Cuspy dark matter haloes and the Galaxy

The microlensing optical depth to Baade's Window constrains the minimum total mass in baryonic matter within the Solar circle to be greater than ∼     , assuming the inner Galaxy is barred with viewing angle ∼20°. From the kinematics of solar neighbourhood stars, the local surface density of dark matter is ∼     . We construct cuspy haloes normalized to the local dark matter density and calculate the circular-speed curve of the halo in the inner Galaxy. This is added in quadrature to the rotation curve provided by the stellar and ISM discs, together with a bar sufficiently massive so that the baryonic matter in the inner Galaxy reproduces the microlensing optical depth. Such models violate the observational constraint provided by the tangent-velocity data in the inner Galaxy (typically at radii     . The high baryonic contribution required by the microlensing is consistent with implications from hydrodynamical modelling and the pattern speed of the Galactic bar. We conclude that the cuspy haloes favoured by the cold dark matter cosmology (and its variants) are inconsistent with the observational data on the Galaxy.     

An Inventory of Gravitational Microlenses Toward the Galactic Bulge

Although microlensing experiments toward the Galactic bulge were originally initiated to check the feasibility of the experiments, they have now become an important tool which allows one to investigate Galactic matter composition. However, previous determination of the lens mass function was not based on the actual number of lenses even for the well-determined population of stellar lenses, but rather on arbitrarily assumed functional forms such as power laws, and thus the derived mass functions were subject to large uncertainties. In this paper, we take a different approach in which we first estimate the event rate distribution expected from observationally well-constrained populations of lenses, and then test other possible lens populations. By comparing the determined event rate distribution Γ( t _E) for various mass function models of lens populations with the observed distribution, we find that stars and white dwarfs explain just ∼ 50 per cent of the total observed events even including very faint stars just above the hydrogen-burning limit. Additionally, the expected time-scale distribution of events caused by these known populations of lenses deviates significantly from the observed distribution, especially in the short time-scale region. However, if the rest of the dynamical mass of the bulge (∼ 2.1 × 10¹⁰ M) is composed of brown dwarfs, the expected event rate distribution matches the observation well.     

Contribution to the search for binaries among Am stars – VIII. New spectroscopic orbits of eight systems and statistical study of a sample of 91 Am stars

Red clump giant (RCG) stars can be used as distance indicators to trace the mass distribution of the Galactic bar. We use RCG stars from 44 bulge fields from the OGLE-II microlensing collaboration data base to constrain analytic triaxial models for the Galactic bar. We find the bar major-axis is oriented at an angle of 24°–27° to the Sun–Galactic Centre line-of-sight. The ratio of semimajor and semiminor bar axis scalelengths in the Galactic plane   x ₀, y ₀  , and vertical bar scalelength z ₀, is   x ₀ :  y ₀ :  z ₀= 10 : 3.5 : 2.6  , suggesting a slightly more prolate bar structure than the working model of Gerhard which gives the scalelength ratios as   x ₀ :  y ₀ :  z ₀= 10 : 4 : 3  .     

