5

Statistical Detections, Galactic Structure, and the Mass Content of the Universe

INTRODUCTION TO THE DARK-MATTER PROBLEM

Most of the matter in the universe is “dark.” Matter in the form of luminous stars accounts for only about 0.5% of the critical density, while all matter together accounts for at least 20%, and perhaps much more, of the critical density. Big-bang nucleosynthesis indicates that ordinary matter (“baryons”) contributes around 5% of the critical density, strongly suggesting that most of the matter is not in the form of baryons. Thus, there are two dark-matter questions (see presentation by M.S. Turner in this chapter):

  1. What are the dark baryons? and

  2. What is the form of the nonbaryonic dark matter?

Even the luminous matter is not fully characterized, e.g., the low-mass end of the stellar mass function (MF) and the brown dwarf MF. Candidates for the baryonic dark matter include dwarf stars and diffuse gas, and the leading candidate for the nonbaryonic matter is long-lived elementary particles left over from the earliest moments of creation. The Milky Way galaxy, with its various luminous components and massive dark halo, provides an ideal testbed for studying the composition of matter in the universe. The Hubble Space Telescope, microlensing, and new surveys are revealing much about the matter content of the universe.

Crucial to understanding the distribution of ordinary matter in astronomical objects is the abundance of low-mass stars and substellar-mass objects, as most of the objects, if not most of the mass, is in this low-mass component. The brown dwarf MF is being probed by four interrelated methods:

  1. Field-star counts to determine the field-star luminosity function (LF), and so the field-star MF;

  2. Photometry of clusters to determine their MFs;

  3. Radial-velocity studies of field stars to measure the MF of secondaries in binary systems; and

  4. Gravitational microlensing toward the Large Magellanic Cloud (LMC), Small Magellanic Cloud (SMC), and the galactic bulge.

The first method has until recently been sensitive primarily to hydrogen-burning stars and so does not directly constrain the brown dwarf MF. However, in combination with the other methods it does provide strong indirect constraints. As is discussed more thoroughly below, it is now possible to draw the following tentative conclusions:



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Failed Stars and Super Planets: A Report Based on the January 1998 Workshop on Substellar-Mass Objects 5 Statistical Detections, Galactic Structure, and the Mass Content of the Universe INTRODUCTION TO THE DARK-MATTER PROBLEM Most of the matter in the universe is “dark.” Matter in the form of luminous stars accounts for only about 0.5% of the critical density, while all matter together accounts for at least 20%, and perhaps much more, of the critical density. Big-bang nucleosynthesis indicates that ordinary matter (“baryons”) contributes around 5% of the critical density, strongly suggesting that most of the matter is not in the form of baryons. Thus, there are two dark-matter questions (see presentation by M.S. Turner in this chapter): What are the dark baryons? and What is the form of the nonbaryonic dark matter? Even the luminous matter is not fully characterized, e.g., the low-mass end of the stellar mass function (MF) and the brown dwarf MF. Candidates for the baryonic dark matter include dwarf stars and diffuse gas, and the leading candidate for the nonbaryonic matter is long-lived elementary particles left over from the earliest moments of creation. The Milky Way galaxy, with its various luminous components and massive dark halo, provides an ideal testbed for studying the composition of matter in the universe. The Hubble Space Telescope, microlensing, and new surveys are revealing much about the matter content of the universe. Crucial to understanding the distribution of ordinary matter in astronomical objects is the abundance of low-mass stars and substellar-mass objects, as most of the objects, if not most of the mass, is in this low-mass component. The brown dwarf MF is being probed by four interrelated methods: Field-star counts to determine the field-star luminosity function (LF), and so the field-star MF; Photometry of clusters to determine their MFs; Radial-velocity studies of field stars to measure the MF of secondaries in binary systems; and Gravitational microlensing toward the Large Magellanic Cloud (LMC), Small Magellanic Cloud (SMC), and the galactic bulge. The first method has until recently been sensitive primarily to hydrogen-burning stars and so does not directly constrain the brown dwarf MF. However, in combination with the other methods it does provide strong indirect constraints. As is discussed more thoroughly below, it is now possible to draw the following tentative conclusions:

