Observational Evidence for the Effect of Amplification Bias in Gravitational Microlensing Experiments

Recently Alard\markcite{alard1996} proposed to detect the shift of a star's image centroid, $\delta x$, as a method to identify the lensed source among blended stars. Goldberg & Wo\'zniak\markcite{goldberg1997} actually applied this method to the OGLE-1 database and found that 7 out of 15 events showed significant centroid shifts of $\delta x \gtrsim 0.2$ arcsec. The amount of centroid shift has been estimated theoretically by Goldberg.\markcite{goldberg1997} However, he treated the problem in general and did not apply it to a particular survey or field, and thus based his estimates on simple toy model luminosity functions (i.e., power laws). In this paper, we construct the expected distribution of $\delta x$ for Galactic bulge events by using the precise stellar LF observed by Holtzman et al.\markcite{holtzman1998} using HST. Their LF is complete up to $M_I\sim 9.0$ ($M_V\sim 12$), corresponding to faint M-type stars. In our analysis we find that regular blending cannot produce a large fraction of events with measurable centroid shifts. By contrast, a significant fraction of events would have measurable centroid shifts if they are affected by amplification-bias blending. Therefore, Goldberg & Wo\'zniak's measurements of large centroid shifts for a large fraction of microlensing events confirms the prediction of Han and Alard that a large fraction of Galactic bulge events are affected by amplification-bias blending.Comment: total 15 pages, including 6 figures, and no Table, submitted to ApJ on Apr 26 1998, email [email protected]

Variable Stars in the Globular Cluster M5. Application of the Image Subtraction Method

We present $V$-band light curves of 61 variables from the core of the globular cluster M5 obtained using a newly developed image subtraction method (ISM). Four of these variables were previously unknown. Only 26 variables were found in the same field using photometry obtained with DoPHOT software. Fourier parameters of the ISM light curves have relative errors up to 20 times smaller than parameters measured from DoPHOT photometry. We conclude that the new method is very promising for searching for variable stars in the cores of the globular clusters and gives very accurate relative photometry with quality comparable to photometry obtained by HST. We also show that the variable V104 is not an eclipsing star as has been suggested, but is an RRc star showing non-radial pulsations.Comment: submitted to MNRAS, 9 pages, 4 figure

The relationship between CK and CV chondrites: a single parent body source?

The relationship between CK and CV3 chondrites is examined. Both groups may represent a single continuum and have been derived from the same parent body

Microlensing toward crowded fields: Theory and applications to M31

We present a comprehensive treatment of the pixel-lensing theory and apply it to lensing experiments and their results toward M31. Using distribution functions for the distances, velocities, masses, and luminosities of stars, we derive lensing event rates as a function of the event observables. In contrast to the microlensing regime, in the pixel-lensing regime (crowded or unresolved sources) the observables are the maximum excess flux of the source above a background and the full width at half-maximum (FWHM) time of the event. To calculate lensing event distribution functions depending on these observables for the specific case of M31, we use data from the literature to construct a model of M31, reproducing consistently photometry, kinematics and stellar population. We predict the halo- and self-lensing event rates for bulge and disk stars in M31 and treat events with and without finite source signatures separately. We use the M31 photon noise profile and obtain the event rates as a function of position, field of view, and S/N threshold at maximum magnification. We calculate the expected rates for WeCAPP and for a potential Advanced Camera for Surveys (ACS) lensing campaign. The detection of two events with a peak signal-to-noise ratio larger than 10 and a timescale larger than 1 day in the WeCAPP 2000/2001 data is in good agreement with our theoretical calculations. We investigate the luminosity function of lensed stars for noise characteristics of WeCAPP and ACS. For the pixel-lensing regime, we derive the probability distribution for the lens masses in M31 as a function of the FWHM timescale, flux excess and color, including the errors of these observables.Comment: 45 pages, 27 figures LaTeX; corrected typos; published in the Astrophysical Journal Supplemen

Towards Locating the Brightest Microlensing Events on the Sky

It is estimated that a star brighter than visual magnitude 17 is undergoing a detectable gravitational microlensing event, somewhere on the sky, at any given time. It is assumed that both lenses and sources are normal stars drawn from a standard Bahcall-Soneira model of our Galaxy. Furthermore, over the time scale of a year, a star 15th magnitude or brighter should undergo a detectable gravitational lens amplification. Detecting and studying the microlensing event rate among the brightest 10$^8$ stars could yield a better understanding of Galactic stellar and dark matter distributions. Diligent tracking of bright microlensing events with even small telescopes might detect planets orbiting these stellar lenses.Comment: 19 pages, 4 figures, accepted by Ap

