arXiv subjects

Andrew Gould

Publications and source records attributed to Andrew Gould.

At least 379 records · Page 21Linked to original sources

arXiv1996

Star Counts From HST: Implications for Dark Matter

Star counts made with the Hubble Space Telescope (HST) probe four populations that are important for dark matter: disk, halo, bulge, and intergalactic. The disk mass function falls for masses M<0.6 Msun in sharp contrast to the rising Salpeter function usually assumed. The amount of ``observed'' disk material is therefore lower than commonly believed which implies the need for disk dark matter. Halo stars contribute no more than a few percent of the dark matter. Disk and halo together contribute no more than 10% of the observed microlensing optical depth toward the Large Magellanic Cloud. The bulge luminosity function is similar to that of the disk down to $M_V ~ 10$. If this similarity continues to the bottom of the main sequence, the bulge microlensing events can only be explained by a large population of brown dwarfs. Intergalactic stars in the Local Group have a density lower than the local halo density by at least $10^{-3.5}$.

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arXiv1996

M Dwarfs From Hubble Space Telescope Star Counts III: The Groth Strip

We analyze the disk M dwarfs found in 31 new fields observed with the Wide Field Camera (WFC2) on the Hubble Space Telescope (HST) together with the sample previously analyzed from 22 WFC2 fields and 162 prerepair Planetary Camera (PC1) fields. The new observations, which include the 28 high-latitude fields comprising the Large Area Multi-Color Survey (``Groth Strip''), increase the total sample to 337 stars, and more than double the number of late M dwarfs (M_V>13.5) from 23 to 47. The mass function changes slope at M~0.6 Msun, from a near-Salpeter power-law index of α=-1.21 to α=0.44. In both regimes the mass function at the Galactic plane is given by ${d^3 N / d\log M d M_V d V} = 8.1\times 10^{-2}\pc^{-3} ({M / 0.59 M_\odot})^α$. The correction for secondaries in binaries changes the low-mass index from α=0.44 to α\sim 0.1. If the Salpeter slope continued to the hydrogen-burning limit, we would expect 500 stars in the last four bins (14.5<M_V<18.5), instead of the 25 actually detected. The explanation of the observed microlensing rate towards the Galactic bulge requires either a substantial population of bulge brown dwarfs or that the disk and bulge mass functions are very different for stars with M~< 0.5 Msun.

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arXiv1996

Microlensing: Prospects for the Future

Four ongoing microlensing experiments have produced important new results but also big puzzles, the major one being that the expected classes of lenses cannot account for the observed distribution of time scales. I discuss future experiments that could resolve these puzzles. By far the most important would be to launch a parallax satellite into solar orbit. I also discuss a number of non-dark-matter applications of microlensing, including searching for planets, measuring the rotation speeds of giant stars, and imaging a black hole at the center of a quasar.

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arXiv1996

Measuring the Rotation Speed of Giant Stars From Gravitational Microlensing

During some gravitational lensing events, the lens transits the face of the star. This causes a shift in the apparent radial velocity of the star which is proportional to its rotation speed. It also changes the magnification relative to what would be expected for a point source. By measuring both effects, one can determine the rotation parameter $v\sin i$. The method is especially useful for K giant stars because these have turbulent velocities that are typically large compared with their rotation speed. By making a series of radial velocity measurements, one can typically determine $v\sin i$ to the same accuracy as the individual radial velocity measurements. There are approximately 10 microlensing transit events per year which would be suitable to make these measurements.