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Failed Stars and Super Planets: A Report Based on the January 1998 Workshop on Substellar-Mass Objects Brown dwarfs do not make a major contribution to the dark halo of the Milky Way galaxy; In most environments (globular and open clusters, the solar neighborhood, and the galactic bulge) the MF for low-mass stars (#DXGT#0.1 solar masses) is approximately “flat”; i.e., the number per log-mass interval is constant; and To the extent that it can be directly measured, the MF for brown dwarfs continues the flat behavior seen for low-mass stars. Brown dwarfs should therefore constitute a large fraction of all stellar objects, but only a small fraction of the total mass in such objects. However, the data, particularly the microlensing data, contain several major puzzles whose resolution may ultimately undermine this simple picture.1 CURRENT UNDERSTANDING OF THE MASS FUNCTIONS OF LOW-MASS STARS AND SMOs The Hubble Space Telescope's (HST's) Wide-Field/Planetary Camera has been used to measure the LF of the solar neighborhood to V = 18 and the LF of the bulge to V = 12. Since both populations are approximately solar in metallicity, 2 one can convert from LF to MF using the local solar-metallicity, mass-luminosity relation derived empirically from nearby binary stars. Theoretical stellar models are in almost perfect agreement with these empirical mass measurements, within the accuracy of the scatter of the observations on a Hertzsprung-Russell (H-R) diagram. In both cases, the MFs (after correction for unseen binary companions) are consistent with flat down to the limit of the observations (0.1 solar masses for the solar-neighborhood MF and 0.3 solar masses for the bulge MF). The 2-Micron All Sky Survey (2MASS) and Deep Near-Infrared Survey of the Southern Sky (DENIS) are both sensitive to nearby field brown dwarfs provided that they are sufficiently young (and so are luminous). Only about 1% of the data have been analyzed, but already three brown dwarfs have been confirmed by detection of lithium in their spectra. Because of small-number statistics, no attempt has yet been made to estimate the local brown dwarf MF, although this should be possible in the relatively near future. About 10 globular cluster LFs have now been measured down to (or in some cases nearly to) the bottom of the hydrogen-burning main sequence using HST. In particular, it is possible to use proper motions to separate the cluster main sequence from contaminating field stars and so demonstrate that the cluster sequence ends before the limit of detectability. Stellar models predict the shape of the cluster color-magnitude diagram very well and (together with their empirically tested predictions for solar-metallicity stars) give confidence that the theoretical mass-luminosity relations are correct. The resulting MFs reveal a range of behavior from flat to falling moderately (number per log mass interval proportional to mass). At the present time it is not known whether the underlying (initial) MF is universally flat and the observed differences among clusters reflect different histories, with some clusters losing their low-mass stars due to dynamical evolution; or whether there is some intrinsic variety among initial MFs.3 In either 1   For a recent review, see, for example, A. Gould, “Microlensing and the Stellar Mass Fanction,”Publications of the Astronomical Society of the Pacific, 108: 465, 1996. 2   A. McWilliam and R.M. Rich, “The First Detailed Abundance Analysis of Galactic Bulge K Giants in Baade's Window,”Astrophysical Journal Supplement, 91: 749, 1994. 3   K.L. Luhman and G.H. Rieke, “The Low-Mass Initial Mass Function in Young Clusters: L1495E,” Astrophysical Journal, 497: 354, 1998.

