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Andrew Gould

Publications and source records attributed to Andrew Gould.

At least 325 records · Page 18Linked to original sources

Microlens Parallaxes of Binary Lenses Measured from a Satellite

Caustic-crossing binary lenses make up about 5% of all detected microlenses. The relative proper motion of a caustic-crossing binary lens can be measured with observations from a single terrestrial telescope. Thus, uniquely, binary lenses can be completely solved with only the addition of a measurement of the microlensing parallax. This solution will yield the mass, distance, and transverse velocity of the lens relative to the source. To date, only one of the $\sim 1000$ observed microlensing events has been so solved. We examine the ability of a parallax satellite combined with ground-based observations to solve these events. To measure both components of the vector parallax, the lens must be observed near two different caustics. Thus, the final accuracy is determined mostly by whether one can intensively monitor part of the first caustic crossing, by the magnification pattern, and by the path of the source with respect to the lens geometry. We find that vector parallaxes can be measured far more easily for binary lenses than single lenses, requiring 1-3 orders of magnitude fewer photons. They may thus yield a large number of completely solved lenses relatively cheaply.

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Astrometry Survey Missions Beyond the Magnitude Limit

Three planned astrometry survey satellites, FAME, DIVA, and GAIA, all aim at observing magnitude-limited samples. We argue that substantial additional scientific opportunities are within the reach of these mission if they devote a modest fraction of their catalogs to selected targets that are fainter than their magnitude limits. We show that the addition of ~10^6 faint (R>15) targets to the 40 10^6 object FAME catalog can improve the precision of the reference frame by a factor 2.5, to 7 micro-as/yr, increase Galactocentric distance at which halo rotation can be precisely (2 km/s) measured by a factor 4, to 25 kpc, and increase the number of late M dwarfs, L dwarfs, and white dwarfs with good parallaxes by an order of magnitude. In most cases, the candidate quasars, horizontal branch stars, and dim dwarfs that should be observed to achieve these aims are not yet known. We present various methods to identify candidates from these classes, and assess the efficiencies of these methods. The analysis presented here can be applied to DIVA with modest modifications. Application to GAIA should be deferred until the characteristics of potential targets are better constrained.

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Millisecond Pulsars as Probes of Mass Segregation in the Galactic Center

We propose a simple test for the existence of a cluster of black hole remnants around Sgr A* that is based on a small sample of any type of Galactic Center objects, provided they are substantially less massive than the black holes and constitute part of an old (> 1 Gyr) population. The test relies on the fact that, under the presence of such a cluster of heavy remnants and because of energy equipartition, lower mass objects would be expelled from the central regions and settle into a distribution very different than the cusp expected to be induced by the supermassive black hole alone. We show that with a sample of just 50 objects and using only their angular positions on the sky relative to Sgr A* it is possible to clearly differentiate between a distribution consistent with the presence of the cluster of black holes and a power-law cusp distribution. We argue that millisecond pulsars might currently be the best candidate to perform this test, because of the large uncertainties involved in the age determination of less exotic objects. In addition, by measuring their first and second period derivatives, millisecond pulsars offer the rare opportunity of determining the complete phase space information of the objects. We show that this extra information improves the detection of mass segregation by about 30%.

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Microlensing by Stellar Black Holes Around Sgr A*

We show that at any given time, the Galactocentric black hole Sgr A* is expected to be microlensing N(lens)=1.7 bulge stars if the threshold of detectability of the fainter image is K(thr)=21, and about N(lens)=8 sources if K(thr)=23. The lensed images then provide a unique way to detect stellar-mass black holes predicted to cluster around Sgr A*. If a black hole passes close to a microlensed image, it will give rise to a short (weeks long) microlensing event. We show that the mass and projected velocity of the stellar-mass black hole can both be measured unambiguously from such an event, provided that either a caustic crossing is observed or the astrometric displacement is measured. For K(thr)=23 and moderate magnifications by Sgr A*, the microlensing event rate from a cluster of 20000 black holes within a radius of 0.7 pc is only 0.06 events per year; however, if highly magnified images of a star were found, the rate of events by the stellar black holes would be much higher. In addition, the N(lens) sources lensed by Sgr A* provide a unique probe of extinction behind the Galactic center along 2N(lens) lines of sight.

