Astronomy 292

Week 8: Active Galaxies

Monday, February 23: Superclusters and Voids

The structure of the universe is hierarchical; there is structure on a wide range of length scales.

Stars are found mainly in gravitationally bound galaxies.
Galaxies are found mainly in gravitationally bound clusters.
Clusters are found mainly in superclusters, which are currently collapsing.

For superclusters to be collapsing today, they must have a freefall time comparable to the Hubble time, H₀^-1. This implies that their density must be
rho ~ 3 pi H₀²/(32 G) ~ 2x10^-26kg/m³ ~ 3x10¹¹ M_sun/Mpc³.

Superclusters are most easily seen in three-dimensional maps made using the redshifts of galaxies to estimate their distance: d = (c/H₀)z. A ``wedge diagram'' shows the distribution of galaxies in space:

The two wedges shown above contain 9500 galaxies out to a redshift of z=0.05 (corresponding to a distance of 215 Mpc). The largest structures seen in redshift surveys are superclusters about 100 Mpc long. The Local Group and the Virgo Cluster are both contained within the Local Supercluster.

Properties of superclusters:

Elongated filaments or walls, not spheres.
Maximum size ~ 100 Mpc (Larger objects have not yet had time to collapse, so there are no ``superduperclusters''.)

Properties of voids (low-density regions between superclusters):

Roughly spherical in shape, making the universe look ``bubbly'' or ``frothy'' on large scales.
Maximum size ~ 100 Mpc.
Free of bright galaxies; dark matter content not well known.

Redshift surveys should be used with the caveat that not all redshifts are due to the expansion of the universe. For instance, rich clusters in wedge diagrams show the ``finger of God'' effect; they tend to be elongated in the radial direction. This elongation received its curious name because the grossly stretched-out cluster is jokingly compared to the finger of God pointing accusingly at the observer, while God thunders, `You are WRONG!'. What you've done wrong, in this case, is assume that the redshift z measured for each cluster galaxy can be converted to a distance d = (c/H₀)z. In fact, if a cluster at a distance d has a velocity dispersion sigma along the line of sight, some galaxies will have a radial speed of +sigma with respect to the center of mass of the cluster, while others will have a radial speed of -sigma. Thus, two galaxies quite close to each other in the cluster can have redshifts that differ by
Delta z ~ 2 sigma / c.
If we naively convert observed redshifts to distances, we will conclude that the finger of God has a length
Delta d ~ (c/H₀) Delta z ~ 2 sigma / H₀.
Thus, the Coma cluster, which has sigma ~ 900 km/s, appears to be stretched to a length of Delta d ~ 30 Mpc in a wedge diagram, when its actual diameter is only 3 Mpc.

Since the largest structures in the universe are 100 Mpc superclusters, the region within a few hundred Mpc of the Galaxy is expected to be a fair sample of the universe at the present day. Within this region, the galaxy luminosity function is found to have a power-law form with an exponential cutoff:
Phi(L) dL = Phi_* (L/L_*)^a exp (-L/L_*) dL/L_*,
where Phi is the number of galaxies per cubic Mpc per unit interval in luminosity. The exponential cutoff kicks in at a luminosity
L_* ~ 2x10¹⁰L_sun ~ L_MW.
At luminosities below the cutoff, the luminosity function is a power law of index
a ~ -1.2.
The overall normalization of the luminosity function is
Phi_* ~ 0.01 Mpc^-3.
The form of the luminosity function is poorly known for L < 0.1 L_*; determining the number of dwarf galaxies in the universe is extremely difficult. The total luminosity density of the universe, found by integrating Phi(L) times L from L=0 to L=infinity, is
rho_L ~ 2x10⁸ L_sun/Mpc³.
This is equivalent to a single 40-watt light bulb within a sphere 1 A.U. in radius. By terrestrial standards, the universe is a shockingly poorly lit place.

Tuesday, February 24: Active Galactic Nuclei

How do you tell an active galaxy from a normal galaxy? Here are some of the attributes of active galaxies:

The galaxy has high luminosity: L > 10³⁷ watts (L > 3x10¹⁰ L_sun)
Much of the emission is nonthermal, as compared to the thermal emission from stars and warm dust.
Much of the emission is from the central nucleus.
The luminosity of the nucleus is variable on short time scales (t < 1 month).
Jets lead away from the nucleus.
The spectrum of the nucleus shows emission lines.

