The Sunyaev-Zeldovich effect (SZE) is an observed anisotropy in the cosmic microwave background (CMB) spectrum, caused by Compton scattering of microwave photons by ions in the gas that fills clusters of galaxies. Although it is a less important perturbation of the microwave background in comparison to that caused by primordial density fluctuations, the SZE is important in astronomy and cosmology. Theorized by Soviet physicists Rashid Sunyaev and Yakov Zel'dovich in 1969, the SZE can be used to calibrate the Hubble constant.

Thermal Sunyaev-Zeldovich effect

The universe is filled with galaxies. By all accounts, there are likely billions of them. Many of these galaxies lie within clusters that formed from the densest regions of the primordial universe. Today, we see these clusters as aggregations of thousands of galaxies, all gravitationally bound and orbiting about the center of the cluster. What is not evident to the eye is that these clusters are also filled with very hot gas. The gas can have temperatures of several million Kelvins, and can be very bright in X-rays. However, this gas also has an effect on the CMB.

As light from the microwave background passes though these galaxy clusters, the microwave photons are scattered by electrons in the intra-cluster gas, giving low-energy photons much higher energy in the process. This results in a fainter CMB spectrum at low photon energies, which appears as a cooler microwave background in the direction of the galaxy cluster. This is called the thermal Sunyaev-Zeldovich effect, because the CMB is being distorted by the thermal motions of electrons within the cluster gas.

By measuring how much the spectrum is changed, you can make a good guess as how large the cluster is. This measurement is important, because we have no simple way to measure distances in the universe. Measuring the linear size of the cluster and the angular size (as it appears to us on the sky) lets us use trigonometry to determine the distance to the cluster. If we then measure the redshift of the cluster, we can calibrate the Hubble constant, i.e. What Hubble constant is required to obtain the measured redshift for the cluster at known distance?

In reality, using the SZE to measure the Hubble constant is very difficult, and requires several critical assumptions. In particular, it requires that one knows the distribution of hot gas within the galaxy cluster, since the density of the gas determines how the CMB photons will scatter. One must also assume a specific cosmological model for the universe, particularly for the deceleration parameter, q0. Neither of these is particularly well-known, though the distribution of gas in the cluster can be roughly measured with the X-ray radiation it emits. Measuring the redshift of the cluster is also difficult, because the individual galaxies within the cluster have their own large pecular velocities in addition to the Hubble velocity of the cluster.

The Sunyaev-Zeldovich effect has been used many times to measure the Hubble constant, and values derived from the SZE method seem to agree with those measured from other means (e.g. extragalactic Cepheid variables and high-redshift supernovae). The current best-guess for the Hubble constant is about 65 ± 10 km/s/megaparsec.

Kinetic Sunyaev-Zeldovich effect

There is a second, weaker effect observed in some galaxy clusters, called the kinetic Sunyaev-Zeldovich effect. Like the thermal SZE, the cluster gas has an effect on the CMB, but in this case, there is a further modification to the spectrum caused by the bulk motion of the cluster itself, relative to the Hubble expansion. In the thermal effect, we assumed that the cluster was moving relative to us only because of the expansion of the universe. In fact, this was an important assumption because we assume that the redshift we measure is purely due to the Hubble effect. However, the cluster itself may have a peculiar motion, particularly if it is gravitationally interacting with something else. You then have to take into account scattering by a gas moving at the velocity of the cluster relative to the Hubble flow, which may be several thousand kilometers per second. This actually produces a tiny brightening of the spectrum, but the increase is about a factor of ten smaller than the dimming caused by the thermal effect.

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