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Searching for Failed Supernovae With Astrometric Binaries

Stars in the mass range 8 Msun<M<30 Msun are thought to end their lives as luminous supernovae that leave behind a neutron star. However, if a substantial fraction of these stars instead ended as black-hole remnants, without producing a supernova (a `failed' supernova), how would one know? We show that, under plausible assumptions, the Hipparcos catalog should contain about 30 f_{fail} astrometric binaries with black-hole companions, where f_{fail} is the fraction of supernovae that fail. Since no black-hole astrometric binaries are found in Hipparcos, one might like to conclude that such failed supernovae are very rare. However, the most important assumption required for this argument, the initial companion mass function (ICMF) of G stars (the majority of Hipparcos stars) in the high-mass companion regime, is without any observational basis. We show how the ICMF of G stars can be measured using the Full-Sky Astrometric Explorer (FAME), thereby permitting an accurate measurement of the rate of supernovae that fail.

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Resolving Microlens Blends Using Image Subtraction

Blended light is an important source of degeneracy in the characterization of microlensing events, particularly in binary-lens and high magnification events. We show how the techniques of image subtraction can be applied to form an image of the blend with the source removed. In many cases, it should be possible to construct images with very high signal-to-noise ratio. Analysis of these images can help distinguish between competing models that have different blend fractions, and in some cases should allow direct detection of the lens.

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Microlens Mass Measurement using Triple-Peak Events

We show that one can measure the effects of microlens parallax for binary microlensing events with three well-measured peaks -- two caustic crossings plus a cusp approach, and hence derive the projected Einstein radius. Since the angular Einstein radius is measurable from finite source effects for almost any well-observed caustic crossing, triple-peak events can yield the determination of the lens mass. We note that, to a certain extent, rotation of the binary can mimic the effects of parallax, but it should often be possible to disentangle parallax from rotation by making use of the late-time light curve.

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Analytic Study of Grid Star and Reference Star Selection for the Space Interferometry Mission

Grid stars and reference stars provide the fundamental global and local astrometric reference frames for observations by the Space Interferometry Mission. They must therefore be astrometrically stable at the ~1 uas level. I present simple formulae in closed form to estimate contamination of these frames by motions due to stellar companions that go undetected in a radial-velocity (RV) survey of specified precision. The contamination rate depends almost entirely on the binary-period distribution function and not on the details of the mass or eccentricity distributions. Screening by a modest RV survey (sigma_rv=60 m/s) can reduce the fraction of grid stars having detectable unmodeled accelerations to <<1%. Reference-star selection promises to be much more challenging, partly because the requirements of astrometric stability are more severe and partly because the required density of sources is about 100 times higher, which latter implies that less satisfactory candidates will have to be accepted. The tools presented here can help design a reference-star selection strategy, but a full treatment of the problem will require better knowledge of their companions in the planetary mass range.

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Applications of Microlensing to Stellar Astrophysics

Over the past decade, microlensing has developed into a powerful tool to study stellar astrophysics, especially stellar atmospheres, stellar masses, and binarity. I review this progress. Stellar atmospheres can be probed whenever the source in a microlensing event passes over the caustic (contour of infinite magnification) induced by the lens because the caustic effectively resolves the source. Broad-band observations of four events have yielded limb-darkening measurements, which in essence map the atmospheric temperature as a function of depth. And now, for the first time, spectroscopic observations of one event promise much richer diagnostics of the source atmosphere. In the past two years, a practical method has finally been developed to systematically measure the lens masses in microlensing events. This will permit a census of all massive objects, both dark and luminous, in the Galactic bulge, including low-mass stars, brown dwarfs, white dwarfs, neutron stars, and black holes. The method combines traditional ground-based photometry with astrometric and photometric measurements by the Space Interferometry Mission (SIM) in solar orbit. Using a related technique SIM can also obtain accurate (>~ 1%) mass measurement of a dozen or so nearby stars, thus enabling precision tests of stellar models. Binary lenses can give rise to dramatic and easily detectable microlensing signatures, even for large mass ratios. This makes microlensing a potentially powerful probe of the companion mass distribution, especially in the Galactic bulge where this function is difficult to probe by other techniques.

