Hubble Diagram S George Djorgovski. Encyclopedia of Astronomy & Astrophysics P. Murdin

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1 eaa.iop.org DOI: / /2132 Hubble Diagram S George Djorgovski From Encyclopedia of Astronomy & Astrophysics P. Murdin IOP Publishing Ltd 2006 ISBN: Institute of Physics Publishing Bristol and Philadelphia Downloaded on Tue Jan 31 17:16:31 GMT 2006 [ ] Terms and Conditions

2 Hubble Diagram Initially introduced as a way to demonstrate the expansion of the universe, and subsequently to determine the expansion rate (the HUBBLE CONSTANT H 0 ), the Hubble diagram is one of the classical cosmological tests. It is a plot of apparent fluxes (usually expressed as magnitudes) of some types of objects at cosmological distances, against their REDSHIFTS. It is used as a tool to measure the global geometry of the universe, and as a probe of galactic evolution. As in most other cosmological tests, the observables used in this diagram are really proxies for the expansion factor of the universe (measured as the cosmological redshift) and some independently determined proper distance to the objects used in the test. The observed trend of distance-related quantities (e.g. apparent fluxes, angular diameters, etc) against the redshift can thus, at least in principle, be mapped to the expansion history of the universe, which in turn uniquely determines the COSMOLOGICAL MODEL. The slope of the trend at low redshifts determines the present normalized expansion rate, i.e. the Hubble constant. The shape of the trend at large redshifts determines the global geometry of the universe. In the case of the Hubble diagram, a relativistic version of the inverse square law is used to determine the relative distances to the light sources used. Simply put, the more distant objects of a fixed intrinsic brightness should be fainter, by a factor determined exactly by the geometry of space. Redshifts are measured spectroscopically, and do not depend on the complicating factors which may affect the distance measurements, such as the evolution of sources used, sample selection effects, etc. The distances are much more difficult to determine, and this is where most of the practical problems lie. The objects used as the test particles in a Hubble diagram are often called standard candles, thus expressing the hope of their constancy in time and at different locations. Yet this is hardly ever the case, and much of the effort involved goes into their standardization removal of the various second-order parameters which cause the scatter around the ostensible universal mean luminosity of a given type of object. Hubble (1929) used this diagram to demonstrate the expansion of the universe: fainter and thus on average more distant galaxies were receding from us with larger apparent speeds. Once the universal expansion was generally established, the test acquired other cosmological uses. There are two regimes in which the Hubble diagram is used today, each with its own goals, methods and problems. In the low-redshift regime, the Hubble diagram is used in determinations of the Hubble constant. The local geometry is very close to being Euclidean, and thus the effects of the global curvature can be safely ignored. The look-back times to the objects used are small enough so that evolutionary effects can also be neglected. The local universal expansion is practically linear, producing the well-known HUBBLE S LAW: cz = H 0 D, where c is the speed of light in a vacuum, z is the observed redshift (assuming that the peculiar velocity of the object is negligible), H 0 is the Hubble constant and D is the proper distance. Since distances are not directly measurable, even for the nearest galaxies, a proxy quantity is used; in the case of the Hubble diagram, this is often the magnitude of an object of given class, e.g. a Cepheid variable (or, more accurately, the intercept of the CEPHEID PERIOD LUMINOSITY RELATION), a SUPERNOVA at its peak brightness, etc. If one knows the actual absolute luminosities of the objects used in the test, obtained from some independent calibration procedure, then the slope of the observed relation gives directly the local normalized expansion rate, the Hubble constant H 0. The difficulties in establishing the absolute brightness scale of the objects used for such purposes, and other problems involved in the measurements of H 0,are beyond the scope of this article. In the more distant universe, the global geometry comes into play, causing the trend to deviate from linearity. The shape of the relation becomes a probe of the cosmological parameters; for the standard Friedmann Lemaitre models, these are the density parameter 0 and the cosmological constant 0. (We note in passing that for many years the value of the COSMOLOGICAL CONSTANT was declared to be zero on purely ideological grounds, and only a single parameter, 0, was used to characterize the global geometry, or equivalently, the deceleration parameter q 0.) Since the shape of the trend does not depend on the absolute value of the luminosities, the normalization and the Hubble constant factor out. The curvature of the trend reflects directly the global kinematics of the universe as observed over cosmological time-scales for true standard candles. Consider the effect of an increase in the mean density: it causes the expansion to slow down more, and thus the objects at a given redshift are closer and appear brighter. The same effect is accomplished by the negative values of the cosmological constant (which correspond to a positive energy density), and the opposite effect by the positive values of this parameter, which then acts as a repulsive force, accelerating the expansion. These effects become detectable only over very large look-back times, i.e. at relatively high redshifts, requiring the use of objects bright enough to be detected at such large cosmological distances. Moreover, there is a considerable parameter coupling between 0 and 0, as they can have qualitatively similar effects. A large baseline in redshift is also necessary in order to separate their contributions, since they may dominate the changes in the expansion rate at different epochs. For a source with an intrinsic luminosity L, at a cosmological redshift z, the observed flux is: F = L 4πD 2 (1+z) 2 = L 4πD 2 L where D is the proper distance and z is the source redshift. The quantity D L D(1 +z) is called the Dirac House, Temple Back, Bristol, BS1 6BE, UK 1