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arXiv1996

Planet Parameters in Microlensing Events

A planetary microlensing event occurs when a planet perturbs one of the two images created in a point-mass microlensing event, causing a deviation from the standard Paczyński curve. Determination of the two physical parameters that can be extracted from a planetary microlensing event, the planet/star mass ratio q, and the planet/star separation in units of the stellar Einstein ring, $y_p$, is hampered by several types of degeneracies. There are two distinct and qualitatively different classes of planetary events: major and minor image perturbations. For major image perturbations, there is a potentially crippling continuous degeneracy in q which is of order $δ_d^{-1}$, where $δ_d$ is the maximum fractional deviation of the planetary perturbation. Since the threshold of detection is expected to be $δ_d \sim 5%$, this degeneracy in q can be a factor of $\sim 20$. For minor image perturbations, the continuous degeneracy in q is considerably less severe, and is typically less than a factor 4. We show that these degeneracies can be resolved by observations from dedicated telescopes on several continents together with optical/infrared photometry from one of these sites. There also exists a class of discrete degeneracies. These are typically easy to resolve given good temporal coverage of the planetary event. Unambiguous interpretation of planetary microlensing events requires the resolution of both types of degeneracy. We describe the degeneracies in detail and specify the situations in which they are problematic. We also describe how individual planet masses and physical projected separations can be measured.

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arXiv1996

Satellite Parallaxes of Lensing Events Towards the Galactic Bulge

In order to understand the nature of the lenses that generate microlensing events, one would like to measure their mass, distance, and velocity. Unfortunately, current microlensing experiments measure only one parameter of the events, the characteristic timescale, which is a combination of the underlying physical parameters. Other methods are required to extract additional information. Parallax measurements using a satellite in an Earth-like orbit yield the projected velocity of the lens: ${\bf{\tilde v}} ={\bf{v}}/(1-z)$, where ${\bf{v}}$ is the transverse velocity (speed and direction) of the lens relative to the Earth-source line of sight, and $z$ is the ratio of the distances to the lens and the source. A measurement of ${\bf{\tilde v}}$ could distinguish between lenses belonging to the bulge and disk populations. We show that for photometric precisions of 1% to 2%, it is possible to measure the projected speed, $\tilde v$, to an accuracy of $\leq 10%$ for over 70% of disk lenses and over 60% of bulge lenses. For measuring the projected velocity ${\bf{\tilde v}}$, the percentages are 40% and {30%}, respectively. We find lines of sight $> 2^{\circ}$ away from the ecliptic are preferable, and an Earth-satellite separation in the range $0.7 {\rm{AU}} - 1.9{\rm{AU}}$ is optimal. The requirements of the satellite for measuring the projected velocities of events towards the bulge are similar to those for measurements toward the LMC.

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arXiv1996

The Hollywood Strategy for Microlensing Detection of Planets

Follow the big stars! I review the theory of detection and parameter measurement of planetary systems by follow-up observations of ongoing microlensing events. Two parameters can generically be measured from the event itself: the planet/star mass ratio, $q$, and the planet/star separation in units of the Einstein ring. I emphasize the advantages of monitoring events with giant-star sources which are brighter (thus easier to monitor) and bigger (thus offering the prospect of measuring an additional parameter from finite-source effects: the proper motion $μ$). There is potentially a strong degeneracy between $q$ and $μ$. I present a simple analytic representation of this degeneracy. I then describe how it can be broken using accurate single-band photometry from observatories around the world, or optical/infrared photometry from a single site, or preferably both. Both types of observations are underway or will be soon. Monitoring of giant-star events seen toward the bulge is also the best way to determine the content and structure of the inner Galaxy.

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arXiv1996

Galactic versus Extragalactic Pixel Lensing Events toward M31

A new type of gravitational microlensing experiment toward a field where stars are not resolved is being developed observationally and theoretically: pixel lensing. When the experiment is carried out toward the M31 bulge area, events may be produced both by Massive Compact Halo Objects (MACHOs) in our Galactic halo and by lenses in M31. We estimate that $\sim 10-15\%$ of the total events are caused by Galactic halo MACHOs assuming an all-MACHO halo. If these Galactic events could be identified, they would provide us with an important constraint on the shape of the halo. We test various observables that can be used for the separation of Galactic halo/M31 events. These observables include the Einstein time scale, the effective duration of an event, and the flux at the maximum amplification, but they cannot be used to separate each population events. However, we find that most high maximum-flux Galactic halo events can be isolated through a satellite-based measurement of the flux difference caused by the parallax effect. For the detection of the flux difference, it is required to monitor events with an exposure time of $\sim 20\ {\rm min}$ by a 0.5 m telescope mounted on a satellite. Such observations could be carried out as a minor component of a mission aimed primarily at events seen toward the Galactic bulge and Large Magellanic Cloud. In addition, proper motion can be used to isolate Galactic halo/M31 events, but only for $\sim 5\%$ of high signal-to-noise ratio M31 events and only 1\% of Galactic halo events.

