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B. Scott Gaudi

Publications and source records attributed to B. Scott Gaudi.

At least 235 records · Page 13Linked to original sources
arXiv2003

Probing Structures of Distant Extrasolar Planets with Microlensing

Planetary companions to the source stars of a caustic-crossing binary microlensing events can be detected via the deviation from the parent light curves created when the caustic magnifies the star light reflecting off the atmosphere or surface of the planets. The magnitude of the deviation is delta_p e_p rho_p^{-1/2}, where e_p is the fraction of starlight reflected by the planet and rho_p is the angular radius of the planet in units of angular Einstein ring radius. Due to the extraordinarily high resolution achieved during the caustic crossing, the detailed shapes of these perturbations are sensitive to fine structures on and around the planets. We consider the signatures of rings, satellites, and atmospheric features on caustic-crossing microlensing light curves. We find that, for reasonable assumptions, rings produce deviations of order 10% delta_p, whereas satellites, spots, and zonal bands produce deviations of order 1% delta_p. We consider the detectability of these features using current and future telescopes, and find that, with very large apertures (>30m), ring systems may be detectable, whereas spots, satellites, and zonal bands will generally be difficult to detect. We also present a short discussion of the stability of rings around close-in planets, noting that rings are likely to be lost to Poynting-Robertson drag on a timescale of order 10^5 years, unless they are composed of large (>>1 cm) particles, or are stabilized by satellites.

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arXiv2002

Angular Radii of Stars via Microlensing

We outline a method by which the angular radii of giant and main sequence stars in the Galactic bulge can be measured to a few percent accuracy. The method combines ground-based photometry of caustic-crossing bulge microlensing events, with a handful of precise astrometric measurements of the lensed star during the event, to measure the angular radius of the source, theta_*. Dense photometric coverage of one caustic crossing yields the crossing timescale dt. Less frequent coverage of the entire event yields the Einstein timescale t_E and the angle phi of source trajectory with respect to the caustic. The photometric light curve solution predicts the motion of the source centroid up to an orientation on the sky and overall scale. A few precise astrometric measurements therefore yield theta_E, the angular Einstein ring radius. Then the angular radius of the source is obtained by theta_*=theta_E(dt/t_E) sin(phi). We argue that theta_* should be measurable to a few percent accuracy for Galactic bulge giant stars using ground-based photometry from a network of small (1m-class) telescopes, combined with astrometric observations with a precision of ~10 microarcsec to measure theta_E. We find that a factor of ~50 times fewer photons are required to measure theta_E to a given precision for binary-lens events than single-lens events. Adopting parameters appropriate to the Space Interferometry Mission (SIM), ~7 min of SIM time is required to measure theta_E to ~5% accuracy for giant sources in the bulge. For main-sequence sources, theta_E can be measured to ~15% accuracy in ~1.4 hours. With 10 hrs of SIM time, it should be possible to measure theta_* to ~5% for \~80 giant stars, or to 15% for ~7 main sequence stars. A byproduct of such a campaign is a significant sample of precise binary-lens mass measurements.

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arXiv2002

Microlensing Searches for Extrasolar Planets: Current Status and Future Prospects

I review results from, and future prospects for, microlensing searches for extrasolar planets. Analyses of well-sampled microlensing light curves by several collaborations have demonstrated that current searches are sensitive to Jupiter-mass planets with few AU separations from M-dwarfs in the Galactic bulge. To date, however, no unambiguous planetary detections have been made. Detailed analysis has shown that this null result implies that <33% of typical stars (i.e. M-dwarfs) in the Galactic bulge have Jupiter-mass companions with separations between 1.5 and 4 AU, and <45% have three-Jupiter-mass companions between 1 and 7 AU. The recent dramatic increase in the number of alerts per year will allow ongoing microlensing searches to probe companion fractions of a few percent within a few years.

