Jessica R. Lu

MEASURING DISTANCE AND PROPERTIES OF THE MILKY WAY'S CENTRAL SUPERMASSIVE BLACK HOLE WITH STELLAR ORBITS

We report new precision measurements of the properties of our Galaxys supermassive black hole. Based on astrometric (1995-2007) and radial velocity (RV; 2000-2007) measurements from the W. M. Keck 10m telescopes, a fully unconstrained Keplerian orbit for the short-period star S0-2 provides values for the distance (R_0) of 8.0±0.6 kpc, the enclosed mass (M_(bh)) of 4.1±0.6x10^6 M☉ and the black holes RV, which is consistent with zero with 30 km/s uncertainty. If the black hole is assumed to be at rest with respect to the Galaxy (e. g., has no massive companion to induce motion), we can further constrain the fit, obtaining R_0 = 8.4±0.4kpc and M_(bh) 4.5±0.4x10^6 M☉. More complex models constrain the extended dark mass distribution to be less than 3-4x10^5 M☉ within 0.01 pc, ~100 times higher than predictions from stellar and stellar remnant models. For all models, we identify transient astrometric shifts from source confusion (up to 5 times the astrometric error) and the assumptions regarding the black holes radial motion as previously unrecognized limitations on orbital accuracy and the usefulness of fainter stars. Future astrometric and RV observations will remedy these effects. Our estimates of R_0 and the Galaxys local rotation speed, which it is derived from combining R_0 with the apparent proper motion of Sgr A*, (θ_0 = 229±18 km/s), are compatible with measurements made using other methods. The increased black hole mass found in this study, compared to that determined using projected mass estimators, implies a longer period for the innermost stable orbit, longer resonant relaxation timescales for stars in the vicinity of the black hole and a better agreement with the M_(bh)-σ relation.

Stellar Orbits around the Galactic Center Black Hole

Wepresentnew diffraction-limitedimagesoftheGalacticcenter, obtainedwith theW.M.KeckI10mtelescope. Within0B4oftheGalaxy’scentraldarkmass,17proper-motionstars,withKmagnitudesrangingfrom 14.0to16.8, areidentified,and10ofthesearenewdetections(sixwerealsoindependentlydiscoveredbyothers).Inthissample, three newly identified (S0-16, S0-19, and S0-20) and four previously known (S0-1, S0-2, S0-4, and S0-5) sources have measured proper motions that reveal orbital solutions. Orbits are derived simultaneously so that they jointly constrain the central dark object’s properties: its mass,its position, and, for the first time using orbits, its motion on the plane of the sky. This analysis pinpoints the Galaxy’s central dark mass to within 1.3 mas (10 AU) and limits its propermotionto1:5 � 0:5masyr � 1 (orequivalently60 � 20kms � 1 )withrespecttothecentralstellarcluster.This localizationofthecentraldarkmassisconsistentwithourderivationofthepositionoftheradiosourceSgrA*inthe infrared reference frame (� 10 mas) but with an uncertainty that is a factor of 8 times smaller, which greatly facilitates searches for near-infrared counterparts to the central black hole. Consequently, one previous claim for such a counterpart can now be ascribed to a close stellar passage in 1996. Furthermore, we can place a conservative upper limit of 15.5 mag on any steady state counterpart emission. The estimated central dark mass from orbital motions is 3:7(� 0:2) ;10 6 R0= 8k pc ðÞ ½� 3 M� ; this is a more direct measure of mass than those obtained from velocitydispersion measurements,which are asmuchasafactorof2 smaller.The Galactic center’sdistance,which adds an additional 19% uncertainty in the estimated mass, is now the limiting source of uncertainty in the absolute mass. For stars in this sample, the closest approach is achieved by S0-16, which came within a mere 45 AU (=0:0002 pc ¼ 600Rs) at a velocity of 12,000 km s � 1 . This increases the inferred dark mass density by 4 orders of magnitude compared to earlier analyses based on velocity and acceleration vectors, making the Milky Way the strongest existing case for a supermassive black hole at the center of a normal-type galaxy. Well-determined orbital parameters for these seven Sgr A* cluster stars also provide new constraints on how these apparently massive, young (<10 Myr) stars formed in a region that seems to be hostile to star formation. Unlike the more distant He i emission line stars—another population of young stars in the Galactic center—that appear to have coplanar orbits, the Sgr A* cluster stars have orbital properties (eccentricities, angular momentum vectors, and apoapse directions) that are consistent with an isotropic distribution. Therefore, many of the mechanisms proposed for the formation of the He i stars, such as formation from a preexisting disk, are unlikely solutions for the Sgr A* cluster stars. Unfortunately, alternative theories for producing young stars, or old stars that look young, in close proximity to a centralsupermassiveblackholeareallalsosomewhatproblematic.Understandingtheapparentyouthofstarsinthe Sgr A* cluster, as well as the more distant Hei emission line stars, has now become one of the major outstanding issues in the study of the Galactic center. Subject headingg black hole physics — Galaxy: center — Galaxy: kinematics and dynamics — infrared: stars — techniques: high angular resolution