The G-dwarf problem in the Galactic spheroid

This paper has two parts: one about observational constraints, and the other about chemical evolution models. In the first part, the empirical differential metallicity distribution (EDMD) is deduced from two different samples involving (i) 268 K-giant bulge stars [Sadler, E.M., Rich, R.M., Terndrup, D.M., 1996. AJ 112, 171], and (ii) 149 globular clusters [Mackey, A.D., van den Bergh, S., 2005. MNRAS 360, 631], in addition to previous results (Caimmi, R., 2001b, AN 322, 241 (C01)) related to (iii) 372 solar neighbourhood halo subdwarfs [Ryan, S.G., Norris, J.E., 1991. AJ 101, 1865]. Under the assumption that each distribution is typical for the corresponding subsystem, the EDMD of the Galactic spheroid is determined by weighting the mass. The empirical age-metallicity relation (EAMR) involving absolute ages is deduced from recent results related to a homogeneous sample of globular clusters [De Angeli, F., Piotto, G., Cassisi, S., et al., 2005. AJ 130, 116]. In the second part, models of chemical evolution for the Galactic halo and bulge are computed, assuming the instantaneous recycling approximation. The EDMD data are fitted, to an acceptable extent, by simple models of chemical evolution implying both homogeneous and inhomogeneous star formation, provided that star formation is inhibited during halo formation and enhanced during bulge formation, with respect to the disk solar neighbourhood, taken to be representative of the whole disk. The initial mass function (IMF) is assumed to be a universal power law, which implies the same value of the true yield in different subsystems. The theoretical differential metallicity distribution (TDMD) is first determined for the halo and the bulge separately, and then for the Galactic spheroid by weighting the mass. The EAMR cannot be fitted into the Simple model that implies homogeneous star formation, but shows a non-monotonic trend characterized by large dispersion. On the other hand, simple models involving inhomogeneous star formation yield a theoretical age-metallicity relation (TAMR) which reproduces the data to an acceptable extent. For gas ouflow from the proto-halo, acceptable models give rise to different predictions in different alternatives. If the Galactic spheroid and disk underwent decoupled chemical evolution, i.e. no gas exchange between the related reservoirs, less than one third of the bulge mass outflowed from the proto-halo. If the Galactic spheroid and disk underwent coupled chemical evolution, i.e. some gas exchange between the related reservoirs, the existence of an unseen baryonic halo (or equivalent amount of gas lost by the Galaxy) with mass comparable to bulge mass, is necessarily needed. In this view, the outflowing proto-halo gas which remains bound to the Galaxy, produces both the bulge and the disk.     

Predictions on the detection of the free-floating planet population with K2 and spitzer microlensing campaigns

The K2’s Campaign 9 (K2C9) by the Kepler satellite for microlensing observations towards the Galactic bulge started on April 7, 2016, and is going to last for about three months. It offers the first chance to measure the masses of members of the large population of the isolated dark low-mass objects further away in our Galaxy, free-floating planets (FFPs). Intentionally, this observational period of K2 will overlap with that of the 2016 Spitzer follow-up microlensing project expected to start in June, 2016. Therefore, for the first time it is going to be possible to observe simultaneously the same microlensing events from a ground-based telescope and two satellites. This will help in removing the two-fold degeneracy of the impact parameter and in estimating the FFP mass, provided that the angular Einstein ring radius Θ_E is measured. In this paper we calculate the probability that a microlensing event is detectable by two or more telescopes and study how it depends on the mass function index of FFPs and the position of the observers on the orbit.     

The astrometric signal of microlensing events caused by free floating planets

Astrometric observations of microlensing events can be used to obtain important information about lenses. During these events, the shift of the position of the multiple image centroid with respect to the source star location can be measured. This effect, which is expected to occur on scales from micro-arcseconds to milli-arcseconds, depends on the lens-source-observer system physical parameters. Here, we consider the astrometric and photometric observations by space and ground-based telescopes of microlensing events towards the Galactic bulge caused by free floating planets (FFPs). We show that the efficiency of astrometric signal on photometrically detected microlensing events tends to increase for higher FFP masses in our Galaxy. In addition, we estimate that during five years of the Gaia observations, about a dozen of microlensing events caused by FFPs are expected to be detectable.     

The Chemical Evolution of the Galactic Bulge

In this paper we review the chemical evolution models for the Galactic bulge: in particular, we discuss the predictions of models as compared with the available abundance data and infer the mechanism as well as the time scale for the formation of the Galactic bulge. We show that good chemical evolution models reproducing the observed metallicity distribution of stars in the bulge predict that the [α/Fe] >0 over most of the metallicity range. This is a very important constraint indicating that the bulge of our Galaxy formed at the same time and even faster than the inner Galactic halo. We also discuss predictions for the evolution of light elements such as D and ⁷Li and conclude that the D astration should be maximum due to the high star formation rate required for the bulge whereas the evolution of the abundance of Li should be similar to that observed in the solar neighbourhood, but with an higher Li abundance in the interstellar medium at the present time. This revised version was published online in July 2006 with corrections to the Cover Date.     

