Biases in mass estimates of dSph galaxies

Using a high resolution N-body simulation of a two-component dwarf galaxy orbiting in the potential of the Milky Way, we study two effects that lead to significant biases in mass estimates of dwarf spheroidal galaxies. Both are due to the strong tidal interaction of initially disky dwarfs with their host. The tidal stripping of dwarf stars leads to the formation of strong tidal tails that are typically aligned with the line of sight of an observer positioned close to the host center. The stars from the tails contaminate the kinematic samples leading to a velocity dispersion profile increasing with the projected radius and resulting in an overestimate of mass. The tidal stirring of the dwarf leads to the morphological transformation of the initial stellar disk into a bar and then a spheroid. The distribution of stars in the dwarf remains non-spherical for a long time leading to an overestimate of its mass if it is observed along the major axis and an underestimate if it seen in the perpendicular direction.Comment: 5 pages, 3 figures, contribution to the proceedings of "Hunting for the Dark: The Hidden Side of Galaxy Formation", Malta, 19-23 Oct. 2009, eds. V.P. Debattista & C.C. Popescu, AIP Conference Series, in pres

The stellar structure and kinematics of dwarf spheroidal galaxies formed by tidal stirring

Using high-resolution N-body simulations we study the stellar properties of dwarf spheroidal galaxies resulting from the tidally induced morphological transformation of disky dwarfs on a cosmologically motivated eccentric orbit around the Milky Way. Dwarf galaxy models initially consist of an exponential stellar disk embedded in an extended spherical dark matter halo. Depending on the initial orientation of the disk with respect to the orbital plane, different final configurations are obtained. The least evolved dwarf is triaxial and retains a significant amount of rotation. The more evolved dwarfs are prolate spheroids with little rotation. We show that the final density distribution of stars can be approximated by a simple modification of the Plummer law. The kinematics of the dwarfs is significantly different depending on the line of sight which has important implications for mapping the observed stellar velocity dispersions of dwarfs to subhalo circular velocities. When the dwarfs are observed along the long axis, the measured velocity dispersion is higher and decreases faster with radius. In the case where rotation is significant, when viewed perpendicular to the long axis, the effect of minor axis rotation is detected, as expected for triaxial systems. We model the velocity dispersion profiles and rotation curves of the dwarfs by solving the Jeans equations for spherical and axisymmetric systems and adjusting different sets of free parameters. We find that the mass is typically overestimated when the dwarf is seen along the long axis and underestimated when the observation is along the short or intermediate axis. The effect of non-sphericity cannot however bias the inferred mass by more than 60 percent in either direction, even for the most strongly stripped dwarf which is close to disruption.Comment: 17 pages, 15 figures, revised version accepted for publication in Ap

The anatomy of Leo I: how tidal tails affect the kinematics

We model the recently published kinematic data set for Leo I dSph galaxy by fitting the solutions of the Jeans equations to the velocity dispersion and kurtosis profiles measured from the data. We demonstrate that when the sample is cleaned of interlopers the data are consistent with the assumption that mass follows light and isotropic stellar orbits with no need for an extended dark matter halo. Our interloper removal scheme does not clean the data of contamination completely, as demonstrated by the rotation curve of Leo I. When moving away from the centre of the dwarf, the rotation appears to be reversed. We interpret this behaviour using the results of an N-body simulation of a dwarf galaxy possessing some intrinsic rotation, orbiting in the Milky Way potential and show that it can be reproduced if the galaxy is viewed almost along the tidal tails so that the leading (background) tail contaminates the western part of Leo I while the trailing (foreground) tail the eastern one. We show that this configuration leads to a symmetric and Gaussian distribution of line-of-sight velocities. The simulation is also applied to test our modelling method on mock data sets. We demonstrate that when the data are cleaned of interlopers and the fourth velocity moment is used the true parameters of the dwarf are typically within 1 \sigma errors of the best-fitting parameters. Restricting the fitting to the inner part of Leo I our best estimate for the anisotropy is \beta = -0.2^{+0.3}_{-0.4} and the total mass M = (4.5 +/- 0.7) x 10^7 M_sun. The mass-to-light ratio including the errors in mass, brightness and distance is M/L_V = 8.2 +/- 4.5 solar units.Comment: 10 pages, 10 figures, revised version accepted for publication in MNRA

