Tidal scattering of stars on supermassive black holes in galactic centers

Some of the mass that feeds the growth of a massive black hole (BH) in a galactic center is supplied by tidal disruption of stars that approach it on unbound, low angular momentum orbits. For each star that is disrupted, others narrowly escape after being subjected to extreme tidal distortion, spin-up, mixing and mass-loss, which may affect their evolution and appearance. We show that it is likely that a significant fraction of the stars around massive BHs in galactic centers have undergone such extreme tidal interactions and survived subsequent total disruption, either by being deflected off their orbit or by missing the BH due to its Brownian motion. We discuss possible long-term observable consequences of this process, which may be relevant for understanding the nature of stars in galactic centers, and may provide a signature of the existence of massive BHs there.Comment: 5 pages 4 figures. ApJL in press, minor changes to reflect journal version including redifinition of unbound tidally disturbed stars and additional reference

The Lamé family of connections on the projective line

International audienceThis paper deals with rank two connections on the projective line having four simple poles with prescribed local exponents 1/4 and -1/4. This Lamé family of connections has been extensively studied in the literature. The differential Galois group of a Lamé connection is never maximal: it is either dihedral (finite or infinite) or reducible. We provide an explicit moduli space of those connections having a free underlying vector bundle and compute the algebraic locus of those reducible connections. The irreducible Lamé connections are derived from the rank 1 regular connections on the Legendre elliptic curve w^2=z(z-1)(z-t); those connections having a finite Galois group are known to be related to points of finite order on the elliptic curve. In the paper, we provide a very efficient algorithm to compute the locus of those Lamé connections having a finite Galois group of a given order. We also give an efficient algorithm to compute the minimal polynomial for the corresponding field extension. We do this computation for low order and recover this way known algebraic solutions of the Painlevé VI equation and of the classical Lamé equation. In the final section we compare our moduli space with the classical one due to Okamoto

Bürgerbeteiligung braucht Verstetigung und Verlässlichkeit: Gestaltungselemente einer dauerhaften und systematischen Bürgerbeteiligung in Städten und Gemeinden

Die Proteste um den Stuttgarter Hauptbahnhof haben die Diskussion über das Verhältnis zwischen Bürgern und Politik neu entfacht. In diesem Beitrag argumentieren wir nach einer kritischen Diskussion bisheriger Lösungsansätze für die Implementation eines auf Dauer angelegten, systematischen Konzeptes kooperativer Demokratie. Zum Aufbau von gegenseitigem Vertrauen bedarf es der Verstetigung kooperativer Bürgerbeteiligungsprozesse. Dabei müssen Verbindlichkeiten geregelt sein im Hinblick auf die Beteiligungsprozesse, den Umgang mit jeweiligen Ergebnissen und auf Verantwortlichkeiten. Zentrales Merkmal muss außerdem die prozessuale Verzahnung der beteiligten Akteure sein - vornehmlich der Bürgerschaft, der Politik und der Verwaltung. Auf Basis erster Umsetzungserfahrungen formulieren wir hierzu sechs Gestaltungselemente eines entsprechenden Beteiligungskonzeptes. Sie werden ergänzt um Rahmenbedingungen, die für die Implementation eines solchen Ansatzes notwendig sind.Besides voting, new ways and instruments of citizen participation in local politics have become common in recent years. So far however, these instruments are normally used only sporadically. In this article we make the point for more continuity and reliability in local citizen participation. In order to build up trust between citizens, politicians and the local public administration, reliability of local participatory processes has to be guaranteed with regard to the incitation of these processes, the processes themselves and the handling of the respective results. We formulate six fundamental components of a respective reliable concept of continuous citizen participation. Bases on experiences from a German local participatory project we finally add several contextual factors that seem vital to us for the implementation of such a concept of continuous and reliable citizen participation in local politics

Tidal Disruption of a Star By a Black Hole : Observational Signature

We have modeled the time-variable profiles of the Halpha emission line from the non-axisymmetric disk and debris tail created in the tidal disruption of a solar-type star by a million solar mass black hole. Two tidal disruption event simulations were carried out using a three dimensional relativistic smooth-particle hydrodynamic code, to describe the early evolution of the debris during the first fifty to ninety days. We have calculated the physical conditions and radiative processes in the debris using the photoionization code CLOUDY. We model the emission line profiles in the period immediately after the accretion rate onto the black hole became significant. We find that the line profiles at these very early stages of the evolution of the post-disruption debris do not resemble the double peaked profiles expected from a rotating disk since the debris has not yet settled into such a stable structure. As a result of the uneven distribution of the debris and the existence of a ``tidal tail'' (the stream of returning debris), the line profiles depend sensitively on the orientation of the tail relative to the line of sight. Moreover, the predicted line profiles vary on fairly short time scales (of order hours to days). Given the accretion rate onto the black hole we also model the Halpha light curve from the debris and the evolution of the Halpha line profiles in time.Comment: 20 pages, 9 figures, to appear in ApJ, 1 August 2004 issue; mpeg simulations of tidal disruption available at http://www.astro.psu.edu/users/tamarab/tdmovies.htm

