Quasars and Quasar Evolution

A quasar is the high-luminosity extreme of the active-galactic-nucleus family: a source so compact it was unresolved on early photographic plates — hence "quasi-stellar" — yet whose spectrum shows broad emission lines shifted far to the red by cosmological expansion. When Maarten Schmidt read a redshift of $z=0.158$ off 3C 273 in 1963, the implied luminosity of order $10^{46}\,\mathrm{erg\,s^{-1}}$ was pouring out of a region light-days across, and no stellar process could supply it. The resolution, sketched within a year by Salpeter and Zeldovich, is gravitational: accretion onto a supermassive black hole of $10^{6}$ – $10^{10}\,M_\odot$ , radiating through a geometrically thin, optically thick disk plus a broad-line region, dusty torus, and hot corona. The energetics turn on one number, the efficiency $\eta$ with which rest mass becomes light. For accretion at rate $\dot M$ the luminosity is $L=\eta\dot M c^2$ , with $\eta\approx0.06$ – $0.42$ set by black-hole spin — an order of magnitude better than hydrogen fusion. Steady output is capped at the Eddington luminosity $L_{\rm Edd}\propto M$ , so the brightest quasars demand the most massive holes running near their limit, tying quasar phenomenology directly to thin disks, the Eddington argument, and spin. Quasars are also clocks. Luminous optical quasars were roughly a thousand times more common at $z\sim2$ – $3$ than today, a "quasar epoch" coinciding with peak cosmic star formation — a sign that black holes and their hosts grew together. Fainter nuclei peak later ("downsizing"), so the biggest holes finished first. The demography closes through Soltan's argument: the integrated quasar light, divided by $\eta c^2$ , must equal the mass now locked in dormant black holes weighed through the M–sigma relation — and the two agree for $\eta\sim0.1$ .

Key takeaways

A quasar is the luminous extreme of an active galactic nucleus, powered by accretion onto a $10^{6}$ – $10^{10}\,M_\odot$ black hole, reaching bolometric luminosities up to $\sim10^{47}\,\mathrm{erg\,s^{-1}}$ and outshining the entire host galaxy.
The engine radiates $L=\eta\dot M c^2$ with efficiency $\eta\approx0.06$ (non-spinning) to $0.42$ (maximal spin); steady output is limited by the Eddington luminosity $L_{\rm Edd}=1.26\times10^{38}(M/M_\odot)\,\mathrm{erg\,s^{-1}}$ .
Eddington-limited accretion grows the hole exponentially with an e-folding (Salpeter) time $\sim5\times10^{7}\,\mathrm{yr}$ , so building a billion-solar-mass hole by $z>6$ races against cosmic time.
"Quasar evolution" is the evolution of the population's luminosity function: the comoving density of luminous quasars rises steeply to a peak near $z\approx2.5$ and falls off on both sides.
Soltan's continuity argument equates the integrated quasar light with the local mass density in dormant black holes, closing the accretion history of the Universe and fixing the mean efficiency at $\eta\sim0.1$ .
Key idea: a quasar is a supermassive black hole accreting near its Eddington limit; its luminosity ( $L=\eta\dot M c^2$ ), its cosmic rise-and-fall around $z\sim2$ – $3$ , and its final mass are all governed by accretion physics, and together they reconstruct the growth history of the black-hole population.

Where this lives today

The quasar luminosity function is now measured across almost all of cosmic history. Wide surveys — the Sloan Digital Sky Survey and its extensions, followed by Gaia, DESI, and soon the Vera Rubin Observatory's LSST — catalogue hundreds of thousands of quasars and pin the $z\approx2.5$ peak and its downsizing to high precision. At the frontier, the James Webb Space Telescope has revealed a surprising abundance of accreting black holes at $z>7$ , including compact "little red dots," sharpening the seed-and-growth crisis that Worked Example 2 quantifies. Reverberation mapping weighs the central holes and calibrates the M–sigma relation that anchors the Soltan census. Quasars also serve as cosmic backlights: the Gunn–Peterson trough in the highest-redshift quasars dates reionization. And "quasar-mode" feedback — fast outflows launched near the Eddington limit — is now central to every cosmological galaxy-formation simulation, thought to quench massive galaxies and set the black-hole–galaxy scaling relations.

