Dynamical Cusp Regeneration

After being destroyed by a binary supermassive black hole, a stellar density cusp can regrow at the center of a galaxy via energy exchange between stars moving in the gravitational field of the single, coalesced hole. We illustrate this process via high-accuracy N-body simulations. Regeneration requires roughly one relaxation time and the new cusp extends to a distance of roughly one-fifth the black hole's influence radius, with density rho ~ r^{-7/4}; the mass in the cusp is of order 10% the mass of the black hole. Growth of the cusp is preceded by a stage in which the stellar velocity dispersion evolves toward isotropy and away from the tangentially-anisotropic state induced by the binary. We show that density profiles similar to those observed at the center of the Milky Way and M32 can regenerate themselves in several Gyr following infall of a second black hole; the presence of density cusps at the centers of these galaxies can therefore not be used to infer that no merger has occurred. We argue that Bahcall-Wolf cusps are ubiquitous in stellar spheroids fainter than M_V ~ -18.5 that contain supermassive black holes, but the cusps have not been detected outside of the Local Group since their angular sizes are less than 0.1". We show that the presence of a cusp implies a lower limit of \~10^{-4} per year on the rate of stellar tidal disruptions, and discuss the consequences of the cusps for gravitational lensing and the distribution of dark matter on sub-parsec scales.Comment: Accepted for publication in The Astrophysical Journa

No Supermassive Black Hole in M33?

We analyze optical long-slit spectroscopy of the nucleus of M33 obtained from the Space Telescope Imaging Spectrograph aboard the Hubble Space Telescope. Rather than the steep rise expected within the radius of influence of a supermassive black hole, the velocity dispersion drops significantly within the inner parsec. Dynamical modelling yields an estimated upper limit of 3000 solar masses for the mass of a central compact object. This upper limit is however consistent within the uncertainties with the mass predicted by the M-sigma relation, which is between 2000 and 20,000 solar masses. We therefore can not conclude that the presence of a massive black hole in the nucleus of M33 would require a different formation mechanism from that of the black holes detected in galaxies with more luminous bulges.Comment: 10 pages, 4 postscript figure

Time-Dependent Models for Dark Matter at the Galactic Center

The prospects of indirect detection of dark matter at the galactic center depend sensitively on the mass profile within the inner parsec. We calculate the distribution of dark matter on sub-parsec scales by integrating the time-dependent Fokker-Planck equation, including the effects of self-annihilations, scattering of dark matter particles by stars, and capture in the supermassive black hole. We consider a variety of initial dark matter distributions, including models with very high densities ("spikes") near the black hole, and models with "adiabatic compression" of the baryons. The annihilation signal after 10 Gyr is found to be substantially reduced from its initial value, but in dark matter models with an initial spike, order-of-magnitude enhancements can persist compared with the rate in spike-free models, with important implications for indirect dark matter searches with GLAST and Air Cherenkov Telescopes like HESS and CANGAROO.Comment: Four page

The Low End of the Supermassive Black Hole Mass Function: Constraining the Mass of a Nuclear Black Hole in NGC 205 via Stellar Kinematics

Hubble Space Telescope (HST) images and spectra of the nucleated dwarf elliptical galaxy NGC 205 are combined with 3-integral axisymmetric dynamical models to constrain the mass (M_BH) of a putative nuclear black hole. This is only the second attempt, after M33, to use resolved stellar kinematics to search for a nuclear black hole with mass below 10^6 solar masses. We are unable to identify a best-fit value of M_BH in NGC 205; however, the data impose a upper limit of 2.2x10^4 M_sun (1sigma confidence) and and upper limit of 3.8x10^4 M_sun (3sigma confidence). This upper limit is consistent with the extrapolation of the M_BH-sigma relation to the M_BH < 10^6 M_sunregime. If we assume that NGC 205 and M33 both contain nuclear black holes, the upper limits on M_BH in the two galaxies imply a slope of ~5.5 or greater for the M_BH-sigma relation. We use our 3-integral models to evaluate the relaxation time (T_r) and stellar collision time (T_coll) in NGC 205; T_r~10^8 yr or less in the nucleus and T_coll~10^11 yr. The low value of T_r is consistent with core collapse having already occurred, but we are unable to draw conclusions from nuclear morphology about the presence or absence of a massive black hole.Comment: Latex emulateapj, 15 pages, 16 figures, Version accepted for Publication in ApJ, 20 July 2005, v628. Minor changes to discussion

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

Tax-Free Corporate Acquisitions - The Law and the Proposed Regulations

The quest for interpretation is indeed an ancient one. Our life path is pervaded by a search for meanings. It has been said of the law that it is sometimes better to have a bad rule than to have no rule. I suppose the rationale is that unsatisfactory certainties at least permit action, and are susceptible to a change for the better, the very badness of the rule serving to accelerate the equitable resolution. Being neither philosopher nor historian, I do not know whether that patience which awaits ultimate improvement is always a virtue

The 1953 Bundestag election: evidence from West German public opinion

Der Verfasser untersucht die Gültigkeit ausgewählter Interpretationen zur Erklärung der Bundestagswahlergebnisse des Jahres 1953. Er konfrontiert die einzelnen Interpretationen mit Datenmaterial aus Meinungsumfragen des amerikanischen Hohen Kommissars für Deutschland zu Aspekten der bundesdeutschen Nachkriegspolitik. Der Autor kommt zu den Ergebnissen, daß der Wahlausgang und die Akzeptanz der bundesdeutschen Bevölkerung gegenüber demokratischen Institutionen und dem demokratischen System nach Auswertung des Datenmaterials nicht überrascht. Während die Identifikation mit den politischen Parteien eine untergeordnete Rolle gespielt habe, seien die von Adenauer vertretenen Standpunkte sowie dessen Persönlichkeit ausschlaggebend für den Wahlausgang gewesen. Haben sich Religionszugehörigkeit und soziale Herkunft als bedeutende Determinanten des Wahlverhaltens erwiesen, so läßt nach Ansicht des Autors eine fehlende theoretische Fundierung hingegen Rückschlüsse über ihren Stellenwert verglichen mit anderen Determinanten nicht zu. (RS)'The 1953 Bundestag election is frequently interpreted as a critical milestone in postwar West Germany's political history. Some saw its outcome, which gave Chancellor Adenauer's CDU/CSU 45.2% for the vote (31.0% in 1949) and his coalition 63.8% (and a constitution-changing 68.4% of Bundestag seats), as a major surprise, as proof that west Germans had firmly accepted democacy, or as simply another election, to be explained by the appeal of political issues, party identification, the candidates personalities, special political circumstances (e.g. U.S. intervention), or the sociological characteristics of the voters themselves. The paper looks into the validity of a particular set of public opinion surveys on the 1953 Bundestag election, commissioned by the Evaluation Staff of the Office of Public Affairs, U.S. High Commission for Germany (HICOG). The data from the 1953 election study show that neither the electoral outcome nor the degree of West Germans' acceptance of democratic institutions and practices should have come as a surprise. Specific issues seemed to play little role, but differences in general mood, related to several such issues, were important. Party identification as such was important for only a few. Voters subsequently saw Adenauer's personality and the general mood he represented as the most important element in the outcome; the special circumstances mentioned by several writers were insignificant in the voters' consciousness. The data suggest that social class and religion were important variables determining voters' predispositions, but the lack of theoretic orientation in the study makes impossible any definite conclusion about their weight vis-a-vis other variables such as issues.' (author's abstract