Dynamical Effects of CDM Subhalos on a Galactic Disk

We investigate the dynamical interaction between a galactic disk and surrounding numerous dark subhalos as expected for a galaxy-sized halo in the cold dark matter (CDM) models. Our particular interest is to what extent accretion events of subhalos into a disk are allowed in light of the observed thinness of a disk. Several models of subhalos are considered in terms of their internal density distribution, mass function, and spatial and velocity distributions. Based on a series of N-body simulations, we find that the disk thickening quantified by the change of its scale height, Delta z_d, depends strongly on the individual mass of an interacting subhalo M_{sub}. This is described by the relation, Delta z_d / R_d = 8 Sum_{j=1}^N (M_{sub,j}/M_d)**2, where R_d is a disk scale length, M_d is a disk mass, and N is the total number of accretion events of subhalos inside a disk region (< 3R_d). Using this relation, we find that an observed thin disk has not ever interacted with subhalos with the total mass of more than 15% disk mass. Also, a less massive disk with smaller circular velocity V_c is more affected by subhalos than a disk with larger V_c, in agreement with the observation. Further implications of our results for the origin of a thick disk component are also discussed.Comment: 12 pages, 9 figures, accepted by PAS

Physical symmetries and gauge choices in the Landau problem

Due to a special nature of the Landau problem, in which the magnetic field is uniformly spreading over the whole two-dimensional plane, there necessarily exist three conserved quantities, i.e. two conserved momenta and one conserved orbital angular momentum for the electron, independently of the choice of the gauge potential. Accordingly, the quantum eigen-functions of the Landau problem can be obtained by diagonalizing the Landau Hamiltonian together with one of the above three conserved operators with the result that the quantum mechanical eigen-functions of the Landau problem can be written down for arbitrary gauge potential. The purpose of the present paper is to clarify the meaning of gauge choice in the Landau problem based on this gauge-potential-independent formulation, with a particular intention of unraveling the physical significance of the concept of gauge-invariant-extension of the canonical orbital angular momentum advocated in recent literature on the nucleon spin decomposition problem. At the end, our analysis is shown to disclose a physically vacuous side face of the gauge symmetry.Comment: version to appear in The European Physical Journal

Universal dark halo scaling relation for the dwarf spheroidal satellites

Motivated by a recently found interesting property of the dark halo surface density within a radius, $r_{\rm max}$, giving the maximum circular velocity, $V_{\rm max}$, we investigate it for dark halos of the Milky Way's and Andromeda's dwarf satellites based on cosmological simulations. We select and analyze the simulated subhalos associated with Milky Way-sized dark halos and find that the values of their surface densities, $\Sigma_{V_{\rm max}}$, are in good agreement with those for the observed dwarf spheroidal satellites even without employing any fitting procedures. This implies that this surface density would not be largely affected by any baryonic feedbacks and thus universal. Moreover, all subhalos on the small scales of dwarf satellites are expected to obey the relation $\Sigma_{V_{\rm max}}\propto V_{\rm max}$, irrespective of differences in their orbital evolutions, host halo properties, and observed redshifts. Therefore, we find that the universal scaling relation for dark halos on dwarf galaxy mass scales surely exists and provides us important clues to understanding fundamental properties of dark halos. We also investigate orbital and dynamical evolutions of subhalos to understand the origin of this universal dark halo relation and find that most of subhalos evolve generally along the $r_{\rm max}\propto V_{\rm max}$ sequence, even though these subhalos have undergone different histories of mass assembly and tidal stripping. This sequence, therefore, should be the key feature to understand the nature of the universality of $\Sigma_{V_{\rm max}}$.Comment: 12 pages, 5 figures and 3 tables, submitted to Ap