Annu. Rev. Astron. Astrophys. 1994. 32: 115-52 Copyright © 1994 by Annual Reviews. All rights reserved

2. OVERVIEW: THE MORPHOLOGICAL DEPENDENCE OF FUNDAMENTAL PROPERTIES

In an early study of the integral properties of galaxies, Roberts (1969) analyzed 98 spiral and irregular galaxies for which total mass, neutral hydrogen content, luminosity, color and radius were available. Over the last several decades, the database of observed quantities for extragalactic objects has expanded at an enormous rate. The availability today of large catalogs of galaxies and compilations of data in digital form makes statistical and graphical analysis possible as it has not been before. In preparing this review, we have drawn upon such catalogs to explore several of the morphological dependence issues. In this section, we present the results of our own analysis which we discuss in comparison with the findings of others in later sections.

Construction of Samples for Analysis

For the current purpose, we make use of two primary compilations: first, the RC3 and second, a private catalog maintained by R. Giovanelli and M. Haynes that we refer to by its familiar name, the Arecibo General Catalog (AGC). The latter catalog primarily adds a significant body of HI line data including upper limits for non-detected objects, a variety of measurements of the 21 cm line width, and qualitative indicators of profile shape.

Currently, redshift surveys extend relatively deeper in the north than in the south (as visible in Figure 2 of Giovanelli & Haynes 1991). Because of the northern hemisphere bias in redshift survey depth, we use as the prime deep sample the compilation of objects that are included both in the RC3 and in the Uppsala General Catalogue (Nilson 1973: UGC). We refer to the sample of objects common to both catalogs as the ``RC3-UGC sample'' It should be noted that, because the RC3 is intended to be complete only for objects of high surface brightness, the lowest surface brightness objects are found only in the UGC, and are underrepresented in the current analysis. Likewise, the UGC, being angular-diameter limited, is biased against high surface brightness, compact objects and becomes incomplete for early-type galaxies especially at the larger distances.

When one selects galaxies of fixed flux, the volume element containing the more distant, intrinsically brighter objects is larger than that occupied by the nearer, intrinsically fainter population. This ``Malmquist bias'' affects all galaxy catalogs that are flux-limited. In order to examine (and counteract) the effects of Malmquist bias, we have also constructed a nearby volume-limited one that should be complete but has relatively fewer galaxies. Since the volume occupied by the Local Supercluster has been well-studied by most available multiwavelength techniques, we have identified 4972 RC3 objects with redshifts implying membership in the Local Supercluster V<sub>LG</sub> < 3000 km s<sup>-1</sup>. This subset is referred to as the ``RC3-LSc sample.'' Note that it contains galaxies that are not in the RC3-UGC sample.

Since the backbone of our compilation is the RC3, the reader is referred to its first volume for an explanation of its contents. Our general philosophy has been to use all of the corrected parameters directly from the RC3 when available since its authors have gone to considerable length to reduce parameters obtained from different sources to a standard system. For the present comparative purposes, the consistency of approach is perhaps more critical than absolute prescription. Most parameters as detailed below have been taken directly from the RC3. Additional radial velocities, 21 cm parameters and far infrared data from IRAS come from the AGC.

DISTANCES In order to convert velocities to distances and to further calculate intrinsic parameters, it is necessary to adopt a value of the Hubble constant and a model of the local velocity field. Heliocentric velocities V are taken from the AGC preferentially if a good quality 21 cm spectrum is available; otherwise, the available optical velocity is used. The velocity with respect to the Local Group V_LG was calculated by applying the standard correction to V given in the RC3: 300 sinl cosb. For objects in the Local Supercluster, a non-linear infall model was used to calculate the distance to an object with the observed V_LG. The model adopted follows the outline of Schechter (1980) with the assumptions of a distance of 20.0 Mpc and an overdensity of 2 for Virgo and an infall velocity at the Local Group of 300 km s^-1. The Local Supercluster boundary is taken to be at V_LG = 3000 km s^-1. For more distant objects, distance is computed merely from the Hubble ratio from V_LG and is not referenced to any other frame. The assumptions that we have made are not intended to be an endorsement of any particular solution but are chosen for convenience. Most important is our emphasis on consistency. Throughout this paper, we adopt a Hubble constant H₀ of 50 km s^-1 Mpc^-1.

OPTICAL SIZE, LUMINOSITY AND SURFACE MAGNITUDE The linear size follows from the RC3 and the calculated distance. Likewise, the prescriptions outlined in the RC3 for correcting magnitudes are adopted along with a value of the solar absolute magnitude M_B of +5.48. The surface magnitude _B used here is defined simply as _B = B_T⁰ + 2.5 log ab, with a equal to D₂₅ and b the corresponding minor axis obtained from the RC3 axial ratio.

NEUTRAL HYDROGEN MASS AND SURFACE DENSITY The total neutral hydrogen mass M_HI in solar units is calculated from the integrated 21 cm line emission M_HI = 2.36 x 10⁵ D² SdV, where D is the distance in Mpc and SdV is the HI line flux in Jy kms^-1. For objects for which only a value of the rms noise per velocity interval in the emission spectum is available, the upper limit to M_HI is calculated assuming the emission is rectangular, of amplitude 1.5 times the rms noise and width equal to that expected for an Sa-Sb galaxy of similar luminosity, properly corrected for inclination. The latter relationship was derived from the detected objects. Objects showing emission confused with other sources or HI in absorption cannot be used properly in the analysis and have been ignored. The HI surface density, _HI, has been calculated as M_HI / R² where R is the optical linear radius. Although the use of the optical area makes _HI a hybrid quantity, Hewitt et al. (1983) have shown that on average, the HI and optical sizes scale linearly. Most authors use the quantity _HI or some variant thereof as the indicator of HI content in comparative studies.

FAR INFRARED LUMINOSITY AND SURFACE DENSITY The far infrared luminosity is derived from the fluxes measured by IRAS in the 60 and 100 micron bands F_FIR (Jy) = 2.58 F_60µ + F_100µ, as L_FIR (L) = 3.86 x 10⁵ D² F_FIR. Similar to _HI, a hybrid far infrared luminosity surface density _FIR is calculated as L_FIR / R².

TOTAL MASS AND SURFACE DENSITY FOR SPIRALS For the galaxies for which 21 cm line emission is detected, profiles widths are available to provide an estimate of the circular rotation velocity. Since widths are often measured using different algorithms, we have selected a subset of the available data that meet the following criteria: 1. the level at which the width was measured must be either at 20% of one or more peaks or 50% of the mean intensity; 2. the detection must be a good one, that is, not poor or confused; 3. the inclination must be greater than 40° for the width to be corrected to edge-on. While these restrictions cut down the number of galaxies for which corrected 21 cm line widths are available, they insure greater certainty of the resultant correlations. The total mass M_T is available only for non E-type systems, and is calculated according to M_T(< R) (M) = 2.325 x 10⁵ R V²_rot. As a practical application, we use the corrected 21 cm line width as the measure of 2V_rot and D₂₅ as the indicator of 2 R. Note that we have not applied a correction for turbulent velocity. The total mass surface density _T is likewise calculated as M_T / R².