Cheongho Han
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The organizations/institutes from the scholar's latest article
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Cheongho Han has a total of 2 co-authors. Here are the top co-authors by number of shared publications:
- Andrew Gould
Ohio State University
7 shared publications - Vijay K. Narayanan
Dept. of Astronomy The Ohio State University 43210 Columbus OH
1 shared publication
Latest Publications
- Open Access
- 1 May 1997
- Published by American Astronomical Society in The Astrophysical Journal
- Vol. 480 (1) , 196-202
Einstein Radii from Binary‐Source Lensing Events
We show that the Einstein ring radius and transverse speed of a lens projected on the source plane, ˆ re and ˆ 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 ≫ te, there exists a single two-fold degeneracy in determining ˆ re. However, when P ∼ < te the degeneracy can often be broken by making use of the binary-source system's orbital motion. 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 ∼ 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.
- 1 May 1997
- Published by American Astronomical Society in The Astrophysical Journal
- Vol. 480 (1) , 196-202
Open AccessEinstein Radii from Binary‐Source Lensing Events
We show that the Einstein ring radius and transverse speed of a lens projected on the source plane, ˆ re and ˆ 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 ≫ te, there exists a single two-fold degeneracy in determining ˆ re. However, when P ∼ < te the degeneracy can often be broken by making use of the binary-source system's orbital motion. 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 ∼ 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.
- Open Access
- 10 December 1996
- Published by American Astronomical Society in The Astrophysical Journal
- Vol. 473 (1) , 230-239
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 ~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 observ-ables that can be used for the separation of Galactic halo/M31 events. These observables include the Einstein timescale, the effective duration of an event, and the flux at the maximum amplification, but they cannot be used to separate the two populations of 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 ~20 minutes 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 the Large Magellanic Cloud. In addition, proper motion can be used to isolate Galactic halo/M31 events, but for only ~5% of high signal-to-noise ratio M31 events and only 1% of Galactic halo events.
- 10 December 1996
- Published by American Astronomical Society in The Astrophysical Journal
- Vol. 473 (1) , 230-239
Open AccessGalactic 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 ~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 observ-ables that can be used for the separation of Galactic halo/M31 events. These observables include the Einstein timescale, the effective duration of an event, and the flux at the maximum amplification, but they cannot be used to separate the two populations of 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 ~20 minutes 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 the Large Magellanic Cloud. In addition, proper motion can be used to isolate Galactic halo/M31 events, but for only ~5% of high signal-to-noise ratio M31 events and only 1% of Galactic halo events.
- Open Access
The Effects of Amplification Bias in Gravitational Microlensing Experiments
Although a source star is fainter than the detection limit imposed by crowding, it is still possible to detect an event if the star is located in the seeing disk of a bright star is and gravitationally amplified: amplification bias. Using a well-constrained luminosity function, I show that $\sim 40\%$ of events detected toward the Galactic bulge are affected by amplification bias and the optical depth might be overestimated by a factor $\sim 1.7$. In addition, I show that if one takes amplification bias into consideration, the observed time scale distribution matches significantly better, especially in the short time-scale region, with the distribution expected from a mass-spectrum model in which lenses are composed of the known stellar population plus an additional population of brown dwarfs than it is without the effect of the amplification bias.Open AccessThe Effects of Amplification Bias in Gravitational Microlensing Experiments
Although a source star is fainter than the detection limit imposed by crowding, it is still possible to detect an event if the star is located in the seeing disk of a bright star is and gravitationally amplified: amplification bias. Using a well-constrained luminosity function, I show that $\sim 40\%$ of events detected toward the Galactic bulge are affected by amplification bias and the optical depth might be overestimated by a factor $\sim 1.7$. In addition, I show that if one takes amplification bias into consideration, the observed time scale distribution matches significantly better, especially in the short time-scale region, with the distribution expected from a mass-spectrum model in which lenses are composed of the known stellar population plus an additional population of brown dwarfs than it is without the effect of the amplification bias. - Open Access