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Failed Stars and Super Planets: A Report Based on the January 1998 Workshop on Substellar-Mass Objects case, if the MF power laws extend into the brown dwarf regime, then brown dwarfs contribute only moderately to the mass of globular clusters. The MF of brown dwarfs in clusters could be directly probed by looking for microlensing of background stars, but this approach has not yet been attempted.4 At present, young open clusters are the only systems where the mass function can be measured from low-mass stars across the hydrogen-burning limit into the brown-dwarf regime. To date, the Pleiades is the only cluster where there are enough confirmed brown dwarfs (mainly by lithium detection) to permit a measurement of the brown dwarf MF, although there are detections in several other clusters. The Pleiades MF is consistent with being flat down to 0.03 solar masses. MICROLENSING DETERMINATION OF THE SMO MASS FUNCTION Radial velocity measurements of (M sin i) for the secondaries in short-period (less than 10 years) binaries probe the transition from stellar to substellar objects at least for members of binary systems. The results are consistent with a smooth transition across this boundary. Gravitational microlensing provides a complementary window on the brown dwarf MF, as well as on the composition of the dark halo and other components of the galaxy (see presentation by A. Gould). In contrast to photometric methods, it is sensitive to the mass directly and therefore is equally sensitive to old and young brown dwarfs. Depending on the late evolution (and hence present-day luminosity) of very old brown dwarfs, microlensing may be the only feasible way to detect them. However, a microlensing event does not yield the mass directly, but rather the event time scale, which is a complicated combination of the mass, the distance, and the transverse speed. Thus, to interpret the observed events in terms of MF, one must (at the present stage) incorporate models of the velocity and physical distributions. About 14 events have been detected toward the Large Magellanic Cloud (LMC) (see presentation by C. Alcock). If the lenses are in the halo, the event rate implies that half the halo is in dark stars, with very large uncertainties. The typical time scale (Einstein-radius-crossing time) is about 40 days. Since events lensed by 0.1-solar-mass brown dwarfs would last less than half this time and since the time scale is proportional to the square root of the lens mass, a mass of around 0.5 solar masses is indicated. In addition, searches for short-duration events have turned up no candidates and so can be used to place very strong limits on halo populations from 10-7 to 10-1 solar masses (0.1 Earth masses to 100 MJ). Apparently then, perhaps half or less of the halo exists in the form of dark stars—providing additional, local evidence that the bulk of the dark matter is nonbaryonic—and the precise nature of the lenses is a real puzzle. The lenses cannot be stars in the halo or the population would have been seen. A variety of suggestions have been advanced, including the following: Stars in the LMC itself; Stars in a warped and flaring Milky Way disk; A new dark population in the spheroid or thick disk; Stars in a dwarf galaxy that happens to lie in the line of sight toward the LMC; Halo white dwarfs; Primordial black holes; and 4   B. Paczynski, “Gravitational Microlensing by Globular Cluster Stars,” Acta Astronomica. 44: 235, 1994.

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Failed Stars and Super Planets: A Report Based on the January 1998 Workshop on Substellar-Mass Objects Brown dwarfs in a halo with very non-standard kinematics. However, each of these explanations has serious drawbacks. More than 200 events have been detected toward the galactic bulge, although only about 50 of these have been published. The remaining events are listed on the World Wide Web and were publicly announced via the Global MACHO Alert Network (GMAN). Most of the lenses are in the bulge itself; if one assumes that the bulge is non-axisymmetric (barlike) and has 20 billion solar masses of stars with a Salpeterlike MF (number per log mass proportional to the −1.35 power of the mass), then the observed events are not easily explained. Indeed, some researchers claim that the observed lensing rate toward the bulge is two standard deviations larger than expected even with a 28 billion solar mass bar and a full disk.5 However, as discussed above, the bulge MF is now measured: it is not rising steeply, but rather is flat. The total mass in bulge stars is only about 14 billion solar masses. Using this observed MF and a simple model for bulge kinematics, one can predict the expected time scale distribution of events and compare to the observed distribution. The latter has far too many short (i.e., low-mass) events. Thus, if the measurements of the bulge MF are correct, then either the bulge MF turns up sharply in the brown dwarf regime, or bulge kinematics are very different from what the simplest models predict. DETECTING PLANETS VIA MICROLENSING Significant efforts are under way to detect planets by using gravitational microlensing. Toward the bulge, it is expected that a large fraction of the events are due to stars. If one of these stars has a planet, then the event can be briefly perturbed. The ratio of the duration of the perturbation to the time scale of the whole event is given by the square root of the planet/star mass ratio. Thus, the mass ratio can be extracted from the detected light curve. Planet perturbations are expected to last from about 1 day for Jupiters to about 1 hour for Earths (see presentation by S. Peale). Hence, one must carry, out frequent photometric follow-up in order to get good enough coverage to unambiguously recognize the perturbation as planetary. Since the events are on the order of a day or less, a network of observatories spread over the three southern continents is required. Two such networks are now operating, and each has substantial (nearly dedicated) allocations of observing time at several observatories during the season when the bulge is readily observed. While no unambiguous planetary events have been detected, several other, non-standard microlensing light curves have been traced with 2% precision at several hundred epochs. Hence, the prospects for planet detection are promising. 5   Hongsheng Zhao and Shude Mao, “On the Microlensing Optical Depth of the Galactic Bar,” Monthly Notices of the Royal Astronomical Society, 283: 1197, 1996.

