The distribution of microlensed light-curve derivatives: the relationship between stellar proper motions and transverse velocity

We present a method for computing the probability distribution of microlensed light-curve derivatives both in the case of a static lens with a transverse velocity, and in the case of microlensing that is produced through stellar proper motions. The distributions are closely related in form, and can be considered equivalent after appropriate scaling of the input transverse velocity. The comparison of the distributions in this manner provides a consistent way to consider the relative contribution to microlensing (both large and small fluctuations) of the two classes of motion, a problem that is otherwise an extremely expensive computational exercise. We find that the relative contribution of stellar proper motions to the microlensing rate is independent of the mass function assumed for the microlenses, but is a function of optical depth and shear. We find that stellar proper motions produce a higher overall microlensing rate than a transverse velocity of the same magnitude. This effect becomes more pronounced at higher optical depth. With the introduction of shear, the relative rates of microlensing become dependent on the direction of the transverse velocity. This may have important consequences in the case of quadruply lensed quasars such as Q2237+0305, where the alignment of the shear vector with the source trajectory varies between images.     

On the probability of microlensing in gamma-ray burst afterglows

The declining light curve of the optical afterglow of gamma-ray burst (GRB) GRB000301C showed rapid variability with one particularly bright feature at about t − t ₀=3.8 d. This event was interpreted as gravitational microlensing by Garnavich, Loeb & Stanek and subsequently used to derive constraints on the structure of the GRB optical afterglow. In this paper, we use these structural parameters to calculate the probability of such a microlensing event in a realistic scenario, where all compact objects in the universe are associated with observable galaxies. For GRB000301C at a redshift of z =2.04, the a posteriori probability for a microlensing event with an amplitude of Δ m 0.95 mag (as observed) is 0.7 per cent (2.7 per cent) for the most plausible scenario of a flat Λ-dominated Friedmann–Robertson–Walker (FRW) universe with Ω_m=0.3 and a fraction f ∗=0.2 (1.0) of dark matter in the form of compact objects. If we lower the magnification threshold to Δ m 0.10 mag, the probabilities for microlensing events of GRB afterglows increase to 17 per cent (57 per cent). We emphasize that this low probability for a microlensing signature of almost 1 mag does not exclude that the observed event in the afterglow light curve of GRB000301C was caused by microlensing, especially in light of the fact that a galaxy was found within 2 arcsec from the GRB. In that case, however, a more robust upper limit on the a posteriori probability of ≈5 per cent is found. It does show, however, that it will not be easy to create a large sample of strong GRB afterglow microlensing events for statistical studies of their physical conditions on microarcsec scales.     

Gamma—Ray Bursts：Afterglows and Central Engines

Gamma-ray bursts (GRBs) are the most intense transient gamma-ray events in the sky; this, together with the strong evidence (the isotropic and inhomogeneous distribution of GRBs detected by BASTE) that they are located at cosmological distances, makes them the most energetic events ever known. For example, the observed radiation energies of some GRBs are equivalent to the total convertion into radiation of the mass energy of more than one solar mass. This is thousand times stronger than the energy of a supernova explosion. Some unconventional energy mechanism and extremely high conversion efficiency for these mysterious events are required. The discovery of host galaxies and association with supernovae at cosmoligical distances by the recently launched satellite of BeppoSAX and ground based radio and optical telescopes in GRB afterglow provides further support to the cosmological origin of GRBs and put strong constraints on their central engine. It is the aim of this article to review the possible central engines, energy mechanisms, dynamical and spectral evolution of GRBs, especially focusing on the afterglows in multi-wavebands.     

Microlensing by halo MACHOs with a spatially varying mass function

The main aim of microlensing experiments is to evaluate the mean mass of massive compact halo objects (MACHOs) and the mass fraction of the Galactic halo made by this type of dark matter. Statistical analysis shows that by considering a Dirac-Delta mass function (MF) for the MACHOs, their mean mass is about that of a white dwarf star. This result is, however, in discrepancy with other observations such as those of non-observed expected white dwarfs in the Galactic halo which give rise to metal abundance, polluting the interstellar medium by their evolution. Here we use the hypothesis of the spatially varying MF of MACHOs, proposed by Kerins and Evans to interpret microlensing events. In this model, massive lenses with a lower population contribute to the microlensing events more frequently than do dominant brown dwarfs. This effect causes the mean mass of the observed lenses to be larger than the mean mass of all the lenses. A likelihood analysis is performed to find the best parameters of the spatially varying MF that are compatible with the duration distribution of Large Magellanic Cloud microlensing candidates of the MACHO experiment.     