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arXiv1996

Einstein Radii from Binary Lensing Events

We show that the Einstein ring radius and transverse speed of a lens projected on the source plane, $\hat{r}_{\rm e}$ and $\hat{v}$, can be determined from the light curve of a binary-source event, followed by the spectroscopic determination of the orbital elements of the source stars. The determination makes use of the same principle that allows one to measure the Einstein ring radii from finite-source effects. For the case when the orbital period of the source stars is much longer than the Einstein time scale, $P\gg t_{\rm e}$, there exists a single two-fold degeneracy in determining $\hat{r}_{\rm e}$. However, when $P \lesssim t_{\rm e}$ the degeneracy can often be broken by making use of the binary-source system's orbital motion. %Once $\hat{r}_{\rm e}$, and thus $\hat{v}$ are determined, one can %distinguish self-lensing events in the Large Magellanic Cloud %from Galactic halo events. For an identifiable 8\% of all lensing events seen toward the Large Magellanic Cloud (LMC), one can unambiguously determine whether the lenses are Galactic, or whether they lie in the LMC itself. The required observations can be made after the event is over and could be carried out for the $\sim 8$ events seen by Alcock et al.\ and Aubourg et al.. In addition, we propose to include eclipsing binaries as sources for gravitational lensing experiments.

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arXiv1996

Finite Source Effects in Microlensing Events

The computation of the magnification of a finite source by an arbitrary gravitational lens can be reduced from a two-dimensional to a one-dimensional integral using a generalization of Stoke's theorem. For a large source lensed by a planetary-system whose planet lies at the position where one of the two images would be in the absence of a planet, the integral can be done analytically. If the planet lies at the position of the major (unperturbed) image, the excess flux is the same as it would be for an isolated planet. If the planet lies at the minor image, there is no excess flux.

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arXiv1996

Detection Rates for Close Binaries Via Microlensing

Microlensing is one of the most promising methods of reconstructing the stellar mass function down to masses even below the hydrogen-burning limit. The fundamental limit to this technique is the presence of unresolved binaries, which can in principle significantly alter the inferred mass function. Here we quantify the fraction of binaries that can be detected using microlensing, considering specifically the mass ratio and separation of the binary. We find that almost all binary systems with separations greater than $b \sim 0.4$ of their combined Einstein ring radius are detectable assuming a detection threshold of $3\%$. For two M dwarfs, this corresponds to a limiting separation of $\gsim 1 \au$. Since very few observed M dwarfs have companions at separations $\lsim 1 \au$, we conclude that close binaries will probably not corrupt the measurements of the mass function. We find that the detectability depends only weakly on the mass ratio. For those events for which individual masses can be determined, we find that binaries can be detected down to $b \sim 0.2$.

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arXiv1996

Femtolens Imaging of a Quasar Central Engine Using a Dwarf Star Telescope

We show that it is possible to image the structure of a distant quasar on scales of $\sim 1\,$AU by constructing a telescope which uses a nearby dwarf star as its ``primary lens'' together with a satellite-borne ``secondary''. The image produced by the primary is magnified by $\sim 10^5$ in one direction but is contracted by 0.5 in the other, and therefore contains highly degenerate one-dimensional information about the two-dimensional source. We discuss various methods for extracting information about the second dimension including ``femtolens interferometry'' where one measures the interference between different parts of the one-dimensional image with each other. Assuming that the satellite could be dispatched to a position along a star-quasar line of sight at a distance $r$ from the Sun, the nearest available dwarf-star primary is likely to be at $\sim 15\,\pc\,(r/40\,\rm AU)^{-2}$. The secondary should consist of a one-dimensional array of mirrors extending $\sim 700\,$m to achieve 1 AU resolution, or $\sim 100\,$m to achieve 4 AU resolution.