The physical picture

Think of a quasar as a gravitational furnace. Gas spiralling inward loses potential energy, and by the time it reaches the innermost stable circular orbit (ISCO) it has surrendered several percent of its rest-mass energy as heat and light — roughly ten times more energy per gram than hydrogen fusion delivers, which is why a hole swallowing only a few solar masses a year can outshine a galaxy of $10^{11}$ stars. The disk is hottest at its inner edge and cools outward, so its spectrum is a sum of blackbodies peaking in the ultraviolet — the "big blue bump" of massive-black-hole accretion. The first figure is that engine in cross-section, carrying the master relation $L=\eta\dot M c^2$ and the efficiencies it spans.

Figure

The quasar engine: gas spiralling onto a 10⁶–10¹⁰ M⊙ black hole releases L = η Ṁ c² with η ≈ 0.06 for a non-spinning hole up to 0.42 at maximal spin, so a few M⊙ per year at η ≈ 0.1 already yields 10⁴⁷ erg s⁻¹, outshining the whole host galaxy

The population behaves like a wave sweeping through cosmic time: it builds up as cold gas becomes available to fuel black holes, crests near $z\sim2$ – $3$ , then fades as reservoirs are exhausted and feedback clears them. Any single quasar shines only for a small duty-cycle fraction of the Hubble time — the bright phase is episodic. Because $L=\eta\dot M c^2$ , every photon is a receipt for mass swallowed, so summing the light of all quasars across all redshift measures the total mass that ever fell into black holes. The second figure carries that history — the comoving density of luminous quasars versus redshift.

Figure

The quasar epoch: the comoving space density of luminous quasars climbs by a factor of order 10³ from z = 0 to a broad peak near z ≈ 2.5, then declines toward high redshift, while fainter AGN peak later at lower z — the pattern called downsizing

The core equations

The master relation of the whole subject is the accretion luminosity: light is the ledger of rest mass fed to the hole, discounted by the efficiency $\eta$ with which gravity releases it. Everything downstream — mass floors, growth times, the Soltan budget — is a manipulation of this one line.

L = \eta\,\dot M\, c^2 \qquad (1)

where: $L$ — bolometric luminosity; $\eta$ — radiative efficiency (fraction of rest mass radiated, $0.06$ – $0.42$ ); $\dot M$ — mass accretion rate onto the hole; $c$ — speed of light. Reading it: a larger $\eta$ (higher spin, smaller ISCO) means more light per gram, so a demography that measures light constrains the population's average spin. The efficiency is not free — it is the binding energy released in falling from infinity to the last stable orbit. In Schwarzschild geometry the specific energy at the ISCO is $\sqrt{8}/3\approx0.943$ , so the radiated fraction is one minus that.

\eta = 1-\frac{E_{\rm ISCO}}{mc^2}=1-\frac{\sqrt{8}}{3}\approx0.057\quad(\text{Schwarzschild}),\qquad \eta\approx0.42\ (\text{maximal Kerr}) \qquad (2)

where: $E_{\rm ISCO}$ — specific orbital energy at the ISCO; $m$ — mass of an accreting element. Reading it: spin shrinks the ISCO and raises $\eta$ sevenfold, the hidden variable behind quasar energetics. Steady, roughly spherical accretion cannot radiate arbitrarily hard: at the Eddington luminosity the outward radiation force on electrons balances gravity on the coupled protons, and any excess unbinds the fuel.

L_{\rm Edd}=\frac{4\pi G M m_p c}{\sigma_T}\approx1.26\times10^{38}\left(\frac{M}{M_\odot}\right)\ \mathrm{erg\,s^{-1}} \qquad (3)

where: $M$ — black-hole mass; $m_p$ — proton mass; $\sigma_T$ — Thomson cross section; $G$ — gravitational constant. Reading it: because $L_{\rm Edd}\propto M$ , a measured luminosity sets a hard lower bound on mass — the most-used inference in quasar work. The dimensionless accretion rate — the Eddington ratio — is what actually classifies a source, sorting radiatively efficient quasars from starved, inefficient nuclei.