Microlensing in dark matter haloes

Using eight dark matter haloes extracted from fully self-consistent cosmological N -body simulations, we perform microlensing experiments. A hypothetical observer is placed at a distance of 8.5 kpc from the centre of the halo measuring optical depths, event durations and event rates towards the direction of the Large Magellanic Cloud. We simulate 1600 microlensing experiments for each halo. Assuming that the whole halo consists of massive astronomical compact halo objects (MACHOs),   f = 1.0  , and a single MACHO mass is   m _M= 1.0 M_⊙  , the simulations yield mean values of  τ= 4.7^+5.0_−2.2× 10⁻⁷  and  Γ= 1.6^+1.3_−0.6× 10⁻⁶  events star⁻¹ yr⁻¹. We find that triaxiality and substructure can have major effects on the measured values so that τ and Γ values of up to three times the mean can be found. If we fit our values of τ and Γ to the MACHO collaboration observations, we find   f = 0.23^+0.15_−0.13  and   m _M= 0.44^+0.24_−0.16  . Five out of the eight haloes under investigation produce f and m _M values mainly concentrated within these bounds.     

Microlensing of tidal debris on the Magellanic great circle

Increasing evidence suggests that the Galactic halo is lumpy on kpc scales as a result of the accretion of at least a dozen small galaxies [Large and Small Magellanic Clouds (LMC/SMC), Sgr, Fornax, etc.]. Faint stars in such lumpy structures can significantly microlense a background star with an optical depth of 10⁻⁷–10⁻⁶, which is comparable to the observed value to the LMC. The observed microlensing events towards the LMC can be explained by a tidal debris tail from the progenitor of the Magellanic Clouds and Magellanic Stream. The LMC stars can either lense stars in the debris tail a few kpc behind the LMC, or be lensed by stars in the part of the debris tail in front of the LMC. The models are consistent with an elementary particle dominated Galactic halo without massive compact halo objects (MACHOs). They also differ from Sahu's LMC-self-lensing model by predicting a higher optical depth and event rate and lower concentration of events to the LMC centre.     

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.     

The physical parameters of Markarian 501 during flaring activity

We analyse an N -body simulation of the Small Magellanic Cloud (SMC), that of Gardiner & Noguchi, to determine its microlensing statistics. We find that the optical depth owing to self-lensing in the simulation is low, 0.4×10⁻⁷, but still consistent (at the 90 per cent level) with that observed by the EROS and MACHO collaborations. This low optical depth is due to the relatively small line-of-sight thickness of the SMC produced in the simulation. The proper motions and time-scales of the simulation are consistent with those observed assuming a standard mass function for stars in the SMC. The time-scale distribution from the standard mass function generates a significant fraction of short time-scale events: future self-lensing events towards the SMC may have the same time-scales as events observed towards the Large Magellanic Cloud (LMC). Although some debris was stripped from the SMC during its collision with the LMC about 2×10⁸ yr ago, the optical depth of the LMC owing to this debris is low, a few ×10⁻⁹, and thus cannot explain the measured optical depth towards the LMC.     

The environments of short-duration gamma-ray bursts and implications for their progenitors

The study of short-duration gamma-ray bursts (GRBs) experienced a complete revolution in recent years thanks to the discovery of the first afterglows and host galaxies starting in May 2005. These observations demonstrated that short GRBs are cosmological in origin, reside in both star forming and elliptical galaxies, are not associated with supernovae, and span a wide isotropic-equivalent energy range of ～10⁴⁸–10⁵² erg. However, a fundamental question remains unanswered: What are the progenitors of short GRBs? The most popular theoretical model invokes the coalescence of compact object binaries with neutron star and/or black hole constituents. However, additional possibilities exist, including magnetars formed through prompt channels (massive star core-collapse) and delayed channels (binary white dwarf mergers, white dwarf accretion-induced collapse), or accretion-induced collapse of neutron stars. In this review I summarize our current knowledge of the galactic and sub-galactic environments of short GRBs, and use these observations to draw inferences about the progenitor population. The most crucial results are: (i) some short GRBs explode in dead elliptical galaxies; (ii) the majority of short GRBs occur in star forming galaxies; (iii) the star forming hosts of short GRBs are distinct from those of long GRBs, and instead appear to be drawn from the general field galaxy population; (iv) the physical offsets of short GRBs relative to their host galaxy centers are significantly larger than for long GRBs; (v) there is tentative evidence for large offsets from short GRBs with optical afterglows and no coincident hosts; (vi) the observed offset distribution is in good agreement with predictions for NS–NS binary mergers; and (vii) short GRBs trace under-luminous locations within their hosts, but appear to be more closely correlated with the rest-frame optical light (old stars) than the UV light (young massive stars). Taken together, these observations suggest that short GRB progenitors belong to an old stellar population with a wide age distribution, and generally track stellar mass. These results are fully consistent with NS–NS binary mergers and rule out a dominant population of prompt magnetars. However, a partial contribution from delayed magnetar formation or accretion-induced collapse is also consistent with the data.     

