Possible gravitational microlensing of a star in the Large Magellanic Cloud

C. Alcock^* , C. W. Akerlof ¶, R. A. Allsman^*, T. S. Axelrod^*, D. P. Bennett^* , S. Chan !, K. H. Cook^* , K. C. Freeman !, K. Griest ||, S. L. Marshall §, H-S. Park^*, S. Perlmutter , B. A. Peterson !, M. R. Pratt §, P. J. Quinn !, A. W. Rodgers !, C. W. Stubbs § & W. Sutherland

^* Lawrence Livermore National Laboratory, Livermore, California 94550. USA
Center for Particle Astrophysics, University of California, Berkeley, California 94720, USA
! Mt Stromlo and Siding Spring Observatories, Australian National University, Weston, ACT 2611, Australia
§ Department of Physics, University of California, Santa Barbara, California 93106, USA
|| Department of Physics, University of California, San Diego, California 92039, USA
¶ Department of Physics, University of Michigan, Ann Arbor, Michigan 48109. USA

THERE is now abundant evidence for the presence of large quantities of unseen matter surrounding normal galaxies, including our own^1,2. The nature of this 'dark matter' is unknown, except that it cannot be made of normal stars, dust or gas, as they would be easily detected. Exotic particles such as axions, massive neutrinos or other weakly interacting massive particles (collectively known as WIMPs) have been proposed^3,4, but have yet to be detected. A less exotic alternative is normal matter in the form of bodies with masses ranging from that of a large planet to a few solar masses. Such objects, known collectively as massive compact halo objects⁵ (MACHOs), might be brown dwarfs or 'jupiters' (bodies too small to produce their own energy by fusion), neutron stars, old white dwarfs or black holes. Paczynski⁶ suggested that MACHOs might act as gravitational microlenscs, temporarily amplifying the apparent brightness of background stars in nearby galaxies. We are conducting a microlensing experiment to determine whether the dark matter halo of our Galaxy is made up of MACHOs. Here we report a candidate for such a microlensing event, detected by monitoring the light curves of 1.8 million stars in the Large Magellanic Cloud for one year. The light curve shows no variation for most of the year of data taking, and an upward excursion lasting over 1 month, with a maximum increase of ~2 mag. The most probable lens mass, inferred from the duration of the candidate lensing event, is ~0.1 solar mass.

The MACHO Project^7,8 uses the gravitational microlens signature to search for evidence of MACHOs in the Galactic halo, which is thought to he at least three times as massive as the visible disk². (Two other groups are attempting a similar search^9,10.) If most of our Galaxy's dark matter resides in MACHOs, the 'optical depth' for microlensing towards the Large Magellanic Cloud (LMC) is about 5 × 10^-7 (independent of the mass function of MACHOs), so that at any given time about one star in two million will be microlensed with an amplification factor A > 1.34 (ref. 5). Our survey takes advantage of the transverse motion of MACHOs relative to the line-of-sight from the observer to a background star. This motion causes a transient, time-symmetric and achromatic brightening that is quite unlike any known variable star phenomena, with a characteristic timescale t = 2r_E/n_"¥ where r_E is the Einstein ring radius and n_"¥ is the MACHO velocity transverse to the line-of-sight. For typical halo models the time (where M is the mass of the Sun), The amplification can be large, but these events are extremely rare; for this reason our survey was designed to follow >ten million stars over several years.

The survey employs a dedicated 1.27-m telescope at Mount Stromlo. A field-of-view of 0.5 square degrees is achieved by operating at the prime focus. The optics include a dichroic beam-splitter which allows simultaneous imaging in a 'red' beam (6,300—7,600 Å) and a 'blue' beam (4,500—6,300 Å). Two large charge-coupled device (CCD) cameras¹¹ are employed at the two foci; each contain a 2 × 2 mosaic of 2,048 × 2,048 pixel Loral CCD imagers. The 15-mm pixel size corresponds to 0.63 arcsec on the sky. The images are read out through a 16-channel system, and written into dual ported memory in the data acquisition computer. Our primary target stars are in the LMC. We also monitor stars in the Galactic bulge and the Small Magellanic Cloud. As of 15 September 1993, over 12,000 images have been taken with the system.