\lambda\equiv\frac{L}{L_{\rm Edd}} \qquad (4)

where: $\lambda$ — Eddington ratio. Reading it: $\lambda\sim0.1$ – $1$ is the luminous quasar regime, while $\lambda\lesssim10^{-3}$ is the low-luminosity fate of a starved hole. Feeding the hole at fixed $\lambda$ makes it grow exponentially, because $\dot M\propto L_{\rm Edd}\propto M$ . The e-folding time — the Salpeter time — depends only on $\eta$ and $\lambda$ , not on mass.

M(t)=M_0\,e^{t/t_S},\qquad t_S=\frac{\eta}{(1-\eta)\lambda}\,\frac{\sigma_T c}{4\pi G m_p}\approx5\times10^{7}\,\frac{\eta/0.1}{\lambda}\ \mathrm{yr} \qquad (5)

where: $M_0$ — seed mass; $t_S$ — mass e-folding (Salpeter) time. Reading it: the Universe permits only so many e-folds, so growing a big hole early forces near-continuous high- $\lambda$ accretion or a massive seed. The disk's local effective temperature follows from balancing viscous dissipation against blackbody radiation in each annulus; it falls as $r^{-3/4}$ far out and turns over near the inner edge:

T(r)=\left[\frac{3GM\dot M}{8\pi\sigma_{\rm SB}r^3}\left(1-\sqrt{\frac{r_{\rm in}}{r}}\right)\right]^{1/4}\ \propto\ \left(\frac{\dot M}{M^2}\right)^{1/4}\ \text{at fixed }r/r_g \qquad (6)

where: $\sigma_{\rm SB}$ — Stefan–Boltzmann constant; $r_{\rm in}$ — inner edge, near the ISCO; $r_g=GM/c^2$ . Reading it: lower-mass holes run hotter (soft X-ray/EUV), while $10^9\,M_\odot$ quasars peak in the UV — the big blue bump. The population is described statistically by the luminosity function, a comoving density per unit luminosity whose shape and normalization change with redshift — this is what "quasar evolution" names.

\Phi(L,z)=\frac{\mathrm{d}N}{\mathrm{d}V\,\mathrm{d}L}=\frac{\Phi_\ast(z)}{(L/L_\ast)^{\alpha}+(L/L_\ast)^{\beta}} \qquad (7)

where: $\Phi$ — comoving density per unit luminosity; $V$ — comoving volume; $L_\ast$ — break luminosity; $\alpha,\beta$ — faint- and bright-end slopes. Reading it: the break $L_\ast(z)$ brightens toward $z\sim2$ then dims, and luminous quasars peak at higher $z$ than faint ones (downsizing). Finally, the Soltan integral converts that observed light density into a black-hole mass density — the accreted mass budget of the Universe.

\rho_\bullet=\frac{1-\eta}{\eta c^2}\int_0^\infty\frac{(1+z)\,\mathcal{L}(z)}{H(z)}\,\mathrm{d}z\ \sim\ 4\times10^{5}\left(\frac{0.1}{\eta}\right)M_\odot\,\mathrm{Mpc^{-3}} \qquad (8)

where: $\rho_\bullet$ — local mass density in black holes grown during quasar phases; $\mathcal{L}(z)$ — comoving bolometric luminosity density of quasars; $H(z)$ — Hubble parameter. Reading it: compared with the dormant-hole mass weighed today, this is the global check that pins $\eta\sim0.1$ .

Derivation AMinimum black hole mass of a luminous quasar

The goal here is to extract the single most powerful inference in quasar astrophysics: from nothing but an observed luminosity and the assumption of steady accretion, place a hard lower bound on the central black-hole mass. Because a steady, roughly spherical flow cannot radiate above its Eddington luminosity — beyond that, radiation pressure overwhelms gravity and halts the inflow — the observed $L$ immediately implies a floor on $M$ , with no need to resolve the source or model its spectrum.

Step 1. Impose the Eddington ceiling: a steady flow satisfies $L\le L_{\rm Edd}=1.26\times10^{38}(M/M_\odot)\,\mathrm{erg\,s^{-1}}$ , equivalently $\lambda=L/L_{\rm Edd}\le1$ . Why: above $L_{\rm Edd}$ the outward radiation force on electrons exceeds the inward gravity on the coupled protons, so the fuel is expelled rather than accreted.

