quasar luminosity function
/ QLF /
Suppose you want to know not just that quasars exist, but how many bright ones versus faint ones there are, and whether the universe had more of them long ago than it does today. You need a census — a tally of how common quasars are at each level of brightness, and how that tally changes through cosmic time. That census is the quasar luminosity function.
Formally, the luminosity function gives the number of quasars per unit volume of space at each luminosity. Like most populations, faint quasars vastly outnumber bright ones, so the function falls off steeply toward the high-luminosity end. The crucial twist is that it changes with cosmic epoch. Surveys show that quasars were far more abundant in the past: the cosmic density of bright quasars peaked when the universe was roughly 2 to 3 billion years old (around redshift z = 2 to 3, often called 'cosmic noon') and has declined sharply since. Because looking far away means looking back in time, mapping the luminosity function across redshift reconstructs this rise and fall.
The quasar luminosity function is how astronomers chart the cosmic history of black hole growth. Its rise and peak and decline trace when supermassive black holes did most of their feeding and how the universe's total accretion power evolved — its integral relates directly to the black hole mass built up over cosmic time. It also tells us quasars are not random: their numbers rose with the supply of fresh gas and galaxy mergers in the young universe, then dwindled as that fuel ran low. So 'the universe used to be full of quasars, and now mostly is not' is, quantitatively, exactly what the luminosity function says.
Large surveys like the Sloan Digital Sky Survey have measured millions of quasars and shown their space density peaked around redshift z = 2 to 3 — when the universe was a few billion years old — and is roughly a hundred times lower today. The luminosity function turns that into a precise curve of black hole growth over cosmic time.
A census of quasars by brightness and epoch — charting when black holes fed the most.
The luminosity function measures how common quasars of each brightness are per unit volume — not how bright a single quasar is. Faint quasars hugely outnumber bright ones, so a flux-limited survey easily over-counts rare bright objects unless that selection bias is carefully corrected.