3 luminosity distance. The formula differs from the classical inverse square law by the two powers of the expansion factor, (1 +z): one is due to the energy loss of photons as their wavelengths are redshifted, and one is due to the relativistic time dilation in the photon emission rate, since the source is moving away from us. In the simple Friedmann cosmological models, with a vanishing cosmological constant, 0 = 0, the proper distance is given by the following formulae: D = c H 0 z(1+z/2) 1+z for 0 = 0 D = 2c H 0 (1 1/ 1+z) for 0 = 1 D = 2c z 0 (2 0 ) 1+z 0 H (1+z) otherwise where c is the speed of light in a vacuum, H 0 is the Hubble constant and 0 is the density parameter of the universe, the ratio of the mean density to the critical density at the present epoch. HUBBLE s pioneering vision of determining the global geometry through this and other tests was frustrated by the technology available to him at the time, by not being able to reach out to sufficiently large redshifts where the cosmological effects may be detectable. His quest was then carried out over many years by A SANDAGE and collaborators, as well as many others; for a fascinating historical account, see, e.g., Sandage (1995). Typically, magnitudes of the brightest cluster ELLIPTICAL GALAXIES were used as the standard candles, and the quest was on for finding the ever more distant ones. At low redshifts, suitably defined magnitudes of these objects show an intrinsic scatter of only about 30%, which was considered constant enough. Unfortunately, no conclusive cosmological results were achieved in these studies despite much effort and observing time spent, in part because they did not reach out to sufficiently large redshifts. QUASARS, discovered in 1963, provided luminous probes of even larger redshifts, but had too much of a spread in intrinsic luminosities and too much variability to be viable for this purpose. Other candidate standard candles tried at cosmological distances include supernovae, the characteristic luminosity (L ) of the galactic luminosity function in distant clusters, etc. The observed apparent magnitude of a source is given by m obs = M +5 5 log D L + K + m sc where M is the absolute magnitude of the source, which may be affected by evolution effects, and D L is the luminosity distance defined above. K is the so-called K correction, which accounts for the difference in the detector bandpass in the observer s frame and in the source restframe. It is given by the ratio of the fluxes of the source, with its spectrum integrated over the observed bandpass and its redshifted counterpart, and expressed Figure 1. The infrared Hubble diagram (in the K band, 2.2 µm effective observed wavelength) for a set of powerful radio galaxies, reaching out to z = 5.19 (indicated with the large triangle). The insert is a zoom-in on the high-z portion of the diagram. Two galactic evolution models are shown, both corresponding to a single burst of star formation starting at z = 20, and assuming a cosmology with H 0 = 65 km s 1 Mpc 1. 0 = 0.3 and 0 = 0. The diagram shows a remarkably small scatter at any redshift, even though every relevant effect we know of would increase the scatter: the variations in star formation histories and formation redshifts, in the contributions from active nuclei, in extinction, line emission, merging rates, etc. While no one is yet brave enough to try to use this diagram to measure the cosmological parameters, the small observed scatter presents a challenge for theoretical models of powerful radio galaxies and their evolution. (Reprinted with permission from van Breugel W et al 1999 Astrophys. J. Lett. 518 L61 The American Astronomical Society.) in the magnitude form. This of course requires the knowledge of the source s spectrum at z = 0; any possible evolutionary effects are not included. m sc is an empirical correction used to standardize the candle, i.e., remove statistically some other observable effects which may be correlated with M. In the case of the brightest cluster ellipticals, such corrections include subtle dependences on the cluster richness and morphology; in the case of supernovae, shapes of their light curves are used to derive such corrections. As in the case of most other cosmological tests, the use of the Hubble diagram as a probe of the global geometry was severely undermined by the inevitable cosmic evolution of whatever objects are used as the test particles. The light from galaxies comes from their STELLAR POPULATIONS, which must evolve in time, in brightness and in color. By the late 1970s it became clear that the effects of galactic evolution will dominate over the cosmological effects for any type of galaxy at sufficiently large redshifts. Dirac House, Temple Back, Bristol, BS1 6BE, UK 2