Step 2. Invert for the mass floor: rearranging gives $M\ge L/(1.26\times10^{38})\,M_\odot$ . Why: since $L_{\rm Edd}$ is strictly proportional to $M$ , the brightest thing a hole of a given mass can be is fixed, so a bright source cannot hide behind a small mass.

Step 3. Evaluate for a luminous quasar. Taking $L=10^{47}\,\mathrm{erg\,s^{-1}}$ gives $M\gtrsim10^{47}/(1.26\times10^{38})\approx7.9\times10^{8}\,M_\odot$ — essentially a billion solar masses. Why: the most luminous quasars are inescapably billion-solar-mass objects, and finding them at $z>6$ , when the Universe was under a gigayear old, is a genuine crisis for seed-and-growth models. *Verified: $L_{\rm Edd}/M=1.259\times10^{38}\,\mathrm{erg\,s^{-1}}/M_\odot$ recomputed from $4\pi G m_p c/\sigma_T$ ; $M\ge7.94\times10^{8}\,M_\odot$ for $L=10^{47}$ (Carroll & Ostlie ch. 28).*

Go deeper · Derivation B · 1 minExponential growth and the Salpeter time

Derivation BExponential growth and the Salpeter time

The aim is to show that feeding a black hole at a fixed fraction of its Eddington limit makes it grow exponentially, and to read off the e-folding time that decides whether the Universe is old enough to build the quasars we see. The chain is short: the luminosity fixes the accretion rate through $\eta$ ; the accretion rate minus what is radiated is the mass actually added; and because $L_{\rm Edd}\propto M$ , the growth rate is proportional to the current mass — exponential growth with a mass-independent timescale.

Step 1. Convert luminosity to accretion rate. Radiating at $L=\lambda L_{\rm Edd}$ requires supplying mass at $\dot M_{\rm acc}=L/(\eta c^2)=\lambda L_{\rm Edd}/(\eta c^2)$ . Why: equation (1) is a two-way street — fixing the light fixes the throughput, once $\eta$ is chosen.

Step 2. Subtract the radiated part. The hole itself gains only $\dot M_\bullet=(1-\eta)\dot M_{\rm acc}=(1-\eta)\lambda L_{\rm Edd}/(\eta c^2)$ , since a fraction $\eta$ of the rest mass leaves as radiation and never crosses the horizon. Why: it is the mass that actually falls in, not the mass processed, that grows the hole, so the bookkeeping factor $(1-\eta)$ matters at the tens-of-percent level for high-spin holes.

Step 3. Use $L_{\rm Edd}\propto M$ . Dividing by $M$ gives $\dot M_\bullet/M=[(1-\eta)\lambda/\eta]\,(4\pi G m_p/\sigma_T c)$ , a constant at fixed $\eta,\lambda$ . Integrating, $M(t)=M_0\,e^{t/t_S}$ with $t_S=[\eta/((1-\eta)\lambda)]\,(\sigma_T c/4\pi G m_p)$ . Why: a growth rate proportional to the current mass is exponential growth, with an e-folding time independent of mass — the same $\sim5\times10^7$ yr for a seed or a monster.

Step 4. Count the e-folds. With $\eta=0.1$ , $\lambda=1$ , the pure Eddington time is $\sigma_T c/4\pi G m_p\approx0.45\,\mathrm{Gyr}$ , so $t_S\approx5\times10^{7}\,\mathrm{yr}$ . Growing a $100\,M_\odot$ seed to $10^9\,M_\odot$ is a factor $10^7$ , i.e. $\ln(10^7)\approx16$ e-folds, or about $0.8\,\mathrm{Gyr}$ of unbroken Eddington accretion. Why: the age of the Universe at $z\simeq7$ is only $\sim0.8\,\mathrm{Gyr}$ , so a stellar-mass seed has essentially no slack — the observations push toward massive direct-collapse seeds or episodes of super-Eddington growth. *Verified: $t_S=5.0\times10^{7}\,\mathrm{yr}$ ( $\eta=0.1,\lambda=1$ ); $\ln(10^7)=16.1$ e-folds → $0.81\,\mathrm{Gyr}$ ; pure Eddington time $0.451\,\mathrm{Gyr}$ .*