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arXiv2002

Survey for Transiting Extrasolar Planets in Stellar Systems (STEPSS): The Frequency of Planets in NGC 1245

We present first results from the Survey for Transiting Extrasolar Planets in Stellar Systems (STEPSS). Our goal is to assess the frequency of close-in extrasolar planets around main-sequence stars in several open clusters. By concentrating on main-sequence stars in clusters of known (and varied) age, metallicity, and stellar density, we will gain insight into how these various properties affect planet formation, migration, and survival. We show preliminary results from our 19 night photometric campaign of the old, solar metallicity cluster NGC 1245. Taking into account the photometric precision, observational window function, transit probability, and total number of stars monitored, we estimate that we should be able to probe planetary companion fractions of <1% for separations of a<0.03 AU. If 1% of the stars in the cluster have Jupiter-sized companions evenly distributed in log(a) between 0.03 and 0.3 AU, we expect to find ~2 transits. A preliminary search of our light curve data has revealed a transit with a depth ~4%. Based on its shape, it is likely to be a grazing binary eclipse rather than a planetary transit, emphasizing the need for high temporal resolution in transit surveys.

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arXiv2002

Gravitational Microlensing Near Caustics II: Cusps

We present a rigorous, detailed study of the generic, quantitative properties of gravitational microlensing near cusp catastrophes. We derive explicit formulas for the total magnification and centroid of the images created for sources outside, on, and inside the cusped caustic. We obtain results on how the image magnifications scale with respect to separation from the cusped caustic for arbitrary source positions. Along the axis of symmetry of the cusp, the total magnification $μ$ scales as $μ\propto u^{-1}$, where $u$ is the distance of the source from the cusp, whereas perpendicular to this axis, $μ\propto u^{-2/3}$. When the source passes through a point $\bu_0$ on a fold arc abutting the cusp, the image centroid has a jump discontinuity; we present a formula for the size of the jump in terms of the local derivatives of the lens potential. The total magnifications for a small extended source located both on, and perpendicular to, the axis of symmetry are also derived, for both uniform and limb darkened surface brightness profiles. We find that the difference in magnification between a finite and point source is $< 5%$ for separations of $> 2.5$ source radii from the cusp point, while the effect of limb-darkening is $< 1%$ in the same range. Our predictions for the astrometric and photometric behavior of both pointlike and finite sources passing near a cusp are illustrated and verified using numerical simulations of the cusp-crossing Galactic binary-lens event MACHO-1997-BUL-28. We discuss several possible applications of our results to Galactic binary lenses and quasar microlensing.

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arXiv2002

Microlensing Constraints on Low-Mass Companions

Microlensing is sensitive to binary, brown dwarf, and planetary companions to normal stars in the Galactic bulge with separations between about 1-10 AU. The accurate, densely-sampled photometry of microlensing events needed to detect planetary companions has been achieved by several follow-up collaborations. Detailed analysis of microlensing events toward the bulge demonstrates that less than 45% of M-dwarfs in the bulge have Jupiter-mass companions between 1 and 5 AU. Detection of binary and brown-dwarf companions using microlensing is considerably easier; however, the interpretation is hampered by their non-perturbative influence on the parent lightcurve. I demonstrate that ~25% of brown-dwarf companions with separations 1-10 AU should be detectable with survey-quality data (~1 day sampling and ~5% photometry). Survey data is more amenable to generic, brute-force analysis methods and less prone to selection biases. An analysis of the ~1500 microlensing events detected by OGLE-III in the next three years should test whether the BD desert exists at separations 1-10 AU from M-dwarfs in the Galactic bulge.

