Towards relativistic orbit fitting of Galactic center stars and pulsars

The S stars orbiting the Galactic center black hole reach speeds of up to a few percent the speed of light during pericenter passage. This makes, for example, S2 at pericenter much more relativistic than known binary pulsars, and opens up new possibilities for testing general relativity. This paper develops a technique for fitting nearly-Keplerian orbits with perturbations from Schwarzschild curvature, frame dragging, and spin-induced torque, to redshift measurements distributed along the orbit but concentrated around pericenter. Both orbital and light-path effects are taken into account. It turns out that absolute calibration of rest-frame frequency is not required. Hence, if pulsars on orbits similar to the S stars are discovered, the technique described here can be applied without change, allowing the much greater accuracies of pulsar timing to be taken advantage of. For example, pulse timing of 3 microsec over one hour amounts to an effective redshift precision of 30 cm/s, enough to measure frame dragging and the quadrupole moment from an S2-like orbit, provided problems like the Newtonian "foreground" due to other masses can be overcome. On the other hand, if stars with orbital periods of order a month are discovered, the same could be accomplished with stellar spectroscopy from the E-ELT at the level of 1 km/s.Comment: 22 pages, 9 figures, published in the Ap

A nova origin of the gas cloud at the Galactic Center ?

The recent discovery by Gillessen and collaborators of a cloud of gas falling towards the Galactic Center on a highly eccentric orbit, diving nearly straight into the immediate neighborhood of the central supermassive black hole, raises the important question of its origin. Several models have already been proposed. Here we suggest that a recent nova outburst has ejected a ring-like shell of gas. Viewed at high inclination, that could account for the mass, head and tail structure, and the unusually high eccentricity of the observed cloud in a natural way, even as the nova moves on an orbit quite normal for the young stars in the close neighborhood of the Galactic Center. We illustrate this by calculating orbits for the head and tail parts of the ejecta and the nova that has produced it. We briefly discuss some of the questions that this model, if true, raises about the stellar environment close to the Galactic Center.Comment: 4 pages, 1 figure, Journal reference, correction of a minor erro

Medienerziehung - Wege zu mehr Schülerkompetenz

Um in der Schule Medien und Pädagogik in Einklang zu bringen, ist es zum einen notwendig, dass Schule ihren Schülern vielfältige Gelegenheiten für selbstständige Lernerfahrungen mit Medien bietet. Die Ganztagsschule ermöglicht dies bisher durch freie Lernorte (der Raum als „dritter Pädagoge“) und den zunehmenden Einbezug außerschulischer Lernerfahrungen der Schüler im Fachunterricht. […] Durch die explizite Verzahnung der pragmatischen, auf Fachinhalte bezogenen Mediennutzung auf der einen Seite und der Förderung strategischen Denkens und Lernens mit Medien auf der anderen Seite können Schüler Grundlagen selbstregulierter Medienhandlungen entwickeln. (DIPF/Orig.

The orbit of the star S2 around SgrA* from VLT and Keck data

Two recent papers (Ghez et al. 2008, Gillessen et al. 2009) have estimated the mass of and the distance to the massive black hole in the center of the Milky Way using stellar orbits. The two astrometric data sets are independent and yielded consistent results, even though the measured positions do not match when simply overplotting the two sets. In this letter we show that the two sets can be brought to excellent agreement with each other when allowing for a small offset in the definition of the reference frame of the two data sets. The required offsets in the coordinates and velocities of the origin of the reference frames are consistent with the uncertainties given in Ghez et al. (2008). The so combined data set allows for a moderate improvement of the statistical errors of mass of and distance to Sgr A*, but the overall accuracies of these numbers are dominated by systematic errors and the long-term calibration of the reference frame. We obtain R0 = 8.28 +- 0.15(stat) +- 0.29(sys) kpc and M(MBH) = 4.30 +- 0.20(stat) +- 0.30(sys) x 10^6 Msun as best estimates from a multi-star fit.Comment: submitted to ApJ

Fe Ka line emission from the Arches cluster region - evidence for ongoing particle bombardment?