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M Dwarfs from Hubble Space Telescope Star Counts. IV

We study a sample of about 1400 disk M dwarfs that are found in 148 fields observed with the Wide Field Camera 2 (WFC2) on the Hubble Space Telescope and 162 fields observed with pre-repair Planetary Camera 1 (PC1), of which 95 of the WFC2 fields are newly analyzed. The method of maximum likelihood is applied to derive the luminosity function and the Galactic disk parameters. At first, we use a local color-magnitude relation and a locally determined mass-luminosity relation in our analysis. The results are consistent with those of previous work but with considerably reduced statistical errors. These small statistical errors motivate us to investigate the systematic uncertainties. Considering the metallicity gradient above the Galactic plane, we introduce a modified color-magnitude relation that is a function of Galactic height. The resultant M dwarf luminosity function has a shape similar to that derived using the local color-magnitude relation but with a higher peak value. The peak occurs at $M_V \sim 12$ and the luminosity function drops sharply toward $M_V \sim 14$. We then apply a height-dependent mass-luminosity function interpolated from theoretical models with different metallicities to calculate the mass function. Unlike the mass function obtained using local relations, which has a power-law index $α= 0.47$, the one derived from the height-dependent relations tends to be flat ($α= -0.10$). The resultant local surface density of disk M dwarfs (12.2 +/- 1.6 M_sun pc^{-2}) is somewhat smaller than the one obtained using local relations (14.3 +/- 1.3 M_sun pc^{-2}). Our measurement favors a short disk scale length, H = 2.75 +/- 0.16 (statistical) +/- 0.25 (systematic) kpc.

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Theory of Microlensing

I present a somewhat selective review of microlensing theory, covering five major areas: 1) the derivation of the basic formulae, 2) the relation between the observables and the fundamental physical parameters, 3) binaries, 4) astrometric microlensing, and 5) femtolensing.

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Nearby Microlensing Events - Identification of the Candidates for the SIM

The Space Interferometry Mission (SIM) is the instrument of choice when it comes to observing astrometric microlensing events where nearby, usually high-proper-motion stars (``lenses''), pass in front of more distant stars (``sources''). Each such encounter produces a deflection in the source's apparent position that when observed by SIM can lead to a precise mass determination of the nearby lens star. We search for lens-source encounters during the 2005-2015 period using Hipparcos, ACT and NLTT to select lenses, and USNO-A2.0 to search for the corresponding sources, and rank these by the SIM time required for a 1% mass measurement. For Hipparcos and ACT lenses, the lens distance and lens-source impact parameter are precisely determined so the events are well characterized. We present 32 candidates beginning with a 61 Cyg A event in 2012 that requires only a few minutes of SIM time. Proxima Centauri and Barnard's star each generate several events. For NLTT lenses, the distance is known only to a factor of 3, and the impact parameter only to 1''. Together, these produce uncertainties of a factor ~10 in the amount of SIM time required. We present a list of 146 NLTT candidates and show how single-epoch CCD photometry of the candidates could reduce the uncertainty in SIM time to a factor of ~1.5.

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The Ratio of Total to Selective Extinction Toward Baade's Window

We measure the ratio of total to selective extinction, R_{VI}=A_V/E(V-I), toward Baade's Window by comparing the VIK colors of 132 Baade's Window G and K giants from Tiede, Frogel, & Terndrup with the solar-neighborhood (V-I),(V-K) relation from Bessell & Brett. We find R_{VI}=2.283 +/- 0.016, and show that our measurement has no significant dependence on stellar type from G0 to K4. Adjusting the Paczynski et al. determination of the centroid of the dereddened Baade's Window clump for this revised value of $R_{VI}$, we find I_{0,RC}=14.43 and (V-I)_{0,RC}=1.058. This implies a distance to the Baade's Window clump of d_{BW} = 8.63 +/- 0.16 kpc, where the error bar takes account of statistical but not systematic uncertainties.