Go deeper · Derivation C · 1 minThe Soltan argument — closing the accretion budget

Derivation CThe Soltan argument — closing the accretion budget

The purpose of this derivation is to weigh the black holes of the Universe two independent ways and demand that the answers agree. The first is a light budget: every erg a quasar radiates is a receipt for accreted rest mass, so integrating the quasar luminosity density over cosmic history and dividing by $\eta c^2$ gives the total mass that fell into holes. The second is a mass census: the M–sigma relation, applied galaxy by galaxy today, sums the dormant holes directly. Consistency between the two is a nontrivial test of the accretion paradigm — and it fixes the average radiative efficiency.

Step 1. Write the accreted mass-rate density. At each epoch $\dot\rho_{\rm acc}(t)=\mathcal{L}(t)/(\eta c^2)$ , where $\mathcal{L}$ is the comoving bolometric luminosity density of all quasars. Why: this is equation (1) promoted from a single object to the whole population per unit comoving volume — light density in, mass-throughput density out.

Step 2. Integrate over cosmic time and keep what stays. The mass locked in holes is $\rho_\bullet=\frac{1-\eta}{\eta c^2}\int_0^{t_0}\mathcal{L}(t)\,\mathrm{d}t$ , with the $(1-\eta)$ again removing the part that escaped as radiation. Recast as a redshift integral this is equation (8). Why: it is the accumulated mass, not the instantaneous rate, that we can weigh locally, so we must sum over all epochs the quasars were shining.

Step 3. Evaluate the light side. Integrating the observed quasar luminosity function over luminosity and redshift gives $\rho_\bullet\sim4\times10^{5}(0.1/\eta)\,M_\odot\,\mathrm{Mpc^{-3}}$ . Why: the integral is dominated by the $z\sim2$ – $3$ peak and by luminosities near the break $L_\ast$ , so it is well constrained by bright, well-surveyed quasars.

Step 4. Compare with the local census. Independently, integrating the local black-hole mass function from M–sigma gives $\rho_\bullet^{\rm local}\sim(4$ – $5)\times10^{5}\,M_\odot\,\mathrm{Mpc^{-3}}$ . Matching the two forces $\eta\sim0.1$ . Why: the agreement is the punchline — dormant holes in today's galaxies are the burnt-out relics of past quasar activity, and their mean spin was moderate, since $\eta\sim0.1$ is neither non-spinning nor maximal. *Verified: order-of-magnitude match of the light-integral $\rho_\bullet\sim4\times10^5\,M_\odot\,\mathrm{Mpc^{-3}}$ ( $\eta=0.1$ ) against the local M–sigma mass density (Soltan 1982; Yu & Tremaine 2002).*

Limiting cases

Quasar behaviour is organized almost entirely by the Eddington ratio $\lambda=L/L_{\rm Edd}$ , which selects the accretion mode and hence the geometry, efficiency, and spectrum:

Case	Result	Meaning
Radiatively efficient (quasar mode)	$0.01\lesssim\lambda\lesssim1$	Geometrically thin, optically thick Shakura–Sunyaev disk; $\eta\sim0.1$ ; the classic luminous quasar with a big blue bump and broad lines.
Super-Eddington / slim disk	$\lambda\gtrsim1$	Photons trapped and advected inward, so $L$ is only mildly super-Eddington and saturates logarithmically; a route to rapid growth of the highest- $z$ quasars.
Radiatively inefficient (ADAF)	$\lambda\lesssim10^{-3}$	Advection-dominated flow: hot, geometrically thick, dim; the fate of a starved former quasar such as a low-luminosity AGN or Sgr A*.
Eddington ceiling	$L\le L_{\rm Edd}=1.26\times10^{38}(M/M_\odot)\,\mathrm{erg\,s^{-1}}$	Steady spherical accretion cannot exceed this, so a $10^{47}\,\mathrm{erg\,s^{-1}}$ quasar needs $M\gtrsim10^{9}\,M_\odot$ at $\lambda\sim1$ .
Spin: none → maximal	$\eta:0.057\to0.42$	Spin sets the ISCO and hence efficiency; a maximal Kerr hole yields sevenfold more light per gram.