Repeating microlensing events in the OGLE data

Microlensing events are usually selected among single-peaked non-repeating light curves in order to avoid confusion with variable stars. However, a microlensing event may exhibit a second microlensing brightening episode when the source or/and the lens is a binary system. A careful analysis of these repeating events provides an independent way to study the statistics of wide binary stars and to detect extrasolar planets. Previous theoretical studies predicted that 0.5–2 per cent of events should repeat due to wide binary lenses. We present a systematic search for such events in about 4000 light curves of microlensing candidates detected by the Optical Gravitational Lensing Experiment (OGLE) towards the Galactic bulge from 1992 to 2007. The search reveals a total of 19 repeating candidates, with six clearly due to a wide binary lens. As a by-product, we find that 64 events (∼2 per cent of the total OGLE-III sample) have been misclassified as microlensing; these misclassified events are mostly nova or other types of eruptive stars. The number and importance of repeating events will increase considerably when the next-generation wide-field microlensing experiments become fully operational in the future.     

The structure of the Galactic bar

We present a deep near-infrared wide-angle photometric analysis of the structure of the inner Galactic bar and central disc. The presence of a triaxial structure at the centre of the Galaxy is confirmed, consistent with a bar inclined at  22°± 55  from the Sun—Galactic Centre line, extending to approximately 2.5 kpc from the Galactic Centre and with a rather small axis ratio. A feature at  ℓ=−98  not aligned with this triaxiality suggests the existence of a second structure in the inner Galaxy, a double triaxiality or an inner ring. We argue that this is likely to be the signature of the end of the Galactic bar, at approximately 2.5–3 kpc, which is circumscribed by an inner pseudo-ring. No thick dust lane preceding the bar is detected and a hole in the dust distribution of the disc inside the bar radius is inferred.     

Can Jupiters be found by monitoring Galactic bulge microlensing events from northern sites?

In 1998 the EXPORT team monitored microlensing event light curves using a charge-coupled device (CCD) camera on the IAC 0.8-m telescope on Tenerife to evaluate the prospect of using northern telescopes to find microlens anomalies that reveal planets orbiting the lens stars. The high airmass and more limited time available for observations of Galactic bulge sources make a northern site less favourable for microlensing planet searches. However, there are potentially a large number of northern 1-m class telescopes that could devote a few hours per night to monitor ongoing microlensing events. Our IAC observations indicate that accuracies sufficient to detect planets can be achieved despite the higher airmass.     

New constraints on a triaxial model of the Galaxy

We determine the most likely values of the free parameters of an N -body model for the Galaxy developed by Fux via a discrete–discrete comparison with the positions on the sky and line-of-sight velocities of an unbiased, homogeneous sample of OH/IR stars. Via Monte Carlo simulation, we find the plausibility of the best-fitting models, as well as the errors on the determined values. The parameters that are constrained best by these projected data are the total mass of the model and the viewing angle of the central bar, although the distribution of the latter has multiple maxima. The other two free parameters, the size of the bar and the (azimuthal) velocity of the Sun, are less well-constrained. The best model has a viewing angle of ∼ 44°, a semimajor axis of 2.5 kpc (corotation radius 4.5 kpc, pattern speed 46 km s⁻¹ kpc⁻¹), a bar mass of 1.7×10¹⁰ M_⊙ and a tangential velocity of the local standard of rest of 171 km s⁻¹. We argue that the lower values that are commonly found from stellar data for the viewing angle (∼25°) arise when too few coordinates are available, when the longitude range is too narrow or when low latitudes are excluded from the fit. The new constraints on the viewing angle of the Galactic bar from stellar line-of-sight velocities decrease further the ability of the distribution of the bar to account for the observed microlensing optical depth toward Baade's window: our model reproduces only half the observed value. The signal of triaxiality diminishes quickly with increasing latitude, fading within approximately 1 scaleheight (≲3°). This suggests that Baade's window is not a very appropriate region in which to sample bar properties.     

