24-2 Supermassive black holes are the “central engines” that power active galactic nuclei

What produces the intense emission from quasars? The basic model of quasar emission involves accretion—the gravitational accumulation of matter—around a supermassive black hole. In this section, we look at what quasar behavior pointed to a central role for black holes, and how to estimate the black hole masses.

Size of the Light Source

One characteristic that is common to all types of active galactic nuclei is variability. For example, Figure 24-5 shows brightness fluctuations of the quasar 3C 273 as determined from 29 years of observations. The brightness of 3C 273 increased by 60% from the beginning to the end of 1982, then declined to the starting value in just five months. Other AGN undergo even greater fluctuations in brightness (by a factor of 25 or more) that occur even more rapidly (X-ray observations reveal that some AGN vary in brightness over time intervals as short as 3 hours).

Figure 24-5: Brightness Variations of an AGN This graph shows variations over a 29-year period in the apparent brightness of the quasar 3C 273 (see Figure 24-2a, b). Note the large outburst in 1982–1983 and the somewhat smaller ones in 1988 and 1992.

(Adapted from M. Türler, S. Paltani, and T. J.-L. Courvoisier)

The crucial aspect of these fluctuations in brightness is that they allow astronomers to place fundamental limits on the maximum size of a light source. This strict limit arises because an object cannot vary in brightness faster than light can travel across that object. For example, an object that is 1 light-year in diameter cannot vary significantly in brightness over a period of less than 1 year.

To understand this limitation, imagine an object that measures 1 light-year across, as in Figure 24-6. Suppose the entire object suddenly brightens, emitting a brief flash of light. Photons from that part of the object nearest Earth arrive at our telescopes first. Photons from the middle of the object arrive at Earth 6 months later. Finally, light from the far side of the object arrives a year after the first photons. Although the object emitted a sudden flash of light, we observe only a gradual increase in brightness that lasts a full year. In other words, the flash is stretched out over an interval equal to the difference in the light travel time between the nearest and farthest observable regions of the object.

Figure 24-6: A Limit on the Speed of Variations in Brightness The rapidity with which the brightness of an object can vary significantly is limited by the time it takes light to travel across the object. If an object 1 light-year in size emits a sudden flash of light, the flash will be observed from Earth to last a full year. If the object is 2 light-years in size, brightness variations will last at least 2 years as seen from Earth, and so on.

The rapid flickering exhibited by active galactic nuclei means that they emit their energy from a small volume—in some cases less than half a light-day across (which is about the diameter of Neptune’s orbit). Thus, from quasar variability, astronomers discovered that a region about the size of our solar system can emit more energy per second than a thousand galaxies! More than anything else, this size-constraint points to supermassive black holes, as no other known object can power the release of so much energy from such a small volume.

While the light-emitting region in a quasar might be about the size of our solar system, the black hole is smaller still. Just how big and massive are the black holes in quasars? Surprisingly, the size and mass of the black hole can be estimated from great distances where nothing is seen but the light from its hot accreting gas.

The Eddington Limit and Black Hole Sizes

There is a relationship between the size of a black hole and the luminosity emitted by the hot gas falling into it. Even if there is plenty of gas around to act as “fuel,” there is a natural limit to the luminosity that can be radiated by accretion onto a compact object like a black hole. This limit is called the Eddington limit, after the British astrophysicist Sir Arthur Eddington. The Eddington limit applies to any object held together by its own gravity and applies to stars as well as quasars.

The accretion of fuel by a black hole is thought to be a smooth and steady process, but let’s imagine what might happen if a quasar were to suddenly brighten. If the luminosity exceeds the Eddington limit, there is so much radiation pressure—the pressure produced by photons streaming outward from the infalling material—that the surrounding gas is pushed outward rather than falling inward onto the black hole. Without a source of gas to provide energy, the luminosity naturally decreases to below the Eddington limit, at which point gas can again fall inward. Thus, the Eddington limit represents the balance between radiation pushing gas-fuel outward and gravity pulling the gas inward. This limit allows us to calculate the minimum mass of the black hole in a quasar.

Numerically, the Eddington limit is

The Eddington limit

• L_Edd = maximum luminosity that can be radiated by accretion around a black hole
• M = mass of the black hole
• M_⊙ = mass of the Sun
• L_⊙ = luminosity of the Sun

The tremendous luminosity of a quasar must be less than or equal to its Eddington limit (or it would blow away its accreting gas), so this limit must be very high indeed. Hence, the mass of the black hole must also be quite large. For example, consider the quasar 3C 273, which has a luminosity of about 3 × 10¹³ L_⊙. To calculate the minimum mass of a black hole that could continue to attract gas to power the quasar, assume that the quasar’s luminosity equals the Eddington limit. Inserting L_Edd = 3 × 10¹³ L_⊙ into the above equation, we find that M = 10⁹ M_⊙. Therefore, if a black hole is responsible for the energy output of 3C 273, its mass must be greater than a billion Suns!

Astronomers have indeed found evidence for such super-massive black holes at the centers of many nearby normal galaxies (see Section 22-5), and these are thought to be the remnants of AGN. As we saw in Section 22-6, at the center of our own Milky Way Galaxy lies what is almost certainly a black hole of about 4.1 × 10⁶ solar masses—supermassive in comparison to a star, but less than 1% the mass of the behemoth black hole at the center of 3C 273.

Unlike stellar-mass black holes, which require a supernova to produce them, supermassive black holes can be produced without extreme densities. Recall (Section 21-5) that matter with an average density no greater than water could form a 500 million M_⊙ black hole if this matter coalesced into a sphere with a radius about the Earth–Sun distance (1 AU). Some astronomers suspect that galaxy collisions produced massive black holes that accreted their way to even larger sizes, but the origin of supermassive black holes, and the AGN they powered, remains a mystery.