The orientation and kinematics of inner tidal tails around dwarf galaxies orbiting the Milky Way

Using high-resolution collisionless N-body simulations we study the properties of tidal tails formed in the immediate vicinity of a two-component dwarf galaxy evolving in a static potential of the Milky Way (MW). The stellar component of the dwarf is initially in the form of a disk and the galaxy is placed on an eccentric orbit motivated by CDM-based cosmological simulations. We measure the orientation, density and velocity distribution of the stars in the tails. Due to the geometry of the orbit, in the vicinity of the dwarf, where the tails are densest and therefore most likely to be detectable, they are typically oriented towards the MW and not along the orbit. We report on an interesting phenomenon of `tidal tail flipping': on the way from the pericentre to the apocentre the old tails following the orbit are dissolved and new ones pointing towards the MW are formed over a short timescale. We also find a tight linear relation between the velocity of stars in the tidal tails and their distance from the dwarf. Using mock data sets we demonstrate that if dwarf spheroidal (dSph) galaxies in the vicinity of the MW are tidally affected their kinematic samples are very likely contaminated by tidally stripped stars which tend to artificially inflate the measured velocity dispersion. The effect is stronger for dwarfs on their way from the peri- to the apocentre due to the formation of new tidal tails after pericentre. Realistic mass estimates of dSph galaxies thus require removal of these stars from kinematic samples.Comment: 8 pages, 7 figures, accepted for publication in MNRA

Tidal stirring of Milky Way satellites: a simple picture with the integrated tidal force

Most of dwarf spheroidal galaxies in the Local Group were probably formed via environmental processes like the tidal interaction with the Milky Way. We study this process via N-body simulations of dwarf galaxies evolving on seven different orbits around the Galaxy. The dwarf galaxy is initially composed of a rotating stellar disk and a dark matter halo. Due to the action of tidal forces it loses mass and the disk gradually transforms into a spheroid while stellar motions become increasingly random. We measure the characteristic scale-length of the dwarf, its maximum circular velocity, mass, shape and kinematics as a function of the integrated tidal force along the orbit. The final properties of the evolved dwarfs are remarkably similar if the total tidal force they experienced was the same, independently of the actual size and eccentricity of the orbit.Comment: 5 pages, 2 figures, contribution to the proceedings of JENAM 2010 in Lisbon, Symposium 2 "Environment and the formation of galaxies: 30 years later", comments welcom

Formation and evolution of dwarf galaxies in the CDM Universe

We first review the results of the tidal stirring model for the transformation of gas-rich dwarf irregulars into dwarf spheroidals, which turns rotationally supported stellar systems into pressure supported ones. We emphasize the importance of the combined effect of ram pressure stripping and heating from the cosmic ultraviolet background in removing the gas and converting the object into a gas poor system as dSphs. We discuss how the timing of infall of dwarfs into the primary halo determines the final mass-to-light ratio and star formation history. Secondly we review the results of recent cosmological simulations of the formation of gas-rich dwarfs. These simulations are finally capable to produce a realistic object with no bulge, an exponential profile and a slowly rising rotation curve. The result owes to the inclusion of an inhomogeneous ISM and a star formation scheme based on regions having the typical density of molecular cloud complexes. Supernovae-driven winds become more effective in such mode, driving low angular momentum baryons outside the virial radius at high redshift and turning the dark matter cusp into a core. Finally we show the first tidal stirring experiments adopting dwarfs formed in cosmological simulations as initial conditions. The latter are gas dominated and have have turbulent thick gaseous and stellar disks disks that cannot develop strong bars, yet they are efficiently heated into spheroids by tidal shocks.Comment: 14 pages, 4 Figures, o appear in the proceedings of the CRAL conference, Lyon, June 2010, "A Universe of Dwarf Galaxies", eds. Philippe Prugniel & Mina Koleva; EDP Sciences in the European Astronomical Society Publications Series. (invited talk