Common trapA quasar's redshift is a recession Doppler shift, its "evolution" is one object aging, and it needs super-Eddington accretion to be so bright

All three are wrong. First, a quasar's large redshift is cosmological — a stretching of wavelength by the expansion of space, encoding look-back time, not the local velocity of an ejected fragment; the discredited "local" hypothesis of the 1960s foundered on exactly this point. Second, "quasar evolution" is a statement about the population: the comoving luminosity function $\Phi(L,z)$ changes with redshift, peaking near $z\approx2.5$ . An individual quasar does not slide along that curve as it ages; it flickers on for a duty-cycle fraction of the Hubble time and then goes dark. Third, extreme luminosity does not require super-Eddington accretion — a $10^9\,M_\odot$ hole at its Eddington limit already produces $\sim10^{47}\,\mathrm{erg\,s^{-1}}$ ; super-Eddington episodes are invoked only to grow such holes fast enough at $z>6$ .

Worked examples

1 · Weighing a luminous quasar from its light alone (fully worked)

A quasar has bolometric luminosity $L=10^{47}\,\mathrm{erg\,s^{-1}}$ . Assuming it radiates at its Eddington limit, find the black-hole mass, and for a radiative efficiency $\eta=0.1$ find the accretion rate in solar masses per year.

Step 1. Apply the Eddington relation as an equality ( $\lambda=1$ ): $M=L/L_{\rm Edd,\odot}=10^{47}/(1.26\times10^{38})\,M_\odot$ . Evaluating, $M\approx7.9\times10^{8}\,M_\odot$ — a billion-solar-mass hole, the generic weight of the brightest quasars.

Step 2. Get the accretion rate from equation (1), with $c^2=9\times10^{20}\,\mathrm{cm^2\,s^{-2}}$ in CGS: $\dot M=L/(\eta c^2)=10^{47}/(0.1\times9\times10^{20})=1.1\times10^{27}\,\mathrm{g\,s^{-1}}$ .

Step 3. Convert to astronomer's units: $\dot M=1.1\times10^{27}\,\mathrm{g\,s^{-1}}\times(3.16\times10^{7}\,\mathrm{s\,yr^{-1}})/(1.99\times10^{33}\,\mathrm{g}/M_\odot)\approx\mathbf{18\ M_\odot\,yr^{-1}}$ . So a billion-solar-mass hole devouring only about 18 solar masses a year outshines an entire galaxy — the whole point of gravitational accretion as an engine. M ≈ 7.9×10⁸ M⊙, Ṁ ≈ 18 M⊙ yr⁻¹.

2 · Can a stellar seed become a quasar by z ≈ 7? (fully worked)

A $100\,M_\odot$ black-hole seed accretes continuously at the Eddington limit with $\eta=0.1$ . How long does it take to reach $10^9\,M_\odot$ , and is that feasible before $z\approx7$ , where the Universe is $\sim0.8\,\mathrm{Gyr}$ old?

Step 1. Fix the e-folding time from equation (5): with $\eta=0.1$ , $\lambda=1$ , $t_S=[\eta/((1-\eta)\lambda)]\times0.45\,\mathrm{Gyr}=(0.1/0.9)\times0.45\,\mathrm{Gyr}\approx\mathbf{5\times10^{7}\,yr}$ .

Step 2. Count the required e-folds: the growth factor is $10^9/100=10^7$ , so $N=\ln(10^7)=7\ln10\approx\mathbf{16.1}$ e-folds.

Step 3. Multiply: $t=N\,t_S=16.1\times5\times10^{7}\,\mathrm{yr}\approx\mathbf{8\times10^{8}\,yr}=0.8\,\mathrm{Gyr}$ .

Step 4. Compare with cosmic time. That $0.8\,\mathrm{Gyr}$ is essentially the entire age of the Universe at $z\approx7$ , and it assumes uninterrupted Eddington accretion from a stellar seed — no gaps, no sub-Eddington lulls, no feedback shutoff. The margin is effectively zero, which is why observed $z>7$ quasars push the field toward massive ( $10^4$ – $10^5\,M_\odot$ ) direct-collapse seeds or brief super-Eddington bursts. t ≈ 0.8 Gyr for 16 e-folds — feasible only in principle, with no slack.