The data are reduced with a crowded-field photometry routine known as Sodophot, derived from Dophot¹². First, one image of each field that was obtained in good seeing is reduced in a manner similar to Dophot to produce a 'template' catalogue of star positions and magnitudes. Normally, bright stars are matched with the template and used to determine an analytic point spread function (PSF) and a coordinate transformation. Photometric fitting is then performed on each template star in descending order of brightness, with the PSF for all other stars subtracted from the frame. When a star is found to vary significantly, it and its neighbours undergo a second iteration of fitting. The output consists of magnitudes and errors for the two colours, and six additional useful parameters (such as the c² of the PSF fit and crowding information). These are used to flag questionable measurements, that arise from cosmic ray events in the CCDs, bad pixels and so on.

These photometric data are subjected to an automatic time-series analysis which uses a set of optimal filters to search for microlensing candidates and variable stars (which we have detected in abundance¹³). For each microlensing candidate a light curve is fitted, and the final selection is done automatically using criteria (for example, signal-lo-noise, quality of fit, wavelength independence of the light curve and colour of the star) that were established empirically using Monte Carlo addition of fake events into real light curves.

This analysis has been done on four fields near the centre of the LMC, containing 1.8 million stars, with approximalely 250 observations for each star. The candidate event reported here occurs in the light curve of a star at coordinates a a = 05 h 14 min 44.5 s, d = -68°48 2 00 3 (J2000). (A finding chart is available on request from C.A.). The star has median magnitudes V ~19.6, R ~19.0, consistent with a clump giant (metal-rich helium core burning star) in the LMC. These magnitudes are estimated using colour transformations from our filters to V and R that have been derived from observations of standard stars.

Our photometry for this star, from July 1992 to July 1993, is shown in Fig. 1, and the candidate event is shown on an expanded scale in Fig. 2, along with the colour light curve. The colour changes by <0.1 mag as it brightens and fades (the candidate 'event'). A mosaic, showing portions of some of the CCD images used, is shown in Fig. 3, with the relevant star at the centre. The integrated number of PSF photoelectrons detected above the sky background in the template image is ~10⁴, for a 300 s exposure. The increase in counts during the peak is highly significant, as is clear from the figures. Also shown in Fig. 2 is a fit to the theoretical microlensing light curve (see ref. 6). The four parameters fit are (1) the baseline flux, (2) the maximum amplification A_max = 6.86 ± 0.11, (3) the duration t = 33.9 ± 0.26 d, (4) the centroid in time 433.55 ± 0.04 d. The quoted errors are formal fit errors. Using the PSF fit uncertainties as determined by the photometry program, the best-fit microlensing curve gives a c² per degree of freedom of 1.6 (for 443 d.f.).

Fig. 1 The observed light curve with estimated ±1s errors. a Shows Ablue, the flux (in linear units) divided by the median observed flux, in the blue passband. b Is the same, for the red passband. | high-resolution version |

Fig. 3 Selected red CCD frames centred on the microlens candidate, showing observations before, during and after the event. The numbers on each frame indicate the days after 2 January 1992. | high-resolution version |

A number of features of the candidate event are consistent with gravitational microlensing: the light curve is achromatic within measurement error, and it has the expected symmetrical shape. If this is a genuine microlensing event, the mass of the deflector can be estimated. Because the duration depends upon the lens mass, the relative velocity transverse to the line-of-sight and the distance to the lens (none of which are known), the lens mass cannot be uniquely determined from the duration. But by using a model of the mass and velocity distributions of halo dark matter, one can find the relative probability that a MACHO of mass M_macho gave rise to the event. Thus, if this is genuine microlensing, Fig. 9 of ref. 5 implies the most likely mass is ~0.12 M, with masses of 0.03 M and 0.5 M being roughly half as likely. However, this method does not properly take into account our detection efficiencies, and should be considered only a rough estimate.

The mass range given above includes brown dwarfs and main sequence stars. Any microlensing star is very unlikely to be a red dwarf of the Galactic stellar halo, because one can show that the optical depth t_s for microlensing by main sequence stars of the stellar halo is very low. Even if the mass function of the stellar halo rises as steeply as dN/dM M^-4, as suggested recently¹⁴ (here N is the number of stars per unit stellar mass interval), t_s is still a few hundred times smaller than the 5×10^-7 optical depth estimated for MACHO microlensing. The chance of finding such a stellar microlensing event among our 1.8 million stars is therefore very small.

The prospects for direct observation of a lensing object are not favourable. Even a star of 0.5 M, for example, would have V~24, and for many years would be within a small fraction of an arcsecond of the much brighter LMC star.

