Attributes of Gravitational Lensing Parallax

The cosmological density of compact objects in the range 10 10 is currently uncertain. Potentially important components to the density of the universe include stars, MAssive Compact Halo Objects (MACHOs), and massive black holes. Here one hypothetical path to estimating the space density of these objects is proposed: the simultaneous measurement by separated observers of compact sources at cosmological distances. A population of compact objects of ΩL would cause a slight gravitational lens induced brightness difference that would be recoverable by sufficiently sensitive photometry. As this method hinges on well calibrated observations by separated observers, it will be referred to as “gravitational lensing parallax” or just “lensing parallax.” Lensing parallax observations of cosmological sources were first suggested by Refsdal (1966), who discussed what generic information about lensing events could be obtained by two platforms separated in the solar system. That lensing parallax observations of QSOs could determine the transverse velocity of galaxies was pointed out by Grieger, Kayser & Refsdal (1986). Gould (1992, 1994, 1995) suggested the method could better constrain the transverse velocities of lenses in MACHO searches. GRBs were discovered in the late 1960s (Klebesadel, Strong, & Olson, 1973). In 1997, GRBs were found to have counterparts in wavelength bands from the radio to the X-ray (Costa et al., 1997; van Paradijs et al., 1997). For simplicity, these event will all be referred to as GRBs, however. In general, GRB emission lasts longer and peaks later at longer wavelengths. At the time of this writing, one GRB was found to have an absorption line placing the event at cosmological distances (Metzger et al. 1997). Microlensing of GRBs had been proposed by Paczynski (1986). A search for gravitational lensing effects in GRB data has been ongoing since 1993 (Nemiroff et al., 1993; Marani, 1997; Marani et al., 1998). Nemiroff & Gould (1995) first suggested lensing parallax observations of gamma-ray bursts (GRBs), and showed how limits could be placed on a cosmological abundance of lens masses from 10 M⊙ to 10 M⊙. Loeb & Perna (1998) recently discussed how lensing parallax observations of GRB afterglows could confirm a microlensing amplification bump or a lensinduced polarization signature.