Supernovae-optical precursors of short gamma-ray bursts

The probability of observing “supernova-gamma-ray burst” (GRB) pair events and recurrent GRBs from one galaxy in a time interval of several years has been estimated. Supernova explosions in binary systems accompanied by the formation of a short-lived pair of compact objects can be the sources of such events. If a short GRB is generated during the collision of a pair, then approximately each of ∼300 short GRBs with redshift z must have an optical precursor—a supernova in the observer’s time interval <2(1 + z) yr. If the supernova explosion has the pattern of a hypernova, then a successive observation of long and short GRBs is possible. The scenario for the generation of multiple GRBs in collapsing galactic nuclei is also discussed.     

Cosmological models of gamma-ray bursts

We review models of cosmological gamma-ray bursts (GRBs). The statistical and -ray transparency issues are summarized. Neutron-star and black-hole merger scenarios are described and estimates of merger rates are summarized. We review the simple fireball models for GRBs and the recent work on non-simple fireballs. Alternative cosmological models, including models where GRBs are analogs of active galactic nuclei and where they are produced by high-field, short period pulsars, are also mentioned. The value of neutrino astronomy to solve the GRB puzzle is briefly reviewed.     

Bright bursts and the GRB distance scale

We discuss the use of selected characteristics of the burster population (e.g. the distribution of peak fluxes, or durations) to derive the GRB distance scale within the framework of cosmological models. The effects of the cosmological expansion on GRBs are briefly noted and it is shown that intrinsic GRB properties may strongly complicate the search for (and the interpretation of) purely cosmological effects. In this context, bright GRBs provide a sample of reference; they are almost free of cosmological influences and they have been studied for a long time. We also emphasize the need for a GRB distance indicator which could be used for individual events; several recent studies suggest that such a quantity may exist.     

Dense star clusters as the sources of gamma-ray-burst progenitors

Two independent sets of arguments lead us to conclude that the progenitors of superintense bursts (with an energy yield larger than that for ordinary supernovae by one or two orders of magnitude) are born in massive dense star clusters, but generally flare up only after they have left the cluster; these are the same objects that are the progenitors of gamma-ray bursts (GRBs). Each of the giant stellar arcs which are grouped into multiple systems of stellar complexes in the LMC and NGC 6946 could only be produced by a single powerful energy release near its center. The progenitors of these systems of arc-shaped stellar complexes must have had a common source nearby, and it could only be a massive star cluster. Such clusters are actually known near both systems. On the other hand, calculations of the dynamical evolution of star clusters show that close binary systems of compact objects are formed in the dense central parts of the clusters and are then ejected from them during triple encounters. Mergers of the components of such systems are believed to be responsible for GRBs. Since their progenitors are ejected from the cluster before merging, the arc-shaped stellar complexes produced by GRBs are observed near (but not around) the parent clusters. If a considerable fraction of the GRB progenitors are formed as a result star encounters in massive star clusters, and if the GRBs themselves trigger star formation near the parent clusters, then observations of GRBs in star-forming regions are consistent with their origin during mergers of pairs of compact objects.     

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.     

Are there cosmological evolution trends on gamma-ray burst features?

The variability of a gamma-ray burst (GRB) is thought to be correlated with its absolute peak luminosity, and this relation had been used to derive an estimate of the redshifts of GRBs. Recently, Amati et al. presented the results of spectral and energetic properties of several GRBs with known redshifts. Here, we analyse the properties of two groups of GRBs: one group with known redshift from afterglow observation and another group with redshift derived from the luminosity–variability relation. We study the redshift dependence of various GRBs features in their cosmological rest frames, including the burst duration, the isotropic luminosity and radiated energy, and the peak energy E_p of ν F _ν spectra. We find that, for these two groups of GRBs, their properties are all redshift-dependent, i.e. their intrinsic duration, luminosity, radiated energy and peak energy E_p are all correlated with the redshift, which means that there are cosmological evolution effects on gamma-ray burst features, and this can provide an interesting clue to the nature of GRBs. If this is true, then the results also imply that the redshift derived from the luminosity–variability relation may be reliable.     

