Internal Kinematics of the Fornax Dwarf Spheroidal Galaxy

TL;DR

This study expands the Fornax dSph kinematic data with 176 new radial velocities (206 overall; 176 members) to test for rotation, map the velocity-dispersion profile, and infer the mass distribution. After correcting for perspective using published proper motions, rotation is marginal and not robust, while the velocity dispersion remains flat across radii, arguing against simple tidal disturbance. Single-component, mass-follows-light King models fail to match the data; isotropic two-component King models with an extended dark halo reproduce the flat dispersion, yielding global M/L_V ~ 10–40 and total masses ~4–18×10^8 M☉. A non-parametric Jeans-based mass estimator supports a substantial dark-matter halo, with M/L_V ~ 15 inside r < 1.5 kpc, consistent with a dark-matter–dominated Fornax and highlighting the value of non-parametric mass estimation for dSphs.

Abstract

We present new radial velocity results for 176 stars in the Fornax dwarf spheroidal galaxy, of which at least 156 are probable Fornax members. We combine with previously published data to obtain a radial velocity sample with 206 stars, of which at least 176 are probable Fornax members. We detect the hint of rotation about an axis near Fornax's morphological minor axis, though the significance of the rotation signal in the galactic rest frame is sensitive to the adopted value of Fornax's proper motion. Regardless, the observed stellar kinematics are dominated by random motions, and we do not find kinematic evidence of tidal disruption. The projected velocity dispersion profile of the binned dataset remains flat over the sampled region, which reaches a maximum angular radius of 65 arcmin. Single-component King models in which mass follows light fail to reproduce the observed flatness of the velocity dispersion profile. Two-component (luminous plus dark matter) models can reproduce the data, provided the dark component extends sufficiently beyond the luminous component, and the central dark matter density is of the same order as the central luminous density. These requirements suggest a more massive, darker Fornax than standard core-fitting analyses have previously concluded, with M/L_V over the sampled region reaching 10 to 40 times the M/L_V of the luminous component. We also apply a non-parametric mass estimation technique, introduced in a companion paper. Though it is designed to operate on datasets containing velocities for $>$1000 stars, the estimation yields preliminary results suggesting M/L_V ~ 15 inside r < 1.5 kpc.

Figures (12)

• Figure 1: Fornax red giant branch. a) includes all stars measured photometrically in a 110' $\times$ 90' region of sky centered on the Fornax dSph. b) shows only those stars observed spectroscopically, and illustrates the boundaries of our color-magnitude target selection region. Filled circles are probable Fornax members, based on velocity criteria described in section \ref{['subsec:membership']}. Open circles are probable foreground contaminants. Open triangles represent stars with marginal membership status. Points located outside the CMD selection region represent stars observed for this study before the photometry comprising this CMD was available, and so were chosen based on the photometry described in Mateo et al. (1991).
• Figure 2: Maps of (a) all stars meeting the selection criteria discussed in Section \ref{['subsec:membership']}; overplotted are the boundaries of the 31 photometric fields observed. (b) maps stars for which we measured radial velocities. Filled circles represent stars later determined to be probable Fornax members. Open circles represent stars rejected as probable foreground contaminants on the basis of their radial velocities. Open triangles represent stars having velocities marginally consistent with Fornax membership (see section \ref{['subsec:membership']}). The inner and outer ellipses are the King core and tidal radii, respectively, which have published semi-major axis values $r_{core}=13.7\arcmin \pm 1.2\arcmin$ and $r_{tide}=71.1\arcmin \pm 4.0\arcmin$, with ellipticity $\epsilon=0.30\pm0.01$ (Irwin $\&$ Hatzidimitriou 1995). The standard coordinate system is centered on the Fornax dSph such that ($\xi$,$\eta$)=(0,0) corresponds to $\alpha_{2000}$=2:39:52, $\delta_{2000}$=-34:28:09. North is toward the top of the figure, east is to the left.
• Figure 3: Heliocentric radial Velocity distribution of a) all 176 Fornax candidate member stars whose velocities are presented in Table \ref{['tab:results']}. Stars that were later rejected by an iterative membership determination algorithm are numbered according to which iteration rejected them (e.g., "1"= 1st iteration); b) the 156 stars determined to be probable Fornax members; c) all 209 Fornax candidate member stars after combining our data with that of M91. Again, numbers specify which iteration removed probable nonmembers; d) the 176 probable Fornax members from the combined data set. In (b) and (d), a thick vertical line marks the mean velocity of members calculated using maximum likelihood statistics. The regions enclosed by dotted lines in (b) and (d) represent those stars rejected in iterations 2,3 and 4. We consider these to be borderline members.
• Figure 4: Rotation signal of Fornax. The difference between the radial velocity of Fornax members on either side of a line passing through Fornax's center is plotted as a function of the position angle of that line. a) computed using the measured heliocentric rest frame radial velocities, uncorrected for perspective-induced rotation (see Section \ref{['subsec:rotation']}). b) computed from GRF radial velocities obtained using the Fornax proper motion measurement of Piatek et al. (2002). c) computed from GRF radial velocities obtained using the Fornax proper motion measurement of Dinescu et al. (2004). d) computed from GRF radial velocities obtained under the assumption that Fornax does not rotate.
• Figure 5: Radial velocity dispersion as a function of angular radius for three levels of Fornax membership discrimination (see section \ref{['subsec:membership']}). Filled squares and errorbars correspond to HRF radial velocity dispersion. Open triangles and open circles indicate the GRF radial velocity dispersion calculated using, respectively, the Piatek et al. (2002) and Dinescu et al. (2004) values for Fornax's proper motion. The plots in the top row are constructed using circular annuli, while those in the bottom row use elliptical annuli with $\epsilon \equiv 1-b/a=0.3$, semimajor axis $a=R$ and PA=41$^{\circ}$. a) Calculated using only the 176 stars with velocities surviving all four iterations of the bi-weight rejection algorithm. b) Calculated using the 182 stars with velocities surviving the first two rejection iterations. c) calculated using the 186 stars with velocities surviving the first rejection algorithm. Bins contain approximately equal numbers of stars.