Nereid
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The LF (luminosity function) is the (2D) relationship between intrinsic luminosity and volume density; crudely, how many quasars are there, per cubic Mpc (megaparsec), in the intrinsic luminosity range [Mi, Mi+1], over all Mi? In the Strauss video (and paper that it largely comes from), the vertical axis is logarithmic in Mpc-3 mag-1, and goes from ~10^-9 to ~10^-6 (for z>2 quasars). The horizontal axis (absolute magnitude, representing luminosity) goes from ~-24 to ~-29 (or perhaps -30).granpa said:what does 'The luminosity function curve slope changes fairly abruptly after redshift z~3' mean?
(if you'd like a quick tutorial on 'magnitude', 'luminosity', etc, just holler)
For quasars, the current paradigm is to fit them with 'a broken power law', meaning that on the graph/plot/chart I have described, fitting two straight lines, one for the high-luminosity objects, and one of the lower luminosity objects, with a break-point (where the two line intersect). For the quasars under discussion here (those with z>3, and observed in SDSS DR3), the fainter-luminosity line is not so relevant.
The slope of the LF line (for higher-luminosities) is estimated by making a fit to the datapoints (in some statistical sense); such estimates are made (in the Strauss video) at z = 2.01, 2.40, 2.80, 3.25, 3.75, 4.25, and 4.75, by some binning of the data. Formal (1σ) error bars are calculated. When the fitted slopes are plotted, against z, they show a (z) trend, from ~-3.2 (z<3) to ~-2.1 (z=4.25), with the datapoint at z = 4.75 as an outlier (and with huge error bars). For z<3, the fitted slopes have values ~-3, with some scatter, but more or less within the error bars.
And that's it.
Perhaps you'd be interested in what astronomers interpret this set of (very substantially processed) material means?
If so - or if any other reader is interested - I'd be happy to try to explain ...