4 Figure 2. An example of a Hubble diagram for type Ia supernovae, with peak magnitudes corrected using the light curve shapes. Several cosmological models are drawn through the points, with the corresponding values of the parameters 0 and 0 as indicated. The best fit to these data indicates a low-density universe with a positive cosmological constant. The top panel shows the diagram itself. The bottom panel shows the residuals from the best-fit model, and the bottom panel shows the photometric deviations from the model in units of the standard deviations. (Reprinted with permission from Perlmutter S et al 1999 Astrophys. J The American Astronomical Society.) This is especially true at the observed visual wavelengths, which correspond to the ultraviolet light restframe, which may be dominated by a few luminous, young and shortlived stars. Moreover, galactic merging and interactions, which must have been more frequent at higher redshifts, further complicate the interpretation of observations: galaxies may grow in time, and undergo merger-induced bursts of star formation (see GALAXIES: INTERACTIONS AND MERGERS). The Hubble diagrams thus became a probe of galactic evolution, where a set of cosmological parameters was often assumed out of necessity in order to measure the rate of galactic evolution. More recently, the Hubble diagram has made a comeback as a potential cosmological tool, as described below. Even if the evolutionary effects can be controlled, an additional difficulty is the possible (likely?) presence of sample selection effects. Typically, brighter representatives of any class of objects would be found at larger redshifts, as the fainter ones may not make it into a fluxlimited sample. Such biases are hard to correct, since one never knows how many objects are not even detected, let alone what is their brightness distribution. Reducing the scatter of observed luminosities at a given redshift (i.e. using a more standard candle) helps, but some bias is always present. Understanding the sample completeness is essential. In addition, it is sometimes hard to guarantee even Dirac House, Temple Back, Bristol, BS1 6BE, UK 3

5 the homogeneity of the samples, i.e. that the same type of objects are being selected both at high redshifts, and as their ostensible low-redshift progeny. Additional problems include possible effects of GRAVITATIONAL LENSING by the intervening masses, and interstellar extinction corrections, both in our Galaxy and in the distant galaxies used in the test. Some hope came with technological advances in near-infrared measurements (see INFRARED TELESCOPES). The advantages of infrared observations are considerable. They probe the restframe wavelengths of normal galaxies which are much less affected by a possible flicker of massive star formation. The infrared light is typically dominated by the relatively stable and slowly changing stellar subpopulations such as the red giants. Thus, the effects of galactic evolution effects should be minimized. Infrared observations are also much less sensitive to interstellar extinction. One example is the infrared Hubble diagram for powerful RADIO GALAXIES at high redshifts (figure 1). The advantages of radio galaxies are that they can be identified at very large redshifts (as of this writing, at z > 5), and that they are generally believed to be progenitors of at least some giant ellipticals today. Their chief disadvantage is the presence of a powerful active nucleus, which may be contaminating the observed brightness and affecting the host galaxy in uncertain ways. Perhaps the infrared observations of normal, quiescent cluster ellipticals (known out to z 1.3, as of mid-1999), or magnitude intercepts of their fundamental plane correlations may be more promising. There has been much excitement in recent years about the use of distant supernovae as possible standard candles to measure the global geometry of the universe. At their peak, supernovae of type Ia reach an absolute magnitude M B 19.5, and are thus sufficiently luminous to be detected at redshifts approaching unity, where the effects of cosmic geometry should be readily detectable. Furthermore, the shape of the supernova light curve is found to correlate with the peak luminosity, thus providing a handy observational way to lower the scatter of the peak magnitudes by correcting for this second parameter. Scatter as low as 15% or even less may be achieved (this made type Ia supernovae also a viable tool in the efforts to measure H 0 at low redshifts). Since the physics of the supernova explosions should be universal, this novel standard candle clearly has a lot of promise as a cosmological tool. Note, however, that some evolution in the observable properties of supernovae is possible, e.g. due to the slowly changing metallicities of the stellar populations from which these supernovae originate. Using this approach, two groups have recently measured the values of the cosmological parameters 0 and 0 (figure 2), with mutually consistent results (Schmidt et al 1998, Perlmutter et al 1999). Both groups found that the best fit to their observations is consistent with a zero-curvature universe, preferred by the theoretical prejudice of inflation models, but with a positive cosmological constant, which was something of a surprise. If this result is confirmed by future observations and tests, it would be of profound cosmological significance. It remains to be seen if any other types of luminous objects turn out to be good standard candles, or if new ways of standardizing the old ones are invented. In any case, the Hubble diagrams will remain a useful probe of galactic evolution, and possibly even of the global geometry of the universe. Bibliography The first-hand historical account of the initial uses of the Hubble Diagrams can be found in Hubble E 1929 Proc. Natl Acad. Sci., USA This work was summarized in a much more accessible and easier to find book Hubble E 1936 The Realm of the Nebulae (New Haven, CT: Yale University Press) (reprinted in 1982) An excellent scientific and historical outline of the use of the Hubble Diagrams from the early days until about early 1990s is given in Sandage A 1995 The Deep Universe, (Saas-Fee Advanced Course 23) (Berlin: Springer) Two modern papers describing the use of the Hubble diagrams of type Ia supernovae, along with the more modern references are Perlmutter S et al 1999 Astrophys. J Schmidt B et al 1998 Astrophys. J S George Djorgovski Dirac House, Temple Back, Bristol, BS1 6BE, UK 4

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