The Cosmic Distance Ladder

The Cosmic Distance Scale Physics of Galaxies 2012 part 4 1 How big is the Universe? We want to understand how big the Universe is! Why? Scale: how big are distant things, like galaxies? Time: we’ll see that recession speed is proportional to distance, so our estimate of the age of the Universe depends on how far apart galaxies are! 2 Absolute vs. relative distance measures Absolute methods: those that can determine a precise distance (usually through geometrical means or timing) generally only work nearby! Relative methods: those that refer to a standard candle or standard ruler — e.g., comparing stars with similar brightnesses or galaxies with similar sizes work out to very large distances! 3 Direct distance measures Parallax: apparent motion of distant stars caused by orbital motion of earth currently limited to ~100 pc for bright stars after Gaia (~2018 or so), will reach out to ~150 kpc for the brightest stars and ~3 kpc for the faintest (V~20) stars 4 Consider the Earth, 1 AU away from the Sun at position E1. Six months ϖ later, the Earth is at position E2, but the star has remained in the same d place relative to the Sun. Then, as seen from Earth, the star appears to have 1 AU subtended an angle 2ϖ E1 E2 Sun on the sky. 5 Then if r (=1 AU) is the radius of the Earth’s orbit, r we find = tan rad d ≈ because ϖ is clearly small; then converting to seconds of arc, = 206265 rad 206265 Defining 1 AU such that d = AU and 1 parsec as the distance at which a star would have a parallax of 1″: 1 pc = 206265 AU = 3.086 1013 km = 3.26 light years The distance to a star with× observed parallax ϖ″ 1 is then d = pc 6 Secular parallax: Instead of using the Earth’s motion around the Sun, use the Sun’s motion relative to nearby stars: v⊙≈20 km/s, so the Sun moves about 4 AU/year twice as large a distance as the Earth moves in six months! use long time baselines to get very long distance baselines Problem: the other stars move too! 7 By averaging over proper motions (i.e., a component of space velocity) in the right way, we can determine an average secular parallax for a group of stars µ ∼ v An extension of this is statistical parallax, where the stars are distant enough to have roughly random motions (see BM2.2.4) 8 Baade–Wesselink method 2 4 Recall that the luminosity of a star is L =4πR σTeff So its absolute magnitude is M = 10 log T 5 log R + C bol − eff − So if we know the apparent magnitude m, temperature Teff, and radius R, we have a direct distance measurement 9 Now, we can generally find Teff from colors or the spectrum of a star How do we find R? In a variable star (or a supernova), the spectral lines shift as a function of time due to the expansion (or contraction) of the atmosphere with some velocity vlos(t), so the change in size of the atmosphere is t1 ∆r = p v (t)dt this is just rate x time = distance! 1 − los t0 where p corrects for the fact that the expansion happens all over the atmosphere, not just along the line of sight, and the negative sign comes from fact that the lines are blue-shifted 10 Therefore the apparent magnitude must change between t0 and t1: m m = 5[log(r +∆r ) log r ] 10[log T log T ] 0 − 1 − 0 1 − 0 − eff,1 − eff,0 So if we can measure the change in magnitudes and the effective temperates, we have r0 and therefore M0. This method doesn’t work perfectly, but detailed stellar atmosphere modeling of supernovae atmospheres has made it useful for distances to some supernovae, like SN 1987A in the LMC: d=55±5 kpc 11 Distances from time delays If you can measure the same signal at two different times — the “delay time” — then you can measure a distance: d c∆t ∼ 12 Supernova light echo Consider a supernova explosion at some time t that is seen at position A Now imagine that some time t0 later a signal (say, strong spectral lines) is seen at position B, and at C an even later time t1 exactly the same signal is seen at position C A i this is light from the SN reprocessed by an inclined ring, as seen by HST for SN1987A observer To B 13 The time delay from A to B is r t = ring (1 sin i) 0 c − while the time delay from A to C is r t = ring (1 + sin i) 1 c The ring radius rring and C inclination i are then easy to find: for SN1987A, t0~90 days and t1~400 days, so i=(42±5)º A i and rring=(0.42±0.03) pc r Now, the size of the ring is observer To B measured to be θ=1.66±0.03 arcsec, so d=52±3 kpc 14 Gravitational lensing Quasars lensed into multiple images by foreground galaxies (usually ellipticals) show correlated brightness variations in the light of each component The delay time of these variations with