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2.3. Rotation Curve Decomposition. III. Galaxy Selection Criteria

We take DM parameters from published decompositions with as few changes as possible consistent with the assumption that halos are isothermal, with a uniform distance scale, and with the following selection criteria:

1 - Morphological types are restricted to Sc - Im and dSph, as noted above. Late-type and spheroidal galaxies are physically related (Kormendy 1985, 1987c; Binggeli & Cameron 1991; Ferguson & Binggeli 1994). Most dSph companions of our Galaxy have had episodes of star formation in the past 1 - 8 Gyr (Da Costa 1994 and Mateo 1998 provide reviews); they presumably turned from irregulars into spheroidals since that time (Kormendy & Bender 1994). In fact, the distinction between galaxy types has blurred as HI gas has been found in or near a few spheroidals (e.g., Sculptor: Knapp et al. 1978; Carignan et al. 1998; see Mateo 1998 for a review). It seems physically reasonable to include Sc - Im and dSph galaxies in the same parameter correlation diagrams.

2 - We discard most galaxies with inclinations i < 40°. Broeils (1992) remarks that HI rotation curve derivations are less accurate when the galaxy is too face-on. Also, there is some danger that oval distortions (Bosma 1978; Kormendy 1982) result in incorrect estimates of inclinations. Because they provide much-needed leverage at high luminosities, we kept four i < 40° galaxies from ABP: M101, NGC 5236, NGC 6946, and IC 342. Inclination is not a critical selection criterion; most nearly face-on galaxies satisfy the DM correlations.

3 - The most important selection cut is to ensure that rotation curves reach large enough radii to constrain the DM parameters. After some experimentation, we decided to require that the rotation curve measurements reach out to at least 4.5 exponential scale lengths of the disk. The peak in V(r) for an exponential occurs at 2.2 scale lengths (Freeman 1970), so the above choice ensures that the outer disk rotation curve drops significantly over the radius range in which we have velocity data. Observing a flat rotation curve then provides good constraints on DM parameters. The fussy choice of the ratio 4.5 resulted from a desire to keep a few galaxies that provide leverage at the high-luminosity end of the correlations. The radius cut is not applied slavishly; we keep a few galaxies that slightly violate the above criterion (ratio 3.5 - 4.4) but that are sufficiently halo dominated that the DM parameters are well determined. These galaxies are DDO 127, DDO 154, DDO 168, NGC 247, and IC 2574. In general, the radius cut is important; if we do not use it, we get a substantially larger galaxy sample, and it mostly is consistent with the DM correlations, but it shows considerably larger scatter than Figures 2 - 4.

Besides the selection cuts, we adopt the following procedures to make parameters from different sources be as consistent with each other as possible.

Following Broeils (1992), we base distances on the Virgocentric flow model of Kraan-Korteweg (1986). However, the zeropoint is based on distances from Cepheids and from surface brightness fluctuations (Ferrarese et al. 2000; Tonry et al. 2001). The distance to the Virgo Cluster is taken to be D = 16.5 Mpc, corresponding to a Hubble constant of H0 = 70 km s-1 Mpc-1. The center of the Virgo Cluster is assumed to be at (l, b) = (281°, 75°) (Binggeli, Tammann, & Sandage 1987). The Virgocentric infall velocity of the Local Group is assumed to be 220 km s-1. When accurate distances of our galaxies are known, e.g., from Cepheids, they are adopted. Most sources used essentially the above distance scale; when an author did not, we assumed that rc propto D and that rho0 propto D-2. This is not strictly correct, because gas and dynamical masses scale differently with distance. But the errors are small on the scales of Figures 2 - 4.

Galactic absorption corrections are from Burstein & Heiles (1984) or equivalently from the RC3 (de Vaucouleurs et al. 1991). Absolute magnitudes are corrected for internal absorption as in Tully & Fouqué (1985).

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