.527T .257. The Astrophysical Journal, 257:527-537, 1982 June 15 . © 1982. The American Astronomical Society. All rights reserved. Printed in U.S.A. 1982ApJ. A COLOR-MAGNITUDE RELATION FOR SPIRAL GALAXIES R. Brent Tully Institute for Astronomy, University of Hawaii J. R. Mould Kitt Peak National Observatory1 AND M. Aaronson Steward Observatory, University of Arizona Received 1981 September 10; accepted 1981 December 17 ABSTRACT Tight correlations are found between blue-to-infrared colors and either the H i line profile widths (masses) or the intrinsic luminosities of spiral galaxies. The correlations are derived from samples of galaxies which range in type from Sa to Im. The dispersions in the relationships are not affected by type dependencies except at a marginally significant level. Since colors are distance independent, the color-magnitude correlation can be used as a measuring stick. A distance modulus of 31.04 ±0.16 mag is found for the Virgo Cluster, if we adopt the Sandage-Tammann distance scale for nearby galaxies. The tight relationships between color and mass or luminosity, essentially independent of galaxy type, suggest that the Hubble morphological sequence is predominantly dependent on a single parameter: total mass. The color-magnitude diagram can be qualitatively understood if the initial specific star formation rate in spirals decreases with decreasing mass and, at the same time, chemical abundances decrease and/or the initial mass function flattens with decreasing mass. Spiral and lenticular galaxies inhabit quite separate regions on the color-magnitude diagram. If galaxies evolve between the two branches, the probability seems to be low of viewing them in the intermediate state. It is proposed that a gas-rich galaxy will He on the spiral branch at a location specified by its total mass and, once its gas is depleted or lost, will rapidly evolve to a location on the lenticular branch that is specified by its total mass. Subject headings: galaxies: evolution — galaxies: photometry I. PREFACE discussing an idea whose moment has come, because the After this article was submitted for publication, the relationship has been independently discovered by Wyse report of the discovery of a color-magnitude relationship (1982). for spiral galaxies by Visvanathan (1981) came to our attention. We will be discussing the same phenomenon, although our color (the difference of broad-band ob- II. A COLOR-MASS RELATIONSHIP FOR SPIRAL GALAXIES servations at 0.45 /im and 1.6 jam) achieves better separation between young and old stellar populations It has become firmly established that there are tight than the color used by Visvanathan (based on observa- correlations between the global H I profile widths of tions at 0.55 jam and 1.0 jam), and, consequently, the spiral galaxies and the intrinsic luminosities of these relationship is even better defined. As a result, we are systems, whether the luminosities are at optical wave- more optimistic about the utilization of color dependen- lengths (Tully and Fisher 1977) or in the near infrared cies for the determination of the distances of galaxies. (Aaronson, Huchra, and Mould 1979). These correla- Visvanathan has qualitatively anticipated some of our tions can be understood physically because the H I conclusions regarding the physical underpinning of the profile width is a measure of the mass of a galaxy, and it correlation between color and magnitudes. We will be is expected that total mass and total luminosity are closely coupled. The observed relationships between the H I line pro- 1 Operated by the Association of Universities for Research in Astronomy, Inc. under contract with the National Science Founda- file width and blue magnitudes or 1.6 jam “H” magni- tion. tudes follow power laws, but, for the two cases, the © American Astronomical Society • Provided by the NASA Astrophysics Data System .527T .257. 