IMPROVING GALACTIC CENTER ASTROMETRY BY REDUCING THE EFFECTS OF GEOMETRIC DISTORTION

We present significantly improved proper motion measurements of the Milky Way’s central stellar cluster. These improvements are made possible by refining our astrometric reference frame with a new geometric optical distortion model for the W. M. Keck II 10 m telescope’s adaptive optics camera (NIRC2) in its narrow field mode. For the first time, this distortion model is constructed from on-sky measurements and is made available to the public in the form of FITS files.When applied to widely dithered images, it produces residuals in the separations of stars that are a factor of ~3 smaller compared with the outcome using previous models. By applying this new model, along with corrections for differential atmospheric refraction, to widely dithered images of SiO masers at the Galactic center (GC), we improve our ability to tie into the precisely measured radio Sgr A*-rest frame. The resulting infrared reference frame is ~2–3 times more accurate and stable than earlier published efforts. In this reference frame, Sgr A* is localized to within a position of 0.6 mas and a velocity of 0.09 mas yr^(−1), or ~3.4 km s^(−1) at 8 kpc (1σ). Also, proper motions for members of the central stellar cluster are more accurate, although less precise, due to the limited number of these wide field measurements. These proper motion measurements show that, with respect to Sgr A*, the central stellar cluster has no rotation in the plane of the sky to within 0.3 mas yr^(−1) arcsec^(−1), has no net translational motion with respect to Sgr A* to within 0.1 mas yr^(−1), and has net rotation perpendicular to the plane of the sky along the Galactic plane, as has previously been observed. While earlier proper motion studies defined a reference frame by assuming no net motion of the stellar cluster, this approach is fundamentally limited by the cluster’s intrinsic dispersion and therefore will not improve with time.We define a reference frame with SiO masers and this reference frame’s stability should improve steadily with future measurements of the SiO masers in this region (∝t^(−3/2)). This is essential for achieving the necessary reference frame stability required to detect the effects of general relativity and extended mass on short-period stars at the GC.

An x-ray, infrared, and submillimeter flare of Sagittarius A*

Energetic flares are observed in the Galactic supermassive black hole Sagittarius A* from radio to X-ray wavelengths. On a few occasions, simultaneous flares have been detected in IR and X-ray observations, but clear counterparts at longer wavelengths have not been seen. We present a flare observed over several hours on 2006 July 17 with the Chandra X-Ray Observatory, the Keck II telescope, the Caltech Submillimeter Observatory, and the Submillimeter Array. All telescopes observed strong flare events, but the submillimeter peak is found to occur nearly 100 minutes after the X-ray peak. Submillimeter polarization data show linear polarization in the excess flare emission, increasing from 9% to 17% as the flare passes through its peak, consistent with a transition from optically thick to thin synchrotron emission. The temporal and spectral behavior of the flare require that the energetic electrons responsible for the emission cool faster than expected from their radiative output. This is consistent with adiabatic cooling in an expanding emission region, with X-rays produced through self-Compton scattering, although not consistent with the simplest model of such expansion. We also present a submillimeter flare that followed a bright IR flare on 2005 July 31. Compared to 2006, this event had a larger peak IR flux and similar submillimeter flux, but it lacked measurable X-ray emission. It also showed a shorter delay between the IR and submillimeter peaks. Based on these events we propose a synchrotron and self-Compton model to relate the submillimeter lag and the variable IR/X-ray luminosity ratio.

The Shortest-Known–Period Star Orbiting Our Galaxy’s Supermassive Black Hole

Close to a Black Hole At the center of our Galaxy, there is a black hole that is 4 million times as massive as the Sun. Using data from the Keck Observatory, Meyer et al. (p. 84) detected a star orbiting this black hole with a period of 11.5 years, the shortest period among the stars orbiting it. The star is the second well-sampled star with an orbital period under 20 years. Having detailed knowledge about two stars with short periods and full orbit coverage will be crucial in testing Einsteins theory of general relativity in the gravitational field close to a massive black hole. A star can help probe Einstein’s general relativity theory close to a black hole that is 4 million times as massive as the Sun. Stars with short orbital periods at the center of our Galaxy offer a powerful probe of a supermassive black hole. Over the past 17 years, the W. M. Keck Observatory has been used to image the galactic center at the highest angular resolution possible today. By adding to this data set and advancing methodologies, we have detected S0-102, a star orbiting our Galaxy’s supermassive black hole with a period of just 11.5 years. S0-102 doubles the number of known stars with full phase coverage and periods of less than 20 years. It thereby provides the opportunity, with future measurements, to resolve degeneracies in the parameters describing the central gravitational potential and to test Einstein’s theory of general relativity in an unexplored regime.

