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Register a new userStatistical mechanics of collisionless orbits. IV. Distribution of angular momentum
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Added by
Liliya L. R. Williams
Publication date
2014
fields
Physics
and research's language is
English
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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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We present an equilibrium statistical mechanical theory of collisionless self-gravitational systems with isotropic velocity distributions. Compared to existing standard theories, we introduce two changes: (1) the number of possible microstates is computed in energy (orbit) space rather than phase space and (2) low occupation numbers are treated more appropriately than using Stirlings approximation. Combined, the two modifications predict that the relaxed parts of collisionless self-gravitating systems, such as dark-matter halos, have a differential energy distribution N(E) ~ [exp(phi_0 - E) - 1], dubbed DARKexp. Such systems have central power-law density cusps rho(r) ~ r^-1, which suggests a statistical mechanical origin of cusps in simulated dark-matter halos.
The final giant-impact phase of terrestrial planet formation is believed to begin with a large number of planetary embryos on nearly circular, coplanar orbits. Mutual gravitational interactions gradually excite their eccentricities until their orbits cross and they collide and merge; through this process the number of surviving bodies declines until the system contains a small number of planets on well-separated, stable orbits. In this paper we explore a simple statistical model for the orbit distribution of planets formed by this process, based on the sheared-sheet approximation and the ansatz that the planets explore uniformly all of the stable region of phase space. The model provides analytic predictions for the distribution of eccentricities and semimajor axis differences, correlations between orbital elements of nearby planets, and the complete N-planet distribution function, in terms of a single parameter, the dynamical temperature, that is determined by the planetary masses. The predicted properties are generally consistent with N-body simulations of the giant-impact phase and with the distribution of semimajor axis differences in the Kepler catalog of extrasolar planets. A similar model may apply to the orbits of giant planets if these orbits are determined mainly by dynamical evolution after the planets have formed and the gas disk has disappeared.
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.
We study the dark and luminous mass distributions, circular velocity curves (CVC), line-of-sight kinematics, and angular momenta for a sample of 42 cosmological zoom simulations of massive galaxies. Using a temporal smoothing technique, we are able to reach large radii. We find that: (i)The dark matter halo density profiles outside a few kpc follow simple power-law models, with flat dark matter CVCs for lower-mass systems, and rising CVCs for high-mass haloes. The projected stellar density distributions at large radii can be fitted by Sersic functions with n>10, larger than for typical ETGs. (ii)The massive systems have nearly flat total CVCs at large radii, while the less massive systems have mildly decreasing CVCs. The slope of the CVC at large radii correlates with v_circ itself. (iii)The dark matter fractions within Re are in the range 15-30% and increase to 40-65% at 5Re. Larger and more massive galaxies have higher dark matter fractions. (iv)The short axes of simulated galaxies and their host dark matter haloes are well aligned and their short-to-long axis ratios are correlated. (v)The stellar vrms(R) profiles are slowly declining, in agreement with planetary nebulae observations in the outer haloes of most ETGs. (vi)The line-of-sight velocity fields v show that rotation properties at small and large radii are correlated. Most radial profiles for the cumulative specific angular momentum parameter lambda(R) are nearly flat or slightly rising, with values in [0.06,0.75] from 2Re to 5Re. (vii)Stellar mass, ellipticity at 5Re, and lambda(5Re) are correlated: the more massive systems have less angular momentum and are rounder, as for observed ETGs. (viii)More massive galaxies with a large fraction of accreted stars have radially anisotropic velocity distributions outside Re. Tangential anisotropy is seen only for galaxies with high fraction of in-situ stars. (Full abstract in PDF)
We study the spatially-resolved stellar specific angular momentum $j_*$ in a high-quality sample of 24 CALIFA galaxies covering a broad range of visual morphology, accounting for stellar velocity and velocity dispersion. The shape of the spaxel-wise probability density function of normalised $s=j_*/j_{*mean}$, PDF($s$), deviates significantly from the near-universal initial distribution expected of baryons in a dark matter halo and can be explained by the expected baryonic effects in galaxy formation that remove and redistribute angular momentum. Further we find that the observed shape of the PDF($s$) correlates significantly with photometric morphology, where late-type galaxies have PDF($s$) that is similar to a normal distribution, whereas early types have a strongly-skewed PDF($s$) resulting from an excess of low-angular momentum material. Galaxies that are known to host pseudobulges (bulge Sersic index $n_b <2.2$) tend to have less skewed bulge PDF($s$), with skewness $(b_{1rb})lesssim0.8$. The PDF($s$) encodes both kinematic and photometric information and appears to be a robust tracer of morphology. Its use is motivated by the desire to move away from traditional component-based classifications which are subject to observer bias, to classification on a galaxys fundamental (stellar mass, angular momentum) properties. In future, PDF($s$) may also be useful as a kinematic decomposition tool.
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