- 1 August 1996
- Published by American Astronomical Society in The Astrophysical Journal
- Vol. 467, 540
Statistical Determination of the MACHO Mass Spectrum
The mass function of 51 Massive Compact Objects (MACHOs) detected toward the Galactic bulge is statistically estimated from Einstein ring crossing times $t_{ m e}$. For a Gaussian mass function, the best fitting parameters are $langle log (m/M_{odot}) angle = -1.12$ and $sigma_{log (m/M_{odot})} = 0.57$. If the mass function follows a power-law distribution, the best fitting mass cut-off and power are $m_{ m cut} = 0.04 M_{odot}$ and $p = -2.1$. Both mass spectra indicate that a significant fraction of events are caused by MACHOs in substellar mass range. Both best determined mass functions are compared with that obtained from Hubble Space Telescope (HST) observations. The power law is marginally favored ($2.3sigma$) over the Gaussian mass function, and significantly over HST mass function ($5.5sigma$), indicating that MACHOs have a different mass function from stars in the solar neighborhood. In addition, the fact that all the models have very poor fits to the longest four events with $t_{e} geq 70 { m days}$ remains a puzzle.Comment: 18 pages including 5 figures, revise- 1 August 1996
- Published by American Astronomical Society in The Astrophysical Journal
- Vol. 467, 540
Open AccessStatistical Determination of the MACHO Mass Spectrum
The mass function of 51 Massive Compact Objects (MACHOs) detected toward the Galactic bulge is statistically estimated from Einstein ring crossing times $t_{ m e}$. For a Gaussian mass function, the best fitting parameters are $langle log (m/M_{odot}) angle = -1.12$ and $sigma_{log (m/M_{odot})} = 0.57$. If the mass function follows a power-law distribution, the best fitting mass cut-off and power are $m_{ m cut} = 0.04 M_{odot}$ and $p = -2.1$. Both mass spectra indicate that a significant fraction of events are caused by MACHOs in substellar mass range. Both best determined mass functions are compared with that obtained from Hubble Space Telescope (HST) observations. The power law is marginally favored ($2.3sigma$) over the Gaussian mass function, and significantly over HST mass function ($5.5sigma$), indicating that MACHOs have a different mass function from stars in the solar neighborhood. In addition, the fact that all the models have very poor fits to the longest four events with $t_{e} geq 70 { m days}$ remains a puzzle.Comment: 18 pages including 5 figures, revise - Open Access
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.Open AccessEinstein 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. - Open Access
Pixel Lensing Experiment toward the M31 Bulge
I demonstrate that one can detect pixel gravitational microlensing events at the rate $\sim 180\ {\rm events}\ {\rm yr}^{-1}$ and that some fraction of events ($\sim 15$) will be good enough to measure time scales at the $20\%$ level if the experiment is carried out toward the central M31 bulge region with a dedicated 1 m telescope and a $2{\rm K}\times2{\rm K}$ CCD. I also show that the event rate could be significantly increased (up to a factor 6.5) if more aggressive observation strategies are adopted. These aggressive strategies include multiple observation sites, using a bigger telescope, and reduction of seeing differences among images. A few years of observation could provide a data set big enough to extract important information about the M31 bulge such as the optical depth distribution, the mass spectrum of M31 MACHOs, and the luminosity function, which currently cannot be obtained by other methods. Additionally, I find that the extinction of M31 bulge light by dust in the disk is {\it not} important and can be approximated by the model in which only $20\%$ of light in $V$ band is extinguished over most of the bulge area.Open AccessPixel Lensing Experiment toward the M31 Bulge
I demonstrate that one can detect pixel gravitational microlensing events at the rate $\sim 180\ {\rm events}\ {\rm yr}^{-1}$ and that some fraction of events ($\sim 15$) will be good enough to measure time scales at the $20\%$ level if the experiment is carried out toward the central M31 bulge region with a dedicated 1 m telescope and a $2{\rm K}\times2{\rm K}$ CCD. I also show that the event rate could be significantly increased (up to a factor 6.5) if more aggressive observation strategies are adopted. These aggressive strategies include multiple observation sites, using a bigger telescope, and reduction of seeing differences among images. A few years of observation could provide a data set big enough to extract important information about the M31 bulge such as the optical depth distribution, the mass spectrum of M31 MACHOs, and the luminosity function, which currently cannot be obtained by other methods. Additionally, I find that the extinction of M31 bulge light by dust in the disk is {\it not} important and can be approximated by the model in which only $20\%$ of light in $V$ band is extinguished over most of the bulge area. - 1 August 1995
- Published by American Astronomical Society in The Astrophysical Journal
- Vol. 449, 521
Statistics of Microlensing Optical Depth