Discovery of Precursor Luminous Blue Variable Outbursts in Two Recent Optical Transients: The Fitfully Variable Missing Links UGC 2773-OT and SN 2009ip

We present progenitor-star detections, light curves, and optical spectra of supernova (SN) 2009ip and the 2009 optical transient in UGC 2773 (U2773-OT), which were not genuine SNe. Precursor variability in the decade before outburst indicates that both of the progenitor stars were luminous blue variables (LBVs). Their pre-outburst light curves resemble the S Doradus phases that preceded giant eruptions of the prototypical LBVs η Carinae and SN 1954J (V12 in NGC 2403), with intermediate progenitor luminosities. Hubble Space Telescope detections a decade before discovery indicate that the SN 2009ip and U2773-OT progenitors were supergiants with likely initial masses of 50-80 M ☉ and 20 M ☉, respectively. Both outbursts had spectra befitting known LBVs, although in different physical states. SN 2009ip exhibited a hot LBV spectrum with characteristic speeds of 550 km s–1, plus evidence for faster material up to 5000 km s–1, resembling the slow Homunculus and fast blast wave of η Carinae. In contrast, U2773-OT shows a forest of narrow absorption and emission lines comparable to that of S Dor in its cool state, plus [Ca II] emission and an infrared excess indicative of dust, similar to SN 2008S and the 2008 optical transient in NGC 300 (N300-OT). The [Ca II] emission is probably tied to a dusty pre-outburst environment, and is not a distinguishing property of the outburst mechanism. The LBV nature of SN 2009ip and U2773-OT may provide a critical link between historical LBV eruptions, while U2773-OT may provide a link between LBVs and the unusual dust-obscured transients SN 2008S and N300-OT. Future searches will uncover more examples of precursor LBV variability of this kind, providing key clues that may help unravel the instability driving LBV eruptions in massive stars.

An Overabundance of Transient X-Ray Binaries within 1 Parsec of the Galactic Center

During 5 years of Chandra observations, we have identified seven X-ray transients located within 23 pc of Sgr A*. These sources each vary in luminosity by more than a factor of 10 and have peak X-ray luminosities greater than 5 × 1033 ergs s-1, which strongly suggests that they are accreting black holes or neutron stars. The peak luminosities of the transients are intermediate between those typically considered outburst and quiescence for X-ray binaries. Remarkably, four of these transients lie within only 1 pc of Sgr A*. This implies that, compared to the numbers of similar systems located between 1 and 23 pc, transients are overabundant by a factor of 20 per unit stellar mass within 1 pc of Sgr A*. It is likely that the excess transient X-ray sources are low-mass X-ray binaries that were produced, as in the cores of globular clusters, by three-body interactions between binary star systems and either black holes or neutron stars that have been concentrated in the central parsec through dynamical friction. Alternatively, they could be high-mass X-ray binaries that formed among the young stars that are present in the central parsec.

STELLAR POPULATIONS IN THE CENTRAL 0.5 pc OF THE GALAXY. II. THE INITIAL MASS FUNCTION

The supermassive black hole at the center of the Milky Way plays host to a massive, young cluster that may have formed in one of the most inhospitable environments in the Galaxy. We present new measurements of the global properties of this cluster, including the initial mass function (IMF), age, and cluster mass. These results are based on Keck laser-guide-star adaptive optics observations used to identify the young stars and measure their Kp-band luminosity function as presented in Do et al. 2013. A Bayesian inference methodology is developed to simultaneously fit the global properties of the cluster utilizing the observations and extensive simulations of synthetic star clusters. We find that the slope of the mass function for this cluster is \alpha = 1.7 +/- 0.2, which is steeper than previously reported, but still flatter than the traditional Salpeter slope of 2.35. The age of the cluster is between 2.5-5.8 Myr with 95% confidence, which is a younger age than typically adopted but consistent within the uncertainties of past measurements. The exact age of the cluster is difficult to determine since our results show two distinct age solutions (3.9 Myr and 2.8 Myr) due to model degeneracies in the relative number of Wolf-Rayet and OB stars. The total cluster mass is between 14,000 - 37,000 \msun above 1 \msun and it is necessary to include multiple star systems in order to fit the observed luminosity function and the number of observed Wolf-Rayet stars. The new IMF slope measurement is now consistent with X-ray observations indicating a factor of 10 fewer X-ray emitting pre-main-sequence stars than expected when compared with a Salpeter IMF. The young cluster at the Galactic center is one of the few definitive examples of an IMF that deviates significantly from the near-universal IMFs found in the solar neighborhood.