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Failed Stars and Super Planets: A Report Based on the January 1998 Workshop on Substellar-Mass Objects MICROLENSING: AN OBSERVATIONAL OVERVIEW Charles Alcock Lawrence Livermore National Laboratory A number of groups are searching for evidence that the dark matter in the halo of the Milky Way is made up of objects of astrophysical (planetary or stellar) mass, such as brown dwarfs, planets, ancient degenerate dwarfs, neutron stars, or black holes. These objects have come to be known as MACHOs, for massive compact halo objects. The signature of these objects is the occasional magnification of the light from extragalactic stars by gravitational lensing. The magnification can be large, but events are extremely rare: it is necessary to monitor photometrically several million stars for a period of years in order to obtain a useful detection rate. The majority of microlensing events have been seen by the MACHO project; significant results have also been reported by two other projects, the Optical Gravitational Lensing Experiment (OGLE) and Experience pour la Recherche d'Objets Sombres (EROS). The MACHO project built a two-channel system that employs eight, 2048-by-2048 charge-coupled devices, mounted on the 50-inch telescope at Mt. Stromlo, Australia. The high data rate (#DXGT#5 gigabytes per night) is accommodated by custom electronics and online data reduction. More than 65,000 images have been taken with this system; the dataset is #DXGT#5 terabytes in size. Reduction of part of these data has yielded databases containing light curves in two colors for more than 20 million stars. Careful analysis has revealed ~200 microlensing events, out of which ~14 are toward the primary target, the Large Magellanic Cloud. The current best estimate of the fraction of the dark halo that is composed of MACHOs is ~50%, but with substantial uncertainties. Perhaps more surprising, the typical mass of these objects is ~0.5 M?. Lower-mass objects, such as brown dwarfs and planets, are not significant contributors to the total. The microlensing-event rate toward the galactic-center region turns out to be relatively large, and this has had a significant impact on models of the inner parts of the Milky Way. Preliminary analysis of this data indicates that most of the events are caused by low-mass stars in the central bulge of our galaxy. MICROLENSING AS A PROBE OF THE INITIAL MASS FUNCTION AND GALACTIC STRUCTURE Andrew Gould Ohio State University Microlensing observations toward the galactic bulge and the Large Magellanic Cloud (LMC) pose two, perhaps related, puzzles. Toward the bulge, there are many short events, with Einstein-radius-crossing times of te~10 days. For fixed bulge geometry and kinematics, the lens mass M scales as Mate2. Hence, these short events would most simply be explained as low-mass bulge stars with a Salpeter mass function of dN/dM aM2.35. Unfortunately, the bulge mass function has now been measured for M#DXGT# 0.3 M? and has several times too few low-mass stars to explain the observed events. Logically, there are five possibilities:

