Phase Transitions in Neutron Stars and Maximum Masses

Using the most recent realistic effective interactions for nuclear matter with a smooth extrapolation to high densities including causality, we constrain the equation of state and calculate maximum masses of rotating neutron stars. First and second order phase transitions to, e.g., quark matter at high densities are included. If neutron star masses of $\sim 2.3M_\odot$ from quasi-periodic oscillations in low mass X-ray binaries are confirmed, a soft equation of state as well as strong phase transitions can be excluded in neutron star cores.Comment: Replaced with revised version, 7 pages, 3 figs. To appear in Ap. J. Let

Statistical mechanics of collisionless orbits. II. Structure of halos

In this paper, we present the density, \rho, velocity dispersion, \sigma, and \rho/\sigma^3 profiles of isotropic systems which have the energy distribution, N(E)\propto[\exp(\phi_0-E)-1], derived in Paper I. This distribution, dubbed DARKexp, is the most probable final state of a collisionless self-gravitating system, which is relaxed in terms of particle energies, but not necessarily in terms of angular momentum. We compare the DARKexp predictions with the results obtained using the extended secondary infall model (ESIM). The ESIM numerical scheme is optimally suited for the purpose because (1) it relaxes only through energy redistribution, leaving shell/particle angular momenta unaltered, and (2) being a shell code with radially increasing shell thickness it has very good mass resolution in the inner halo, where the various theoretical treatments give different predictions. The ESIM halo properties, and especially their energy distributions, are very well fit by DARKexp, implying that the techniques of statistical mechanics can be used to explain the structure of relaxed self-gravitating systems.Comment: 17 pages, 8 figure

Statistical mechanics of collisionless orbits. I. Origin of central cusps in dark-matter halos

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 Stirling's 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.Comment: 6 pages, 2 figure

Statistical mechanics of collisionless orbits. III. Comparison with N-body simulations

We compare the DARKexp differential energy distribution, N(E) \propto \exp(\phi_0-E)-1, obtained from statistical mechanical considerations, to the results of N-body simulations of dark matter halos. We first demonstrate that if DARKexp halos had anisotropic velocity distributions similar to those of N-body simulated halos, their density and energy distributions could not be distinguished from those of isotropic DARKexp halos. We next carry out the comparison in two ways, using (1) the actual energy distribution extracted from simulations, and (2) N-body fitting formula for the density distribution as well as N(E) computed from the density using the isotropic Eddington formula. Both the methods independently agree that DARKexp N(E) with \phi_0\approx 4-5 is an excellent match to N-body N(E). Our results suggest (but do not prove) that statistical mechanical principles of maximum entropy can be used to explain the equilibrated final product of N-body simulations.Comment: 17 pages, 7 figures; ApJ, in pres

Dynamics of merging: Post-merger mixing and relaxation of an Illustris galaxy

During the merger of two galaxies, the resulting system undergoes violent relaxation and seeks stable equilibrium. However, the details of this evolution are not fully understood. Using Illustris simulation, we probe two physically related processes, mixing and relaxation. Though the two are driven by the same dynamics---global time-varying potential for the energy, and torques caused by asymmetries for angular momentum---we measure them differently. We define mixing as the redistribution of energy and angular momentum between particles of the two merging galaxies. We assess the degree of mixing as the difference between the shapes of their N(E)s, and their N(L^2)s. We find that the difference is decreasing with time, indicating mixing. To measure relaxation, we compare N(E) of the newly merged system to N(E) of a theoretical prediction for relaxed collisionless systems, DARKexp, and witness the system becoming more relaxed, in the sense that N(E) approaches DARKexp N(E). Because the dynamics driving mixing and relaxation are the same, the timescale is similar for both. We measure two sequential timescales: a rapid, 1 Gyr phase after the initial merger, during which the difference in N(E) of the two merging halos decreases by ~80%, followed by a slow phase, when the difference decreases by ~50% over ~8.5 Gyrs. This is a direct measurement of the relaxation timescale. Our work also draws attention to the fact that when a galaxy has reached Jeans equilibrium it may not yet have reached a fully relaxed state given by DARKexp, in that it retains information about its past history. This manifests itself most strongly in stars being centrally concentrated. We argue that it is particularly difficult for stars, and other tightly bound particles, to mix because they have less time to be influenced by the fluctuating potential, even across multiple merger events.Comment: accepted for publication in JCA

Ubiquity of density slope oscillations in the central regions of galaxy and cluster-sized systems