Physics of the portrait

Quasars are the meeting point of three revolutions — luminous distant "stars," a black-hole engine, and a population that evolved across cosmic time — and one person sits at the origin of all three.

Origins · 1 minMaarten Schmidt and how this was discovered

Maarten Schmidt

1929–2022 · the discovery of quasar redshifts and the evolution of the quasar population

In 1963 the Dutch–American astronomer Maarten Schmidt, at Caltech and Palomar, stared at the puzzling optical spectrum of the radio source 3C 273. Its emission lines matched no known element until he recognized them as ordinary hydrogen Balmer lines redshifted by $z=0.158$ — an enormous shift for something that looked stellar. In a single-page Nature note he turned an oddity into a cosmological object: at that redshift 3C 273 radiated some $10^{46}\,\mathrm{erg\,s^{-1}}$ , hundreds of times a whole galaxy, from a region small enough to vary in months. Within a year Edwin Salpeter and Yakov Zeldovich independently proposed accretion onto a supermassive black hole, and Donald Lynden-Bell in 1969 made the disk picture quantitative, arguing that dead quasar engines must lurk in the centres of ordinary galaxies. Schmidt did not stop at discovery. Asking whether quasars were spread uniformly through space or concentrated in the past, he devised the $V/V_{\rm max}$ test, a clean statistic for whether sources crowd toward the edge of a flux-limited survey. It showed decisively that quasars were far more numerous in the early Universe — the first quantitative evidence for cosmological evolution of a source population, and the seed of the entire modern enterprise of the quasar luminosity function. His statistical legacy underlies every measurement of the $z\sim2.5$ peak today.

History

1963

— Schmidt identifies the redshift z = 0.158 of 3C 273, revealing quasars as ultraluminous distant objects

1964

— Salpeter and Zeldovich independently propose accretion onto supermassive black holes as the power source

1969

— Lynden-Bell models quasars as accretion disks and predicts dormant black holes in normal galaxies

1982

— Soltan ties the integrated quasar light to the local black-hole mass budget

2002

— Yu and Tremaine close the Soltan argument with SDSS demographics, fixing the mean efficiency near 0.1

Going further

Texts. Carroll & Ostlie, An Introduction to Modern Astrophysics, 2nd ed., ch. 28 (Active Galaxies) · Mo, van den Bosch & White, Galaxy Formation and Evolution, ch. 14 (AGN and accretion) · Binney & Tremaine, Galactic Dynamics, 2nd ed. (galactic nuclei and central black holes) · Peterson, An Introduction to Active Galactic Nuclei (1997) · Ryden, Introduction to Cosmology, 2nd ed. (redshift, comoving volume) · Dodelson, Modern Cosmology (cosmological framework and structure growth).

Provenance. The Eddington luminosity, accretion efficiency, Salpeter time, thin-disk temperature, and Soltan integral follow standard treatments and were re-verified numerically here: $L_{\rm Edd}/M=1.259\times10^{38}\,\mathrm{erg\,s^{-1}}/M_\odot$ from $4\pi G m_p c/\sigma_T$ ; the Schwarzschild ISCO efficiency $\eta=1-\sqrt{8}/3=0.0572$ ; the pure Eddington time $\sigma_T c/4\pi G m_p=0.45\,\mathrm{Gyr}$ so $t_S\approx5\times10^7\,\mathrm{yr}$ at $\eta=0.1,\lambda=1$ ; the billion-solar-mass floor $M\ge7.9\times10^8\,M_\odot$ for $L=10^{47}\,\mathrm{erg\,s^{-1}}$ ; and the Soltan density $\rho_\bullet\sim4\times10^5\,M_\odot\,\mathrm{Mpc^{-3}}$ cross-checked against the local black-hole mass function (Soltan 1982, MNRAS 200, 115; Yu & Tremaine 2002). The $z\sim2$ – $3$ density peak and downsizing are established from SDSS/2dF luminosity-function fits.