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arXiv2002

Gravitational Microlensing Near Caustics I: Folds

We study the local behavior of gravitational lensing near fold catastrophes. Using a generic form for the lensing map near a fold, we determine the observable properties of the lensed images, focusing on the case when the individual images are unresolved, i.e., microlensing. Allowing for images not associated with the fold, we derive analytic expressions for the photometric and astrometric behavior near a generic fold caustic. We show how this form reduces to the more familiar linear caustic, which lenses a nearby source into two images which have equal magnification, opposite parity, and are equidistant from the critical curve. In this case, the simplicity and high degree of symmetry allows for the derivation of semi-analytic expressions for the photometric and astrometric deviations in the presence of finite sources with arbitrary surface brightness profiles. We use our results to derive some basic properties of astrometric microlensing near folds, in particular we predict for finite sources with uniform and limb darkening profiles, the detailed shape of the astrometric curve as the source crosses a fold. We find that the astrometric effects of limb darkening will be difficult to detect with the currently planned accuracy of the Space Interferometry Mission. We verify our results by numerically calculating the expected astrometric shift for the photometrically well-covered Galactic binary lensing event OGLE-1999-BUL-23, finding excellent agreement with our analytic expressions. Our results can be applied to any lensing system with fold caustics, including Galactic binary lenses and quasar microlensing.

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arXiv2001

Interpreting the M22 Spike Events

Recently Sahu et al., using the Hubble Space Telescope to monitor stars in the direction of the old globular cluster M22, detected six events in which otherwise constant stars brightened by ~50% during a time of <1 day. They tentatively interpret these unresolved events as due to microlensing of background bulge stars by free-floating planets in M22. I show that if these spike events are due to microlensing, the lensing objects are unlikely to be associated with M22, and unlikely to be part of a smoothly distributed Galactic population. Thus either there happens to be a massive, dark cluster of planets along our line-of-sight to M22, or the spike events are not due to microlensing. The lensing planets cannot be bound to stars in the core of M22: if they were closer than 8 AU, the lensing influence of the parent star would have been detectable. Moreover, in the core of M22, all planets with separations > 1 AU would have been ionized by random stellar encounters. Most unbound planets would have escaped the core via evaporation which preferentially affects such low-mass objects. Bound or free-floating planets can exist in the outer halo of M22; however, for reasonable assumptions, the maximum optical depth to such a population falls short of the observed optical depth, tau ~ 3x10^{-6}, by a factor of 5-10. Therefore, if real, these events represent the detection of a significant free-floating Galactic planet population. The optical depth to these planets is comparable to and mutually exclusive from the optical depth to resolved events measured by microlensing survey collaborations toward the bulge, and thus implies a similar additional mass of lensing objects. Such a population is difficult to reconcile with both theory and observations.

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arXiv2001

Microlensing and the Surface Brightness Profile of the Afterglow Image of GRB 000301C

The optical afterglow of Gamma-Ray Burst (GRB) 000301C exhibited a significant, short-timescale deviation from the power-law flux decline expected in the standard synchrotron shock model. Garnavich, Loeb & Stanek found that this deviation was well-fit by an ad hoc model in which a thin ring of emission is microlensed by an intervening star. We revisit the microlensing interpretation of this variability, first by testing whether microlensing of afterglow images with realistic surface brightness profiles (SBPs) can fit the data, and second by directly inverting the observed light curve to obtain a non-parametric measurement of the SBP. We find that microlensing of realistic SBPs can reproduce the observed deviation, provided that the optical emission arises from frequencies above the cooling break. Conversely, if the variability is indeed caused by microlensing, the SBP must be significantly limb-brightened. Specifically, greater than 60% of the flux must originate from the outer 25% of the area of the afterglow image. The latter requirement is satisfied by the best fit theoretical SBP. The underlying optical/infrared afterglow lightcurve is consistent with a model in which a jet is propagating into a uniform medium with the cooling break frequency below the optical band.

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arXiv2001

Resolving the Image of Gamma-Ray Burst Afterglows with Gravitational Microlensing

