Axisymmetric Schwarzschild models of an isothermal axisymmetric mock dwarf spheroidal galaxy

Abstract

Aims. The goal of this work is to test the ability of Schwarzschild's orbit superposition method in measuring the mass content, scale radius and shape of a flattened dwarf spheroidal galaxy. Until now, most dynamical model efforts have assumed that dwarf spheroidal galaxies and their host halos are spherical. Methods. We use an Evans model (1993) to construct an isothermal mock galaxy whose properties somewhat resemble those of the Sculptor dwarf spheroidal galaxy. This mock galaxy contains flattened luminous and dark matter components, resulting in a logarithmic profile for the global potential. We have tested how well our Schwarzschild method could constrain the characteristic parameters of the system for different sample sizes, and also if the functional form of the potential was unknown. Results. When assuming the true functional form of the potential, the Schwarzschild modelling technique is able to provide an accurate and precise measurement of the characteristic mass parameter of the system and reproduces well the light distribution and the stellar kinematics of our mock galaxy. When assuming a different functional form for the potential, such as a flattened NFW profile, we also constrain the mass and scale radius to their expected values. However in both cases, we find that the flattening parameter remains largely unconstrained. This is likely because the information content of the velocity dispersion on the geometric shape of the potential is too small, since σ is constant across our mock dSph. Conclusions. Our results using Schwarzschild's method indicate that the mass enclosed can be derived reliably, even if the flattening parameter is unknown, and already for samples containing 2000 line-of-sight radial velocities, such as those currently available. Further applications of the method to more general distribution functions of flattened systems are needed to establish how well the flattening of dSph dark halos can be determined.

Forecasts on the Dark Matter Density Profiles of Dwarf Spheroidal Galaxies with Current and Future Kinematic Observations

“…The most common dynamical modeling method using individual stars as tracers of the gravitational potential is spherical Jeans modeling (e.g., Jeans 1915;Binney & Tremaine 2008;Mamon et al 2013;Cappellari 2015;Read & Steger 2017). More sophisticated methods are also used to study these systems such as phase-space methods (e.g., Wojtak & Lokas 2010;Strigari et al 2018), made-tomeasure (e.g., Williams & Evans 2015), action-angle modeling (e.g., Pascale et al 2019) and Schwarzschild modeling (e.g., Schwarzschild 1979;Breddels et al 2013;Hagen et al 2019).…”

Stellar dynamics and dark matter in Local Group dwarf galaxies

“…There are however indications that the amplitude and shape of the σ los radial profile might vary as a function of azimuthal angle [e.g. 73,76,210], hence data-sets mapping the kinematics in 2D could in principle be an asset for the dynamical modelling, due to the larger number of observational constraints to be reproduced.…”

“…For given Φ tot , one constructs a library of numerically integrated orbits, which are then weighted and combined to reproduce ρ . This method has been applied to build both spherical [27,28,[104][105][106] and axisymmetric [73,[88][89][90] models of DGs, but can deal also with triaxial systems. The weights of the superposed orbits can be used to obtain a numerical estimate of the DF and thus of the velocity distribution.…”

Dynamical Modeling of Galaxies and Supermassive Black Holes: Axisymmetry in Triaxial Schwarzschild Orbit Superposition Models

“…Once we perform this operation, it is unnecessary to perform the eight-fold reflections in the original code. A similar rotation scheme was tested on mock data with no central SMBH in Hagen et al (2019).…”

“…This issue should be essentially resolved outside of the axisymmetric limit, or if a black hole or density cusp is included. However, axisymmetric studies that use this code with no central cusp may be affected (Hagen et al 2019).…”