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Astron. Astrophys. 345, 73-80 (1999)

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2. Partial coverage

When an absorbing cloud does not cover the background source completely, the observed residual intensity in the normalized spectrum, [FORMULA], can be written as,

[EQUATION]

where, [FORMULA] and [FORMULA] are the optical depth and covering factor respectively. The latter is the ratio of the number of photons produced by the region of the background source that is occulted by the absorbing cloud to the total number of photons (Srianand & Shankaranarayanan 1999). If two absorption lines with rest-wavelengths [FORMULA] and [FORMULA] originate from the same ion (usually it will be doublets or multiplets), their residual intensities, [FORMULA] and [FORMULA], at any velocity v with respect to the centroid of the lines are related by,

[EQUATION]

where [FORMULA] and [FORMULA] are the covering factors calculated for the two lines and,

[EQUATION]

with [FORMULA] and [FORMULA] the oscillator strengths (see e.g. Petitjean 1999). The value of [FORMULA] is close to 2 for doublets.

Though our intuition says that [FORMULA] it need not be true in general (Srianand & Shankaranarayanan 1999). Indeed due the complex velocity structure in the BLR, photons that could be absorbed by lines 1 and 2 (even in the case of doublets) originate from spatially distinct regions in the BLR. A cloud can thus be black in line 1 (covering the BLR region emitting at the corresponding wavelength [FORMULA]), but not in line 2 if it does not cover at the same time the region emitting photons with wavelength [FORMULA]. Also, the interpretation of the relative covering factors for various ions is not straightforward. Indeed, the covering factor of absorption lines seen over the wavelength range of the QSO spectrum that is dominated by the continuum may be larger than the covering factor of lines present on top of the QSO emission lines as the extension of the BLR is larger than that of the continuum emission region.

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© European Southern Observatory (ESO) 1999

Online publication: April 12, 1999
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