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Failed Stars and Super Planets: A Report Based on the January 1998 Workshop on Substellar-Mass Objects The bulge mass function has been mismeasured; There is a sharp upturn in the mass function for M#DXLT# 0.3 M◉; The events are being misinterpreted due to various observational systematics; The conversion from te to M is wrong because the bulge geometry and kinematics are misunderstood; and There is a new, dark population of objects in the bulge or disk, perhaps brown dwarfs. The first and second possibilities are unlikely and can be directly checked by Hubble Space Telescope (HST) infrared observations of the bulge. The third possibility will be checked over the next several years by comparing results from three independent observational programs, the Optical Gravitational Lensing Experiment (OGLE), the Massive Compact Halo Object (MACHO) collaboration, and Experience pour la Recherche d'Objets Sombres (EROS), and by new reduction and analysis techniques now being put in place. To distinguish between the fourth and fifth possibilities, and to characterize the new dark population (if it exists), new information must be obtained about short-duration microlensing events. The most useful and easily extracted new piece of information would be the angular size of the Einstein ring (θe), which also immediately yields the proper motion, μ = θe/te. For bulge lenses, these observables are approximately related to the underlying physical parameters by: θe2 ≅(4G/Ro2c2)(MDls) and μ ≅ | ν ˔ˏ-ν˔s | /Ro where Ro is the galactocentric distance, Dls is the distance between the lens and the source, and ν˔ˏ and ν˔s, are the transverse velocities of the lens and source, respectively. Hence, θe tells us about the mass scale (modulo uncertainty about the depth of the bulge), and μ gives a direct check on our assumptions about bulge kinematics. The only feasible method for measuring θe, for low-mass lenses is to do frequent accurate photometry of the ~9% of giant-source events in which the lens transits the face of the source star. The shape of the light curve changes during the transit, allowing measurement of θ*/θe. Since θ*, the star's angular radius, is known from Stephan's Law, this yields θe. Using two-channel optical/infrared photometry, this method can be extended to near-transits (within 1.5 stellar radii), about 13% of giant-source events. An aggressive worldwide network of optical/infrared follow-up cameras could measure θe, for ~8 events per year. By themselves, these measurements could not completely resolve the present ambiguities, because they measure only the product MDls and not the mass and source-lens distance separately. However, if these results remained consistent with the hypothesis of a new population of low-mass objects, the mass, distance, and velocity of these events could be separately measured by launching a parallax satellite. Much of the equipment required to carry out follow-up observations is already in place: optical/infrared telescopes to be used for this purpose should be commissioned in Chile and South Africa this spring. Two worldwide follow-up groups—the Probing Lensing Anomalies Network (PLANET) and the Global Microlensing Alert Network (GMAN)—are already established and are gaining access to substantial amounts of telescope time. These networks have as their primary goal the detection of planets, but the hardware and software requirements for measuring θe for low-mass lenses are essentially identical to those of planet searches. Modest additional support in the form of hardware improvements and funding for data analysis would significantly enhance the efficiency of these efforts. By contrast, the events seen toward the LMC are puzzling because their durations are too long to be caused by brown dwarfs and too numerous to be accounted for by known populations

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Failed Stars and Super Planets: A Report Based on the January 1998 Workshop on Substellar-Mass Objects of stars. If these lenses truly belong to the dark halo, they should be asymmetric at the ~1% level due to Earth's parallactic motion. A similar program of intensive follow-up would be able to detect this small effect. Unfortunately, no systematic effort is currently being made to follow LMC events. Such a follow-up program (parallel to the bulge programs) is very much needed. DARK MATTER IN THE UNIVERSE AND MICROLENSING   Michael S. Turner University of Chicago and Fermi National Accelerator Laboratory Dark matter is a central issue in astrophysics and cosmology. Because the universal density of baryons deduced from big-bang nucleosynthesis (5% of the critical density) is much greater than the universal density of luminous matter (about 0.5% of the critical density) and much less than estimates of the total amount of matter (at least 20% of critical), there are two dark matter problems: The nature of the dark baryons; and The nature of the nonbaryonic dark matter. The best candidate for the nonbaryonic dark matter is slowly moving elementary particles left over from the earliest moments (“cold dark matter”), e.g., axions or neutralinos. This idea is supported by a host of data, including the anisotropy of the cosmic microwave background radiation and the evolution of large-scale structure in the universe. The leading candidates for the baryonic dark matter are “dark stars” (e.g., dwarf stars or Jupiters) and diffuse gas. If they exist, both dark stars and cold dark matter should reside in the halo of the Milky Way galaxy. Microlensing of stars in the Magellanic Clouds provides a powerful probe of dark stars in the halo. The simplest interpretation of the microlensing events seen thus far is that one-third of the halo is dark stars of half solar mass; two-thirds is unexplained (and consistent with being cold dark-matter particles), and the baryonic dark matter is dark stars. This interpretation is not without its difficulties, and there is an interesting alternative: the lenses are not dark stars in the halo, but rather are stars in other components of the Milky Way, the Magellanic Clouds themselves, and debris in the Magellanic Stream; the dark halo is almost all cold dark-matter particles, and the bulk of the baryonic dark matter is diffuse hot gas (as it is in clusters of galaxies). MICROLENSING AND THE SEARCH FOR PLANETS Stanton Peale University of California, Santa Barbara If a single star acting as a gravitational lens has a planet whose projected separation is not excessively far from the Einstein ring radius RE of the lens (in the lensing zone), the bell-