Microlensing of a gamma-ray burst afterglow by an intervening star can be used to infer the radial structure of the afterglow image. Near the peak of the microlensing event, the outer edge of the image is more highly magnified than its central region, whereas the situation is reversed at later times due to the rapid radial expansion of the image on the sky. Thus, the microlensed afterglow light curve can be inverted to recover the self-similar radial intensity profile of the afterglow image. We calculate the expected errors in the recovered intensity profile as a function of the number of resolution elements, under the assumption that the afterglow and microlensing event parameters are known. For a point-mass lens and uniform source, we derive a simple scaling relation between these parameters and the resultant errors. The afterglow need not be monitored for its entire duration; rather, observations from the peak magnification time t_p of the microlensing event until 7 t_p are sufficient to resolve the majority of the image. Thus, microlensing events can be alerted by relatively infrequent observations of afterglows and then monitored intensively, without significant loss of information about the afterglow intensity profile. The relative intensity profile of about 1% of all afterglows can be measured with 10 resolution elements to an accuracy of 1% in the optical and 10% in the infrared, using 4m-class telescopes. Weak microlensing events with large impact parameters are more common; we estimate that for about 10% of afterglows the image profile may be inverted to a fractional accuracy 20% through frequent optical observations. We also calculate the effects of external shear due to the host galaxy or a binary companion, and contamination by background light from the host galaxy.

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arXiv2000

Planetary Transits Toward the Galactic Bulge

The primary difficulty with using transits to discover extrasolar planets is the low probability a planet has of transiting its parent star. One way of overcoming this difficulty is to search for transits in dense stellar fields, such as the Galactic bulge. Here I estimate the number of planets that might be detected from a monitoring campaign toward the bulge. A campaign lasting 10 nights on a 10 meter telescope (assuming 8 hours of observations per night and a 5'x5' field of view) would detect about 100 planets with radius $\rp=1.5 \rjup$, or about 30 planets with $\rp=1.0 \rjup$, if the frequency and distribution of planets in the bulge is similar to that in the solar neighborhood. Most of these planets will be discovered around stars just below the turn-off, i.e. slightly evolved G-dwarfs. Campaigns involving 1- or 4-m class telescopes are unlikely to discover any planets, unless there exists a substantial population of companions with $\rp > 1.5 \rjup$.

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arXiv2000

Microlensing Constraints on the Frequency of Jupiter Mass Planets

Microlensing is the only technique likely, within the next 5 years, to constrain the frequency of Jupiter-analogs. The PLANET collaboration has monitored nearly 100 microlensing events of which more than 20 have sensitivity to the perturbations that would be caused by a Jovian-mass companion to the primary lens. No clear signatures of such planets have been detected. These null results indicate that Jupiter mass planets with separations of 1.5-3 AU occur in less than 1/3 of systems. A similar limit applies to planets of 3 Jupiter masses between 1-4 AU.

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arXiv2000

Direct Detection of Giant Close-In Planets Around the Source Stars of Caustic-Crossing Microlensing Events

We propose a direct method to detect close-in giant planets orbiting stars in the Galactic bulge. This method uses caustic-crossing binary microlensing events discovered by survey teams monitoring the bulge to measure light from a planet orbiting the source star. When the planet crosses the caustic, it is more magnified than the source star; its light is magnified by two orders of magnitude for Jupiter size planets. If the planet is a giant close to the star, it may be bright enough to make a significant deviation in the light curve of the star. Detection of this deviation requires intensive monitoring of the microlensing light curve using a 10-meter class telescope for a few hours after the caustic. This is the only method yet proposed to directly detect close-in planets around stars outside the solar neighborhood.

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arXiv1999

Detection Efficiencies of Microlensing Datasets to Stellar and Planetary Companions

Microlensing light curves are now being monitored with the precision required to detect small perturbations due to planetary companions of the primary lens. Microlensing is complementary to other planetary search techniques in its potential for measuring the statistical frequency of planets beyond the solar neighborhood. We present an algorithm to analyze the efficiency with which the presence of binaries can be detected in real microlensing datasets. Such an analysis is required in order to draw statistical inferences about lensing companions. We apply the method to artificial (but realistic) data to explore the dependence of detection efficiencies on observational parameters, the impact parameter of the event, the finite size of the background source, the amount of unlensed (blended) light, and the criterion used to define a detection. We find that: (1) the integrated efficiency depends strongly on the impact parameter distribution of the monitored events, (2) calculated detection efficiencies are robust to changes in detection criterion for strict criteria and large mass ratios, (3) finite sources can dramatically alter detection efficiencies to companions with small mass ratios, and (4) accurate determination of the blended light fraction is crucial for the accurate determination of the detection efficiency of individual events. Suggestions are given for addressing complications associated with computing accurate detection efficiencies of real datasets.

