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Kinematic Constraints on the Stellar and Dark Matter Content of Spiral

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Kinematic Constraints on the Stellar and Dark Matter Content of Spiral SUMMARY KINEMATIC CONSTRAINTS ON THE STELLAR AND By comparing the predicted kinematics of mass models of disk galaxies to their observed stellar kinematics, we con- strain their K -band stellar mass-to-light ratios and dark DARK MATTER CONTENT OF SPIRAL AND S0 GALAXIES S matter fractions. The median (M/L)Ks for the sample is . with an rms scatter of .. The median dark matter fraction is % within one eective radius and % within R . The Ss [email protected], in our sample are systematically fainter for a given circular velocity, a finding that is consistent with models of galaxy evolution in which Ss are the faded descendents of spirals. INTRODUCTION 30 RESULTS DISCUSSION 20 This work has two principal goals: to constrain the near- 10 In all cases, these simple models are able to reproduce the NEAR-INFRARED M/L RATIOS infrared mass-to-light ratios and stellar masses of a sample of 0 wide range of observed stellar kinematics, which extend to Near-infrared mass-to-light ratios are particularly useful be- local disk galaxies, and to constrain the fraction of the total (arcsec) 2-3 eective radii or, equivalently, 0.5- R . cause it is at these wavelengths that the eects of dust are z −10 25 mass of those galaxies that is dark matter. minimized and light most closely corresponds to stellar mass. −20 In Fig. 2 we show contours of χ2 for the sample. This dem- Unfortunately, the calibration of stellar population synthesis We present mass models of 4 spiral and 4 lenticular (S0) −30 onstrates the constraints we are able to place on (M/L) and Ks models in the near-infrared is particularly uncertain because galaxies. By comparing the predicted kinematics of the M for each galaxy (χ2 is not a strong function of β in DM z of the diculty of modelling the thermally pulsing asymp- models to observed stellar kinematics, we constrain their 200 v these rotationally supported galaxies). rms ) totic giant branch (in addition to the usual uncertainties 1 , stellar and dark matter content. − μ The median (M/L) for the sample is .7 with an rms scat- about the IMF). Dynamical estimates of the stellar mass-to- 150 2 Ks Each mass model is comprised of an axisymmetric stellar (km s ter of 0.36. Our preliminary comparisons show this is con- light ratio that correctly account for dark matter are there- (km s c 100 component based on observed K -band photometry (Bureau v sistent with the predictions of two stellar population models fore of great interest This work is the largest sample of dy- S − , 1 v ) et al. 2006) and an NFW halo (Navarro et al. 997). The stel- 50 (Bell & de Jong 200, Maraston 2005). namically determined stellar population mass-to-light ratios lar component is assigned a constant mass-to-light ratio, 2.85 NGC 3957 The median M for the sample is 0 M with an rms at KS-band and avoids the assumption of a maximal disk. In a (M/L) . The halo is assumed to follow a correlation between 0 DM ☉ Ks scatter of 0.7 dex. This is equivalent to halo concentrations future work we will compare in detail these dynamical esti- halo mass M and concentration c (Macció et al. 2008). 60 50 40 30 20 10 0 10 20 30 40 50 60 DM vir R (arscec) between 7 and 9. The mass models contain a median dark mates to the predictions of population models. The Jeans equations for the corresponding potential are matter fraction of 6% within one eective radius and 50% solved under the assumption of constant anisotropy in the FIGURE within R . DARK HALOES ☝ 25 Our mass models are constrained by kinematics only within meridional plane, β (Cappellari 2008). Example data and model (NGC ). The top panel shows z Models without a dark halo are able to reproduce the ob- the optical parts of the galaxy. The parameter M of our the observed K -band image (filled contours) and the model DM This yields a prediction of the second velocity moment, S served kinematics satisfactorily in most cases. The