Engineering topics
Publications and source records attributed to Paczynski, B..
With SIM, we will break the microlensing degeneracy, and allow detailed interpretation of individual microlensing events. We will thus develop a detailed census of the dark and luminous stellar population of the Galaxy.
Models of stationary, axisymmetric, non-self-gravitating tori around stellar mass Kerr black holes are calculated. Such objects may form as a result of a merger between two neutron stars, a neutron star and a stellar mass black hole, or a 'failed supernova' collapse of a single rapidly rotating star. We explore a large range of parameters: the black hole mass and angular momentum, the torus mass, angular momentum and entropy. Physical conditions within the tori are similar to those in young and hot neutron stars, but their topology is different, and the range of masses and energies is much larger.
Surface brightness maps for thin accretion disks around Schwarzschild and Kerr black holes are presented. These disks are a few times smaller than those used by Rauch and Blandford (1991), and some of the present models are slightly less luminous than theirs. Example of microlensed light curves are calculated by convolving these accretion disk maps with the magnification patterns obtained from microlensing calculations. The light curves exhibit eventlike variations with amplitudes and time scales comparable to those observed in QSO 2237 + 0305. It is concluded that thin thermal accretion disk models are not in contradiction with the observed microlens-induced variations of QSO 2237 + 0305.
Typical light curves and the corresponding color curves are shown for the present model of QSO 2237 + 0305 A, the image that has been reported to vary. Probabilities are presented for color changes of certain amplitudes as functions of the observed magnitude changes for different intervals between the two observational epochs, different source sizes, and different source size ratios. It may be possible to find the ratio of the continuum source sizes in the two color bands, once a color change correlated with a continuum change is found.
The rate of collisions between the neutron stars is about 0.0001/yr in the galaxy and about 0.00001/yr within the Hubble distance. The collisions are the final phases of binary orbit decay driven by gravitational radiation and may produce gamma-ray bursts detectable at extragalactic distances. If strange stars exist then their collisions must release about 10 to the 50th ergs in gamma rays over 0.2 s. Such events should be detectable out to 1 Gpc with the current instruments. The distance to the majority of gamma-ray bursts is not known at this time. The Burst and Transient Source Experiment (BATSE) on Gamma Ray Observatory should determine the distance scale by determining the angular distribution of very weak bursts. If the majority of gamma-ray bursts turn out to be extragalactic, and if their distances are about 1 Gpc, then the collisions between strange stars may be the least speculative events that might account for so energetic bursts.
The optical depth to microlensing on the ordinary disk stars is about 4 x 10 to the -7th for the Galactic bulge stars visible in Baade's window. This means that at any given time one out of about 2.5 x 10 to the 6th bulge stars must be brightened by at least 0.3 mag. The duration of events is proportional to the square root of mass of the lensing star, and it is in the range of 1 week to 1 month for the lensing stars of 0.1-1.0 solar mass. The average number of events with the amplitude exceeding 0.3 mag is expected to be about 4 per year per million bulge stars. If there are brown dwarfs in the Galactic disk with masses in the range 0.01-0.1 solar mass, with the total mass density equal to the total mass density of the ordinary stars, then the combined optical depth to microlensing of the bulge stars is about 8 x 10 to the -7th, the average number of events with the amplitude exceeding 0.3 mag is expected to be about 17 per year per million bulge stars, and the time scales of events are in the range of 3-20 days.
A model of microlensing for image A of the gravitationally lensed QSO 2237 + 0305 for which Irwin et al. reported in 1989 an increase of the apparent luminosity by about 0.5 mag on a time scale of a few months is presented. The model, with the Salpeter mass function over the mass range of 0.1-1.0 solar mass and the transverse velocity of the lens (or observer) of 600 km/s, can reproduce the reported luminosity variation if the source of the optical continuum has a radius smaller than about 2 x 10 to the 15th cm. This size is compatible with the accretion disk interpretation of the big ultraviolet bump in quasar spectra. The model demonstrates a very large diversity of light curves while the source crosses individual microcaustics or clusters of microcaustics. It will take more than 100 yr before the full variety of light curves will be sampled by the observations.
