Upper bounds on the cosmological density of compact objects with sub-solar masses from the variability of QSOs

Details Upper bounds on the cosmological density of compact objects with sub-solar masses from the variability of QSOs Upper bounds on the cosmological density of compact objects with sub-solar masses from the variability of QSOs

Nov 1993

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993a%26a...279....1s&link_type=abstract

Astronomy and Astrophysics (ISSN 0004-6361), vol. 279, no. 1, p. 1-20

Astronomy and Astrophysics

Astrophysics

37

Astronomical Models, Dark Matter, Density (Number/Volume), Gravitational Lenses, Missing Mass (Astrophysics), Quasars, Star Distribution, Variability, Cosmology, Limits (Mathematics), Mass Distribution, Mass Spectra, Mathematical Models, Maxima, Range (Extremes), Velocity Distribution

Scientific paper

If the universe is filled with compact objects in the mass range 10-4 solar mass approximately less than M approximately less than 1 solar mass, relative motion of these objects transverse to the line-of-sight to distant QSOs will lead to time-variable gravitational lensing of the sources, yielding observable flux variations of the QSOs. Although for singly-imaged QSOs, microlens-induced variability cannot be separated from intrinsic variability, observed variations in a QSO sample yield upper limits for the variations that can be attributed to microlensing. Using an approximate method for calculating the expected variability in dependence of the assumed cosmological density of compact objects, their mass (or mass spectrum) and the distribution of random velocities, one can predict the fraction of QSOs which should vary in a given timespan by more than a certain threshold. Using a recently published sample of QSOs which have been selected on the basis of variaiblity, and considering their variability as an upper bound to the microlensing variability, one can obtain upper limits on the cosmological density of compact objects. In particular, the density parameter of compact objects in the mass range 10-3 solar mass approximately less than M approximately less than 10-2 solar mass can be constrained to be smaller than about OmegaL approximately less than 0.1 if the blue continuum-emitting region has a typical size of approximately 1015 cm. Future prospects of this method are discussed; it is argued that future observations of QSO variability (or its absence) can yield even tighter constraints on OmegaL. In two appendices, a simple approximation formula is obtained for the magnification of an extended source by a point-mass lens, and the magnification probability distribution in the multiplication approximation is investigated, complementing recent work by Pei.

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