arXiv subjects

Cheongho Han

Publications and source records attributed to Cheongho Han.

At least 235 records · Page 13Linked to original sources

arXiv2000

Comparison of the Two Followup Observation Strategies for Gravitational Microlensing Planet Searches

There are two different strategies of followup observations for the detection of planets by using microlensing. One is detecting the light curve anomalies affected by the planetary caustic from continuous monitoring of all events detected by microlensing survey programs (type I strategy) and the other is detecting anomalies near the peak amplification affected by the central caustic from intensive monitoring of high amplification events (type II strategy). It was shown by Griest & Safizadeh that the type II strategy yields high planet detection efficiency per event. However, it is not known the planet detection rate by this strategy can make up a substantial fraction of the total rate. In this paper, we estimate the relative planet detection rates expected under the two followup observation strategies. From this estimation, we find that the rate under the type II strategy is substantial and will comprise $\sim 1/4$ -- 1/2 of the total rate. We also find that compared to the type I strategy the type II strategy is more efficient in detecting planets located outside of the lensing zone. We determine the optimal monitoring frequency of the type II strategy to be $\sim 20$ times/night, which can be easily achieved by the current microlensing followup programs even with a single telescope.

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arXiv2000

Colour Change Measurements of Gravitational Microlensing Events by Using the Difference Image Analysis Method

Detecting colour changes of a gravitational microlensing event induced by the limb-darkened extended source effect is important to obtain useful information both about the lens and source star. However, precise measurements of the colour changes are hampered by blending, which also causes colour changes of the event. In this paper, we show that although the colour change measured from the subtracted image by using the recently developed photometric method of the ``difference image analysis'' (DIA) differs from the colour change measured by using the conventional method based on the extraction of the individual source stars' point spread functions, the curve of the colour changes (colour curve) constructed by using the DIA method enables one to obtain the same information about the lens and source star, but with significantly reduced uncertainties due to the absence of blending. We investigate the patterns of the DIA colour curves for both single lens and binary lens events by constructing colour change maps.

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arXiv2000

Additional Information from Astrometric Gravitational Microlensing Observations

Astrometric observations of microlensing events were originally proposed to determine the lens proper motion with which the physical parameters of lenses can be better constrained. In this proceeding, we demonstrate that besides this original usage astrometric microlensing observations can be additionally used in obtaining various important information about lenses. First, we demonstrate that the lens brightness can be determined with astrometric observations, enabling one to know whether the event is caused by a bright star or a dark lens. Second, we show that with additional information from astrometric observations one can resolve the ambiguity of the photometric binary lens fit and thus uniquely determine the binary lens parameters. Finally, we propose two astrometric methods that can resolve the degeneracy in the photometric lens parallax determination. Since one can measure both the proper motion and the parallax by these methods, the lens parameters of individual events can be uniquely determined.

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arXiv2000

Better Astrometric Deblending of Gravitional Microlensing Events by Using the Difference Image Analysis Method

Due to the choice of very dense star fields for a higher event rate, the current microlensing searches suffer from large uncertainties caused by blending effect. To measure light variations of microlensing events free from the effect of blending, a newly developed method of Differential Image Analysis (DIA) was proposed for microlensing searches. However, even with the light variation curve obtained by using the DIA method, dramatic reduction of the uncertainty in the determined Einstein time scale is not expected due to the difficulty in determining the baseline flux of a source star. However, we show in this paper that if the blending effect is investigated by detecting the shift of a source star image centroid, the DIA method will allow one to detect the blending effect with a significantly enhanced efficiency compared the efficiency of the current method based on PSF photometry (PSF method). This is because for a given event the centroid shift measurable by using the DIA method, $δθ_{\rm c,DIA}$, is {\it always} larger than the centroid shift measurable by using the PSF method, $δθ_{\rm c,PSF}$. We find that the ratio $δθ_{\rm c,DIA}/δθ_{\rm c,DIA}$ rapidly increases with increasing fraction of blended light. In addition, for events affected by the same fraction of blended light, the ratio $δθ_{\rm c,DIA}/ δθ_{\rm c,DIA}$ is larger for the event with a lower amplification. Therefore, centroid shift measurements by using the DIA method will be an efficient method to detect the blending effect especially of highly blended events, for which the uncertainties in the determined Einstein time scale are large, as well as of low amplification events, for which the current method is highly inefficient.