Not every active galaxy possesses every one of these attributes. There are different classes of active galaxies, classified according to the properties they display. (Galaxies with highly luminous nuclei are generically called AGNs -- short for Active Galactic Nucleus).

One class of active galaxies is Seyfert Galaxies. Seyfert galaxies are spiral galaxies which have very luminous, variable nuclei with emission-line spectra. Type 1 Seyferts have broad Balmer emission lines (v > 5000 km/s). Type 2 Seyferts have narrower Balmer emission lines (v < 400 km/s).

Another class of active galaxies is BL Lac objects. BL Lacertae, the prototype of this class, was initially mistaken for a variable star. This is because BL Lac objects have extraordinarily luminous nuclei which vary on time scales of 1 day. It is probable that BL Lac objects are elliptical galaxies, but it's hard to determine their morphology because their nuclei are so bright. BL Lac objects have a nonthermal continuum spectrum, with no emission lines.

Yet another class of active galaxies is radio galaxies. The brightest objects in the sky at radio wavelengths are all radio galaxies. A galaxy is classified as a radio galaxy if it has L_radio > 10³³ watts, but that's a fairly arbitrary dividing line. Strong radio sources are usually associated with elliptical galaxies, but some radio galaxies (like Centaurus A) are just plain peculiar in morphology. Extended radio galaxies have large jets, which can be much larger than the galaxy as seen at visible wavelengths. Cygnus A, for instance, has radio jets roughly half a megaparsec long. Compact radio galaxies have short jets and a nuclear radio source. The giant elliptical galaxy M87, in the Virgo Cluster, goes under the alias ``Virgo A''; it is the brightest radio source in the constellation Virgo. M87 has a jet 2 kpc long. Its central nucleus is surrounded by a gas disk of radius r = 16 pc = 4.9x10¹⁷m. The inclination of the disk is roughly i = 42 degrees. The disk is rotating, with a circular speed of v_c = 460 km/s / sin i = 690 km/s. The mass inside the disk is thus
M = v_c² r / G = (6.9x10⁵)² 4.9x10¹⁷ / 6.67x10^-11 = 4x10³⁹kg = 2x10⁹M_sun.
The compact mass at the center of M87 is, in all likelihood, a supermassive black hole, 800 times more massive than the black hole at the center of our galaxy.

The Unified Model of AGNs states that every AGN has a supermassive black hole at its center. The black hole is surrounded by a thick accretion disk of gas and dust. Jets of matter are ejected along magnetic field line in two directions, perpendicular to the disk.

If we view the AGN straight along a jet, we see a BL Lac object; the spectrum is dominated by the synchrotron emission from the hot, magnetized jet.
If we view the AGN at a slight angle to the jet, we see a Type 1 (broad emission line) Seyfert. At this angle, we can see all the way to the Broad Line Region close to the black hole, where speeds are rapid and the resulting Doppler broadening of emission lines is large.
If we view the AGN at a larger angle to the jet, we see a Type 2 (narrow emission line) Seyfert. At this angle, the thick dusty disk blocks our view of the Broad Line Region, so we see only material with slower speeds and less Doppler broadening of the emission lines.

How much matter must be fed into a black hole to maintain the AGN's luminosity. If a bit of matter (mass = m) is lowered toward a black hole of mass M, then if the matter starts at a radius much greater than the Schwarzschild radius, the amount of gravitational potential energy it has lost by the time it reaches the Schwarzschild radius is
Delta E = G M m / R_s = G M m / ( 2 G M / c² ) = 0.5 m c².
In the real universe, not all the gravitational potential energy is converted into photons (some goes into the kinetic energy of the jet, for instance). It is customary to write the photon energy produced as
Delta E_phot = eta m c²,
where eta is a dimensionless number less than 1/2, known as the ``efficiency''. For a typical AGN, it is thought that eta ~ 0.1. (Feed a gram of stuff into a black hole, and get 9 trillion joules of energy in return, in the form of photons.)