Difference image photometry with bright variable backgrounds

Over the last two decades the Andromeda Galaxy (M31) has been something of a test-bed for methods aimed at obtaining accurate time-domain relative photometry within highly crowded fields. Difference imaging methods, originally pioneered towards M31, have evolved into sophisticated methods, such as the Optimal Image Subtraction (OIS) method of Alard & Lupton (1998), that today are most widely used to survey variable stars, transients and microlensing events in our own Galaxy. We show that modern difference image (DIA) algorithms such as OIS, whilst spectacularly successful towards the Milky Way bulge, may perform badly towards high surface brightness targets such as the M31 bulge. Poor results can occur in the presence of common systematics which add spurious flux contributions to images, such as internal reflections, scattered light or fringing. Using data from the Angstrom Project microlensing survey of the M31 bulge, we show that very good results are usually obtainable by first performing careful photometric alignment prior to using OIS to perform point-spread function (PSF) matching. This separation of background matching and PSF matching, a common feature of earlier M31 photometry techniques, allows us to take full advantage of the powerful PSF matching flexibility offered by OIS towards high surface brightness targets. We find that difference images produced this way have noise distributions close to Gaussian, showing significant improvement upon results achieved using OIS alone. We show that with this correction light-curves of variable stars and transients can be recovered to within ~10 arcseconds of the M31 nucleus. Our method is simple to implement and is quick enough to be incorporated within real-time DIA pipelines. (Abridged)Comment: 12 pages. Accepted for publication in MNRAS. Includes an expanded discussion of DIA testing and results, including additional lightcurve example

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.Comment: 18 pages, revised version, submitted to Ap

The Optical Gravitational Lensing Experiment. Monitoring of QSO 2237+0305

We present results from 2 years of monitoring of Huchra's lens (QSO 2237+0305) with the 1.3 m Warsaw telescope on Las Campanas, Chile. Photometry in the V band was done using a newly developed method for image subtraction. Reliable subtraction without Fourier division removes all complexities associated with the presence of a bright lensing galaxy. With positions of lensed images adopted from HST measurements it is relatively easy to fit the variable part of the flux in this system, as opposed to modeling of the underlying galaxy. For the first time we observed smooth light variation over a period of a few months, which can be naturally attributed to microlensing. We also describe automated software capable of real time analysis of the images of QSO 2237+0305. It is expected that starting from the next observing season in 1999 an alert system will be implemented for high amplification events (HAE) in this object. Time sampling and photometric accuracy achieved should be sufficient for early detection of caustic crossings.Comment: 8 pages (including 4 figures and table), latex, emulateapj, submitted to ApJ, revised version - minor change

Microlensing in the double quasar SBS1520+530

We present the results of a monitoring campaign of the double quasar SBS1520+530 at Maidanak observatory from April 2003 to August 2004. We obtained light curves in V and R filters that show small-amplitude \Delta m~0.1 mag intrinsic variations of the quasar on time scales of about 100 days. The data set is consistent with the previously determined time delay of \Delta t=(130+-3) days by Burud et al. (2002). We find that the time delay corrected magnitude difference between the quasar images is now larger by (0.14+-0.03) mag than during the observations by Burud et al. (2002). This confirms the presence of gravitational microlensing variations in this system.Comment: 6 pages, 7 figures. Accepted for publication in A&

A New Channel for the Detection of Planetary Systems Through Microlensing: II. Repeating Events

In the companion paper we began the task of systematically studying the detection of planets in wide orbits ($a > 1.5 R_E$) via microlensing surveys. In this paper we continue, focusing on repeating events. We find that, if all planetary systems are similar to our own Solar System, reasonable extensions of the present observing strategies would allow us to detect 3-6 repeating events per year along the direction to the Bulge. Indeed, if planetary systems with multiple planets are common, then future monitoring programs which lead to the discovery of thousands of stellar-lens events will likely discover events in which several different planets within a single system serve as lenses, with light curves exhibiting multiple repetitions. In this paper we discuss observing strategies to maximize the discovery of all wide-orbit planet-lens events. We also compare the likely detection rates of planets in wide orbits to those of planets located in the zone for resonant lensing. We find that, depending on the values of the planet masses and stellar radii of the lensed sources (which determine whether or not finite source size is important), and also on the sensitivity of the photometry used by observers, the detection of planets in wide orbits may be the primary route to the discovery of planets via microlensing. We also discuss how the combination of resonant and wide-orbit events can help us to learn about the distribution of planetary system properties (S 6.1). In addition, by determining the fraction of short-duration events due to planets, we indirectly derive information about the fraction of all short-duration events that may be due to low-mass MACHOs (S 6.2).Comment: 51 pages, 7 figures. To be published in the Astrophysical Journal, 20 February 1999. This completes the introduction to the discovery of planets in wide orbits begun in astro-ph/9808075, also to appear in ApJ on 20 February 199