RADIO SOURCES, COSMOLOGY ROGIER A. WINDHORST When the radio window first opened up for astronomical observations, it soon became clear that studies of the cosmos at radio wavelengths would have far-reaching consequences for our models of the universe. In the 1930s, Karl G. Jansky and Grote Reber discovered a celestial signal at long radio wavelengths. This radio hiss has a variable component that appeared to go around the Earth in one solar day and is caused by the Sun, as well as a steady component with a period of one sidereal day which was soon identified with the center and plane of our own galaxy. The postwar refinement of radio antennae and interferometers in the 1950s provided ever-increasing resolution and sensitivity to map this steady signal into two main components. One turned out to be a rather smooth continuum associated with the galactic interstellar medium and is caused by synchrotron emission from cosmic ray electrons circling in interstellar magnetic fields. Super-imposed on this is 21-cm-line radiation from neutral hydrogen (or H*) gas in interstellar clouds. The other component consists of discrete or individual radio sources, which remained largely unresolved at the then-available resolution. A subset of these are concentrated toward the galactic plane and are primarily associated with stars and some H** regions. The majority of discrete sources, however, are uniformly distributed across the entire sky. These sources were also referred to as "radio stars" until the late 1950s, when Sir Martin Ryle discovered that their distribution in space was far from uniform. Their number appeared to increase much more rapidly toward weaker radio levels than could be explained by any nonevolving population in any reasonable world model (cosmology). This result ruled out the Euclidean or steady-state models and implied that the number of radio sources per unit volume must increase strongly toward larger distances, even in any one of the relativistic world models. In the early 1960s, the increased positional accuracy of radio interferometers led to more reliable optical identifications of radio sources at high galactic latitudes. Rudolph L. Minkowski identified some of the strongest radio sources in the sky with optically faint galaxies at redshifts of up to 0.5. This was a great mystery, because if these "radio galaxies" had been at redshifts well beyond 1, they would have been completely invisible to even the largest optical telescopes, while they still would have been among the brightest radio sources in the sky! Not long thereafter, Allan R. Sandage identified some bright radio sources with mysterious stellar objects, whose spectra did not look like normal stars. These were referred to as quasistellar radio sources, or briefly "quasars." Maarten Schmidt identified the unusually strong emission lines in the spectra of several quasars with highly redshifted hydrogen lines, reaching redshifts of up to z = 2.0. It soon became clear that quasars might indeed be the very high redshift counterparts of the more nearby radio galaxies, and that these two classes of radio sources together might cause the excessive increase of sources toward weaker radio levels. This process is commonly referred to as "the cosmological evolution of radio sources" and implies that the radio source population must have had larger radio luminosities or space densities in the past, or a combination thereof. In addition to the Hubble expansion, the microwave background radiation and the observed helium abundance, the discovery of the cosmological evolution of radio sources (and the mild evolution in the optical spectra of galaxies discovered in the 1980s) constitute our best evidence that the universe has not always been the same, but once originated through a hot big bang. We now know that radio galaxies and quasars evolve in most of their radio properties on time scales much longer than the human, but smaller than the Hubble time. Hence we can only observe the evolution of an entire population with cosmic epoch, not that of individual objects. When faint objects are selected from deep radio (or optical) images, they generally occupy a handful of independent pixels, so that the studied properties are usually limited to: (1) their brightness, (2) their density in space, (3) their morphology or characteristic size, and/or (4) their colors or spectra. Each of these parameters may appear to evolve with cosmic epoch, either because of poorly understood systematic observational errors and selection effects, or because of good physical reasons, or both. In the following discussion, we will address how the radio source population evolves with cosmic time in each of these individual properties, and study its impact on cosmology. It must be emphasized that any evolution of these properties dominates the minute observational differences expected from world geometry [H*, **,* (Hubble constant, deceleration parameter, cosmological constant), etc.]