We present the results of eight years of XMM-Newton observations of the region surrounding the Arches cluster in the Galactic Center. We study the spatial distribution and temporal behaviour of the Fe-Ka line emission with the objective of identifying the likely source of the excitation. We investigate the variability of the 6.4-keV line emission of four clouds through spectral fitting of the EPIC MOS data with the use of a modelled background, which avoids many of the systematics inherent in local background subtraction. We also employ spectral stacking of both EPIC PN and MOS data to search for evidence of an Fe-K edge feature imprinted on the underlying X-ray continuum. The lightcurves of the Fe-Ka line from three bright molecular knots close to the Arches cluster are found to be constant over the 8-year observation window. West of the cluster, however, we found a bright cloud exhibiting the fastest Fe-Ka variability yet seen in a molecular cloud in the Galactic Center region. The time-averaged spectra of the molecular clouds reveal no convincing evidence of the 7.1-keV edge feature. The EW of the 6.4-keV line emitted by the clouds near the cluster is found to be ~1.0 keV. The observed Fe-Ka line flux and the high EW suggest the fluorescence has a photoionization origin, although excitation by cosmic-ray particles is not specifically excluded. For the three clouds nearest to the cluster, an identification of the source of photo-ionizing photons with an earlier outburst of Sgr A* is however at best tentative. The hardness of the nonthermal component associated with the 6.4-keV line emission might be best explained in terms of bombardment by cosmic-ray particles from the Arches cluster itself. The relatively short-timescale variability seen in the 6.4-keV line emission from the cloud to the West of the cluster is most likely the result of illumination by a nearby transient X-ray source.Comment: 13 pages, 6 figures, accepted for publication in Astronomy and Astrophysic

Frame-dragging and the kinematics of Galactic-Center stars

We calculate the effects of frame dragging on the Galactic-Center stars. Assuming the stars are only slightly relativistic, we derive an approximation to the Kerr metric, which turns out to be a weak field Schwarzschild metric plus a frame dragging term. By numerically integrating the resulting geodesic equations, we compute the effect on keplerian elements and the kinematics. We find that the kinematic effect at pericenter passage is proportional to (a(1-e^2))^{-2}. For known Galactic-center stars it is of order 10 m/s. If observed this would provide a measurement of the spin of the black hole.Comment: To appear in Ap

Orbits Around Black Holes in Triaxial Nuclei

We discuss the properties of orbits within the influence sphere of a supermassive black hole (BH), in the case that the surrounding star cluster is nonaxisymmetric. There are four major orbit families; one of these, the pyramid orbits, have the interesting property that they can approach arbitrarily closely to the BH. We derive the orbit-averaged equations of motion and show that in the limit of weak triaxiality, the pyramid orbits are integrable: the motion consists of a two-dimensional libration of the major axis of the orbit about the short axis of the triaxial figure, with eccentricity varying as a function of the two orientation angles, and reaching unity at the corners. Because pyramid orbits occupy the lowest angular momentum regions of phase space, they compete with collisional loss cone repopulation and with resonant relaxation in supplying matter to BHs. General relativistic advance of the periapse dominates the precession for sufficiently eccentric orbits, and we show that relativity imposes an upper limit to the eccentricity: roughly the value at which the relativistic precession time is equal to the time for torques to change the angular momentum. We argue that this upper limit to the eccentricity should apply also to evolution driven by resonant relaxation, with potentially important consequences for the rate of extreme-mass-ratio inspirals in low-luminosity galaxies. In giant galaxies, we show that capture of stars on pyramid orbits can dominate the feeding of BHs, at least until such a time as the pyramid orbits are depleted; however this time can be of order a Hubble time.Comment: 20 pages, 15 figure