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arXiv2000

Detection of Stellar Spots from the Observations of Caustic-Crossing Binary-Lens Gravitational Microlensing Events

Recently, Heyrovský & Sasselov (1999) investigated the sensitivity of {\it single-lens} gravitational microlensing event light curves to small spots and found that during source transit events spots can cause deviations in amplification larger than 2%, and thus be detectable. In this paper, we explore the feasibility of spot detection from the observations of {\it caustic-crossing binary-lens} microlensing events instead of single-lens events. For this we investigate the sensitivity of binary-lens event light curves to spots and compare it to that of single-lens events. From this investigation, we find that during caustic crossings the fractional amplification deviations of microlensing light curves from those of spotless source events are equivalent to the deviations of single-lens events, implying that spots can also be detected with a similar photometric precision to that required for spot detection by observing single-lens events. We discuss the relative advantages of observing caustic-crossing binary-lens events over the observations of single-lens events in detecting stellar spots.

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arXiv2000

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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arXiv1999

Chromaticity of Gravitational Microlensing Events

In this paper, we investigate the color changes of gravitational microlensing events caused by the two different mechanisms of differential amplification for a limb-darkened extended source and blending. From this investigation, we find that the color changes of limb-darkened extended source events (color curves) have dramatically different characteristics depending on whether the lens transits the source star or not. We show that for a source transit event, the lens proper motion can be determined by simply measuring the turning time of the color curve instead of fitting the overall color or light curves. We also find that even for a very small fraction of blended light, the color changes induced by the blending effect is equivalent to those caused by the limb-darkening effect, causing serious distortion in the observed color curve. Therefore, to obtain useful information about the lens and source star from the color curve of a limb-darkened extended source event, it will be essential to eliminate or correct for the blending effect. We discuss about the methods for the efficient correction of the blending effect.

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arXiv1999

Distribution of Caustic-Crossing Intervals for Galactic Binary-Lens Microlensing Events

Detection of caustic crossings of binary-lens gravitational microlensing events is important because by detecting them one can obtain useful information both about the lens and source star. In this paper, we compute the distribution of the intervals between two successive caustic crossings, $f(t_{\rm cc})$, for Galactic bulge binary-lens events to investigate the observational strategy for the optimal detection and resolution of caustic crossings. From this computation, we find that the distribution is highly skewed toward short $t_{\rm cc}$ and peaks at $t_{\rm cc}\sim 1.5$ days. For the maximal detection of caustic crossings, therefore, prompt initiation of followup observations for intensive monitoring of events will be important. We estimate that under the strategy of the current followup observations with a second caustic-crossing preparation time of $\sim 2$ days, the fraction of events with resolvable caustic crossing is $\sim 80%$. We find that if the followup observations can be initiated within 1 day after the first caustic crossing by adopting more aggressive observational strategies, the detection rate can be improved into $\sim 90%$.

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arXiv1999

On the Baseline Flux Determination of Microlensing Events Detectable with the Difference Image Analysis Method

To improve photometric precision by removing blending effect, a newly developed technique of difference image analysis (DIA) is adopted by several gravitational microlensing experiment groups. However, the principal problem of the DIA method is that, by its nature, it has difficulties in measuring the baseline flux $F_0$ of a source star, causing degeneracy problem in determining the lensing parameters of an event. Therefore, it is often believed that the DIA method is not as powerful as the classical method based on the PSF photometry in determining the Einstein time scales $t_{\rm E}$ of events. In this paper, we demonstrate that the degeneracy problem in microlensing events detectable from the searches by using the DIA method will not be as serious as it is often worried about. This is because a substantial fraction of events will be high amplification events for which the deviations of the amplification curves constructed with the wrong baseline fluxes from their corresponding best-fit standard amplification curves will be considerable even for a small amount of the fractional baseline flux deviation $ΔF_0/F_0$. With a model luminosity function of source stars and under realistic observational conditions, we find that $\sim 30%$ of detectable Galactic bulge events are expected to have high amplifications and their baseline fluxes can be determined with uncertainties $ΔF_0/F_0\leq 0.5$.

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arXiv1999

Improved Detection Rates for Close Binaries Via Astrometric Observations of Gravitational Microlensing Events

In addition to constructing a Galactic matter mass function free from the bias induced by the hydrogen-burning limit, gravitational microlensing allows one to construct a mass function which is less affected by the problem of unresolved binaries (Gaudi & Gould). However, even with the method of microlensing, the photometric detection of binaries is limited to binary systems with relatively large separations of $b\gtrsim 0.4$ of their combined Einstein ring radius, and thus the mass function is still not totally free from the problem of unresolved binaries. In this paper, we show that by detecting distortions of the astrometric ellipse of a microlensing event with high precision instruments such as the {\it Space Interferometry Mission}, one can detect close binaries at a much higher rate than by the photometric method. We find that by astrometrically observing microlensing events, $\sim 50%$ of binaries with separations of $0.1r_{\rm E}$ can be detected with the detection threshold of 3%. The proposed astrometric method is especially efficient at detecting very close binaries. With a detection threshold of 3% and a rate of 10%, one can astrometrically detect binaries with separations down to $\sim 0.01r_{\rm E}$.