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arXiv1998

Microlensing by Multiple Planets in High Magnification Events

Microlensing is increasingly gaining recognition as a powerful method for the detection and characterization of extra-solar planetary systems. Naively, one might expect that the probability of detecting the influence of more than one planet on any single microlensing light curve would be small. Recently, however, Griest & Safizadeh (1998) have shown that, for a subset of events, those with minimum impact parameter $u_{min} \lsim 0.1$ (high magnification events), the detection probability is nearly 100% for Jovian mass planets with projected separations in the range 0.6--1.6 of the primary Einstein ring radius $R_E$, and remains substantial outside this zone. In this Letter, we point out that this result implies that, regardless of orientation, all Jovian mass planets with separations near 0.6--1.6$R_E$ dramatically affect the central region of the magnification pattern, and thus have a significant probability of being detected (or ruled out) in high magnification events. The probability, averaged over all orbital phases and inclination angles, of two planets having projected separations within 0.6--$1.6R_E$ is substantial: 1-15% for two planets with the intrinsic orbital separations of Jupiter and Saturn orbiting around 0.3--1.0$M_\odot$ parent stars. We illustrate by example the complicated magnification patterns and light curves that can result when two planets are present, and discuss possible implications of our result on detection efficiencies and the ability to discriminate between multiple and single planets in high magnification events.

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arXiv1998

Spectrophotometric Resolution of Stellar Atmospheres with Microlensing

Microlensing is a powerful tool for studying stellar atmospheres because as the source crosses regions of formally infinite magnification (caustics) the surfaceof the star is resolved, thereby allowing one to measure the radial intensity profile, both photometrically and spectroscopically. However, caustic crossing events are relatively rare, and monitoring them requires intensive application of telescope resources. It is therefore essential that the observational parameters needed to accurately measure the intensity profile are quantified. We calculate the expected errors in the recovered radial intensity profile as a function of the unlensed flux, source radius, spatial resolution the recovered intensity profile, and caustic crossing time for the two principle types of caustics: point-mass and binary lenses. We demonstrate that for both cases there exist simple scaling relations between these parameters and the resultant errors. We find that the error as a function of the spatial resolution of the recovered profile, parameterized by the number of radial bins, increases as $N_R^{3/2}$, considerably faster than the naive $N_R^{1/2}$ expectation. Finally, we discuss the relative advantages of binary caustic-crossing events and point-lens events. Binary events are more common, easier to plan for, and provide more homogeneous information about the stellar atmosphere. However, a sub-class of point-mass events with low impact parameters can provide dramatically more information provided that they can be recognized in time to initiate observations.

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arXiv1997

Planetary Microlensing Perturbations: True Planets or Binary Sources?

A planetary microlensing event is characterized by a short-lived perturbation to the standard Paczyński curve. Planetary perturbations typically last from a few hours to a day, and have maximum amplitudes, $\dmax$, of $5-20%$ of the standard curve. There exist a subset of binary-source events that can reproduce these main features, and thus masquerade as planetary events. These events require a binary source with a small flux ratio, $\epsil \sim 10^{-2}-10^{-4}$, and a small impact parameter for the fainter source, $β_2 \lsim \epsil / \dmax$. The detection probability of events of this type is $\sim β_2$, and can be as high as $\sim 30%$; this is comparable to planetary detection rates. Thus a sample of planetary-like perturbations could be seriously contaminated by binary-source events, and there exists the possibility that completely meaningless physical parameters would be derived for any given perturbation. Here I derive analytic expressions for a binary-source event in the extreme flux ratio limit, and use these to demonstrate the basic degeneracy between binary source and planet perturbations. I describe how the degeneracy can be broken by dense and accurate sampling of the perturbation, optical/infrared photometry, or spectroscopic measurements.

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