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Astron. Astrophys. 338, 777-780 (1998)

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4. Results and discussions

Knowing the analytic expressions for the lensing cross-sections in general FLRW cosmologies, we can explore in detail the influences of cosmological parameters by numerical computation. We compute the probability [FORMULA] so as to investigate whether the background objects (like quasars) counts are significantly contaminated. Eq. 18contains three factors, namely, the µ-dependent term, the galaxies term and the cosmological term, associated with [FORMULA]. Here we concentrate on the cosmological term by adopting the maximum value [FORMULA] (Kochanek 1996) and a moderate magnification of [FORMULA].

Fig. 1 shows how the probability [FORMULA] depends on the normalized cosmological parameters [FORMULA] and [FORMULA] for an open ([FORMULA], [FORMULA]) and a flat ([FORMULA]) universe respectively. In our calculations, the source has been set at [FORMULA] or [FORMULA] respectively, and a moderate magnification of [FORMULA] has been used. Indeed, the probability [FORMULA] depends sensitively on cosmological parameters [FORMULA] and [FORMULA]. However, even for a [FORMULA]-dominated ([FORMULA]) flat universe, only a small fraction ([FORMULA]) of the sky can be moderately ([FORMULA]) lensed by galaxies.

[FIGURE] Fig. 1a and b. The probability, [FORMULA], that the sources located at [FORMULA] (solid-lines) and [FORMULA] (dashed-lines) are magnified by the factor greater than [FORMULA] as a function of [FORMULA] for a an open universe with [FORMULA], [FORMULA], and b a flat universe with [FORMULA].

Of course, by taking somewhat lower value for µ the probability of the magnification can siginificantly increase. In order to get a more robust conclusion, we now estimate what value of magnification would affect the current observations of quasar count, i.e., we calculate the value of [FORMULA] which makes [FORMULA]. The resulting magnification, which depends on both the cosmological model and the source redshift, is shown in Fig. 2. Since the magnification is generally much lower than 1.1, our result reinforces the hypothesis that the quasar counts are not seriously contaminated by the galactic lenses.

[FIGURE] Fig. 2a and b. The magnification [FORMULA], which makes the probability of the sources located at [FORMULA] (solid-lines) and [FORMULA] (dashed-lines) [FORMULA], as a function of [FORMULA] for a an open universe with [FORMULA], [FORMULA], and b a flat universe with [FORMULA].

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© European Southern Observatory (ESO) 1998

Online publication: September 17, 1998
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