Methoden der Entfernungsmessung

Transkript

1 Methoden der Entfernungsmessung UE Aufbau und Entwicklung der Galaxis II SS2013 Gerhard Weihs NASA Gerhard Weihs / Methoden der Entfernungsmessung / UE Entwicklung der Galaxis II / slide 1

2 Content Distance Ladder Measuring Galactic and Extragalactic Distances Sun s neighborhood (nearby stars) Milky Way and nearby galaxies More distant galaxies Summary References Gerhard Weihs / Methoden der Entfernungsmessung / UE Entwicklung der Galaxis II / slide 2

3 Distance Ladder (Camenzid) Gerhard Weihs / Methoden der Entfernungsmessung / UE Entwicklung der Galaxis II / slide 3

4 Measuring Galactic Distances Solar system Radar Ranging (distances of inner planets ) Solar Neighborhood (nearby stars) 10 kpc Trigonometric parallax (Earth Orbit): pc Secular parallax (moving cluster method) 1 kpc Spectroscopic parallax (distance modulus) 10 kpc Milky Way and nearby Galaxies 30 Mpc Cepheid method. TRGB (Tip of the red giant branch) method. Maser galaxies. Gerhard Weihs / Methoden der Entfernungsmessung / UE Entwicklung der Galaxis II / slide 4

5 Measuring Extragalactic Distances More distant galaxies Mpc Max. luminosities of Type Ia supernovae > 400 Mpc. Tully-Fisher relation -100 Mpc. Surface Brightness Fluctuation (SBF) method. Methods for deep space distances - Gravitational Microlensing The Sunyaev-Zel dovich Effect Hubble s Law Gerhard Weihs / Methoden der Entfernungsmessung / UE Entwicklung der Galaxis II / slide 5

6 Solar neighborhood Trigonometric parallax (Earth Orbit): pc Secular parallax (moving cluster method) 1 kpc Spectroscopic parallax (distance modulus) 10 kpc Gerhard Weihs / Methoden der Entfernungsmessung / UE Entwicklung der Galaxis II / slide 6

7 Trigonomic Parallax 500 pc The parallax is the angle at which the radius of Earth s orbit appears from the star. If the parallax of one arcsecond (1/3600 of a degree), this distance is referred to as a 1 parsec ( 1pc = 3.26 lj). Baseline for Parallax = 2 AU, d(pc) = 1/π (arcsec) Measurement of stars by HIPPARCOS with an accuracy of mas within 500 pc. Gerhard Weihs / Methoden der Entfernungsmessung / UE Entwicklung der Galaxis II / slide 7

8 Secular Parallax 1 kpc Sun is moving with respect to the local field of stars in the direction of Vega at a speed of about 20 km/s. Over a year, the Sun moves a distance of a little over 4 AU. This method can only be used to measure the average distance to a set of stars, because for a set of stars their peculiar motion with respect to the Sun averages approximately to zero. This statistical method is called secular parallax. Gerhard Weihs / Methoden der Entfernungsmessung / UE Entwicklung der Galaxis II / slide 8

9 Spectroscopic Parallax 10 kpc Luminosity distance d L using the distance modulus m M = 5 log d L 5 + A with m = rel., M = absolute magitude, A = extinction (d derived from Stefan-Boltzmann law ) L 4πF d L = L Gerhard Weihs / Methoden der Entfernungsmessung / UE Entwicklung der Galaxis II / slide 9

10 Milky Way and nearby galaxies - 30 Mpc Cepheid method 30 Mpc. TRGB (Tip of the red giant branch) method. Maser galaxies. Gerhard Weihs / Methoden der Entfernungsmessung / UE Entwicklung der Galaxis II / slide 10

11 The CepheidMethod The Cepheid variables are a class of variable stars, which are named after the star δ Cephei in the constellation Cepheus. Cepheids change their luminosity strictly periodic, thereby also changing their surface temperature and thus their spectral Leavitt s law. This empirical law was discovered and stated by Henrietta Swan Leavitt in 1908 Gerhard Weihs / Methoden der Entfernungsmessung / UE Entwicklung der Galaxis II / slide 11

12 The CepheidMethod Gerhard Weihs / Methoden der Entfernungsmessung / UE Entwicklung der Galaxis II / slide 12

13 Cepheid Calibration Steps Galactic Cepheids were absolute calibrated by trigonometric parallaxes (circled green dots) using Hipparcos astrometry satellite. and LMC Cepheids (open blue circles) brought into coincidence with the Galactic calibration. HST KP = key project The reddening-free period-luminosity (W-PL) relation Gerhard Weihs / Methoden der Entfernungsmessung / UE Entwicklung der Galaxis II / slide 13

14 Cepheid Method Calibration Calibration of Cepheid and TRGB Gerhard Weihs / Methoden der Entfernungsmessung / UE Entwicklung der Galaxis II / slide 14

15 TRGB (tipof the redgiant branch) The TRGB method uses the discontinuity in the luminosity function of stars evolving up the red giant branch in old, metal-poor stellar populations II (stars M sun ). Calibration using galaxies with Cepheids distances 250 galaxies distances measured by the TRGB method 57 galaxies with Cepheid distances. Cite: Gerhard Weihs / Methoden der Entfernungsmessung / UE Entwicklung der Galaxis II / slide 15

