Power-law Sérsic profiles in hydrostatic stellar galaxy discs

Abstract

Previously, we showed that surface density profiles of the form of a power-law times a Sérsic function satisfy the hydrostatic Jeans equations, a variety of observational constraints, and the condition of a minimal radial entropy profile in two-dimensional galaxy discs with fixed power-law, halo potentials. It was assumed that such density profiles are generated by star scattering by clumps, waves, or other inhomogeneities. Here we generalize these models to self-gravitating discs. The cylindrically symmetric Poisson equation imposes strong constraints. Scattering processes favor smoothness, so the smoothest solutions, which minimize entropy gradients, are preferred. In the case of self-gravitating discs (e.g., inner discs), the gravity, surface density and radial velocity dispersion in these smoothest models are all of the form 1/r times an exponential. When vertical balance is included, the vertical velocity dispersion squared has the same form as the surface density, and the scale height is constant. In combined selfgravitating plus halo gravity cases, the radial dispersion has an additional power-law term. Nonetheless, the surface density profile has the same form at all radii, without breaks, satisfying the 'disc-halo conspiracy'. The azimuthal velocity and velocity dispersions are smooth, though the former can have a distinct peak. In these models the vertical dispersion increases inwards, and scattering may mediate a transition to a secular bulge. If halo gravity dominates vertically in the outer disc, it flares. The models suggest a correlation between disc mass and radial scale length. The combination of smoothness, simplicity, ability to match generic observational features and physical constraints is unique to these models.

Stellar scattering and the formation of exponential discs in self-gravitating systems

“…In Figure 5, the radial velocity dispersion and the vertical velocity dispersion both decline with increasing galactic radius. This decrease looks like an exponential profile and the profile agrees with the expectation made by Martinsson et al (2013) and Struck & Elmegreen (2019). More discussion on the velocity dispersion is in Section 4.4.…”

“…The profile evolution due to scattering can make a nearexponential disc under various initial density distributions. The appearance of a central cusp in the final profile makes the equilibrium distribution resemble a function of 1/r times an exponential, like that derived by analytic work assuming a minimum entropy gradient of the stellar system (Struck & Elmegreen 2019;Elmegreen & Struck 2016) or assuming a maximum entropy in specific angular momentum distribution (Herpich et al 2017). Marr (2020) also showed that an equilibrium galactic disc is a microcanonical ensemble with maximum entropy and that the equilibrium disc density profile is a lognormal distribution, which can fit with a near-exponential profile well.…”

“…Elmegreen & Struck (2016) showed in a random walk model that stars experiencing random scatterings in a disc reach an equilibrium state distribution that is 1/r times an exponential when the scattering has an inward bias. Struck & Elmegreen (2019) then proved in the context of equilibria of collisionless systems that a surface density profile of the same form is the zero entropy gradient solution to the cylindrically symmetric Poisson equation. Because scattering processes prefer a maximum entropy, scattering nudges a disc towards a profile of 1/r times an exponential, which is very close to an exponential over a disc except for the innermost region where the factor of 1/r could make a noticeable difference.…”

From giant clumps to clouds I: the impact of gas fraction evolution on the stability of galactic discs

“…The density profiles of all components in all the discs are compatible with an exponential form. However, we note that such a profile is imposed in the initial conditions, and therefore the convergence toward the exponential shape cannot be rigorously demonstrated here (but see Elmegreen & Struck 2013;Struck & Elmegreen 2019). Despite having a massive central clump, the gaseous components of the F25 and F40 cases yield shallower density profiles than at low gas fraction.…”

The principle of maximum entropy and the distribution of mass in galaxies

“…This well known difficulty of the CDM model is bypassed invoking physical processes which essentially shorten the timescale to reach TE, making it shorter than the Hubble time. The proposed pathways to thermalization are of very different nature (Sect 6): feedback of the baryons on the DM particles through gravitational forces [27][28][29], scattering with massive gas clumps [30,31], forcing by a central bar [32], merger of two super massive black holes [SMBHs; 26,33,34], or assuming an artificially large DM to DM collision cross section [35][36][37]. Whether or not it is collision-less, the DM seems to find a way for thermalization faster than the inefficient two-body relaxation collisions, an observational fact that weakens the original criticism.…”