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Failed Stars and Super Planets: A Report Based on the January 1998 Workshop on Substellar-Mass Objects shaped light curve characteristic of a single lens can be perturbed in a nonsubtle way—revealing the planet's presence and yielding the planet-star mass ratio and the projected separation in terms of RE. Estimated probabilities of detection of a planet during an event, averaged over orbital inclination and phase and along a uniform distribution of lenses along the line of sight, reach as high as 17% for a Jupiter-mass object in orbit about a solar-mass star.6 But the probability can be unity for ranges of planet-star mass ratios and projected separations spanning the lensing zone for high-amplification events (A #DXGT# 20).7 These latter probabilities will drop when averaged over the orbital inclinations and phase of the planet and over a distribution of lenses along the line of sight, but will remain high. Microlensing is sensitive to Earth-mass planets, but the effects of the finite angular size of a source has profound effects on their detection probability. Still, the probabilities are a few percent when the planet is close to RE.8 Because of the many assumptions required and other uncertainties, the probabilities of detection must remain approximate. The probabilities are still being developed, and they will change as more constraints become available. Still, they are already sufficiently secure to investigate consequences. Using only the Gould and Loeb probabilities scaled for a greater concentration of lenses closer to the galactic center and to an arbitrary planet-star mass ratio for averaging over the mass function, Peale found that the statistical distribution of masses of planets could be constrained to within a factor of three in an intensive search program.9 The projected planet-star separations yield a rough estimate of the distribution of semimajor axes with planetary mass. The short time scale of the planetary perturbations and usually small perturbation amplitudes requires the events to be observed every 1 to 2 hours with 1% photometric accuracy in two colors with observations every few minutes during a perturbation. The yield of detections was about 3% under the assumptions of solar-system-like distributions of planets orbiting only half of the lenses. This yield required a set of four or five dedicated 2-meter telescopes distributed in longitude around the Southern Hemisphere, where realistic observing constraints allow only about 60% high-time-resolution coverage. The yield is completely model dependent, but it gives some indication of the necessary effort required to obtain meaningful statistics. If 5% of the events have A #DXGT# 20 and half of these lenses had a Jupiter- or Uranus-mass object in the lensing zone, the yield might have reached a still model-dependent 5%. The estimates of the probabilities of detection used in determining these model-dependent expectations could be made more realistic if a minimum signal-to-noise ratio were used as a detection criterion rather than the customary minimum-percentage perturbation. Also the probabilities must be recalculated using distributions of lenses and sources along the line of sight that are consistent with the optical depth and frequencies of particular time-scale events from the current microlensing data. Optical depth to a particular source location depends only on the mass density of the lenses, but the actual probability that a source is within RE of a lens depends on the distribution of lenses and sources along the line sight. The distribution of frequencies of particular time scales for events, however, depends on the velocity dispersions of lenses and sources, the mass function of the lenses, as well as the distribution of lenses and 6   A. Gould and A. Loeb, “Discovering Planetary Systems Through Gravitational Microlenses,” Astrophysical Journal, 396: 104, 1992. 7   K. Griest and N. Safizadeh, “The Use of High-magnification Microlensing Events in Discovering Extra-Solar Planets,” Astrophysical Journal, in press, 1998. 8   D. Bennett and S. Rhie, “Detecting Earth-Mass Planets with Gravitational Microlensing,”Astrophysical Journal, 472: 660, 1996. 9   S.J. Peale, “Expectations from a Microlensing Search for Planets,” Icarus, 127: 269, 1997.

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Failed Stars and Super Planets: A Report Based on the January 1998 Workshop on Substellar-Mass Objects sources along the line of sight, where lenses and sources come from the same distribution from this point of view. The refinement of the detection probabilities including all important geometries is more likely to increase the overall probabilities of detection from current calculations than otherwise—perhaps sufficiently to motivate the creation of the necessary telescope array for a dedicated search. As about 3% of nearby stars have giant planets orbiting within 0.2 AU, possibly migrating there from further away, the most important contribution of an intensive microlensing search for planets may be the verification that many Jupiters are located where they are likely to have formed, thereby preserving the space closer to the stars for terrestrial planets.