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The Sunyaev-Zeldovich Effect

The hot gas found in galaxy clusters in principle gives us an opportunity to measure distances within the universe through purely physical processes. The reason is that we see the effects of the hot gas in two way: through the emission of x-rays from a cluster, and the modification of the microwave background by a cluster. This gives use two measurements to disentangle two unknowns: the density of the hot gas, and the physical size of the system. By measuring the physical size of the system and comparing it to the angle the cluster subtends on the sky, we can derive a distance. This method may one day provide an alternative to the standard candle methods used to determine the distance to high-redshift galaxies.

The x-ray emission seen from clusters of galaxies come primarily through the bremsstrahlung process, which is the creation of x-rays when free electrons scatter with ions. The rate at which this process produces x-rays depends on two parameters: the temperature and density of the gas. The temperature can be determined from the shape of the continuum part of the x-ray spectrum. The second quantity we can measure, the flux produced by the cluster, gives us a measure of the density-squared times the diameter of the hot gas sphere. The trick is to find a measure that will disentangle the density from the diameter.

Fortunately, the hot gas in a cluster does more than just emit x-rays: it also scatters the microwave background. The microwave background is remnant radiation from the early age of our universe. This radiation is isotropic and thermal, with a temperature of 2.73°K. When this radiation scatters with the hot electrons, a process called Compton scattering, it acquires energy from the electrons. This scattering distorts the shape of the microwave background in the direction of a galaxy cluster, an effect that is called the Sunyaev-Zeldovich effect, after the two Russian scientists who pointed it out. The amount of distortion depends on three properties: the temperature of the electrons, which we know from x-ray observations, the density of electrons, and the diameter of the hot gas sphere. By measuring the distortion of the microwave background in the direction of a galaxy cluster, we have a measure of the density times the diameter.

The x-ray observations provide us with a measurement of η2D, where η is the electron density and D is the diameter of the gas sphere, and microwave measurements provide a measurement of ηD. These observations therefore give us a direct measure of the diameter of the hot gas sphere. Combining this with the angle that the sphere subtends on the sky, and we have a measurement of the distance to the galaxy cluster. All so simple, and all independent of the ladder of parallax measurements and standard candle sources.

So why are we still fooling around with supernovae and Cephied variables to relate redshift to distance? While the basic idea behind the Sunyaev-Zeldovich effect is very simple, applying this idea to real galaxy clusters is a difficult. Part of the difficulty is theoretical, and part is instrumental.

The description of the method treated the hot gas as simply a uniform sphere. In reality, of course, the gas is sitting at the bottom of a deep gravitational potential created by the galaxies in the cluster. This gas supports itself against gravity by its pressure. This means that the density of the gas is greatest at the center of the sphere. As one moves away from the center, the pressure must drop, which means that either the density or the pressure must drop. Into this mix must be added the mechanisms that heat the gas versus the mechanisms that cool the gas. None of these complications invalidate the basic idea. The complications do mean that we must compare a theoretical model of the gas in a galaxy cluster to x-ray observations by telescopes that can resolve the structure of the gas sphere.

On the observational side, the instruments necessary to measure this effect are just now improving to the point that reasonable measurements of Hubble's constant can be made. The current x-ray instruments used to study x-ray clusters are the Chandra X-ray observatory and the Newton-XMM observatory. These instruments have very good spatial resolution combined with excellent spectral resolution. The greatest uncertainty in measuring the characteristics of the hot gas in the cluster is in precisely measuring the x-ray flux. This uncertainty is systematic in nature, meaning that they arise from the calibration of the instrument rather than from the statistical fluctuations of counting photons. This error is estimated to be around 10% of a measured value for current instruments. Measurements of the actual Sunyaev-Zeldovich effect itself has improved greatly as the microwave telescopes have improved. As with the x-ray telescopes, the principal error is a systematic error in calibration. This error is estimated to be 2.5% in current instruments.

Despite these errors, distances to galaxy clusters have been measured with this method. From these measurements, a value for the Hubble constant has been found, although the value depends on what one assumes for the density of the universe. For an open universe with a density that is 0.3 of the closure density, the Hubble constant is H0 = 56 km s-1 Mpc-1. This differs only slightly from the H0 = 60 km s-1 Mpc-1 value found from type 1a supernovae studies. The difference is values is undoubtedly from systematic errors. The scientific community places more faith in the supernovae-derived value, but with continued improvements in instrumentation, we may one day place as much faith in the Hubble constant derived from the Sunyaev-Zeldovich effect as that from the supernovae studies.

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