Lecture Four: Knowing the distances to galaxies is fundamental for a lot of problems. The Cosmic Distance Scale e.g., are two galaxies going to interact? or are they just conicidental on the sky? or understanding the large scale structure in the Universe, and whether the Universe has always expanded at the same rate. https://www.astro.rug.nl/~etolstoy/pog16/ or Sparke & Gallagher, chapter 2 simply determining absolute luminosities http://www.astro.ucla.edu/~wright/distance.htm 20th April 2016 Distance Scales The Cosmological Distance Ladder: starts with distances to the nearest stars, ends with distances to the furthest galaxies 1-100pc <100kpc <3Mpc <3000Mpc Distance Indicators 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, which work out to very large distances! ZELDOVICH Pathways to Extra-galactic Distances Mostly “secondary or tertiary”: higher rungs Mostly “primary”: first rung pc Jacoby et al. 1992 PASP, 104, 599 Direct distance measures (PRIMARY) x? Distances within the Milky Way infer from understanding of physical process distance? x θ = tan θ distance you How to use perspective effectively… (PRIMARY) Parallax: apparent motion of distant stars caused by orbital motion of earth Stellar Parallax One astronomical unit (1 AU) is the Earth’s mean distance from the Sun, about 150 million kilometers or 8.3 light-minutes Determining Distances r (=1 AU) is the radius of the Earth’s orbit, we find As the Earth orbits the Sun, our viewing r position changes, and closer stars appear to In1838 using a heliometer Bessel measured the = tan rad move relative to more distant objects. In the first parallax of a star, 61 Cygni, of 0.314 d ≈ course of a year, a nearby star traces out an elliptical path against the background of arcseconds, indicating that the star is 10.3 ly ϖ is clearly small; so converting to seconds of arc, distant stars. The angle ϖ on the sky is the away (current measurement 11.4 ly). parallax. = 206265 rad 206265 defining 1 AU d = AU ϖ 1 parsec is the distance at which a star would have a parallax of 1″: 1 rad =1pc = 206265 AU = 3.086 x 1013 km = 3.26 light years d Proxima Centauri, the nearest star, has ϖ = 0.8′′, so its distance is 1.3 pc or 4.3 light-years. The distance to a star with observed parallax ϖ″ is then Friedrich Wilhelm Bessel 1 (1784-1846) d = pc 1 AU E1 E2 Sun There are ~25 stars within 3.5pc of us. ϖ currently limited to ~100 pc for bright stars Moving clusters: when stars are in a stable star cluster whose physical size is not Distances within the Galaxy changing, like the Pleiades then the apparent motions of the stars within the cluster can be used to determine the distance to the cluster. All stars move towards convergent point - perspective effect. Trigonometric Parallax: The Future "Gaia" European Mission: 2013-2020 Radial velocities and proper motions for ~109 stars (about 1% The transverse velocity, VT, (sideways motion) of the cluster can be found using of the Galaxy) VT/VR = tan(ϴ). The distance of the cluster is then D = VT / (d(ϴ)/dt) Reach V~20 (c.f. ! V~12 limit of D[in pc] = (VR/4.74) [km/sec] * tan(ϴ) / (d(ϴ)/dt) [in "/yr] Hipparcos) with ! The odd constant 4.74 km/sec is one au/year. Because a time interval of 100 years can be -4 precision ~2 x 10 " used to measure d(ϴ)/dt, precise distances to nearby star clusters are possible. This method has been applied to the Hyades cluster giving a distance of 45.53 +/- 2.64 pc 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, which is twice as large a distance as the Earth moves in six months! and can use long time baselines to get very long distance baselines. Problem: the other stars move too! Thus, the position of any one star changes on the celestial sphere both because of the Sun's motion and because of the motion of the star and we can't disentangle the two without further information The mean proper motion of the stars, dθ/dt, will have a mean component proportional Cosmological Distances to sin θ, if the slope of this line is, μ, then the distance D is D[in pc] = 4.16/(μ [in "/yr]) 4.16 is the Solar motion in au/yr (PRIMARY) 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 Gravitational Lensing description of the age, geometry and fate of the Universe. The central binding mass (M), presumably in the form of a supermassive Maser distance, using Micro-wave Amplification by the Stimulated Emission of Radiation sources, 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 highly beamed and coherent (H2O maser at 22 GHz). 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 By examining the rotation curve of the masers, it can be seen that the masers rotate in a thin disk with a hole in the center with an inner radius at ➢ the path of light is bent as it passes a gravitating mass (General Relativity) θin θin=4.1 milliarcsec and a velocity of vin=1080 km/s ➢ this effect can cause an amplification of the light source as well as multiple images of the background source (eg. Q0957+561 and another ~40 systems) After a time span of a few years, accelerations were measured with a magnitude of 1 1 v˙ =9.5 1.1kms− yrFigure− 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 ➢ if the source varies in intrinsic brightness (i.e. flickers), ± warped-disk model superposed on actual maser positions as measured by the upper2 panel) and LOS velocities of these masers imply that they subtend ,88 of Equating this acceleration with the VLBAcentripetal of the NRAO, with acceleration, top as North. The ®lled we square see marks that the centre of thev˙ =diskv azimuth/r centredin about the LOS to the central mass, and the observed then the differing light paths of multiple images leads disk, as determined from a global disk-®tting analysis8. The ®lled triangles show accelerationin (8±10 km s-1 yr-1) of these features14,15 unambiguously places them to a time lag in their light curves the positions of the high-velocity masers, so called because they occur at along the near edge of the disk.