Chromatic and spectroscopic signatures of microlensing events as a tool for the gravitational imaging of stars

The detection of microlensing events from stars in the Large Magellanic Cloud and in the Galactic bulge raises important constraints on the distribution of dark matter and on galactic structure, although some events may be the result of a new type of intrinsic variability. When lenses are relatively close to the sources, we predict that chromatic and spectroscopic effects are likely to appear for a significant fraction of the microlensing events. These effects are due to the differential amplification of the limb and the centre of the stellar disc, and present a systematic dependence with wavelength and time that provides an unambiguous signature of a microlensing event (as opposed to a new type of intrinsic stellar variability). We present detailed predictions of the effects, using realistic model atmospheres. The observations of these effects provide a direct constraint on stellar atmospheres, allowing a three-dimensional reconstruction or imaging of its structure, a unique tool with which to test the current models of stellar atmospheres.     

The polarization signature from microlensing of circumstellar envelopes in caustic crossing events

In recent years, it has been shown that microlensing is a powerful tool for examining the atmospheres of stars in the Galactic bulge and Magellanic Clouds. The high gradient of magnification across the source during both small impact parameter events and caustic crossings offers a unique opportunity for determining the surface brightness profile of the source. Furthermore, models indicate that these events can also provide an appreciable polarization signal: arising from differential magnification across the otherwise symmetric source. Earlier work has addressed the signal from a scattering photosphere for both point mass lenses and caustic crossings. In a previous paper, polarimetric variations from point lensing of a circumstellar envelope were considered, as would be suitable for an extended envelope around a red giant. In this work, we examine the polarization in the context of caustic crossing events, the scenario that represents the most easily accessible situation for actually observing a polarization signal in Galactic microlensing. Furthermore, we present an analysis of the effectiveness of using the polarimetric data to determine the envelope properties, illustrating the potential of employing polarimetry in addition to photometry and spectroscopy with microlensing follow-up campaigns.     

Stochastic distributions of lens and source properties for observed galactic microlensing events

A comprehensive new approach is presented for deriving probability densities of physical properties characterizing the lens and source that constitute an observed galactic microlensing event. While previously encountered problems are overcome, constraints from event anomalies and model parameter uncertainties can be incorporated into the estimates. Probability densities for given events need to be carefully distinguished from the statistical distribution of the same parameters among the underlying population from which the actual lenses and sources are drawn. Using given model distributions of the mass spectrum, the mass density, and the velocity distribution of Galactic disc and bulge constituents, probability densities of lens mass, distance, and the effective lens–source velocities are derived, where the effect on the distribution that arises from additional observations of annual parallax or finite-source effects, or the absence of significant effects, is shown. The presented formalism can also be used to calculate probabilities for the lens to belong to one or another population and to estimate parameters that characterize anomalies. Finally, it is shown how detection efficiency maps for binary-lens companions in the physical parameters, such as companion mass and orbital semimajor axis, arise from values determined for the mass ratio and dimensionless projected separation parameter, including the deprojection of the orbital motion for elliptical orbits. Compared to the naive estimate based on 'typical values', the detection efficiency for low-mass companions is increased by mixing in higher detection efficiencies for smaller mass ratios (i.e. smaller masses of the primary).     

Another channel to detect close-in binary companions via gravitational microlensing

Gaudi & Gould showed that close companions of remote binary systems can be efficiently detected by using gravitational microlensing via the deviations in the lensing light curves induced by the existence of the lens companions. In this paper, we introduce another channel to detect faint close-in binary companions by using microlensing. This method utilizes a caustic-crossing binary lens event with a source also composed of binary stars, where the companion is a faint star. Detection of the companion is possible because the flux of the companion can be highly amplified when it crosses the lens caustic. The detection is facilitated since the companion is more amplified than the primary because it, in general, has a smaller size than the primary, and thus experiences less finite source effect. The method is an extension of the previous one suggested to detect close-in giant planets by Graff & Gaudi and Lewis & Ibata and further developed by Ashton & Lewis. From the simulations of realistic Galactic bulge events, we find that companions of K-type main-sequence or brighter stars can be efficiently detected from the current type of microlensing follow-up observations by using the proposed method. We also find that compared with the method of detecting lens companions for which the efficiency drops significantly for binaries with separations ≲0.2 of the angular Einstein ring radius, θ _E, the proposed method has an important advantage of being able to detect companions with substantially smaller separations down to ∼     .     