We emphasize that the observed stellar brightening could be due to some previously unknown source of intrinsic stellar variability. The fit discrepancy near the peak is not yet understood; a more refined analysis of the data is under way. We do not yet have a spectrum of the star. A crucial test of the hypothesis that we are seeing gravitational microlensing by MACHOs in the galactic halo will be the detection of other candidates. So far, we have analysed only ~15% of our first year's frames and we plan to continue observations until 1996; this should allow us to determine if microlensing is really the cause. Additional events should show the theoretical distribution of maxima, and should be representative of both the colour-magnitude diagram and the spatial structure of the LMC. No repeats should be seen in any given star. (While this paper was in preparation, we were informed by J. Rich (personal communication) of the candidate events reported by the EROS collaboration. Note that the two groups use different definitions of characteristic time.)

If such candidates do result from microlensing we should be able to determine the contribution of MACHOs to the dark matter in the Galactic halo. The results presented here encourage us to believe this will happen.

Received 22 September: accepted 30 September 1993.

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12. Schechter, P. L., Saha, A. & Mateo, M. L. Publs astr. Soc. Pacif. (in the press).
13. Cook, K. H. et al. Bull. Am. Astr. Soc. 24, 1179 (1993).
14. Richer, H. B. & Fahlman, G. G. Nature 358, 383–386 (1992).

ACKNOWLEDGEMENTS. We are grateful for the support given our project by the technical staff at the Mt Stromlo Observatory. Work performed at LLNL is supported by the DOE. Work performed by the Center for Particle Astrophysics on the UC campuses is supported in part by the Office of Science and Technology Centers of the NSF. Work performed at MSSSO is Supported by the Bilateral Science and Technology Program of the Australian Department of Industry, Technology and Commerce. K.G. acknowledges a DOE OJI grant, and C.W.S. thanks the Sloan Foundation for their support.

Evidence for gravitational microlensing by dark objects in the Galactic halo

E. Aubourg^*, P. Bareyre^*, S. Bréhin^*, M. Gros^*, M. Lachièze-Rey^*, B. Laurent^*, E. Lesquoy^*, C. Magneville^*, A. Milsztajn^*, L. Moscoso^*, F. Queinnec^*, J. Rich^*, M. Spiro^*, L. Vigroux^*, S. Zylberajch^*, R. Ansari , F. Cavalier , M. Moniez , J.-P. Beaulieu !, R. Ferlet !, Ph. Grison !, A. Vidal-Madjar !, J. Guibert§, O. Moreau§, F. Tajahmady§, E. Maurice||, L. Prévôt|| & C. Gry¶

^* DAPNIA, Centre d'Études de Saclay, 91191 Gif-sur-Yvette, France
Laboratoire de l'Accélérateur Linéaire, Centre d'Orsay, 91405 Orsay, France
! Institut d'Astrophysique de Paris, 98bis Boulevard Arago, 75014 Paris, France
§ Centre d'Analyse des Images de l'Institut National des Sciences de l'Univers, Observatoire de Paris, 61 avenue de l'Observatoire, 75014 Paris, France
|| Observatoire de Marseille, 2 place Le Verrier, 13248 Marseille 04, France
¶ Laboratoire d'Astronomie Spatiale de Marseille, Traverse du Siphon, Les Trois Lucs, 13120 Marseille, France

THE flat rotation curves of spiral galaxies, including our own, indicate that they are surrounded by unseen haloes of 'dark matter'^1,2. In the absence of a massive halo, stars and gas in the outer portions of a galaxy would orbit the centre more slowly, just as the outer planets in the Solar System circle the Sun more slowly than the inner ones. So far, however, there has been no direct observational evidence for the dark matter, or its characteristics. Paczynski³ suggested that dark bodies in the halo of our Galaxy can be detected when they act as gravitational 'microlenses', amplifying the light from stars in nearby galaxies. The duration of such an event depends on the mass, distance and velocity of the dark object. We have been monitoring the brightness of three million stars in the Large Magellanic Cloud for over three years, and here report the detection of two possible microlensing events. The brightening of the stars was symmetrical in time, achromatic and not repeated during the monitoring period. The timescales of the two events are about thirty days and imply that the masses of the lensing objects lie between a few hundredths and one solar mass. The number of events observed is consistent with the number expected if the halo is dominated by objects with masses in this range.

