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Register a new userGalactic disc profiles and a universal angular momentum distribution from statistical physics
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Jakob Herpich n MPIA
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We show that the stellar surface-brightness profiles in disc galaxies---observed to be approximately exponential---can be explained if radial migration efficiently scrambles the individual stars angular momenta while conserving the circularity of the orbits and the total mass and angular momentum. In this case the discs distribution of specific angular momenta $j$ should be near a maximum-entropy state and therefore approximately exponential, $dNproptoexp(-j/langle jrangle)dj$. This distribution translates to a surface-density profile that is generally not an exponential function of radius: $Sigma(R)proptoexp[-R/R_e(R)]/(RR_e(R))(1+dlog v_c(R)/dlog R)$, for a rotation curve $v_c(R)$ and $R_e(R)equivlangle jrangle/v_c(R)$. We show that such a profile matches the observed surface-brightness profiles of disc-dominated galaxies as well as the empirical exponential profile. Disc galaxies that exhibit population gradients cannot have fully reached a maximum-entropy state but appear to be close enough that their surface-brightness profiles are well-fit by this idealized model.
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I review the insights emerging from recent large kinematic surveys of galaxies at low redshift, with particular reference to the SAMI, CALIFA and MaNGA surveys. These new observations provide a more comprehensive picture of the angular momentum properties of galaxies over wide ranges in mass, morphology and environment in the present-day universe. I focus on the distribution of angular momentum within galaxies of various types and the relationship between mass, morphology and specific angular momentum. I discuss the implications of the new results for models of galaxy assembly.
The relations between the specific angular momenta ($j$) and masses ($M$) of galaxies are often used as a benchmark in analytic models and hydrodynamical simulations as they are considered to be amongst the most fundamental scaling relations. Using accurate measurements of the stellar ($j_ast$), gas ($j_{rm gas}$), and baryonic ($j_{rm bar}$) specific angular momenta for a large sample of disc galaxies, we report the discovery of tight correlations between $j$, $M$, and the cold gas fraction of the interstellar medium ($f_{rm gas}$). At fixed $f_{rm gas}$, galaxies follow parallel power laws in 2D $(j,M)$ spaces, with gas-rich galaxies having a larger $j_ast$ and $j_{rm bar}$ (but a lower $j_{rm gas}$) than gas-poor ones. The slopes of the relations have a value around 0.7. These new relations are amongst the tightest known scaling laws for galaxies. In particular, the baryonic relation ($j_{rm bar}-M_{rm bar}-f_{rm gas}$), arguably the most fundamental of the three, is followed not only by typical discs but also by galaxies with extreme properties, such as size and gas content, and by galaxies previously claimed to be outliers of the standard 2D $j-M$ relations. The stellar relation ($j_{ast}-M_{ast}-f_{rm gas}$) may be connected to the known $j_ast-M_ast-$bulge fraction relation; however, we argue that the $j_{rm bar}-M_{rm bar}-f_{rm gas}$ relation can originate from the radial variation in the star formation efficiency in galaxies, although it is not explained by current disc instability models.
[Abridged] We study the angular-momentum profiles of a statistical sample of halos drawn from a high-resolution N-body simulation of the LCDM cosmology. We find that the cumulative mass distribution of specific angular momentum, j, in a halo of mass Mv is well fit by a universal function, M(<j) = Mv mu j/(j_0+j). This profile is defined by one shape parameter (mu or j_0) in addition to the global spin parameter lambda. It follows a power-law over most of the mass, and flattens at large j, with the flattening more pronounced for small values of mu. Compared to a uniform sphere in solid-body rotation, most halos have a higher fraction of their mass in the low- and high-j tails of the distribution. The spatial distribution of angular momentum in halos tends to be cylindrical and is well-aligned within each halo for ~80% of the halos. We investigate two ideas for the origin of this profile. The first is based on a revised version of linear tidal-torque theory combined with extended Press-Schechter mass accretion, and the second focuses on j transport in minor mergers. Finally, we briefly explore implications of the M(<j) profile on the formation of galactic disks assuming that j is conserved during an adiabatic baryonic infall. The implied gas density profile deviates from an exponential disk, with a higher density at small radii and a tail extending to large radii. The steep central density profiles may imply disk scale lengths that are smaller than observed. This is reminiscent of the angular-momentum problem seen in hydrodynamic simulations, even though we have assumed perfect j conservation. A possible solution is to associate the central excesses with bulge components and the outer regions with extended gaseous disks.
Throughout the Hubble time, gas makes its way from the intergalactic medium into galaxies fuelling their star formation and promoting their growth. One of the key properties of the accreting gas is its angular momentum, which has profound implications for the evolution of, in particular, disc galaxies. Here, we discuss how to infer the angular momentum of the accreting gas using observations of present-day galaxy discs. We first summarize evidence for ongoing inside-out growth of star forming discs. We then focus on the chemistry of the discs and show how the observed metallicity gradients can be explained if gas accretes onto a disc rotating with a velocity 20-30% lower than the local circular speed. We also show that these gradients are incompatible with accretion occurring at the edge of the discs and flowing radially inward. Finally, we investigate gas accretion from a hot corona with a cosmological angular momentum distribution and describe how simple models of rotating coronae guarantee the inside-out growth of disc galaxies.
It has been shown in previous work that DARKexp, which is a theoretically derived, maximum entropy, one shape parameter model for isotropic collisionless systems, provides very good fits to simulated and observed dark-matter halos. Specifically, it fits the energy distribution, N(E), and the density profiles, including the central cusp. Here, we extend DARKexp N(E) to include the distribution in angular momentum, L^2, for spherically symmetric systems. First, we argue, based on theoretical, semi-analytical, and simulation results, that while dark-matter halos are relaxed in energy, they are not nearly as relaxed in angular momentum, which precludes using maximum entropy to uniquely derive N(E,L^2). Instead, we require that when integrating N(E,L^2) over squared angular momenta one retrieves the DARKexp N(E). Starting with a general expression for N(E,L^2) we show how the distribution of particles in L^2 is related to the shape of the velocity distribution function, VDF, and velocity anisotropy profile, beta(r). We then demonstrate that astrophysically realistic halos, as judged by the VDF shape and beta(r), must have linear or convex distributions in L^2, for each separate energy bin. The distribution in energy of the most bound particles must be nearly flat, and become more tilted in favor of radial orbits for less bound particles. These results are consistent with numerical simulations and represent an important step towards deriving the full distribution function for spherically symmetric dark-matter halos.
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