. Hence the impact of radio astronomy on cosmology is indirect: It follows only after a fairly complete picture has been formed of the evolutionary history of the radio source population. RADIO SOURCE COUNTS AND COSMOLOGICAL EVOLUTION The intensity of a radio source received by a telescope on Earth is called "flux density," or briefly "flux." It is measured in units of 1 Jy (1 jansky), equivalent to 10** W Hz** m** (so 1 mJy=10** Jy;1 *Jy=10* Jy). One could sum up the integrated flux in all components of an extragalactic radio source (i.e., the radio core and the two opposing radio jets and lobes) and do this for all radio sources in the sky. The resulting number of sources as a function of flux is called the "radio source count," which can be directly compared with the predictions for a given world model and the radio luminosity function (or RLF, which describes their space density * as a function of radio power P). To obtain a reliable source count, one should first estimate the fraction of weak sources with angular sizes much larger than the instrumental beam size, because such sources would be resolved out and missed in a complete sample. In the next section, we describe the radio source angular size distribution, from which one can determine a correction for the fraction of large sources missed. For this reason, radio surveys have been made during the last three decades with instrumental beam sizes similar to the expected angular size at every flux level. In the 1960s, primarily single dish telescopes were used to survey areas of steradian size, typically down to levels of 100 mJy. Interferometers were used in the 1970s to survey areas of many square degrees typically down to a few mJy, and in the 1980s to make ultradeep surveys currently reaching noise values as weak as a few *Jy. Important contributions were made by the UK Cambridge One Mile Telescope, the Dutch Westerbork Synthesis Radio Telescope (WSRT), and the U.S. Very Large Array (VLA). Figure 1 shows the differential source counts at 1.41 GHz (or 21 cm), normalized to those expected in a homogeneous, nonevolving Euclidean universe. In Euclidean space, a population of radio sources of constant radio power P (in W Hz**) and constant space density * (numbers Gpc**) would result in observed numbers N that increase with distance proportional to R*, whereas their observed flux S decreases with distance proportional to R**. So when we count the integral number of sources N brighter than a certain flux S, we expect N(>S)* S** in Euclidean space, or ,dN/dS * S** in differential form. Hence the differential counts in a Euclidean universe would be a straight horizontal line in Fig. 1. The observed counts are clearly not Euclidean. Let us consider the source counts from bright to weak radio fluxes (from right to left in Fig. 1). Only at the brightest levels (between 100 and 10 Jy) are the counts approximately Euclidean, because these sources are indeed radio galaxies at local redshifts where space curvature and evolutionary effects are unimportant. Between about 10 and 1 Jy, the source counts show an enormous excess over Euclidean, which discovery won Ryle the Nobel Prize. (The observed counts are even more in excess of the prediction in a nonevolving relativistic world model, not shown in Fig. 1.) This excess of sources is caused by the cosmological evolution of the radio source population. For some reason, galaxies and quasars produced much more powerful radio sources, or much more frequently were radio sources, in the past. In the preceding example, this means that their radio power P and space density * are not constant, but must have been much larger in the past, causing the excess of sources at those bright flux levels. At flux levels between 1 Jy and a few mJy, the differential source counts decline steadily, diving well below the Euclidean prediction. Because the counts shown are differential, the integral number of sources still does increase toward weaker radio fluxes, but not as quickly as at brighter flux levels. Optical identification work has shown that radio sources down to fluxes of 10 mJy consist of one fairly homogeneous population (primarily giant elliptical galaxies and quasars). The fact that the integral counts from this dominant source population converge so strongly down to 10 mJy is our beet evidence that space cannot be Euclidean. One expects exactly this decline in a relativistic world model for a population with a given (epoch-dependent) RLF. The counts converge, because at weaker radio fluxes one has seen increasingly more of the whole source population, and the available volume per unit redshift is much less than in the Euclidean case, certainly for **1. The peak in the differential source counts around 1 Jy must then be caused by those sources with statistically the largest redshifts, which was only confirmed by observations in the late 1980s. At fluxes below a few milli-Janskys, the 1.4-GHz counts slowly turn up again, although they never quite attain the (horizontal) Euclidean slope. This gradual change in slope was measured in the mid-1980s by independent surveys with different radio telescopes at different frequencies of the same and different areas of sky. Hence the upturn in the weak source counts is not due to instrumental effects, but is a property of the universe. It starts below 10 mJy and is visible in all survey fields that contribute significantly below a few milli-Jansky. This upturn is significant, because it cannot easily be attributed to the canonical giant elliptical radio galaxies or quasars, which dominate the counts only above 10 mJy. Neither can it be explained by normal spiral, or Seyfert galaxies, unless these objects have undergone significant cosmological evolution in the recent past. Various models have been developed to explain the steeper differential slope of the weak source counts, such as local, nonevolving, low-luminosity radio galaxies, or evolving Seyfert, spiral, or starburst galaxies. The most likely explanation is that spiral or starburst galaxies underwent cosmological evolution similar to that of giant ellipticals and quasars, which would bring the number of evolving populations to at least two. If these two evolving populations do not evolve into each other, one can extrapolate their epoch-dependent RLFs beyond the redshift to which it was measured, and reach 100% of the source counts for fairly low redshift values. At a maximum redshift of 2*0.5, about 95% of the sources would have been seen. Some researchers have identified this redshift as the formation epoch of luminous galaxies, where they formed the bulk of their stars