528 TULLY, MOULD, AND AARONSON Vol. 257 . TABLE 1 Local Calibrators 1982ApJ. mo j)b, i -1 rrabs b Name /7L 0.5 íj y B-H (km s ) Mo “-0.5 M s‘ NGC 224... SAb 0.91 3.58 2.67 552 24.38 -23.47 -20.80 NGC 247... SXd 7.69 8.99 1.30 230 27.57 -19.88 -18.58 NGC 253 ... SXc 4.74 7.11 2.37 438 27.57 -22.83 -20.46 NGC 598... SAcd 4.38 5.84 1.46 253 24.82 -20.44 -18.98 NGC 2366 . IBm 10.82 10.70 -0.12 124 27.82 -17.00 -17.12 NGC 2403 . SXcd 6.45 8.34 1.89 306 27.82 -21.37 -19.48 NGC 3031 . SAab 4.38 7.20 2.82 531 27.82 -23.44 -20.62 UGC 5666 a SXm 10.07 10.66 0.59 126 27.82 -17.75 -17.16 NGC 4236 . SBdm 9.08 9.22 0.14 197 27.82 -18.74 -18.60 NGC 5204 . SAm 10.30 11.47 1.17 155 29.56 -19.26 -18.09 UGC 8837b SBm 12.49 12.63 0.14 106 29.56 -17.07 -16.93 NGC 5585 . SXd 10.15 11.24 1.09 211 29.56 -19.41 -18.32 aUGC 5666 = IC 2574. bUGC 8837= Holmberg IV. slopes are different. The correlation between the depro- It may be that we can understand the slope of the jected H i profile width at 20% of maximum intensity infrared relationship following the arguments given by and blue magnitudes corrected for inchnation effects Aaronson, Huchra, and Mould (1979), or it may be that and galactic obscuration is shown by Fisher and Tully the situation is more complex as Burstein (1982) argues. (1977) and by Sandage and Tammann (1976). Using In any event, the point already made by Bottinelli et al updated blue magnitudes and H i profile widths (see (1980) can be emphasized: the slope between luminosity data in Table 1), we now find that and the H i profile width varies with passband in the 2 interval between blue light and the infrared. LB~{WÍ,) \ (O The implication in the difference in slope between the where LB are blue luminosities and are deprojected blue and the infrared relationships is that there is a H i profile widths.2 The dependence between and strong correlation between B — H color and the mass of the infrared magnitude H^q 5 is displayed by Aaronson, spiral galaxies. It is demonstrated in Figure 1 that this Mould, and Huchra (1980) for the same set of calibrat- claim is correct. The two distance-independent parame- ing galaxies. They accept: ters, B — H color and deprojected line profile width, are compared. Data for the sample of 94 galaxies satisfies 4 0 2 rw~(»2o) ' . ( ) the following conditions: 1. //-os measured by Aaronson, Mould, and 2 Rubin, Burstein, and Thonnard (1980) found a considerably Huchra (1980); Mould, Aaronson, and Huchra (1980); steeper slope for a sample of 21 Sc galaxies. Small number statis- or Aaronson e/«/. (1982û). tics may affect their results, as de Vaucouleurs etal. 1982 have suggested. Alternatively, the manner in which the Rubin etal. 2. W2q measured by Fisher and Tully (1981) or sample was compiled might have contributed to the steeper slope. otherwise available in the literature. They considered galaxies within a small window in apparent 3. Bt based on a measurement by Holmberg (1958) dimensions (which would correlate roughly with a common ap- or a photoelectric determination cited in the Second parent luminosity) and tried to sample the widest possible range in intrinsic properties by selecting galaxies over the widest possible Reference Catalogue (de Vaucouleurs, de Vaucouleurs, range of redshifts. By thus populating the extrema in luminosities and Corwin 1976; hereafter RC2). in a nonrepresentative way, the relationship would be steepened. 4. Galaxies inclined such that 45o</<80° and The Rubin et al sample includes the “largest identified Sc galaxy” galaxies greater than 30° from the galactic plane. (Rubin, Ford, and Thonnard 1980), and two galaxies in a sample A least-squares linear regression analysis of the data of 21 are intrinsically more luminous than any of 535 Sbc through Sd galaxies in the “ volume-limited” sample considered by Fisher in Figure 1 provides the fit: and Tully 1981. The much larger samples of both de Vaucouleurs et al and Aaronson et al 1982 a yield a shallower slope for the H I c profile-luminosity relationship. B^f - H _0 5 = 4.53 log JF¿) -9.51. (3) Rubin, Ford, and Thonnard 1980 and Roberts 1978 also report a strong type dependence in the H i profile-luminosity relationship From equations (1) and (2), a slope of 4.5 could have using blue magnitudes, although no significant effect is found by de Vaucouleurs etal 1982. In any event, the type depen- been anticipated. Two details may be noted: dence found using infrared magnitudes appears to be small (see 1. Galaxies with morphological classifications Sa Aaronson et al 1982 ¿>). through Sb may lie slightly to the red of the mean © American Astronomical Society • Provided by the NASA Astrophysics Data System .527T .257. No. 2, 1982 COLOR-MAGNITUDE RELATION FOR SPIRALS 529 . 1982ApJ. Fig. 1.—Blue-toinfrared color-H i line profile width relationship. Morphological types are distinguished by different symbols. Open circles'. Sa-Sb; filled circles: Sbc-Scd; crosses: Sd-Im. The least-squares regression fit is shown. regression line, but the significance of this effect is only 1. It suggests that stellar populations are tightly cou- 2 a; otherwise, there is no evidence for a type depen- pled with mass. The 1 o scatter in Figure 1 is 19% in dence in equation (3). and 0.34 mag in B — H. Suppose mass and H magni- 2.