Models of microlensing are presented for the four images of QSO 2237 + 0305, with the surface mass density and shear for each image based on the macrolensing model developed by Schneider et al. (1988). The computations were done with a new code that makes use of the hierarchical tree method. The high efficiency of this approach makes it possible to include up to 60,000 lensing stars with different masses. Examples are given of amplification maps, light curves, correlation functions, and amplification probabilities. All these are very strongly affected by the shear due to macrolensing. The observed changes in the luminosity of the four images of QSO 2237 + 0305 are most likely induced by microlensing.
It is proposed that some, perhaps most, gamma-ray bursters are at cosmological distances, like quasars, with a redshift of about 1 or 2. This proposition requires a release of supernova-like energy of about 10 to the 51st ergs within less than 1 s, making gamma-ray bursters the brightest objects known in the universe, many orders of magnitude brighter than any quasars. This power must drive a highly relativistic outflow of electron-positron plasma and radiation from the source. It is proposed that three gamma-ray bursts, all with identical spectra, detected from B1900 + 14 by Mazets, Golenetskii, and Gur'yan and reported in 1979, were all due to a single event multiply imaged by a gravitational lens. The time intervals between the successive bursts, 10 hr to 3 days, were due to differences in the light travel time for different images.
Small random deflections of a narrow beam of radiation due to gravitational scattering by stars randomly distributed within the deflector plane are considered. Using a Fouriere transform method, the probability of scattering is obtained as a function of scattering angle for an arbitrary number of stars with an arbitrary distribution of masses. The probability density, expressed in proper units, depends on one parameter only: the effective number of stars. At small scattering angles the density is a Gaussian, and at large angles it falls off as the scattering angle to the minus fourth power. The probability distribution for scatterings is simply related to the angular distribution of the surface brightness of a macroimage, averaged over many microimages. The isophotes are ellipses, with the ratio of the major axis to the minor axis, determined by the dimensionless surface mass density and the shear of the lensing system. The number of stars that has to be included in the modeling of microlensing is proportional to the amplification due to the macrolens, and to the square of the dimensionless surface mass density.
The consequences of the hypothesis that a supermassive black hole can serve as a gravitational lens are analytically studied. It is shown that the presence of a black hole could be established by the unique property that it would appear against the microwave background as a black spot with a diameter of 0.1 arcsec or greater. The only instrument capable of either resolving the black spot or at least noticing it as a negative luminosity source is the Very Large Array.
A simple model of microlensing by massive objects that might be present in the halo of the Galaxy is presented. It is shown that in any nearby galaxy one star out of a million is strongly microlensed by a 'dark' object located in the Galactic halo, if the halo is made up of objects more massive than about 10 to the -8th solar mass. Monitoring the brightness of a few million stars in the Magellanic Clouds over a time scale between two hours and two years may lead to a discovery of 'dark halo' objects between 10 to the -6th and 10 to the -2nd solar mass, or it may put strong upper limits on the number of such objects.
A large number of numerical models of gravitational microlensing by stars in the lensing galaxy have been calculated, and properties of the models are described. The expected light intensity variations are more rapid when optical depth to microlensing is large, but the time scale is a few years in the best cases, and much longer in a typical case. However, microlensing introduces considerable scatter, up to two or three orders of magnitude, to the intensity of macroimages expected at any given time, and this may considerably complicate the analysis of the observed lenses. It is shown that macroimage is surrounded with a faint 'halo' made of a large number of microimages from individual stars with average surface brightness falling off as R to the -4th. It is also shown that a high surface mass density of continuously distributed matter may affect very strongly properties of microlensing, making possible very large declines in observed intensity, up to two or three orders of magnitude.
Preliminary results are reported for detailed calculations of ten successive helium flashes in Population I stars of 3 and 3.3 solar masses. The calculations have been conducted to determine whether an inner-shell convection zone that is driven outward from the center of the helium-burning shell by the flashes can penetrate into the hydrogen-rich zones of a star. Based on the present incomplete calculations, the process of flash evolution is outlined, the relationship between core mass and interflash period is described together with the relationship between core mass and intershell mass, and nucleosynthesis during helium-shell flash burning is considered. The results thus far indicate that the flashes increase in strength and consist of up to five subcomponents, the mass of the degenerate carbon-oxygen core may determine the interflash period as well as the intershell mass, and that helium flash burning produces mostly C-12 and a small amount of O-16.