and first turned on as radio sources. The cosmological evolution of the radio source population has been rather well established over the last two decades by studying the evolution of their RLFs, but this process is still poorly understood physically. It is now generally agreed upon that the most powerful radio sources, giant ellipticals and quasars, have undergone strong cosmological evolution in their RLFs. They were at least 100 times more powerful and/or more numerous in the past. At radio powers below the characteristic break in the RLF (or P1) at frequencies much greater than 1 GHz because the most energetic synchrotron electrons (which radiate mostly at the highest frequencies) lose their energy more quickly. This results in convex (downward-turning) spectra. A typical synchrotron source ages on time scales of 10*-10* yr, yielding spectra that steepen with time. In addition to these physical considerations, the whole radio source population might show spectra whose slope changes on average with redshift due to cosmological effects. At frequencies around 1 GHz, one samples primarily the steep spectrum class at any flux level. The observed median spectral index *** measured in many surveys (between * 0.5 and 5 GHz) shows a behavior with flux density much like Fig. 1. At the brightest flux levels, we find ***** 0.8, Steepening to ***** 0.9 around 1 Jy where the differential source counts reach their maximum excess (with respect to the Euclidean model), whereas at lower fluxes **** flattens again to approximately 0.75 or less. The most straightforward explanation is that the redshift distribution of radio sources causes the observed **** to steepen with redshift, just like it causes the excessive number of radio sources around 1 Jy. Remember that the median redshift follows a similar trend as a function of radio flux, reaching a maximum of ***1.2-1.5 around 1 Jy (see the previous section). Is this steepening of **** with redshift necessarily caused by evolution in the spectral index, or does it just indicate that one samples different parts of the source spectra at different redshifts, because many spectra are not a straight power law, but convex? This would result in a nonnegligible radio K correction for sources at the highest redshifts, much like the well-known K correction for optical galaxies. Especially for surveys around 1 Jy, we expect a substantial radio K correction, because they have the largest median redshift so that spectral curvature at high frequencies will affect the observed value of * the most. A combination of many surveys (with radio spectra measured between frequencies that correspond as much as possible to the same rest frame frequencies) suggests that the median spectral index is apparently a strong function of redshift and only weakly dependent on radio power, roughly as following: ***************************** (3) (with *****in W Hz** for H*=50, **=0 and log**=25.O W Hz**). Because the radio spectrum of a typical extended synchrotron source maximally steepens by approximately 0.5 (from 0.75-1.25) between frequencies of approximately 1 and several GHz, the corresponding spectral curvature can account for most of the second term in Eq.(3) through the radio K correction. Hence radio sources have not necessarily undergone any evolution in their radio spectra at all. However, the third or log * term itself may have a hidden dependency on redshift if the cosmological evolution of radio sources is caused by pure luminosity evolution, so that P(z)=P(0)(1+z)*, with **4 as in Eq.(1). In that case, the second term of Eq.(3) has an additional term of +0.12 log(1+z), so that the expected K correction does not explain all of the apparent spectral steepening with redshift. The apparent dependence of **** on redshift is then in a sense an artifact of the cosmological evolution of the radio source population, and the true physics lies in the relations between **** and log P***, plus log P**, and redshift. The former may be explained by stronger synchrotron losses for more powerful sources (because they radiate their energy more quickly), the latter by an epoch-dependent fueling that was somehow more efficient in the past. Equation (3) also explains why astronomers in the late 1980s were so successful in finding the highest-redshift galaxies among strong radio sources with the steepest spectra. Additional Reading Condon, J.J.(1988). Radio sources and cosmology. In Galactic and Extragalactic Radio Astronomy, 2nd ed., G.L,. Verschuur and K.I. Kellermann, eds. Springer-Verlag, New York, p. 641. Longair, M.S.(1978). Radio astronomy and cosmology. In Observational Cosmology, Eighth Advanced Course of the Swiss Society of Astronomy and Astrophysics, A. Maeder, L. Martinet, and G.A. Tammann, eds. Geneva Observatory, Geneva, p. 127. Minkowski, R.(1975). The identification of radio sources. In Stars and Stellar Systems: Galaxies and the Universe, A. Sandage, M. Sandage, and J. Kristian, eds. University of Chicago Press, Chicago, p. 177. Ryle, M.(1957). The spatial distribution of radio stars. In Radio Astronomy, IAU Symp. 4, H.C. van der Hulst, ed. Cambridge University Press, Cambridge, p. 221. Scheuer, P.A.G.(1975). Radio astronomy and cosmology. In Stars and Stellar Systems: Galaxies and the Universe, A.Sandage, M. Sandage, and J. Kristian, eds. University of Chicago Press, Chicago, p. 725. Schmidt, M.(1972). Statistical studies of the evolution of extragalactic radio sources. III. Interpretation of source counts and discussion. Ap. J. 176 303. Windhorst, R.A., Mathis, D.F., and Neuschaefer, L.W.(1989). The evolution of weak radio galaxies at radio and optical wavelengths. In The Evolution of the Universe of Galaxies, Edwin Hubble Centennial Symposium, R.G. Kron, ed. ASP Conference Series. Book Crafters, Inc., Provo, UT, p.389.