Wednesday, February 25: Quasars

The luminosity of an accreting black hole is:
L = eta (dm/dt) c²,
where dm/dt is the infall rate. If we know an AGN's luminosity, we can deduce its infall rate:
dm/dt = L / (eta c²) = 0.02 M_sun/yr (L / 10³⁷W) (eta/0.1)^-1.
The inflow rate will probably not be steady; the luminosity of an accreting black hole will leap upward, for instance, if a star is tidally shredded and swallowed by the black hole.

What is the maximum possible luminosity of an accreting black hole? The maximum luminosity is imposed by the fact that outflowing photons exert a force on the inflowing gas. Consider an accreting black hole with mass M and luminosity L; it is surrounded by ionized hydrogen. At a distance r from the black hole, the outgoing photons carry an energy flux
f = L / (4 pi r²).
Since an individual photon of energy E has a momentum p = E/c, the outgoing photons also carry a momentum flux
f_p = L / (c 4 pi r²) .
Because the photons carry momentum, they exert force on the electrons and protons. The force exerted on each particle (that is, the rate at which momentum is transferred to it) depends on its cross-section for interactions with photons. The cross-section for an electron is the Thomson cross-section:
sigma_T = 6.65x10^-29m².
(The cross-section for protons is smaller by a factor of 1/3,000,000.)

An electron will feel an outward force due to interactions with photons. The amplitude of this radiation force is
F_rad = f_p sigma_T = (L sigma_T) / (c 4 pi r²).
As the electron is accelerated, it drags the nearest proton along with it, preserving charge neutrality.

An electron-proton pair will feel an inward force due to gravity. The amplitude of this gravitational force is
F_g = - (G M [m_p+m_e])/r² ~ - (G M m_p)/r².
The maximum possible luminosity for the accreting black hole is called the Eddington luminosity. It's the luminosity for which the inward and outward forces balance:
(L_E sigma_T)/(c 4 pi r²) = (G M m_p)/r²,
or
L_E = (4 pi G m_p c M)/ sigma_T = 1.3x10³¹ watts (M/M_sun) = 33,000 L_sun (M/M_sun).
For accreting black holes the existence of a maximum luminosity implies a maximum accretion rate:
(dm/dt)_E = 20 M_sun/yr (M / 10⁹ M_sun) (eta/0.1)^-1.

(The Eddington luminosity also applies to stars. The reason why hypermassive stars don't exist is that for very massive stars, the luminosity is greater than the Eddington luminosity, and ionized gas in the outer layers of the star is blown away.)

The question of how luminous an AGN can be is important when we discuss the most luminous AGNs of all: quasars (short for ``quasistellar objects''). A quasar is an AGN which is very luminous (L ~ 10³⁸ to 10⁴¹ watts) and typically very far away from us (d ~ c/H₀ in many cases).

Quasars were first discovered in the 1960s. Astronomers were puzzled by mysterious unresolved (``quasistellar'') radio sources. Their visible spectra had broad emission lines which no one could identify until Maarten Schmidt released that they were highly redshifted Balmer lines. The first quasar identified, 3C 273, has z=0.158, corresponding to a radial speed v_r ~ cz = 47,000 km/s and a distance d ~ (c/H₀)z = 680 Mpc. The current range of known quasar redshifts is z=0.06 to z=6.4. (For quasars with redshifts comparable to or greater than 1, the classical approximations break down, and relativistic formulae need to be used for radial speed and distance.)

How do we know quasars are AGNs? They are highly luminous. They have nonthermal emission. Most of their luminosity comes from an unresolved nucleus. The nucleus luminosity is variable on time scales as short as a day. Many quasars have jets. The spectrum of the quasar has strong, broad emission lines. All of these are symptomatic of an active galactic nucleus.

Now, about one in 10⁶ bright galaxies harbors a quasar. However, if you look outward to z~3, you find that in the past, one in 10³ bright galaxies harbored a quasar. Where have all the quasars gone? The supermassive black holes are still lurking in the hearts of galaxies; it's just that now their accretion rates are slower. The most luminous quasars had L~10⁴¹W; their accretion rates were thus dm/dt ~ 200 M_sun/yr. Images of the galaxies hosting quasars frequently show merging galaxies; during the merger process, gas falls to the centers of the two galaxies and feeds their central black holes at a rapid rate. In the past, when galaxies were closer together, mergers were more frequent than they are today.

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Updated: 2004 Feb 25 [bsr]