Dark matter and the Tully-Fisher relations of spiral and S0 galaxies
aa r X i v : . [ a s t r o - ph . GA ] D ec Dark matter and the Tully-Fisher relations ofspiral and S0 galaxies
Michael J. Williams ∗ ,† , Martin Bureau ∗ and Michele Cappellari ∗ ∗ Sub-department of Astrophysics, Denys Wilkinson Building, Keble Road, Oxford OX1 3RH, UK † ESO, Karl-Schwarzschild-Str. 2, D-85748 Garching bei München, Germany
Abstract.
We construct mass models of 28 S0–Sb galaxies. The models have an axisymmetricstellar component and a NFW dark halo and are constrained by observed K S -band photometry andstellar kinematics. The median dark halo virial mass is 10 . M ⊙ , and the median dark/total massfraction is 20% within a sphere of radius r / , the intrinsic half-light radius, and 50% within R .We compare the Tully-Fisher relations of the spirals and S0s in the sample and find that S0s are0.5 mag fainter than spirals at K S -band and 0.2 dex less massive for a given rotational velocity. Weuse this result to rule out scenarios in which spirals are transformed into S0s by processes whichtruncate star formation without affecting galaxy dynamics or structure, and raise the possibility of abreak in homology between spirals and S0s. MASS MODELS
In [1] we presented mass models for a sample of 28 edge-on early-type disk galaxies(S0–Sb). The models are composed of an axisymmetric stellar component, based on ob-served K S -band photometry [2] assuming a constant stellar mass-to-light ratio ( M / L ) K S ,and a spherical NFW dark halo [3] of mass M DM . The model parameters are constrainedby solving the Jeans equations assuming a constant anisotropy in the meridional plane b z ≡ − s z / s R , which yields a prediction of the second velocity moment, and compar-ing to observed stellar kinematics [5]. These simple models are able to reproduce thewide range of observed stellar kinematics, which extend to 2–3 effective radii.The median ( M / L ) K S for the sample is 1.09 (solar units) with an rms scatter of 0.33.The median M DM for the sample is 10 . M ⊙ with an rms scatter of 0.7 dex. This isequivalent to halo concentrations between 7 and 9. The mass models have a mediandark/total mass fraction of 20% within a sphere of radius r / , the intrinsic half-lightradius (approximately equal to 1.33 R e , where R e is the projected half-light (or effective)radius and 50% within R . All but two models are consistent with being maximal [6],although they were not constructed under this assumption. Models without a dark haloare also able to reproduce the observed kinematics satisfactorily in most cases, but theimprovements when halos are added are statistically significant. Moreover, a preliminarycomparison shows that the stellar mass-to-light ratios of mass models without darkmatter very significantly exceed the predictions of stellar population models for plausibleinitial mass functions, but this effect is significantly reduced for our preferred massmodels with dark haloes. We will use these results to measure the normalization anduniversality of the IMF in more detail in the future. IGURE 1.
Tully-Fisher relations of the sample of 28 disk galaxies, shown as functions of K S -bandluminosity, stellar mass and dynamical mass. Spirals are shown as blue triangles, S0s as red circles.Median error bars are shown in the top left of each plot. THE TULLY-FISHER RELATION
Using the circular velocities of the models, we constructed Tully-Fisher relations (TFRs)as functions of luminosity, stellar mass, and dynamical mass for the S0s and spiralsseparately (Fig. 1). We find that S0s are 0.5 mag fainter than spirals at K S -band for agiven rotational velocity. In stellar population synthesis models in which star formationis truncated, this fading would take ∼ REFERENCES
1. M. J. Williams, M. Bureau, and M. Cappellari,
MNRAS , 1665 (2009)2. M. Bureau, et al.,
MNRAS , 753 (2006),3. J. F. Navarro, C. S. Frenk, and S. D. M. White,
ApJ , 493 (1997)4. M. Cappellari,
MNRAS , 71 (2008)5. A. Chung, and M. Bureau, AJ , 3192 (2004)6. P. D. Sackett, ApJ , 103 (1997)7. A. Dressler, et al.,
ApJ , 577 (1997),8. G. Fasano, et al.,
ApJ , 673 (2000)9. S. Courteau, et al.,
ApJ , 203 (2007)10. M. J. Williams, M. Bureau, and M. Cappellari,