Prerequisites. Active Galactic Nuclei: Unified Model · Supermassive Black Holes · Eddington Luminosity and Accretion Limits · Thin Accretion Disks and the Shakura–Sunyaev Model. Leads to. M–sigma Relation and Black Hole–Galaxy Coevolution · AGN Feedback · Blazars and Relativistic Beaming · Black Hole Spin and the Ergosphere.

Ask the tutor: Ask me to walk through the Eddington mass floor for any observed quasar luminosity, or to trace how the Soltan argument turns a survey of quasar light into the mass locked in today's dormant black holes.

What is the difference between a quasar and an active galactic nucleus?

An active galactic nucleus (AGN) is any galaxy centre made luminous by accretion onto a supermassive black hole; a quasar is the high-luminosity extreme of that family, bright enough to outshine its host and appear point-like. In the unified model the differences between AGN types — Seyferts, radio galaxies, blazars, quasars — are largely a matter of luminosity, orientation, and radio loudness rather than of the underlying engine. Historically "quasar" meant the radio-loud quasi-stellar radio sources and radio-quiet ones were called QSOs, but modern usage treats them together.

Why can't nuclear fusion power a quasar?

Two reasons: efficiency and compactness. Hydrogen fusion converts only about $0.7\%$ of rest mass to energy, whereas accretion onto a black hole releases $6$ – $42\%$ — more than ten times as much per gram — so fusion is too weak a battery for $10^{47}\,\mathrm{erg\,s^{-1}}$ . Just as decisive, the luminosity varies on timescales of days to months, so the emitting region is only light-days across; packing enough fusing gas into that volume would collapse it into a black hole anyway. Gravitational accretion is the only mechanism supplying that energy from so tiny a volume.

If quasars "evolve," what exactly is changing?

The population, not the individual. "Quasar evolution" means that the comoving luminosity function $\Phi(L,z)$ — how many quasars of each luminosity exist per unit volume — depends strongly on redshift. Luminous quasars were roughly a thousand times more common at $z\approx2.5$ than today. A given quasar does not slowly climb or descend that curve; it switches on when fuel arrives, shines for a small fraction of the Hubble time, and switches off. So the "evolution" is demographic — the birth, brightening, and dying-out of a whole population — not the biography of one object.

How can billion-solar-mass black holes already exist less than a gigayear after the Big Bang?

This is one of the sharpest open problems in the field. Eddington-limited growth from a stellar-mass seed needs about sixteen e-foldings, or nearly the entire age of the Universe at $z\approx7$ , with no interruptions — an implausibly perfect run. The leading ways out are massive "direct-collapse" seeds of $10^4$ – $10^5\,M_\odot$ that give growth a head start, or episodes of super-Eddington accretion where photon trapping lets the hole gain mass faster than the naive limit. JWST's discovery of abundant accreting holes at $z>7$ has made this puzzle more acute, not less.

Can a quasar exceed the Eddington luminosity?

Briefly and modestly, yes — the Eddington limit assumes steady, roughly spherical accretion, and real flows violate those assumptions. In a "slim disk" at very high accretion rate, photons are trapped in the inflowing gas and advected across the horizon before they escape, so the radiated luminosity grows only logarithmically with $\dot M$ and stays within a factor of a few of $L_{\rm Edd}$ even as the throughput soars. Non-spherical geometry helps too: radiation escapes along the poles while gas keeps falling in through the disk plane. These mildly super-Eddington phases matter for rapid early growth, but a quasar cannot sit at a hundred times Eddington for long — it would blow its own fuel away.

Are quasars still forming today?

Genuine quasars — the most luminous, $\sim10^{47}\,\mathrm{erg\,s^{-1}}$ sources — are essentially a phenomenon of the past; their comoving density has fallen by roughly a factor of a thousand since $z\approx2.5$ . The reason is fuel: the cold-gas reservoirs that fed vigorous accretion have largely been consumed or heated, and the biggest black holes finished growing long ago (downsizing). What remain nearby are lower-luminosity active nuclei and mostly dormant holes, occasionally flickering back to life during a merger or a tidal disruption event. The quasar era was a specific chapter of cosmic history, and we live well after its close.