Microlensing of an extended source by a power-law mass distribution

Microlensing promises to be a powerful tool for studying distant galaxies and quasars. As the data and models improve, there are systematic effects that need to be explored. Quasar continuum and broad-line regions may respond differently to microlensing due to their different sizes; to understand this effect, we study microlensing of finite sources by a mass function of stars. We find that microlensing is insensitive to the slope of the mass function but does depend on the mass range. For negative-parity images, diluting the stellar population with dark matter increases the magnification dispersion for small sources and decreases it for large sources. This implies that the quasar continuum and broad-line regions may experience very different microlensing in negative-parity lensed images. We confirm earlier conclusions that the surface brightness profile and geometry of the source have little effect on microlensing. Finally, we consider non-circular sources. We show that elliptical sources that are aligned with the direction of shear have larger magnification dispersions than sources with perpendicular alignment, an effect that becomes more prominent as the ellipticity increases. Elongated sources can lead to more rapid variability than circular sources, which raises the prospect of using microlensing to probe source shape.     

Cosmic microwave background constraints on the epoch of reionization

We use a compilation of cosmic microwave anisotropy data to constrain the epoch of reionization in the Universe, as a function of cosmological parameters. We consider spatially flat cosmologies, varying the matter density Ω₀ (the flatness being restored by a cosmological constant), the Hubble parameter h and the spectral index n of the primordial power spectrum. Our results are quoted both in terms of the maximum permitted optical depth to the last-scattering surface, and in terms of the highest allowed reionization redshift assuming instantaneous reionization. For critical-density models, significantly tilted power spectra are excluded as they cannot fit the current data for any amount of reionization, and even scale-invariant models must have an optical depth to last scattering of below 0.3. For the currently favoured low-density model with Ω₀=0.3 and a cosmological constant, the earliest reionization permitted to occur is at around redshift 35, which roughly coincides with the highest estimate in the literature. We provide general fitting functions for the maximum permitted optical depth, as a function of cosmological parameters. We do not consider the inclusion of tensor perturbations, but if present they would strengthen the upper limits that we quote.     

Gamma-Ray Bursts: Should cosmologists care?

Gamma-Ray Burst (GRB) locations are distributed isotropically on the sky, but the intensity distribution of the bursts seems clearly incompatible with spatial homogeneity. Of the scenarios that attempt to provide an explanation, there are two that enjoy current popularity: (1) GRBs are produced by high-velocity neutron stars that have formed an extended (100 kpc) spherical halo or corona around our galaxy. (2) The bursters are at cosmological distances, with redshifts near unity for the weaker events. The major evidence used to argue for or against each of these scenarios remains inconclusive. Assuming, not unreasonably, that the cosmological scenario is correct, one can discuss the advantages and disadvantages of studying GRBs as opposed to other objects at moderate redshift. We find that the advantages of GRBs-high intensity, penetrating radiation, rapid variability, and no expected source evolution-are offset by observational difficulties pertaining to the extraction of cosmological information from GRB data. If the cosmological scenario proves to be correct and if the observational difficulties are overcome, then cosmologists certainly should care.     

Delay of emission from extragalactic gamma-ray burst sources as a test for selecting a model of the universe

We obtained an order-of-magnitude estimate for the dispersion of light caused by the effect of quantum fluctuations on the propagation of electromagnetic waves in four-dimensional spacetime. We calculated the delay of the photons from cosmological gamma-ray bursts (GRBs) for the flat, open, and closed cosmological models. This delay is attributable to the effect of expansion of the Universe on the propagation of a dispersive light wave in space. Analysis shows that the delay of GRB photons contains a regular component related to the expansion of the Universe. We conclude that cosmological models of the Universe can be selected by the delay of emission of various energies from GRBs; the accuracy of measuring the parameter Δt/ΔE _γ must be no lower than 10^?6 s MeV^?1.     

The transparency of the Universe limited by Lyα clouds

The brightnesses of supernovae are commonly understood to indicate that cosmological expansion is accelerating due to dark energy. However the entire discussion presumes a perfectly transparent universe because no effects of reddening associated with the interstellar extinction law are seen. We note that with two kinds of dark matter (baryonic and nonbaryonic) strongly dominating the known mass of the universe, it is seriously premature to assume that these dark matter components have not reduced the transmission of the universe for cosmological sources. We show that the long‐known Lyα clouds, if nucleated by the population of baryonic dark matter primordial planetoids indicated by quasar microlensing, would act as spherical lenses and achromatically fade cosmologically distant sources. We attempt to estimate the amount of this cosmological fading, but ultimately the calculation is limited by lack of a satisfactory model for the tenuous outer parts of a primordial planetoid. We also consider the effects of such cosmological fading on the light of quasars. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)