Effects of gravitational microlensing of binary and multiple stars

The observation of microlensing events towards the Large Magellanic Cloud and Galactic Bulge discovers a new population of our Galaxy which is that of dark bodies with masses of the order of 0.1M . Astronomy has now a unique ability: one can use the microlensing as a space telescope with extremely high angular resolution. Here we discuss the opportunity of the application of this ability to observation of close binaries. Stars in a binary system move around their barycenter and as a result the apparent motion is modulated by binary motion. The light curve of this microlensing event becomes nonsymmetrical. If a binary has two stars with different spectral types, one can expect significant variation of color during microlensing effect. Accurate light curves for some typical binaries have been calculated and are presented here. The total fraction of binaries in our Galaxy is around 50%. Therefore one can expect half of the microlensing events to have nonsymmetrical and wavelength depending light curves which would indicate that background star is binary. Our opinion is that the absence of these light curves are due to some selection effect. This leads to an underestimation of the density of the dark body population in our Galaxy by a factor of about two.     

Search for exotic matter from gravitational microlensing observations of stars

We consider small-scale spheroidal clusters of weakly interacting massive particles in our Galaxy as non-compact gravitational microlenses and predict the appearance of caustics in the plane of a lensed source. The crossing of these caustics by a lensed star can produce a large variety of light curves, including some observed in actual microlensing events that have been interpreted as manifestations of binary gravitational lenses. We consider also observable effects during the gravitational microlensing of stars of non-zero angular size with a given brightness distribution across their disks by such an exotic objects as natural wormholes and objects whose space-time environment is described with the NUT metric. We demonstrate that, under certain conditions, the microlensing light curves, chromatic and polarizational effects due to the properties of the lens and the star disk brightness distributions can differ considerably from those observed for a Schwarzschild gravitational lens, so that their analysis can facilitate the identification of such objects.     

Rotating haloes and the microlensing MACHO mass estimate

We investigate the implications of a bulk rotational component of the Galactic halo velocity distribution for MACHO mass estimates. We find that for a rotating halo to yield a MACHO mass estimate significantly below that of the standard spherical case, its microlensing must be highly concentrated close to the Sun. We examine two classes of models fitting this criterion: a highly flattened 1/ r ² halo, and a spheroid-like population the density of which falls off as 1/ r ^3.5. The highly flattened 1/ r ² models can decrease the implied average MACHO mass only marginally, and the spheroid models not at all. Generally, rotational models cannot bring the MACHO mass implied by the current microlensing data down to the substellar range.     

The direct detection of non-baryonic dark matter in the Galaxy?

It has been argued in a number of recent papers that dark matter is in the form of Jupiter-mass primordial black holes that betray their presence by microlensing quasars. This lensing accounts for a number of characteristic properties of quasar light curves, in both single quasars and gravitationally lensed multiple systems, that are not explained on the basis of intrinsic variation. One prediction of this idea is that Jupiter-mass bodies will be detected by the MACHO experiment as short events of about 2 d duration, although the expected frequency of detection is still very hard to estimate. However, the recent report by the MACHO group of the detection of a Jupiter-mass body in the direction of the Galactic bulge is consistent with this prediction, and is possibly the first direct detection of non-baryonic matter in the Galaxy.     

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 the Galactic halo and self-lensing gravitational microlensing 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, ℓ, 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 〈 M 〉∼0.5 M_⊙, the optimal binary separation range of Galactic halo events of 3.5 au≲ℓ≲14 au matches well with that of a Magellanic Cloud self-lensing event caused by a binary lens with a total mass of M ∼1 M_⊙; 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.