previous work. All galaxies meeting these requirements are 2 two are cataloged galaxies for which po- listed in either Table 1 or 2. There is no sitions and other data can be found in 1 ◦ ′ the NASA Extragalactic Database (NED). Compare with 11H 54M , +49 30 found 115400+4836 (KDG 310A) is a companion by Biviano et al. (1990). PT used the same south preceding NGC 3985 (KDG 310B). center coordinates as Biviano et al. along ◦ We do not know of published data on with a cluster radius of 7.5 and effective −1 115640+5059. These two galaxies are velocity limits 628 <V < 1138 km s . h among the ones excluded from our Tully- 2 All galaxies in Tables 1 and 2 except Fisher sample and were not observed. Page 4 Peletier and Willner Tully (1987).3 This group has 57 mem- March used a two-lens reimaging optical bers, and other authors of nearest-neighbor system giving a scale of 1 .′′641 per pixel, analyses (Geller and Huchra 1983, Huchra while those in 1992 March used a three- and Geller 1982, Turner and Gott 1976) lens optical system giving 1 .′′757 per pixel. consider it a sub-group of their somewhat Sky frames were observed along with each larger groups. The difference seems to arise galaxy, separated from object frames by because the latter authors are interested >3 arcmin depending on the galaxy size. in larger structures and accordingly have Data calibration began by removing set their density thresholds lower. For this dark current and star images from sky study, we need to be sure all the galaxies frames and averaging sky frames to create are at the same distance, so the most re- a flat field. Each object frame, including strictive definition is appropriate. those for standard stars, was divided by a Two of the galaxies in Table 1 lack in- flat field frame. The observations of stan- frared magnitudes. UGC 6917 has a bright dard stars showed a variation of up to 30% star superposed on the galaxy, rendering peak-to-peak in 1991 and 20% in 1992 de- the current observations useless, and we pending on where the standard star fell on failed to observe NGC 4218. A total of 27 the object frame. The variation was re- galaxies are thus available for analysis. peatable and mostly in the East-West di- rection. We attribute it to the incomplete 3. Observations long-wavelength blocking of the 1.65 µm bandpass filter; the sky frames thus con- All of the observations were made with tain a component at ∼5 µm, while the the 1.2-m telescope at Mt.