We show that the statistical error, $sigma_{ au}$, in estimating the optical depth, $ au$, due to microlensing is substantially higher than the naive Poisson estimate: $sigma_{ au} = sqrt{eta / N} au$, where $N$ is the number of detections and $1.65 leq eta lsim 3$. We construct a ``microlensing map'' using an observationally well-constrained barred bulge model and compare this with a map based on a spherical bulge model. The result indicates a significant differences in the distribution of optical depths. If the optical depths are determined over a wide range of positions around the Galactic center, one could make a rudimentary determination of the geometry of the mass distribution of the Galactic bulge by observing $sim 200$ events. About 800 events are required to determine the relative contributions to the event rate by bulge and disk Machos.Comment: 13 pages, 2 figures, 1 tables, request hard copy of preprint to cheongho@payne.mps.ohio-state.edu, OSU-TA-23/9- 1 August 1995
- Published by American Astronomical Society in The Astrophysical Journal
- Vol. 449, 521
Statistics of Microlensing Optical Depth
We show that the statistical error, $sigma_{ au}$, in estimating the optical depth, $ au$, due to microlensing is substantially higher than the naive Poisson estimate: $sigma_{ au} = sqrt{eta / N} au$, where $N$ is the number of detections and $1.65 leq eta lsim 3$. We construct a ``microlensing map'' using an observationally well-constrained barred bulge model and compare this with a map based on a spherical bulge model. The result indicates a significant differences in the distribution of optical depths. If the optical depths are determined over a wide range of positions around the Galactic center, one could make a rudimentary determination of the geometry of the mass distribution of the Galactic bulge by observing $sim 200$ events. About 800 events are required to determine the relative contributions to the event rate by bulge and disk Machos.Comment: 13 pages, 2 figures, 1 tables, request hard copy of preprint to cheongho@payne.mps.ohio-state.edu, OSU-TA-23/9- Open Access
Lunar Occultation of MACHOs
Lunar occultation can be used to measure the proper motions of some of the long time scale microlensing events, $t_{e} \gsim 70$ days, now being detected toward the Galactic bulge. The long events are difficult to explain within the context of standard models of the mass distribution and dynamics of the Galaxy. Han & Gould (1995b) have suggested that they may be due to a kinematically cold population near the Sun. To resolve the mass, distance, and velocity of individual events and so to determine their nature, one must measure parallaxes and proper motions. For long events, parallaxes can be often obtained from ground-based measurements, but proper motions can only rarely be determined using conventional methods. Lunar occultations are therefore key to the understanding of the long events. We carry out realistic simulations to estimate the uncertainty of these measurements and show that proper motions could be measured for about one long event per year.Open AccessLunar Occultation of MACHOs
Lunar occultation can be used to measure the proper motions of some of the long time scale microlensing events, $t_{e} \gsim 70$ days, now being detected toward the Galactic bulge. The long events are difficult to explain within the context of standard models of the mass distribution and dynamics of the Galaxy. Han & Gould (1995b) have suggested that they may be due to a kinematically cold population near the Sun. To resolve the mass, distance, and velocity of individual events and so to determine their nature, one must measure parallaxes and proper motions. For long events, parallaxes can be often obtained from ground-based measurements, but proper motions can only rarely be determined using conventional methods. Lunar occultations are therefore key to the understanding of the long events. We carry out realistic simulations to estimate the uncertainty of these measurements and show that proper motions could be measured for about one long event per year. - Open Access
The Mass Spectrum Of Machos From Parallax Measurements
We demonstrate that by making satellite-based parallax measurements of Macho events, it is possible to distinguish disk from bulge Machos and to determine individual masses of disk Machos to an accuracy of $0.2$ in the log. This is at least a 3-fold improvement over what can be done without parallaxes, i.e., just from the observed time scale of the events. In addition, we show that the physical distribution of disk Machos can be found from `reduced' velocities determined by parallax measurements.Open AccessThe Mass Spectrum Of Machos From Parallax Measurements
We demonstrate that by making satellite-based parallax measurements of Macho events, it is possible to distinguish disk from bulge Machos and to determine individual masses of disk Machos to an accuracy of $0.2$ in the log. This is at least a 3-fold improvement over what can be done without parallaxes, i.e., just from the observed time scale of the events. In addition, we show that the physical distribution of disk Machos can be found from `reduced' velocities determined by parallax measurements.