respect to each other is another geometrical distance measurement But! Uncertainty in mass profiles of lens galaxies means large uncertainties in distance determinations; and finding correlated variations not straightforward 15 letters to nature routine, but estimates of absolute distances are rare1. In the vicinity of the Sun, direct geometric techniques for obtaining Ageometricdistancetothe absolute distances, such as orbital parallax, are feasible, but such techniques have hitherto been dif®cult to apply to other galaxies. galaxy NGC4258 from orbital As a result, uncertainties in the expansion rate and age of the Universe are dominated by uncertainties in the absolute calibra- motions in a nuclear gas disk tion of the extragalactic distance ladder2. Here we report a geometric distance to the galaxy NGC4258, which we infer from J. R. Herrnstein*², J. M. Moran², L. J. Greenhill², the direct measurement of orbital motions in a disk of gas P. J. Diamond*³, M. Inoue§, N. Nakai§, M. Miyoshik, surrounding the nucleus of this galaxy. The distance so deter- C. Henkel¶ & A. Riess# minedÐ7:2 6 0:3 MpcÐis the most precise absolute extragalac- * National Radio Astronomy Observatory, PO Box O, Socorro, New Mexico 87801, tic distance yet measured, and is likely to play an important role in USA future distance-scale calibrations. ² Harvard-Smithsonian Center for Astrophysics, Mail Stop 42, 60 Garden Street, NGC4258 is one of 22 nearby active galactic nuclei (AGN) known Cambridge, Massachusetts 02138, USA to possess nuclear water masers (the microwave equivalent of 12 ³ Merlin and VLBI National Facility, Jodrell Bank, Maccles®eld, lasers). The enormous surface brightnesses ( ) 10 K), relatively Cheshire SK11 9DL, UK small sizes ( ( 1014 cm) and narrow linewidths (a few km s-1) of § Nobeyama Radio Observatory, National Astronomical Observatory, these masers make them ideal probes of the structure and dynamics Minamimaki, Minamisaku, Nagano 384-13, Japan of the molecular gas in which they residue. Very-long-baseline k VERA Project Of®ce, National Astronomical Observatory, Mitaka, Tokyo, interferometry (VLBI) observations of the NGC4258 maser have 181-8588, Japan provided the ®rst direct images of an AGN accretion disk, revealing ¶ Max Planck Institut fuÈr Radioastronomie, Auf dem Hugel 69, D-53121, Bonn, a thin, subparsec-scale, differentially rotating warped disk in the Germany nucleus of this relatively weak Seyfert 2 AGN3±6. Two distinct # Department of Astronomy, University of California at Berkeley, Berkeley, populations of masers exist in NGC4258. The ®rst are the high- California 94720, USA velocity masers. These masers amplify their own spontaneous ......................................................................................................................... emission and are offset 61,000 km s-1 and 4.7±8.0 mas (0.16± The accurate measurement of extragalactic distances is a central 0.28 pc for a distance of 7.2 Mpc) on either side of the disk centre. challenge of modern astronomy, being required for any realistic The keplerian rotation curve traced by these masers requires a description of the age, geometry and fate of the Universe. The central binding mass (M), presumably in the form of a supermassive 7 2 2 measurement of relative extragalactic distances has become fairly black hole, of 3:9 6 0:1 3 10 D=7:2 Mpc sin is=sin 82 Maser distance The nearby active galaxy NGC 4258 possesses an accretion disk containing water masers orbiting in a thin disk, nearly on the plane of the sky as seen in ultra-high resolution VLBI radio imaging Figure 1 The NGC4258 water maser. The upper panel shows the best-®tting centred about the systemic velocity of the galaxy. The positions (®lled circles in warped-disk model superposed on actual maser positions as measured by the upper panel) and LOS velocities of these masers imply that they subtend ,88 of VLBA of the NRAO, with top as North. The ®lled square marks the centre of the disk azimuth centred about the LOS to the central mass, and the observed disk, as determined from a global disk-®tting analysis8. The ®lled triangles show acceleration (8±10 km s-1 yr-1) of these features14,15 unambiguously places them the positions of the high-velocity masers, so called because they occur at along the near edge of the disk. The approximately linear relationship between frequencies corresponding to Doppler shifts of ,61,000km s-1 with respect to systemic maser impact parameter and LOS velocity demonstrates that the disk is the galaxy systemic velocity of ,470 km s-1.

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