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

Full Three Dimensional Orbits For Multiple Stars on Close Approaches to the Central Supermassive Black Hole

With the advent of adaptive optics on the W. M. Keck 10 m telescope, two significant steps forward have been taken in building the case for a supermassive black hole at the center of the Milky Way and understanding the black hole's effect on its environment. Using adaptive optics and speckle imaging to study the motions of stars in the plane of sky with +-~2 mas precision over the past 7 years, we have obtained the first simultaneous orbital solution for multiple stars. Among the included stars, three are newly identified (S0-16, S0-19, S0-20). The most dramatic orbit is that of the newly identified star S0-16, which passed a mere 60 AU from the central dark mass at a velocity of 9,000 km/s in 1999. The orbital analysis results in a new central dark mass estimate of 3.6(+-0.4)x10^6(D/8kpc)^3 Mo. This dramatically strengthens the case for a black hole at the center of our Galaxy, by confining the dark matter to within a radius of 0.0003 pc or 1,000 Rsh and thereby increasing the inferred dark mass density by four orders of magnitude compared to earlier estimates. With the introduction of an adaptive-optics-fed spectrometer, we have obtained the spectra of these high-velocity stars, which suggest that they are massive (~15 Mo), young (<10 Myr) main sequence stars. This presents a major challenge to star formation theories, given the strong tidal forces that prevail over all distances reached by these stars in their current orbits and the difficulty in migrating these stars inward during their lifetime from further out where tidal forces should no longer preclude star formation.Comment: 7 pages, 5 figures (abridged abstract

Disentangling Confused Stars at the Galactic Center with Long Baseline Infrared Interferometry

We present simulations of Keck Interferometer ASTRA and VLTI GRAVITY observations of mock star fields in orbit within ~50 milliarcseconds of Sgr A*. Dual-field phase referencing techniques, as implemented on ASTRA and planned for GRAVITY, will provide the sensitivity to observe Sgr A* with infrared interferometers. Our results show an improvement in the confusion noise limit over current astrometric surveys, opening a window to study stellar sources in the region. Since the Keck Interferometer has only a single baseline, the improvement in the confusion limit depends on source position angles. The GRAVITY instrument will yield a more compact and symmetric PSF, providing an improvement in confusion noise which will not depend as strongly on position angle. Our Keck results show the ability to characterize the star field as containing zero, few, or many bright stellar sources. We are also able to detect and track a source down to mK~18 through the least confused regions of our field of view at a precision of ~200 microarcseconds along the baseline direction. This level of precision improves with source brightness. Our GRAVITY results show the potential to detect and track multiple sources in the field. GRAVITY will perform ~10 microarcsecond astrometry on a mK=16.3 source and ~200 microarcsecond astrometry on a mK=18.8 source in six hours of monitoring a crowded field. Monitoring the orbits of several stars will provide the ability to distinguish between multiple post-Newtonian orbital effects, including those due to an extended mass distribution around Sgr A* and to low-order General Relativistic effects. Early characterizations of the field by ASTRA including the possibility of a precise source detection, could provide valuable information for future GRAVITY implementation and observation.Comment: Accepted for publication in Ap

A near-IR variability study of the Galactic black hole: a red noise source with no detected periodicity

We present the results of near-infrared (2 and 3 microns) monitoring of Sgr A*-IR with 1 min time sampling using the natural and laser guide star adaptive optics (LGS AO) system at the Keck II telescope. Sgr A*-IR was observed continuously for up to three hours on each of seven nights, between 2005 July and 2007 August. Sgr A*-IR is detected at all times and is continuously variable, with a median observed 2 micron flux density of 0.192 mJy, corresponding to 16.3 magnitude at K'. These observations allow us to investigate Nyquist sampled periods ranging from about 2 minutes to an hour. Using Monte Carlo simulations, we find that the variability of Sgr A* in this data set is consistent with models based on correlated noise with power spectra having frequency dependent power law slopes between 2.0 to 3.0, consistent with those reported for AGN light curves. Of particular interest are periods of ~20 min, corresponding to a quasi-periodic signal claimed based upon previous near-infrared observations and interpreted as the orbit of a 'hot spot' at or near the last stable orbit of a spinning black hole. We find no significant periodicity at any time scale probed in these new observations for periodic signals. This study is sensitive to periodic signals with amplitudes greater than 20% of the maximum amplitude of the underlying red noise component for light curves with duration greater than ~2 hours at a 98% confidence limit.Comment: 37 pages, 2 tables, 17 figures, accepted by Ap

Preventive Care, Care for Children and National Health Insurance

The purpose of this paper is to examine issues related to the coverage of preventive care under national health insurance. Four specific kinds of medical care services are included under the rubric of preventive care: prenatal care; pediatric care, dental care, and preventive physicians' services for adults. We consider whether preventive care should be covered under national health insurance, and if so what is the nature of the optimal plan. Our review of the literature on the effects of medical care on health outcomes suggests that prenatal care and dental care are effective, but pediatric care (except for immunizations) and preventive doctor care for adults are not. Moreover, health outcomes in which care is effective correspond to outcomes in which income-differences in health are observed. These empirical results and the theory of health as the source of consumption externalities indicate that the optimal NHI plan should be characterized by benefits that fall as income rises. In addition, the plan should be selective rather than general with respect to the types of services covered.