improve- mass models is therefore entirely model dependent. Despite of the stellar component (lines). The bottom left panel which we compare to observed stellar kinematics (Chung & ment when a halo is added is statistically signicant, how- this, a preliminary comparison demonstrates that it appears to Bureau et al. 2004) to constrain the three parameters of the shows the observed line-of sight velocity (points) and the ever, and the stellar mass-to-light ratios of mass models with circular velocities of the total mass model (solid line) and its correspond well with the predictions of semi-analytic models model, (M/L)Ks, MDM and βz. An example model for one of dark haloes match the independent expectations of stellar constrained by the local stellar mass function (see Fig. 3) the 28 galaxies is shown in Fig. stellar and dark components (dashed and dotted lines). The population models better. bottom right panel shows the second velocity moment of TULLY-FISHER RELATIONS OF EARLY-TYPE DISKS the model (red line). The model is adjusted to reproduce the 12 The Tully-Fisher relation (TFR, Tully & Fisher 977) re- observed second velocity moment (points). lates the global H line width to the luminosity of spiral gal- axies. Previous authors have demonstrated that S0s lie at cvir(MDM) 18.2 11.8 7.7 5.0 18.2 11.8 7.7 5.0 18.2 11.8 7.7 5.0 18.2 11.8 7.7 5.0 11 fainter magnitudes for a given line width (see, e.g., Bedregal 1.8 FIGURE 1.6 ☜ ) et al. 2006 and references therein). They did this by using 1.4 Contours of χ for the complete sample. χ is defined in ☉ 1.2 1.0 /M the stellar kinematics of S0s to estimate their maximum cir- terms of the dierence between the observed and model * 0.8 10 0.6 NGC 128 ESO 151−G004 NGC 1381 NGC 1596 M cular velocity, which is statistically related to the global line 1.8 second velocity moment. The red contours are the σ confi- 1.6 width used in the normal TFR. 1.4 dence levels. log ( 1.2 1.0 Wang et al. 2006 Our mass models allow us to determine the circular velocity 0.8 9 Croton et al. 2006 0.6 NGC 1886 NGC 2310 ESO 311−G012 NGC 3203 prole directly for both the spirals and S0s in our sample, 1.8 FIGURE Somerville et al. 2008 eliminating the possibility of systematic dierences between 1.6 ☞ Yang et al 2008 1.4 Stellar and virial masses of the mass models. Spiral galaxies 1.2 8 kinematic tracers of rotation. We conrm the nding that 1.0 are blue triangles and Ss are red circles. The predictions of a 0.8 11 12 13 14 15 S0s lie at fainter magnitudes for a given circular velocity 0.6 NGC 3390 NGC 4469 NGC 4710 PGC 44931 number of semi-analytic models are shown for comparison. 1.8 log (M vir/M ) (0.4 mag at K -band, see Fig. 4). This is consistent with Ks ☉ S 1.6 1.4 models of galaxy evolution in which S0s are the faded de- 1.2 (M/L) 1.0 −26 scendents of spirals. 0.8 FIGURE 0.6 ESO 443−G042 NGC 5746 IC 4767 NGC 6722 ☞ 1.8 The Tully-Fisher relations of the early-type spirals and Ss in 1.6 REFERENCES 1.4 −25 1.2 our sample. Ss (red points) are systematically fainter than Bedregal et al. 2006, MNRAS, 373 25 • Bell & de Jong 1.0 0.8 spirals (blue points) at a given circular velocity. The late-type 200, ApJ, 550, 22 • Bureau et al. 2006, MNRAS, 370, 0.6 NGC 6771 ESO 185−G053 IC 4937 ESO 597−G036 −24 1.8 spiral TFR of Tully & Pierce ( ) is shown for comparison 753 • Cappellari 2008, MNRAS, 390, 7 • Chung & 1.6 1.4 Bureau 2004, AJ, 27, 392 • Croton et al. 2006, MNRAS, 1.2 −23 (mag) 1.0 Ks 365, • Macció et al. 2008, MNRAS, 39, 940 • Maras- 0.8 0.6 IC 5096 NGC 1032 NGC 3957 NGC 4703 M ton 2005, MNRAS 362, 799 • Navarro et al. 997, ApJ, 1.8 109 1011 1013 1015 −22 1.6 1.4 3.2 490, 493 • Somerville et al. 2008, MNRAS, 39, 48 • 3.0 1.2 2.8 Tully & Pierce 2000 1.0 2.6 Tully & Fisher 977, A&A, 54, 66 • Tully & Pierce 2000, 0.8 2.4 −21 Spirals 2.2 NGC 5084 NGC 7123 IC 5176 ApJ, 533 744 • Wang et al. 2006, MNRAS, 37, 537 • Yang 0.6 2.0 ESO 240−G011 S0s 9 11 13 15 9 11 13 15 9 11 13 15 9 11 13 15 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 −20 et al. 2008, ApJ, 676, 248 M (M ) DM ☉ 2.0 2.1 2.2 2.3 2.4 2.5 log v c.
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