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arXiv1996

Les Microlentilles Gravitationnelles

Je presente une revue des microlentilles gravitationnelles en quatre lecons. Dans un premier temps, je discute la theorie des microlentilles dans le contexte general des lentilles, en incluant les effets de la taille finie des sources, de la parallaxe, et du retard temporel entre les images. Dans la deuxieme lecon, j'analyse les experiences courantes. Je montre qu'il n'est pas possible d'expliquer les evenements observes avec les etoiles connues, que ce soit en direction du bulbe ou du Grand Nuage de Magellan. Je decris quelques nouvelles experiences qui pourraient nous reveler les caracteristiques des objets detectes. Le troisieme sujet porte sur la methode des pixels, inventee pour observer des evenements de microlentilles sur des sources non resolues. Je presente une analyse generale de la methode, en incluant des problemes d'alignement geometrique, photometrique, et de PSF, du rapport signal sur bruit, et de la nature des informations tirees des observations. Je presente un rapport sur le progres des experiences actuelles et je discute de deux idees pour rechercher des objets sombres dans l'amas de Virgo et des `microlentilles extremes' dans le bulbe. Pour finir, je parle de l'avenir des microlentilles. J'explique comment on peut les utiliser pour rechercher des planetes, pour mesurer les vitesses transverses de galaxies et les vitesses de rotation d'etoiles geantes, et pour rechercher les objets de la masse d'une comete se trouvant de l'autre cote de l'univers. Ce texte est publie sous forme de rapport interne du Laboratoire de Physique Corpusculaire du College de France (LPC 96-23). Il inclue une copie des transparents de ces quatres lecons, copie disponible aupres de Daniele Levaillant: levaillant@cdf.in2p3.fr

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arXiv1996

Hubble Deep Field Constraint on Baryonic Dark Matter

We use a new technique to search for faint red stars in the Hubble Deep Field (HDF) imaged by the Wide Field Camera (WFC2) on the {\it Hubble Space Telescope}. We construct a densely sampled stellar light profile from a set of undersampled images of bright stars in a low-latitude field. Comparison of this stellar light profile to densely sampled profiles of individual objects in the HDF constructed from multiple undersampled dithers allows us to distinguish unambiguously between stars and galaxies to $I=26.3$. We find no stars with $V-I>1.8$ in the outer 90\% of the volume probed. This result places strong and general constraints on the $I$ band luminosity of the constituents of the Galactic dark halo: $$M_I > 15.9 + {5\over 3}\log\biggl(f{0.5 M_\odot\over M}\biggr)\qquad (V-I>1.8),$$ where $M$ is the mass of the objects and $f$ is their density as a fraction of the local halo density, taken to be $ρ_0=9\times 10^{-3}\,M_\odot\,\pc^{-3}$. If the halo is made of white dwarfs, this limit implies that these objects have $M_V\gsim 18.4$ and $V-I\gsim 2.5$. That is, they are $\gsim 2$ magnitudes fainter than the end of the disk white dwarf sequence. Faint red dwarfs account for $<1\%$ of the Galactic dark halo for $M_I<14$, and $<6\%$ for $M_I<15$ at the 95\% confidence level. The density of inter-galactic Local Group stars is at least a factor 3000 smaller than the density of local Population II stars.

