3 Rotation curve fits at Cepheid-based distances

In Fig. 1 we show the MOND rotation curve for all four galaxies from the BBS sample with Cepheid-based distance determinations. NGC 2841 and NGC 7331 both contain central bulges as evidenced in the light distribution, and the radial surface brightness profile has been appropriately decomposed. Here, $a_{\rm o}$ is fixed at the rescaled value of $0.9 \times 10^{-8}$ cm s^-2, and the distance is fixed at the Cepheid-based values as updated and corrected by Freedman et al. (2001). The free parameters of the fit are the disc and, in two cases, bulge masses. The resulting values and the corresponding mass-to-light ratios are given in Table 1 for the four galaxies.

Figure 1: MOND rotation curves compared to observed H  I rotation curves for the four galaxies from the sample of BBS with Cepheid-based distances. The dotted, long-dashed, and short-dashed lines are the Newtonian rotation curves of the stellar disc, bulge, and gaseous components respectively.

Here we see that for two of the galaxies, NGC 2403 and NGC 7331, the MOND rotation curves agree well with the observed curve. In both of these cases, the predicted rotation curve lies somewhat above the observed curve in the inner regions but this could be due to beam-smearing. The implied mass-to-light ratios generally fall within the range that would be considered reasonable for stellar populations (Table 1).

 

 

Table 1: Galaxies with well-defined rotation curves and Cepheid-based distances.

${\rm Galaxy }$	D	LB	$M_{{\rm gas}}$	$M_{{\rm disc}}$	$M_{{\rm disc}}/L_B$	$M_{{\rm bulge}}$	$M_{{\rm bulge}}/L_B$
	$({\rm Mpc}$)	$({\rm 10^{10}}~L_\odot)$	$({\rm 10^{10}}~M_\odot)$	$({\rm 10^{10}}~M_\odot)$		$({\rm 10^{10}}~M_\odot)$
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)
NGC 2403	3.2 $\pm$ 0.2	0.82	0.4	1.34 $\pm$ 0.03	1.6
NGC 2841	14.1 $\pm$ 1.5	4.60	2.7	29.70 $\pm$ 4.3	8.3	1.5	0.83
NGC 3198	13.8 $\pm$ 0.5	2.44	1.6	2.63 $\pm$ 0.1	1.1
NGC 7331	14.7 $\pm$ 0.6	5.26	1.4	13.20 $\pm$ 0.6	2.0	5.7	1.8

(2) The Cepheid-based distance from Freedman et al. (2001).
(3) The B-band luminosity (in ${\rm 10^{10}}~L_\odot$) at the Cepheid distance.
(4) The total gas mass including primordial helium at the Cepheid distance.
(5) The total mass of the stellar disc from the MOND fit.
(6) The implied mass-to-light ratio of the stellar disc.
(7) The total mass of the stellar bulge in those two cases where a bulge is evident.
(8) The implied mass-to-light ratio of the stellar bulge.

For the other two galaxies, there are clear systematic differences between the MOND rotation curve and the observed curves. Basically, the predicted curves have a different shape than the observed curves: for NGC 2841, the predicted curve is significantly higher than observed in the inner regions (by up to 30 km s^-1) and comparably lower in the outer regions. For NGC 3198 the differences are in the opposite sense: about 10 km s^-1 lower in the inner regions and 10 km s^-1 higher in the outer regions. These differences diminish if NGC 2841 is moved further out and if NGC 3198 is moved closer in; i.e., MOND clearly prefers a larger distance to NGC 2841 (as discussed previously by BBS and by Sanders 1996) and a smaller distance to NGC 3198. We now discuss these two cases with respect to the question of whether or not this mismatch can be interpreted as a falsification of MOND. Because the rotation curve of NGC 3198, when taken at the Hubble law distance of 10 Mpc, is very well predicted by MOND, and because the observed curve is thought to be well-determined, this, at first sight, appears to be the more problematic case, and we begin with this object.