1RedshiftsOrion nebulaz = 0Quasar 3C 273v = 0.14c = 44,000 km/sWavelength ÆFlux Æv = 0.86c = 257,000 km/s11)(z11)(zcvcvλ∆λλλλzRedshift22restrestobs++−+=≈=−==HI Lyαλrest= 1215Special relativistic result [CO eqn. 4.38]Distance MeasurementsFrom The Astrophysical Journal, 1929:2Hubble’s Law (1929)• Measure radial velocity v from Doppler shift.• Hubble’s Law:v = Hod•Hois called “Hubble constant”1929 1931today0 1600millions of LYThe Expanding UniverseHomogeneous * IsotropicAs seen from a Wonder Bread raisen As seen from UtahR(t) = 0Now4age of universedtdRRHo1=Ho= velocity/time= km s-1Mpc=1Slope = Ho=oH13The Expanding UniverseHomogeneous * Isotropic• The Hubble Un-constant (blush)Ho= 100h km s-1Mpc-1• Hubble timetH= 1/Ho= 9.78 x 109h-1yr.1929today0 1600millions of LYLarge Distances Needed1929today0 1600millions of LY• Hubble flow: v = Ho d • Peculiar velocities are superimposed on this.4Large Distances Neededtoday0 1600millions of LY• To distinguish between cosmological models• In the example, 0.5 magaccuracy ~ 50% accuracy. 1929[Fig. 29.26]z=0.1Parallaxes• GAIA will be great within Milky Way• but not to cosmological distances5• The problem: always need something measured in absolute units at the object.• Baade-Wesselink method for expanding or pulsating ~BB sources (Cepheids, SNe) • integrate radial velocity curve to find ∆R• measure L2/L1, T2/T1, solve for R, then for L• problems:• stars, SNe not really BB radiators• absorption lines formed at different depths in atmosphere• SN 1987a gives up to factor 2 error.Some other absolute distance measurements (and why they are not accurate enough)2Time delays: the ring around SN 1987A• emission lines from ring respond to variations in ionizing continuum from SN remnant• measure ∆t = light travel time from center to ring• measure angular diameter of ring• works fine, but only tried for this one nearby objectDuring BeforeAfterθD6Gravitational lens time delays• Separations, relative brightnesses of images ==> model of geometry ==> relative values of Dd, Ds, Dds• Absolute measurement is ∆tlens• Problems:• Need accurate measurements of time lags (many years)• Need accurate model of Φ and of lens geometry.• Models not unique ==> factor 10 uncertainty in H0(!)Relative Distance Estimators: The Cosmic Distance Ladder• The historical approach• Still the most accurate (from HST key project)• Starts with absolute measurements of distances to nearby stars• use those to calibrate distances out to nearest examples of moreluminous objects• then those to calibrate distances to still more luminous objects, and so on…• Empirically-based• doesn’t depend on wrong physical models• but lack of physics ==> absolute calibrator needed somewhere.7The Local Baseline • Parallaxes, moving cluster method Î distance to Hyades, etc.• Cluster main sequence fitting• Variable stars• Cepheids MV~ -3 ==> out to Virgo cluster with HST• RR Lyraes MV~ 0.6 ==> only in Local GroupGlobular cluster luminosity functions• Gaussian distribution of L, mean is same in M31, MW, LMC etc.• at large distances, only practical to measure them in E’s• but calibration is from Milky Way, a spiral• ==> uncertain method8• Planetary nebula luminosity functions• strong [O III], Hα emission line • ==> easily detected by narrow-band imaging• luminosity function has sharp cutoff at bright end• can find brightest planetary out as far as Virgo cluster(17 Mpc, v = 1200 km/s, z = 0.004)• Novae• Correlation between L and rate of decline• fainter ones decay more slowlyAlso… brightest stars in galaxies, brightest H II regions, etc.Results: Distances in the Local GroupGalactic center• huge reddening problems Î poor test of distance indicators.LMC• all stars at ~ same distance, yet close. enough to see stars far down the main sequence Î ideal lab for studying relative luminosities.• RR Lyrae distance scale looks wrong.M31• another good lab for comparing, although farther away.• M31 is same mass as distant spirals (unlike LMC).• table appears to be based on ratioof distances M31/LMC.9Former Goal: Calibrate Brightest Cluster Galaxies• To get out to large distances Î want most luminous possible objects.[CO Fig. 27.6]moreluminousSchecter Luminosity Function• But large distances Î large lookback time Î evolution