The anatomy of Leo I: how tidal tails affect the kinematics

We model the recently published kinematic data set for Leo I dwarf spheroidal (dSph) galaxy by fitting the solutions of the Jeans equations to the velocity dispersion and kurtosis profiles measured from the data. We demonstrate that when the sample is cleaned of interlopers the data are consistent with the assumption that mass follows light and isotropic stellar orbits with no need for an extended dark matter halo. Our interloper removal scheme does not clean the data of contamination completely, as demonstrated by the rotation curve of Leo I. When moving away from the centre of the dwarf, the rotation appears to be reversed. We interpret this behaviour using the results of an N-body simulation of a dwarf galaxy possessing some intrinsic rotation, orbiting in the Milky Way potential and show that it can be reproduced if the galaxy is viewed almost along the tidal tails so that the leading (background) tail contaminates the western part of Leo I while the trailing (foreground) tail the eastern one. We show that this configuration leads to a symmetric and Gaussian distribution of line-of-sight velocities. The simulation is also applied to test our modelling method on mock data sets. We demonstrate that when the data are cleaned of interlopers and the fourth velocity moment is used the true parameters of the dwarf are typically within 1σ errors of the best-fitting parameters. Restricting the fitting to the inner part of Leo I our best estimate for the anisotropy is β=−0.2+0.3−0.4 and the total mass M= (4.5 ± 0.7) × 107M⊙. The mass-to-light ratio (M/L) including the errors in mass, brightness and distance is M/LV= 8.2 ± 4.5 solar unit

The orientation and kinematics of inner tidal tails around dwarf galaxies orbiting the Milky Way

Using high-resolution collisionless N-body simulations, we study the properties of tidal tails formed in the immediate vicinity of a two-component dwarf galaxy evolving in a static potential of the Milky Way (MW). The stellar component of the dwarf is initially in the form of a disc and the galaxy is placed on an eccentric orbit motivated by cold dark matter based cosmological simulations. We measure the orientation, density and velocity distribution of the stars in the tails. Due to the geometry of the orbit, in the vicinity of the dwarf, where the tails are densest and therefore most likely to be detectable, they are typically oriented towards the MW and not along the orbit. We report on an interesting phenomenon of ‘tidal tail flipping': on the way from the pericentre to the apocentre, the old tails following the orbit are dissolved and new ones pointing towards the MW are formed over a short time-scale. We also find a tight linear relation between the velocity of stars in the tidal tails and their distance from the dwarf. Using mock data sets, we demonstrate that if dwarf spheroidal (dSph) galaxies in the vicinity of the MW are tidally affected their kinematic samples are very likely contaminated by tidally stripped stars which tend to artificially inflate the measured velocity dispersion. The effect is stronger for dwarfs on their way from the pericentre to the apocentre due to the formation of new tidal tails after pericentre. Realistic mass estimates of dSph galaxies thus require removal of these stars from kinematic sample

Mass modelling of dwarf spheroidal galaxies: the effect of unbound stars from tidal tails and the Milky Way

We study the origin and properties of the population of unbound stars in the kinematic samples of dwarf spheroidal (dSph) galaxies. For this purpose we have run a high-resolution N-body simulation of a two-component dwarf galaxy orbiting in a Milky Way potential. In agreement with the tidal stirring scenario of Mayer et al., the dwarf is placed on a highly eccentric orbit, its initial stellar component is in the form of an exponential disc and it has a NFW-like dark matter (DM) halo. After 10 Gyr of evolution the dwarf produces a spheroidal stellar component and is strongly tidally stripped so that mass follows light and the stars are on almost isotropic orbits. From this final state, we create mock kinematic data sets for 200 stars by observing the dwarf in different directions. We find that when the dwarf is observed along the tidal tails the kinematic samples are strongly contaminated by unbound stars from the tails. We also study another source of possible contamination by adding stars from the Milky Way. We demonstrate that most of the unbound stars can be removed by the method of interloper rejection proposed by den Hartog & Katgert and recently tested on simulated DM haloes. We model the cleaned-up kinematic samples using solutions of the Jeans equation with constant mass-to-light ratio (M/L) and velocity anisotropy parameter. We show that even for such a strongly stripped dwarf the Jeans analysis, when applied to cleaned samples, allows us to reproduce the mass and M/L of the dwarf with accuracy typically better than 25 per cent and almost exactly in the case when the line of sight is perpendicular to the tidal tails. The analysis was applied to the new data for the Fornax dSph galaxy. We show that after careful removal of interlopers the velocity dispersion profile of Fornax can be reproduced by a model in which mass traces light with a M/L of 11 solar units and isotropic orbits. We demonstrate that most of the contamination in the kinematic sample of Fornax probably originates from the Milky Wa