Probing Intermediate Mass Black Holes With Optical Emission Lines from Tidally Disrupted White Dwarfs

We calculate the emission line spectrum produced by the debris released when a white dwarf (WD) is tidally disrupted by an intermediate-mass black hole (IMBH; M\sim 10^{2}-10^{5}\msun) and we explore the possibility of using the emission lines to identify such events and constrain the properties of the IMBH. To this end, we adopt and adapt the techniques developed by Strubbe & Quataert to study the optical emission lines produced when a main sequence (MS) star is tidally disrupted by a supermassive black hole. WDs are tidally disrupted outside of the event horizon of a < 10^{5}\msun black hole, which makes these tidal disruption events good signposts of IMBHs. We focus on the optical and UV emission lines produced when the accretion flare photoionizes the stream of debris that remains unbound during the disruption. We find that the spectrum is dominated by lines due to ions of C and O, the strongest of which are \ion{C}{4} $\lambda$1549 at early times and [\ion{O}{3}] $\lambda$5007 at later times. Furthermore, we model the profile of the emission lines in the [\ion{O}{3}] $\lambda\lambda$4959, 5007 doublet and find that it is highly asymmetric with velocity widths of up to $\sim 2500 \rm{\;km\;s^{-1}}$, depending on the properties of the WD-IMBH system and the orientation of the observer. Finally, we compare the models with observations of X-ray flares and optical emission lines in the cores of globular clusters and propose how future observations can test if these features are due to a WD that has been tidally disrupted by an IMBH.Comment: 19 pages, 9 figures, accepted for publication in The Astrophysical Journa

A new model of a tidally disrupted star

A new semi-analytical model of a star evolving in a tidal field is proposed. The model is a generalization of the so-called 'affine' stellar model. In our model the star is composed of elliptical shells with different parameters and different orientations, depending on time and on the radial Lagrangian coordinate of the shell. The evolution equations of this model are derived from the virial relations under certain assumptions, and the integrals of motion are identified. It is shown that the evolution equations can be deduced from a variational principle. The evolution equations are solved numerically and compared quantitatively with the results of 3D numerical computations of the tidal interaction of a star with a supermassive black hole. The comparison shows very good agreement between the main ``integral'' characteristics describing the tidal interaction event in our model and in the 3D computations. Our model is effectively a one-dimensional Lagrangian model from the point of view of numerical computations, and therefore it can be evolved numerically $10^{2}-10^{3}$ times faster than the 3D approach allows. This makes our model well suited for intensive calculations covering the whole parameter space of the problem.Comment: This version is accepted for publication in ApJ. Stylistic and grammatical changes, new Appendix adde

Hydrodynamical Simulations to Determine the Feeding Rate of Black Holes by the Tidal Disruption of Stars: The Importance of the Impact Parameter and Stellar Structure

The disruption of stars by supermassive black holes has been linked to more than a dozen flares in the cores of galaxies out to redshift $z \sim 0.4$. Modeling these flares properly requires a prediction of the rate of mass return to the black hole after a disruption. Through hydrodynamical simulation, we show that aside from the full disruption of a solar mass star at the exact limit where the star is destroyed, the common assumptions used to estimate $\dot{M}(t)$, the rate of mass return to the black hole, are largely invalid. While the analytical approximation to tidal disruption predicts that the least-centrally concentrated stars and the deepest encounters should have more quickly-peaked flares, we find that the most-centrally concentrated stars have the quickest-peaking flares, and the trend between the time of peak and the impact parameter for deeply-penetrating encounters reverses beyond the critical distance at which the star is completely destroyed. We also show that the most-centrally concentrated stars produced a characteristic drop in $\dot{M}(t)$ shortly after peak when a star is only partially disrupted, with the power law index $n$ being as extreme as -4 in the months immediately following the peak of a flare. Additionally, we find that $n$ asymptotes to $\simeq -2.2$ for both low- and high-mass stars for approximately half of all stellar disruptions. Both of these results are significantly steeper than the typically assumed $n = -5/3$. As these precipitous decay rates are only seen for events in which a stellar core survives the disruption, they can be used to determine if an observed tidal disruption flare produced a surviving remnant. These results should be taken into consideration when flares arising from tidal disruptions are modeled. [abridged]Comment: 16 pages, 13 figures (2 new figures in revised version). Published in ApJ. Latest version incorporates erratum that fixes issue with fitting formulae not including enough significant digit