7. Bratek Ł., Sikora S., Jałocha J., Kutschera M.
Velocity-density twin transforms in the thin disk model
Mon. Not. R. Astron. Soc. , vol. 451, p. 4018 (2015).
[abstract] [preprint] [journal]

Abstract:
Ring mass density and the corresponding circular velocity in thin disc model are known to be integral transforms of one another. But it may be less familiar that the transforms can be reduced to one-fold integrals with identical weight functions. It may be of practical value that the integral for the surface density does not involve the velocity derivative, unlike the equivalent and widely known Toomre's formula.

8. Jałocha J., Bratek Ł., Sikora S., Kutschera M.
Modelling vertical structure in circular velocity of spiral galaxy NGC 4244
Mon. Not. R. Astron. Soc. , vol. 451, p. 3366 (2015).
[abstract] [preprint] [journal]

Abstract:
We study the vertical gradient in azimuthal velocity of spiral galaxy NGC 4244 in a thin disc model. With surface density accounting for the rotation curve, we model the gradient properties in the approximation of quasi-circular orbits. It is worthy to note that the prediction of our model is consistent with the gradient properties inferred recently from a numerical model implementing the position-velocity diagram of this galaxy. The confirmation of our prediction by the future measurement of the gradient would provide support for the expectation that the mass distribution in this galaxy is flattened.

9. Sikora S., Bratek Ł., Jałocha J., Kutschera M.
Motion of halo tracer objects in the gravitational potential of a low-mass model of the Galaxy
Astron. Astrophys. , vol. 579, p. A134 (2015).
[abstract] [preprint] [journal]

Abstract:
Recently, we determined a lower bound for the Milky Way mass in a point mass approximation. We obtain this result for most general spherically symmetric phase-space distribution functions consistent with a measured radial velocity dispersion. As a stability test of these predictions against a perturbation of the point mass potential, in this paper we make use of a representative of these functions to set the initial conditions for a simulation in a more realistic potential of similar mass and to account for other observations. The predicted radial velocity dispersion profile evolves to forms still consistent with the measured profile, proving structural stability of the point mass approximation and the reliability of the resulting mass estimate of ~2.1 × 10^11 M⊙ within 150 kpc. As a byproduct, we derive a formula in the spherical symmetry relating the radial velocity dispersion profile to a directly measured kinematical observable.

10. Bratek Ł., Sikora S., Jałocha J., Kutschera M.
A lower bound on the Milky Way mass from general phase-space distribution function models
Astron. Astrophys. , vol. 562, p. A134 (2014).
[abstract] [preprint] [journal] [download]

Abstract:
We model the phase-space distribution of the kinematic tracers using general, smooth distribution functions to derive a conservative lower bound on the total mass within ≈150−200 kpc. By approximating the potential as Keplerian, the phase-space distribution can be simplified to that of a smooth distribution of energies and eccentricities. Our approach naturally allows for calculating moments of the distribution function, such as the radial profile of the orbital anisotropy. We systematically construct a family of phase-space functions with the resulting radial velocity dispersion overlapping with the one obtained using data on radial motions of distant kinematic tracers, while making no assumptions about the density of the tracers and the velocity anisotropy parameter β regarded as a function of the radial variable. While there is no apparent upper bound for the Milky Way mass, at least as long as only the radial motions are concerned, we find a sharp lower bound for the mass that is small. In particular, a mass value of 2.4e11 solar mass, obtained in the past for lower and intermediate radii, is still consistent with the dispersion profile at larger radii. Compared with much greater mass values in the literature, this result shows that determining the Milky Way mass is strongly model-dependent. We expect a similar reduction of mass estimates in models assuming more realistic mass profiles.

11. Jałocha J., Sikora S., Bratek. Ł, Kutschera M.
Constraining the vertical structure of the Milky Way rotation by microlensing in a finite-width global disk model
Astron. Astrophys. , vol. 566, p. A87 (2014).
[abstract] [preprint] [journal]

Abstract:
We model the vertical structure of mass distribution of the Milky Way galaxy in the framework of a finite-width global disk model. Assuming only the Galactic rotation curve, we tested the predictions of the model inside the solar orbit for two measurable processes that are unrelated to each other: the gravitational microlensing that allows one to fix the disk width-scale by the best fit to measurements, and the vertical gradient of rotation modeled in the quasi-circular orbits approximation. The former is sensitive to the gravitating mass in compact objects, the latter to all kinds of gravitating matter. The analysis points to a small width-scale of the considered disks and an at-most insignificant contribution of non-baryonic dark matter in the solar circle. The predicted high vertical gradient values in the rotation are consistent with the gradient measurements.

12. Sikora S, Bratek Ł., Jałocha J., Kutschera M.
Gravitational microlensing as a test of a finite-width disk model of the Galaxy
Astron. Astrophys. , vol. 546, p. A126 (2012).
[abstract] [preprint] [journal] [download]

Abstract:
The aim of this work is to show, in the framework of a simple finite-width disk model, that the amount of mass seen through gravitational microlensing measurements in the region 0 < R < R◦ is consistent with the dynamical mass ascertained from Galaxy rotation after subtracting gas contribution. Since microlensing only detects compact objects, this result suggests that a non-baryonic mass component may be negligible in this region.