The 'EROS' (Experience de Recherche d'Objets Sombres) collaboration is searching for microlensing events using the European Southern Observatory at La Silla, Chile^4,5. We have two complementary programmes. The first uses 5° × 5° Schmidt plates of the Large Magellanic Cloud (LMC) that allow us to monitor about eight million stars with a sampling rate of no more than two measurements per night. This makes the programme primarily sensitive to lens masses in the range 10^-14 M < M < 1 M (where M is the solar mass), corresponding to mean lensing durations in the range 1 d < t < 100 d. The probability that a given star in the LMC is amplified by more than 0.3 magnitudes at a given time is calculated to be ~0.5 × 10^-16 (refs 3, 6). For a deflector of mass M the typical timescale for the amplification is . The light curve of such an event should be symmetric in time, achromatic, and the event should not be repeated. Over the period 1990 –93, a total of 304 Schmidt plates of the LMC were taken for us at La Silla with red or blue filters. Exposure times were typically one hour, permitting us to monitor stars down to the twentieth magnitude with a mean photometric precision of about 15% (r.m.s.). The transparency of the plates is digitized in 10 mm (0.67 arcsec) steps by the 'MAMA' (Machine Automatique á Mesurer pour l'Astronomie) at the Observatoire de Paris⁷. The relation between transparency and star luminosity has been established using charge-coupled device (CCD) images scattered through the Schmidt-plate field.

The second programme uses a CCD camera consisting of a mosaic of sixteen 579 × 400 pixel Thomson THX 31157 CCDs covering about 1° × 0.4°. It is mounted on a 40-cm reflector (f/10) refurbished with the help of the Observatoire de Haute Provence. We have used this to observe one field in the bar of the LMC from December 1991 to March 1992 and from August 1992 to March 1993. As of March 1993, a total of 8,100 exposures had been taken with red and blue filters. About 100,000 stars are seen on each image, with a mean photometric precision of about 6%. Compared to the Schmidt-plate programme, the number of stars is a factor 80 smaller but the rapid sampling time (an image pair every 22 minutes) makes the CCD programme sensitive to deflector masses in the range 10^-17 M < M < 10^-13 M, corresponding to event durations in the range 1 h < t < 3 d.

After preliminary processing (digitizing the Schmidt plates and flat-fielding the CCD images), the data reduction for both programmes follows basically the same procedure. First, one reference image for each colour was constructed by combining ten plates or 50 CCD images taken with good atmospheric conditions. We used a star finding algorithm to establish a star catalogue for each reference image. Next, each image is aligned with the reference using bright, isolated stars. The positions of the stars on the reference image then serve as input to a photometric fitting programme to determine the luminosity of each catalogue star on the new image. The image is then aligned 'photometrically' with the reference by requiring that the mean luminosity of stars in a given luminosity band equal the mean luminosity in the catalogue. (The small number of intrinsically variable stars in the catalogue does not affect this procedure.) Successive images then add one point to the blue or red light curve of each star in the catalogue.

After data reduction, each light curve is tested for the presence of time variations using a variety of algorithms. For microlensing-like events, we use a simple algorithm that scans curves for sequences of measurements that are significantly above the mean value. The light curve is selected as a microlensing candidate if it exhibits one and only one such sequence simultaneously in both colours. The precise value of the threshold for acceptance is chosen using estimates of measurement errors so that random fluctuations of intrinsically stable stars are not accepted. The photometric errors are estimated as a function of magnitude for each image but may still vary from one star to another by 20% according to the star's environment. We estimate the efficiency of the cuts to accept real microlensing events using Monte Carlo-generated lensing events, produced with the observed photometric resolution and observing sequence. We superimposed the Monte Carlo signature of microlensing events onto both observed (flat) light curves and simulated light curves. These curves were then subjected to the same algorithms as the real data. For simulated events with peak amplifications >1.34 inserted into the data during the period of the observing seasons, the efficiency ranges from ~25% for events with timescales of 6 days to 50% for events with timescales of 30 days. These numbers differ from 100% because of the sampling period and the photometric resolution for faint stars.

Measured curves passing the above selection criteria were then inspected visually and subjected to further analysis to determine their compatibility with the microlensing hypothesis. At this stage, we found it necessary to eliminate only those light curves that exhibit variations on a timescale comparable to that of the total observing period. Such events cannot be tested for the presence of subsequent variations. Remaining events are fitted for the theoretical microlensing light curve. The parameters of the fit are the off-lensing luminosity, the maximum amplification, the time of maximum amplification, and the timescale of the microlensing. The light curves of the two colours are fitted separately (to test for wavelength independence) and then simultaneously.