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arXiv1996

Microlensing and the Stellar Mass Function

Traditional approaches to measuring the stellar mass function (MF) are fundamentally limited because objects are detected based on their luminosity, not their mass. These methods are thereby restricted to luminous and relatively nearby stellar populations. Gravitational microlensing promises to revolutionize our understanding of the MF. It is already technologically feasible to measure the MFs of the Galactic disk and Galactic bulge as functions of position, although the actual execution of this program requires aggressive ground-based observations including infrared interferometry, as well as the launching of a small satellite telescope. Rapid developments in microlensing, including the new technique of ``pixel lensing'' of unresolved stars, will allow one to probe the MF and luminosity function of nearby galaxies. Such observations of M31 are already underway, and pixel-lensing observations of M87 with the {\it Hubble Space Telescope} would permit detection of dark intra-cluster objects in Virgo. Microlensing techniques can also be applied to investigate the star-formation history of the universe and to search for planets with masses as small as the Earth's. Based on an invited talk at the January 1996 AAS meeting in San Antonio. PASP (June 1996) in press, (c) ASP, reproduced with permission.

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arXiv1996

Extreme Microlensing

Extreme microlensing events, defined as events with maximum magnification $A_\max\gsim 200$ are a potentially powerful probe of the mass spectrum and spatial distribution of objects along lines of sight toward the Galactic bulge. About 75 yr${}^{-1}$ such events are expected for main-sequence sources with $I_0<19$. For many of these it is possible to measure both a ``proper motion'' and a ``parallax'' which together would yield individual mass, distance, and transverse-speed determinations of the lensing object. The proper motion is determined from finite-source effects when the lens transits, or nearly transits the source. The parallax is determined by observing the difference in the light curve as seen from two Earth observatories separated by about 1 Earth radius, $R_\oplus$. The size of the parallax effect is $\sim A_\max R_\oplus/\tilde r_e$ where $\tilde r_e$ is the projected Einstein radius. This can be of order 1\%. Detection of candidate events requires a pixel-lensing search of the entire bulge once per day, preferably by at least two observatories on different continents. Follow-up observation must be carried using optical/infrared photometry, with short (e.g.\ 1 minute) exposures on small ($\gsim 1$ m) telescopes. Extreme microlensing observations toward the Large Magellanic Cloud do not appear feasible at the present time.

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arXiv1996

Luminosity Function of the Perigalactocentric Region

We present H and K photometry of 42,000 stars in an area of 250 arcmin$^{2}$ centered on the Galactic center. We use the photometry to construct a dereddened K band luminosity function (LF) for this region, excluding the excessively crowded inner 2' of the Galaxy. This LF is intermediate between the LF of Baade's window and the LF of inner 2' of the Galactic center. We speculate that the bright stars in this region have an age which is intermediate between the starburst population in the Galactic center and the old bulge population. We present the coordinates and mags for 16 stars with K_{0} < 5 for spectroscopic follow up.

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arXiv1996

Theory of Pixel Lensing

Pixel lensing, gravitational microlensing of unresolved stars, is potentially much more sensitive and much more widely applicable than is generally recognized. I give explicit expressions for the pixel noise induced by a time-variable PSF, by photometric and geometric misalignment, and by discrete pixelization, and I show that these can all be reduced below the photon noise. Pixel lensing can be divided into two regimes. In the ``semi-classical'' regime, it is similar to classical lensing in that it measures the time scale of individual events. In the ``spike'' regime, it measures the total optical depth but not individual time scales. I present simple expressions for the boundary between the two regimes and for the event rate in the latter one. These expressions can be used to quickly classify all potential pixel lensing experiments. Pixel lensing can measure the luminosity function as well as the mass function of stars in target galaxies to a distance of a few Mpc. Future space-based pixel lensing could be $\sim 5$ times more effective in the infrared than in the optical, depending on developments in detector technology. Pixel techniques can also be applied to non-pixel-lensing problems including the search for unresolved variable stars and follow up observations of lensing events found in classical lensing searches. To benefit fully from pixel-lensing techniques, follow-up observations should have resolutions of at least 5 pixels per FWHM.

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