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A Cluster of Black Holes at the Galactic Center

If the stellar population of the bulge contains black holes formed in the final core collapse of ordinary stars with M \ga 30 M_{\odot}, then about 25,000 stellar mass black holes should have migrated by dynamical friction into the central parsec of the Milky Way, forming a black hole cluster around the central supermassive black hole. These black holes can be captured by the central black hole when they randomly reach a highly eccentric orbit due to relaxation, either by direct capture (when their Newtonian peribothron is less than 4 Schwarzschild radii), or after losing orbital energy through gravitational waves. The overall depletion timescale is ~ 30 Gyr, so most of the 25,000 black holes remain in the central cluster today. The presence of this black hole cluster would have several observable consequences. First, the low-mass, old stellar population should have been expelled from the region occupied by the black hole cluster due to relaxation, implying a core in the profile of solar-mass red giants with a radius of ~ 2 pc (i.e., 1'). The observed central density cusp (which has a core radius of only a few arc seconds) should be composed primarily of young (\la 1 Gyr) stars. Second, flares from stars being captured by supermassive black holes in other galaxies should be rarer than usually expected because the older stars will have been expelled from the central regions by the black hole clusters of those galaxies. Third, the young (\la 2 Gyr) stars found at distances ~ 3 - 10 pc from the Galactic center should be preferentially on highly eccentric orbits. Fourth, if future high-resolution $K$-band images reveal sources microlensed by the Milky Way's central black hole, then the cluster black holes could give rise to secondary (``planet-like'') perturbations on the main event.

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A Natural Formalism for Microlensing

If the standard microlensing geometry is inverted so that the Einstein ring is projected onto the observer plane rather than the source plane, then the relations between the observables (θ_E,\tilde r_E) and the underlying physical quantities (M,π_rel) become immediately obvious. Here θ_E and \tilde r_E are the angular and projected Einstein radii, M is the mass of the lens, and π_rel is the lens-source relative parallax. I recast the basic formalism of microlensing in light of this more natural geometry and in terms of observables. I then find that the relations between observable and physical quantities assume an exceptionally simple form. In an appendix, I propose a set of notational conventions for microlensing.

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Superluminal Caustics of Close, Rapidly-Rotating Binary Microlenses

The two outer triangular caustics (regions of infinite magnification) of a close binary microlens move much faster than the components of the binary themselves, and can even exceed the speed of light. When $ε> 1$, where $εc$ is the caustic speed, the usual formalism for calculating the lens magnification breaks down. We develop a new formalism that makes use of the gravitational analog of the Liénard-Wiechert potential. We find that as the binary speeds up, the caustics undergo several related changes: First, their position in space drifts. Second, they rotate about their own axes so that they no longer have a cusp facing the binary center of mass. Third, they grow larger and dramatically so for $ε>> 1$. Fourth, they grow weaker roughly in proportion to their increasing size. Superluminal caustic-crossing events are probably not uncommon, but they are difficult to observe.

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Astrometric Resolution of Severely Degenerate Binary Microlensing Events

We investigate whether the "close/wide" class of degeneracies in caustic-crossing binary microlensing events can be broken astrometrically. Dominik showed that these degeneracies are particularly severe because they arise from a degeneracy in the lens equation itself rather than a mere "accidental" mimicking of one light curve by another. A massive observing campaign of five microlensing collaborations was unable to break this degeneracy photometrically in the case of the binary lensing event MACHO 98-SMC-1. We show that this degeneracy indeed causes the image centroids of the wide and close solutions to follow an extremely similar pattern of motion during the time when the source is in or near the caustic. Nevertheless, the two image centroids are displaced from one another and this displacement is detectable by observing the event at late times. Photometric degeneracies therefore can be resolved astrometrically, even for these most severe cases.

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Binary Black Hole Mergers from Planet-like Migrations

If supermassive black holes (BHs) are generically present in galaxy centers, and if galaxies are built up through hierarchical merging, BH binaries are at least temporary features of most galactic bulges. Observations suggest, however, that binary BHs are rare, pointing towards a binary lifetime far shorter than the Hubble time. We show that, regardless of the detailed mechanism, all stellar-dynamical processes are insufficient to reduce significantly the orbital separation once orbital velocities in the binary exceed the virial velocity of the system. We propose that a massive gas disk surrounding a BH binary can effect its merger rapidly, in a scenario analogous to the orbital decay of super-jovian planets due to a proto-planetary disk. As in the case of planets, gas accretion onto the secondary (here a supermassive BH) is integrally connected with its inward migration. Such accretion would give rise to quasar activity. BH binary mergers could therefore be responsible for many or most quasars.

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