One usually thinks of a radial density profile as having a monotonically changing logarithmic slope, such as in NFW or Einasto profiles. However, in two different classes of commonly used systems, this is often not the case. These classes exhibit non-monotonic changes in their density profile slopes which we call oscillations for short. We analyze these two unrelated classes separately. Class 1 consists of systems that have density oscillations and that are defined through their distribution function $f(E)$, or differential energy distribution $N(E)$, such as isothermal spheres, King profiles, or DARKexp, a theoretically derived model for relaxed collisionless systems. Systems defined through $f(E)$ or $N(E)$ generally have density slope oscillations. Class 1 system oscillations can be found at small, intermediate, or large radii but we focus on a limited set of Class 1 systems that have oscillations in the central regions, usually at $\log(r/r_{-2})\lesssim -2$, where $r_{-2}$ is the largest radius where $d\log(\rho)/d\log(r)=-2$. We show that the shape of their $N(E)$ can roughly predict the amplitude of oscillations. Class 2 systems which are a product of dynamical evolution, consist of observed and simulated galaxies and clusters, and pure dark matter halos. Oscillations in the density profile slope seem pervasive in the central regions of Class 2 systems. We argue that in these systems, slope oscillations are an indication that a system is not fully relaxed. We show that these oscillations can be reproduced by small modifications to $N(E)$ of DARKexp. These affect a small fraction of systems' mass and are confined to $\log(r/r_{-2})\lesssim 0$. The size of these modifications serves as a potential diagnostic for quantifying how far a system is from being relaxed.Comment: accepted by the Journal of Cosmology and Astroparticle Physics (JCAP

Liquidations and Reincorporations—Before and After Davant

Liquidations and reincorporations have been utilized in attempts to bail out corporate earnings and profits at capital gains rates. The success of these attempts has been limited by judicial extension of the corporate reorganization sections of the Internal Revenue Code. Professor Hjorth suggests that specific Congressional amendment of section 331 to encompass the liquidation reincorporation problem is preferable to extension of the reorganization provisions which occurred in the recent case of Davant v. Commissioner

Tax Consequences of Post-Dissolution Support Payment Arrangements

The economic settlement accompanying a marriage dissolution may consist of one or both of the following: (1) the initial property settlement, sometimes referred to as a division of property when only community property is involved; and (2) provisions for maintenance payments categorized as alimony, child support, or some combination thereof. The tax problems of property settlements have been analyzed previously by the author. They are considered here only to the extent necessary to distinguish property settlements paid in installments from periodic maintenance payments made for the support of a former spouse, or for children of the marriage, or both. The primary concerns of this article are the tax consequences of alimony and child support payments. Federal income tax law recognizes marriage as a status involving unique tax benefits and burdens. The following are examples of some of the benefits: (1) a wage-earning spouse is not taxed on the imputed income enjoyed from services rendered in the home by the other spouse or by children of the marriage; (2) parents may obtain exemption allowances for their children and certain deductions for expenses of dependents, including expenses for medical care and child care. On the other hand, payments to or for the support of a nonworking spouse or child are not deductible by the payor and are not income to the beneficiaries of such payments. Although this rule may not be a tax burden, it can certainly be considered to be the denial of a plausible tax benefit. Another potential tax burden of marriage was established by the Tax Reform Act of 1969 which applies four separate tax rate schedules in ascending order of severity to: (1) married individuals filing joint returns (and certain surviving spouses); (2) heads of households; (3) unmarried individuals (other than surviving spouses); and (4) married individuals filing separate returns (and estates and trusts). Whether or not these new rate schedules make marriage a tax benefit or burden depends on the taxable income of each spouse. The history and effect of these rate schedules have been examined elsewhere. The fourth category does not apply to unmarried individuals, and married taxpayers will not ordinarily use it because of its high rates. It is available in the case where one spouse, for whatever reason, refuses to sign a joint return with the other spouse. Briefly, considering only the first three categories, the aggregate tax for two individuals having equal incomes will be less if they are unmarried than if they marry. Where incomes are widely disparate, or where one spouse has no income and the other spouse has considerable income, marriage will usually cause the aggregate taxes of the two individuals to be reduced. However, marriage has the general effect of increasing aggregate taxable income of two individuals by forcing them to share one standard deduction and by otherwise limiting their deductions

The Common Agricultural Policy: Crisis in the Common Market

The future of this common agricultural policy, as well as that of the European Economic Community itself, however, has been made somewhat uncertain by France\u27s decree, on July 1, 1965, of a temporary boycott of the meetings of the Council of Ministers of the Community due to a failure to agree upon the method of financing the Community\u27s agricultural policy. This boycott may well have triggered the most serious crisis in the bloc\u27s seven year history, because the dispute is thought by some to be a mere symptom of a more fundamental conflict between France and her Common Market partners. The issue in that conflict is whether the Common Market is to become an integrated entity of member nations, or is rather to be only a loosely-knit organization of states as envisioned by French President De Gaulle. Because the integration of planned agricultural economies requires a greater degree of supranationalism than does the integration of freemarket industrial economies, it is natural that the political differences between De Gaulle and his partners should clash most vividly in the execution of the common agricultural policy. The purpose of this article is to review this common agricultural policy and its implementation. Apart from considerations of European unity, the common agricultural policy is of significance to exporters of American agricultural products. The value of annual exports of these products amounts to about five billion dollars, of which one and three-tenths billion dollars has been sold to Common Market countries alone. The common agricultural policy should also concern legal scholars because it is probably the most highly developed form of supranational law and institutional regulation in the world.\u2