16 Maser Galaxies 10 Mpc Water vapor masers (22-GHz line of ortho-h 2 O ) orbit a supermassive black hole in almost perfect Keplerian rotation (accretion disk). The simple geometry of the source, and the wellordered kinematics, enable estimation of a distance. This measurement is free from the calibration and systematic uncertainties intrinsic to other distance indicators. Example: maser galaxy NGC 4258 (M106), a nearby Seyfert II galaxy 7.2 Mpc ±6% Gerhard Weihs / Methoden der Entfernungsmessung / UE Entwicklung der Galaxis II / slide 16

17 Cosmologic Distances More distant Galaxies: Mpc. Max. Luminousity of Type Ia supernova > 400 Mpc. Tully-Fisher (TF) relation for spiral galaxies. the surface brightness fluctuation (SBF) method. Gerhard Weihs / Methoden der Entfernungsmessung / UE Entwicklung der Galaxis II / slide 17

18 Extragalactic Distance Ladder Gerhard Weihs / Methoden der Entfernungsmessung / UE Entwicklung der Galaxis II / slide 18

19 Supernovae Typ Ia 400 Mpc One of the most accurate means of measuring cosmological distances is the peak brightness of SNe Ia lightcurve. All Type Ia supernovae have a standard blue and visual magnitude of M B ~ M V ~ / public/papers/aasposter198dir/ aaasposter.html Gerhard Weihs / Methoden der Entfernungsmessung / UE Entwicklung der Galaxis II / slide 19

20 Tully-Fisher Relation 100 Mpc The total luminosity of a spiral galaxy is strongly correlated with the galaxy s maximum rotation velocity. (corrected to face-on inclination to account for extinction) β L v max β= 3.0 B-band β= 3.2 I-band β= 4.2 H -band For the distance determination, the I- band is used, because all the stars contribute to the luminosity. Distance is calculated using the distance modulus. Calibration using galaxies with Cepheids distances Cite: Gerhard Weihs / Methoden der Entfernungsmessung / UE Entwicklung der Galaxis II / slide 20

21 Surface Brightness Fluctuation(SBF) Distant Galaxies allow an estimation of the distance using the statistical fluctuation in the number of stars in a pixel (elliptical galaxies and early-type spirals). A nearby galaxy might have 100 stars projected into each pixel of an image, while a more distant galaxy would have a larger number like Distances: the total number of discrete sources contributing to any given pixel increases with the square of the distance. d 2 = L/4πF. (F...mean flux per star) Cite: Gerhard Weihs / Methoden der Entfernungsmessung / UE Entwicklung der Galaxis II / slide 21

22 Comparison of Cepheid and SN Ia A comparison of Cepheid and Type Ia supernovae distances (red points), as described in Riess et al. (2009b). The calibrating galaxy, NGC 4258, is added in blue. Gerhard Weihs / Methoden der Entfernungsmessung / UE Entwicklung der Galaxis II / slide 22

23 Methods for deep space distances Gravitational Microlensing The Sunyaev-Zel dovich Effect Hubble s Constant Gerhard Weihs / Methoden der Entfernungsmessung / UE Entwicklung der Galaxis II / slide 23

24 Gravitational Microlensing Or Gravitational Lens Time Delays When a quasar is viewed through a gravitational lens, multiple images are seen. Einstein Ring Rs = 2GM/c 2 Schwarzschild radius Gerhard Weihs / Methoden der Entfernungsmessung / UE Entwicklung der Galaxis II / slide 24

25 The Sunyaev-Zel dovich Effect hot electrons in the cluster of galaxies scatter a small fraction of the cosmic microwave background photons and replace them with slightly higher energy photons (inverse Compton scattering). The difference between the CMB seen through the cluster and the unmodified CMB seen elsewhere on the sky can be measured. Compton scattering is an inelastic scattering of a photon by a free charged particle, Inverse Compton scattering effect, in which a charged particle transfers part of its energy to a photon. Gerhard Weihs / Methoden der Entfernungsmessung / UE Entwicklung der Galaxis II / slide 25

26 Hubble s Law Hubble s Law (1929) v = H 0.d = c.z Hubble time = H -1 sets the age of the Universe Within the standard model of cosmology ( 0.27/0.73), the current Value (2010) is: Hubble constant: H 0 = 73 ± 2 km s 1 Mpc 1 Hubble time: /- 0.8 Gyr. Gerhard Weihs / Methoden der Entfernungsmessung / UE Entwicklung der Galaxis II / slide 26

27 Summary Gerhard Weihs / Methoden der Entfernungsmessung / UE Entwicklung der Galaxis II / slide 27

28 Thanks for your attention Gerhard Weihs / Methoden der Entfernungsmessung / UE Entwicklung der Galaxis II / slide 28

29 References Freedman W.L., Madore B.F, Hubble Constant. Annu. Rev. Astron. Astrophys : Ferrarese, L. et al.,2000 A Database of Cepheid Distance Moduli and Tip of the Red Giant Branch, Globular Cluster Luminosity Function, Planetary Nebula Luminosity Function, and Surface Brightness Fluctuation Data Useful for Distance Determinations ApJS Cosmic distance ladder. Luminosity. The Extragalactic Distance Scale. Gerhard Weihs / Methoden der Entfernungsmessung / UE Entwicklung der Galaxis II / slide 29