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arXiv1999

Astrometric Properties of Gravitational Binary-Microlens Events and Their Applications

In this paper, we study the astrometric properties of gravitational microlensing events caused by binary lenses. By investigating the centroid shifts for various types of binary-lens events, we find that the deviations of the centroid shift trajectories from the elliptical ones of single-lens events are characterized by distortions, twistings, and big jumps. We study the conditions of binary-lens system configurations and source star trajectories for individual types of deviations. We find dramatic differences in the astrometric centroid shifts for binary-lens microlensing events that would be degenerate had their parameters been determined photometrically. Therefore, when additional astrometric observations of a binary-lens event are available, one can resolve the ambiguity of the binary-lens fit, and uniquely determine the binary-lens parameters.

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arXiv1999

Identification of Bright Lenses from the Astrometric Observations of Gravitational Microlensing Events

When a source star is gravitationally microlensed by a dark lens, the centroid of the source star image is displaced relative to the position of the unlensed source star with an elliptical trajectory. Recently, routine astrometric follow-up measurements of these source star image centroid shifts by using high precision interferometers are proposed to measure the lens proper motion which can resolve the lens parameter degeneracy in the photometrically determined Einstein time scale. When an event is caused by a bright lens, on the other hand, the astrometric shift is affected by the light from the lens, but one cannot identify the existence of the bright lens from the observed trajectory because the resulting trajectory of the bright lens event is also an ellipse. As results, lensing parameters determined from the trajectory differ from those of a dark lens event, causing wrong identification of lens population. In this paper, we show that although the shape and size of the astrometric centroid shift trajectory are changed due to the bright lens, the angular speed of centroid shifts around the apparent position of the unlensed source star is not affected by the lens brightness. Then, one can identify the existence of the bright lens and determine its brightness by comparing the lens parameters determined from the angular speed curve with those determined from the trajectory of observed centroid shifts. Once the lens brightness is determined, one can correct for the lens proper motion. Since the proposed method provides both information about the lens brightness (dark or bright) and the corrected values of the physical parameters of the lens, one can significantly better constrain the nature of MACHOs.

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arXiv1999

Analytic Relations between the Observed Gravitational Microlensing Parameters With and Without the Effect of Blending

When a microlensing light curve is contaminated by blended light from unresolved stars near the line of sight to the lensed star, the light curve shape and corresponding parameterization for the event will differ from the values expected when the event is not affected by blending. As a result, blending makes it difficult to identify the major lens population and to estimate the amount of lensing matter. In order to estimate the effect of blending on the result of lensing experiments, it is, therefore, essential to know how the observed lensing parameters change depending on the fraction of blended light. Previously, the changed lensing parameters were obtained with a statistical method that not only required a large amount of computation time but also was prone to uncertainty. In this paper, we derive analytic relations between the lensing parameters with and without the effect of blending. By using these relations, we investigate the dependence of the observed lensing parameters on the amount of blended light, the impact parameter, and the threshold amplification for event detection.

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arXiv1999

On the Intrinsic Bias in detecting Caustic Crossings between Galactic Halo and Self-lensing Events in the Magellanic Clouds

In this paper, we investigate the intrinsic bias in detecting caustic crossings between Galactic halo and self-lensing events in the Magellanic Clouds. For this, we determine the region for optimal caustic-crossing detection in the parameter space of the physical binary separations, $\ell$, and the total binary lens mass, $M$, and find that the optimal regions for both populations of events are similar to each other. In particular, if the Galactic halo is composed of lenses with the claimed average mass of $ \sim 0.5 M_\odot$, the optimal binary separation range of Galactic halo events of $3.5 AU\lesssim \ell\lesssim 14 AU$ matches well with that of a Magellanic Cloud self-lensing event caused by a binary lens with a total mass $M\sim 1 M_\odot$; well within the mass range of the most probable lens population of stars in the Magellanic Clouds. Therefore, our computation implies that if the binary fractions and the distributions of binary separations of the two populations of lenses are not significantly different from each other, there is no strong detection bias against Galactic halo caustic-crossing events.

