Ay 127, Spring 2013:!Cosmological Tests and!the Contents of the Universe!• Tests for the expansion of the universe!• Classical and modern cosmological tests of global geometry and dynamics!– Except for the CMB fluc’s, to be covered in more detail later!• The “concordance cosmology”!• The nature of different density components (and how do we measure them)!– Except that we’ll leave a more detailed discussion of the nature of the non-baryonic DM and DE for another lecture!Tests for the Expansion of the Universe!• Tolman surface brightness (SB) test!– In a stationary, Euclidean universe SB = const.!– In an expanding universe, SB ~ (1+z)-4!– In a “tired light” model, SB ~ (1+z)-1!• Time dilation of Supernova light curves!– Time stretches by a factor of (1+v/c) = (1+z)!• The match between the energy density and T 4 for the blackbody and the CMBR!– For a blackbody, energy density u ~ T 4!– In an expanding universe, for photons, energy density is u ~ (1+z)4, and since T ~ 1/λ ~ (1+z), u ~ T 4!The Tolman Test!Surface brightness is flux per unit solid angle: ωdfB =222dlDDLBAL=( )422221−+== zdlLDDdlLBLANote that this is independent of cosmology! This is the same as the luminosity per unit area, at some distance D. In cosmology,!In a stationary, Euclidean case, D = DL = DA, so the distances cancel, and SB = const. But in an expanding universe, DL = D (1+z), and DA = D / (1+z), so:!Performing the The Tolman Test!We need a standard (constant) unit of surface brightness = luminosity/area, to observe at a range of redshifts (a “standard fuzz”?) log SB!A good choice is the intercept of surface brightness scaling relations for elliptical galaxies in clusters log R!Cluster 1!at z1!Cluster 2!at z2 > z1!{!The Tolman Test Results!Surface brightness intercept of the Fundamental Plane correlation, for elliptical galaxies in clusters out to z ~ 0.6. It assumes a reasonable galaxy evolution model correction. (from Pahre et al.)Time Dilation of Supernova Lightcurves!Blue dots: a low-z dataset!Red dots: a high-z dataset!After applying the proper stretch factor!(Goldhaber et al.)!All data points!All data points!Binned!Binned!Cosmological Tests: The Why and How"• Model equations are integrated, and compared with the observations!• The goal is to determine the global geometry and the dynamics of the universe, and its ultimate fate!• The basic method is to somehow map the history of the expansion, and compare it with model predictions!• A model (or a family of models) is assumed, e.g., the Friedmann-Lemaitre models, !typically defined by a set of parameters, e.g., H0 , Ω0,m , Ω0,Λ , q0, etc.!measure the past …!… predict the future!The Basis of Cosmological Tests!R(t)/R0 = 1/(1+z)!1!t!t0 now!0!Big bang!D(z)!~ c [t0-t(z)]!0!now!z!Big bang at z = ∞!All cosmological tests essentially consist of comparing some measure of (relative) distance (or look-back time) to redshift. Absolute distance scaling is given by the H0.!Cosmological Tests: Expected Generic Behavior of Various Models!R(t)!t!| t0!0!R(t)/R0! t - t0!0!Models with a lower density and/or positive Λ expand faster, are thus larger, older today, have more volume and thus higher source counts, at a given z sources are further away and thus appear fainter and smaller"Models with a higher density and lower Λ behave exactly the opposite"The Types of Cosmological Tests!• The Hubble diagram: flux (or magnitude) as a proxy for the luminosity distance, vs. redshift - requires “standard candles”!• Angular diameter as a proxy for the angular distance, vs. redshift - requires “standard rulers”!• Source counts as a function of redshift or flux (or magnitude), probing the evolution of a volume element - requires a population of sources with a constant comoving density - “standard populations”!• Indirect tests of age vs. redshift, usually highly model-dependent - “standard clocks”!• Local dynamical measurements of the mass density, Ωm0!• If you measure H0 and t0 independently, you can constrain a combination of Ωm0 and ΩΛ!Cosmological Tests: A Brief History!• A program of “classical” cosmological tests (Hubble diagram, angular diameter test, source counts) was initiated by Hubble, and carried out at Palomar and elsewhere by Sandage and others, from 1950s through 1970s!• Galaxies, clusters of galaxies, and radio sources were used as standard candles, rulers, or populations. Unfortunately, all are subject to strong and poorly constrained evolutionary effects, which tend to dominate over the cosmology - this foiled most of the attempted tests, and became obvious by 1980’s!• In the late 1990’s, Supernova Ia Hubble diagram, and especially measurements of CMBR fluctuations power spectra (essentially an angular diameter test) completely redefined the subject!• The cosmological parameters are now known with a remarkable precision - a few percent; this is the era of “precision cosmology”!Selection Effects and Biases!Flux or Ang. Diam.!redshift!True model!Best fit with biased data!Observations below this line excluded by selection effects!All observations are limited in sensitivity (we miss fainter sources), angular resolution (we miss smaller sources), surface brightness (we miss very diffuse sources, etc.!This inevitably introduces a bias in fitting the data, unless a suitable statistical corrrection is made - but its form may not be always known!!The Hubble Diagram!magnitude!redshift!Model with a lower density and/or Λ > 0!Model with a higher density and/or Λ ≤ 0!Requires a population on non-evolving sources with a fixed luminosity - “standard candles”. Some candidates:!• Brightest cluster ellipticals!• Supernovae of type Ia!• Luminosity functions in clusters!• GRB afterglows ??!• …!The K-Correction!Galaxy spectra of different types!Photometric measurements are always obtained in some bandpass fixed in the observer’s frame, e.g., the U,B,V,R…!But in a redshifted galaxy, this bandpass now samples some other (bluer in the galaxy’s restframe) region of the spectrum, and it is also (1+z) times narrower!The K-Correction!Thus, we integrate the spectrum over the bandpass in the observed!frame, and in the galaxy’s restframe, take a ratio, express it in magnitudes, and that is the!K-correction!It has to be done for all different