A Constant Spectral Index for Sagittarius A* during Infrared/X-Ray Intensity Variations

We report the first time-series of broadband infrared color m easurements of Sgr A*, the variable emission source associated with the supermassive black hole at the Galactic Center. Using the laser and natural guide star adaptive optics systems on the Keck II telescope, we imaged Sgr A* in multiple near-infrared broadband filters with a typical cycle time of ∼3 min during 4 observing runs (2005‐2006), two of which were simultaneous with Chandra X-ray measurements. In spite of the large range of dereddened flux densities for Sgr A* (2 to 30 mJy), all of our near-infrared measurements are consistent with a constant spectral index of � = -0.6 ± 0.2 (F� ∝ � � ). Furthermore, this value is consistent with the spectral i ndices observed at X-ray wavelengths during nearly all outbursts; which is consistent with the sy nchrotron self-Compton model for the production of the X-ray emission. During the coordinated observations, one infrared outburst occurs ≤36 min after a possibly associated X-ray outburst, while several similar infrared outbursts show no elevated X-ray emission. A variable X-ray to IR ratio and constant infrared spectral i ndex challenge the notion that the infrared and X-ray emission are connected to the same electrons. We, therefore, posit that the population of elec trons responsible for both the IR and X-ray emission are generated by an acceleration mechanism that leaves the bulk of the electron energy distribution responsible for the infrared emission unchanged, but has a variable high-energy cutoff. Occasionally a tail of electrons & 1 GeV is generated, and it is this high-energy tail that gives rise to the X-ray outbursts. One possible explanation for this ty pe of variation is from the turbulence induced by a magnetorotational instability, in which the outer scal e length of the turbulence varies and changes the high-energy cutoff. Subject headings:Galaxy: center — infrared: stars — black hole physics — techniques: high angular resolution

The first laser guide star adaptive optics observations of the galactic center : Sgr A*'S infrared color and the extended red emission in its vicinity

We present the first Laser Guide Star Adaptive Optics (LGS-AO ) observations of the Galactic center. LGSAO has dramatically improved the quality and robustness with which high angular resolution infrared images of the Galactic center can be obtained with the W. M. Keck II 10-meter telescope. Specifically, Strehl ratios of 0.7 and 0.3 at L’[3.8 µm] and K’[2.1 µm], respectively, are achieved in these LGS-AO images; these are at least a factor of two higher and a factor of four to five more stable ag ainst atmospheric fluctuations than the Strehl ratios delivered thus far with the Keck Natural Guide Star AO system on the Galactic center. Furthermore, these observations are the first that cover a large area (76 ′′ × 76 ′′ ) surrounding the central black hole at diffractionlimited resolution for an 8-10 meter class telescope. Durin g our observations, the infrared counterpart to the central supermassive black hole, Sgr A*-IR, showed signific ant infrared intensity variations, with observed L’ magnitudes ranging from 12.6 to 14.5 mag and a decrease in fl ux density of a factor of two over an 8 minute interval. The faintest end of our L’ detections, 1.3 m Jy (dereddened), is the lowest level of emission yet observed for this source by a factor of 3. No significant varia tion in the location of SgrA*-IR is detected as a function of either wavelength or intensity. Previous claim s of such positional variations are easily attributable to a nearby (0. 09 or 720 AU, projected), extended, very red source, which we suggest arises from a locally heated dust feature. Near a peak in its intensity, we obtaine d the first measurement of SgrA*-IR’s K’-L’ color; its K’-L’ of 3.0 ± 0.2 mag (observed) or 1.4 ± 0.2 (dereddened) corresponds to an intrinsic spectral index of � -0.5 ± 0.3 for F� � � � . This is significantly bluer than other recent infrared meas urements from the literature, which suggest � = -4 ± 1. Because our measurement was taken at a time when Sgr A* was�6 times brighter in the infrared than the other measurements, we posit that the spectral index of the emission arising from the vicinity of our Galaxy’s central black hole may depend on the strength of the flare, with stronger flares giving rise to a higher fraction of high energy electrons in the emit ting region. Subject headings:black hole physics ‐ Galaxy:center — infrared:stars ‐ techniques:high angular resolution