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arXiv1999

Unique Determination of the Physical Parameters of Individual MACHOs from Astrometric Parallax Measurements

The Einstein time scale, which is the only information obtained from current microlensing experiments, results from a complicated combination of the lens parameters that we want to determine. Of the methods for breaking the lens parameter degeneracy, the most promising and generally applicable method is to measure the lens parallax from simultaneous observations of a lensing event from the ground and a heliocentric satellite (Gould 1994). However, the elegant idea of parallax measurement, which was proposed to resolve the lens parameter degeneracy, paradoxically suffers from its own degeneracy due to the ambiguity of the source star trajectory. In this paper, we propose to measure the lens parallax astrometrically by mounting an interferometer instead of a photometer in the proposed parallax satellite. By simultaneously measuring the source star centroid shifts from a geocentric and an additional heliocentric satellite, one can determine the lens parallax without ambiguity. If the already planned {\it Space Interferometry Mission} will be used as one of the satellites, one simply needs to replace the photometer in the parallax satellite with an instrument for astrometric observation. In addition, since the proposed method can measure both the lens parallax and the proper motion at the same time, one can completely break the lens parameter degeneracy, and therefore uniquely determine the physical parameters of individual lenses.

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arXiv1999

An Additional Application of the Space Interferometry Mission to Gravitational Microlensing Experiments

Despite the detection of a large number of gravitational microlensing events, the nature of Galactic dark matter remains very uncertain. This uncertainty is due to two major reasons: the lens parameter degeneracy in the measured Einstein timescale and the blending problem in dense field photometry. Recently, consideration has been given to routine astrometric followup observations of lensing events using the {\it Space Interferometry Mission} (SIM) as a means of breaking the lens parameter degeneracy in microlensing events. In this paper, we show that in addition to breaking the lens parameter degeneracy, SIM observations can also be used to correct for nearly all types of blending. Therefore, by resolving both the problems of the lens parameter degeneracy and blending, SIM observations of gravitational lensing events will significantly better constrain the nature of Galactic dark matter.

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arXiv1998

The Applicability of the Astrometric Method in Determining the Physical Parameters of Gravitational Microlenses

In this paper, we investigate the applicability of the astrometric method to the determination of the lens parameters for gravitational microlensing events toward both the LMC and the Galactic bulge. For this analysis, we investigate the dependency of the astrometrically determined angular Einstein ring radius, $Δ(θ_{\rm E}/θ_{\rm E,0})$, on the lens parameters by testing various types of events. In addition, by computing $Δ(θ_{\rm E}/θ_{\rm E,0})$ for events with lensing parameters which are the most probable for a given lens mass under the standard models of Galactic matter density and velocity distributions, we determine the expected distribution of the uncertainties as a function of lens mass. From this study, we find that the values of the angular Einstein ring radius are expected to be measured with uncertainties $Δ(θ_{\rm E}/θ_{\rm E,0}) \lesssim 10%$ up to a lens mass of $M\sim 0.1 M_\odot$ for both Galactic disk-bulge and halo-LMC events with a moderate observational strategy. The uncertainties are relatively large for Galactic bulge-bulge self-lensing events, $Δ(θ_{\rm E}/θ_{\rm E,0}) \sim 25%$ for $M\sim 0.1 M_\odot$, but they can be substantially reduced by adopting more aggressive observational strategies. We also find that although astrometric observations can be performed for most photometrically detected Galactic bulge events, a significant fraction ($\sim 45%$) of LMC events cannot be astrometrically observed due to the faintness of their source stars.

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arXiv1998

The Effect of Bright Lenses in the Astrometric Measurements of MACHO Proper Motion

In current microlensing experiments, the information about the physical parameters of individual lenses are obtained from the Einstein timescales. However, the nature of MACHOs is still very uncertain despite the large number of detected events. This uncertainty is mainly due to the degeneracy of the lens parameters in the measured Einstein timescales. The degeneracy can be lifted in a general fashion if the angular Einstein ring radius $θ_{\rm E}$, and thus the MACHO proper motion, can be measured by conducting accurate astrometric measurements of centroid displacement in the source star image. In this paper, we analyze the influence of bright lenses on the astrometric measurements of the centroid displacement and investigate this effect on the determination of $θ_{\rm E}$. We find that if an event is caused by a bright lens, the centroid displacement is distorted by the flux of the lens and resulting astrometric ellipse becomes rounder and smaller with increasing lens brightness, causing an incorrect determination of the angular Einstein ring radius. A lens-blended event cannot be distinguished from a dark lens event from the trajectory of the measured centroid displacements alone because both events have elliptical trajectories: the degeneracy between dark and bright lens events. We also find that even with information from the analysis of the light curve of the event it will still be difficult to resolve the degeneracy caused by the bright lens because the light curve is also affected by lens blending.

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