# Can we measure the slopes of density profiles in dwarf spheroidal galaxies?

Kowalczyk, K; Lokas, E L; Kazantzidis, S; Mayer, L (2013). Can we measure the slopes of density profiles in dwarf spheroidal galaxies? Monthly Notices of the Royal Astronomical Society, 431(3):2796-2807.

## Abstract

Using collisionless N-body simulations of dwarf galaxies orbiting the Milky Way, we construct realistic models of dwarf spheroidal (dSph) galaxies of the Local Group. The dwarfs are initially composed of stellar discs embedded in dark matter haloes with different inner density slopes and are placed on an eccentric orbit typical for Milky Way subhaloes. After a few Gyr of evolution, the stellar component is triaxial as a result of bar instability induced by tidal forces. Observing the simulated dwarfs along the three principal axes of the stellar component, we create mock data sets and determine the corresponding half-light radii and line-of-sight velocity dispersions. Using the estimator proposed by Wolf et al., we calculate the masses within half-light radii. The masses obtained in this way are over(under)estimated by up to a factor of 2 when the line of sight is along the longest (shortest) axis of the stellar component. We then divide the initial stellar distribution into an inner and outer population and trace their evolution in time. The two populations, although strongly affected by tidal forces, retain different density profiles even after a few Gyr of evolution. We measure the half-light radii and velocity dispersions of the stars in the two populations along different lines of sight and use them to estimate the slope of the mass distribution in the dwarf galaxies following the method recently proposed by Walker & Peñarrubia. The inferred slopes are systematically over- or underestimated, depending on the line of sight. In particular, when the dwarf is seen along the longest axis of the stellar component, a significantly shallower density profile is inferred than the real one measured from the simulations. Given that most dSph galaxies in the Local Group are non-spherical in appearance and their orientation with respect to our line of sight is unknown, but most probably random, the method can be reliably applied only to a large sample of dwarfs when these systematic errors are expected to be diminished.

## Abstract

Using collisionless N-body simulations of dwarf galaxies orbiting the Milky Way, we construct realistic models of dwarf spheroidal (dSph) galaxies of the Local Group. The dwarfs are initially composed of stellar discs embedded in dark matter haloes with different inner density slopes and are placed on an eccentric orbit typical for Milky Way subhaloes. After a few Gyr of evolution, the stellar component is triaxial as a result of bar instability induced by tidal forces. Observing the simulated dwarfs along the three principal axes of the stellar component, we create mock data sets and determine the corresponding half-light radii and line-of-sight velocity dispersions. Using the estimator proposed by Wolf et al., we calculate the masses within half-light radii. The masses obtained in this way are over(under)estimated by up to a factor of 2 when the line of sight is along the longest (shortest) axis of the stellar component. We then divide the initial stellar distribution into an inner and outer population and trace their evolution in time. The two populations, although strongly affected by tidal forces, retain different density profiles even after a few Gyr of evolution. We measure the half-light radii and velocity dispersions of the stars in the two populations along different lines of sight and use them to estimate the slope of the mass distribution in the dwarf galaxies following the method recently proposed by Walker & Peñarrubia. The inferred slopes are systematically over- or underestimated, depending on the line of sight. In particular, when the dwarf is seen along the longest axis of the stellar component, a significantly shallower density profile is inferred than the real one measured from the simulations. Given that most dSph galaxies in the Local Group are non-spherical in appearance and their orientation with respect to our line of sight is unknown, but most probably random, the method can be reliably applied only to a large sample of dwarfs when these systematic errors are expected to be diminished.

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