We found no candidates in an analysis performed on the 1991—92 CCD data (20% of the total data). For this data, we expected about three candidates if the halo is entirely comprised of dark objects in the range 10^-17 to 10^-15 M.

A preliminary analysis of 40% of the Schmidt-plate data has revealed two events that are consistent with the microlensing hypothesis. The light curves are shown in Figs 1 and 2, with the event characteristics listed in Table 1. They are the only curves so far analysed that show one significant amplification event with no further variations. (No curves have been found that show two or more examples of microlensing-like behaviour.) The curves are consistent with the theoretical curve; c²s are good within the estimated 20% uncertainty in the photometric errors. The events are wavelength independent at the 10% level, that is within errors. The amplification is near the median amplitude expected (dm = 1.0) for detectable events with these timescales. Neighbouring stars show no variations over the whole observing period. The off-lensing magnitudes of the two stars are near the average for stars in our catalogue. Candidate 2 is on the main sequence while candidate 1 is between the main sequence and giant branch of the colour –magnitude diagram. Only the observation of further events will tell us if there is an accumulation of events in a given region of the diagram indicating variable-star phenomena.

Fig. 1 a, The measured magnitudes for candidate 1 as a function of time. The time is counted from 1 January 1990. The error bars correspond to the estimated 1s errors, b, The light-curve of candidate 1 on an expanded scale. The curve shows the best fit for the microlensing hypothesis. The parameters of the best fit are shown in Table 1. | high-resolution version |

Fig. 2 As Fig. 1, for candidate 2. | high-resolution version |

If the events are interpreted as arising from microlensing, the lensing objects would have a mass between a few × 10^-12 and 1 M. This range is based on simulations with the standard isothermal halo yielding the observed flat rotation curve out to the LMC (refs 2, 6). The range is wide because, for fixed mass, the lensing time varies due to the uncertain distance and speed of the lensing object. The allowed masses include those expected for brown dwarfs and dim main sequence stars. If they are located in the Galactic halo, they would not be detectable. If the halo consists entirely of such objects, we estimate that we would have observed about six events if the dominant mass is 10^-12 M and about one event if it is 1 M, in agreement with the observed number.

Obviously, this interpretation of the events must be confirmed by further observations of the stars in question and, especially, by the discovery of further events, which would permit us to study their statistical properties. In particular, the distribution of amplification magnitudes must be shown to be consistent with the microlensing hypothesis and the microlensed stars must be distributed throughout the observed colour-magnitude diagram and throughout the LMC. Until this is done, it is not possible to rule out the possibility that we are dealing with a new type of variable star. During the preparation of this paper we learned that a similar microlensing event has been observed by the 'MACHO' collaboration (C. Alcock, personal communication).

The EROS collaboration is continuing to collect and analyse data and it is expected that further results will be presented within a year's time.

Note added in proof: We have located in our data the star involved in the candidate microlensing presented by the MACHO collaboration (C. Alcock et al., this issue). Because the star is very faint in the blue band, we have reliable measurements only in the red. (This fact explains the rejection of the event in our analysis.) We confirm in this colour the existence and characteristics of the MACHO event. No other significant luminosity variations are seen in the 1990–91 and 1991–92 seasons, reinforcing the microlensing interpretation of the event.

Received 22 September; accepted 30 September 1993.

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2. Primack, J. R., Seckel, D. & Sadoulet, B. A. Rev. Nucl. Part. Sci. 38, 751–8O7 (1988).
3. Paczynski, B. Astrophys. J. 304, 1–5 (1986).
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8. Alcock, C. et al. Nature 365, 621–623 (1993).

ACKNOWLEDGEMENTS. We thank C. Alcock for discussions at the beginning of this project. We thank A. Bijaoui, Ph. Veron, the staff at the Observatoire de Haute Provence, the ESO staff at La Silla, and the technical staff of the collaborating laboratories for their advice and help. We thank D. Bennett of the MACHO collaboration for help and interesting discussions. This work is based on observations at the European Southern Observatory, La Silla, Chile, and is funded by DSM-CEA, IN2P3-CNRS, INSU-CNRS, with support from ESO.

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