1B11 Foundations of Astronomy Cosmic distance scale Liz Puchnarewicz

1B11 Cosmic distance scale Why is it so important to establish a cosmic distance scale? Measure basic stellar parameters, eg radii, luminosities, masses Explore the distribution of stars, eg Galactic structure Calibrate extragalactic distance scale, eg galaxy scales, quasar luminosities, cosmological models

1B11 Direct methods 1. Trigonometric parallax  d 1AU star Sun Ground-based telescopes – measure  to ~ 0.01” (d=100pc) HipparcosHipparcos – measured  to ~ 0.002” (d=500pc) GaiaGaia – will measure  to 2x10 -5 arcsec (d=50,000pc)

1B11 Sun-Earth distance To measure parallax accurately, we must know the distance from the Earth to the Sun. 1AU The Earth’s orbit is elliptical. An Astronomical Unit is the size of the semi-major axis. In order to measure the length of the semi-major axis, we need a nearby planet, a radar and Kepler’s Third Law, which is: Where T is the orbital period of a planet, and a is the semi-major axis of it’s orbit.

1B11 Measuring an AU We can measure the orbital periods of the planets by tracking them across the sky. So then we can calculate, in units of the Sun-Earth distance, the distances to all of the planets. Wait until the Earth and a planet, eg Venus are a known AU distance apart, eg when they’re closest together. Then bounce a radar signal to Venus and back, measure the time it takes, multiply by the speed of light and you have the distance in, eg, km. At their closest, the Earth and Venus are 0.28AU apart.

1B11 Converting from AU to km 1AU 0.28AU In this position, it takes 280 seconds for light to bounce back from Venus to the Earth. So the distance in km is: So,

1B11 Nova expansion Remember that for the proper motion of a star, , (measured in arcsecs per year), the tangential velocity of the star, v t =4.74  d (where d is in parsecs and v t is in km/s). Instead of a star, consider a nova – an explosion from a star. We assume that the shell thrown off is spherically- symmetric. d  vtvt vrvr nova shell

1B11 Distances from nova shells Using spectroscopy and measuring the Doppler effect: d  vtvt vrvr nova shell  is the proper motion of the shell due only to its expansion and since v t = |v r |, then

1B11 Indirect methods – Cepheid variables Cepheid period-luminosity relation time magnitude P~1-50 days  m ~1mag average mag Cepheid variables are pulsating variable stars with a characteristic lightcurve – named after  Cephei. Henrietta Leavitt (1912) found that the period of variability increased with star brightness.

1B11 Calibrating Cepheids The period-luminosity of Cepheid variables must be calibrated and this has been done by measuring their parallax using Hipparcos. For P in days, The mean magnitude is typically very bright: so they can be seen at very large distances (Henrietta Leavitt was working on a cluster of stars in the Small Magellanic Cloud). Measuring P provides M V, which gives distance via the distance modulus. This is especially important for calibrating extragalactic distance, eg the Hubble Space Telescope Key Project. Hubble Space Telescope Key Project

1B11 Spectroscopic distances – H-R diagram This is a Hertzsprung-Russell diagram – a plot of luminosity against temperature for stars. colour/spectral type => luminosity temperature, K Luminosity (L SUN )

1B11 Distances from H-R diagrams If an H-R diagram is well-calibrated (ie the temperatures and spectral types are well-known), the absolute luminosities can be derived. The distances are then calculated by measuring their apparent magnitudes and applying the distance modulus equation (ie (m V -M V )=5log 10 d-5+A V )). Spectral distances can be calibrated using trigonometric parallaxes.

1B11 Cluster distances from H-R diagrams (B-V) MVMV calibrated main sequence Vertical shift gives (m V -M V ) horizontal shift gives E(B-V) => A V And the distance modulus is (m V -M V )=5log 10 d-5+A V.

1B11 Standard candles If there is a type of object whose intrinsic luminosity we can reliably infer by indirect means, then this is a “standard candle”. We measure its apparent flux, calculate the intrinsic luminosity and the inverse square law gives us the distance. Globular clusters Construct the H-R diagram for a globular cluster of stars and find the spectroscopic distance. Also look for variables in the cluster. Integrated absolute magnitudes can be estimated by assuming M V. Then you can estimate the distances for globular clusters around other galaxies.

1B11 Novae Novae The absolute magnitude of a nova can reach M V ~ -10. And novae which decline faster, are brighter: where R 2 is the decline rate in magnitudes per day, over the first two magnitudes. MVMV t t2t2  m=2 m Calibrate using novae in our Galaxy. Then you can use the relationship to infer extragalactic distances.

1B11 Supernovae Type II supernovae : core collapse of massive star Type Ia supernovae : dumping of matter from secondary star onto a primary star in binary systems. In Type Ia SN, M V (max) reaches approx –20 with only a small variation between different events. So as long as you catch the maximum, you have a good standard candle out to very large extragalactic distances.

1B11 Tully-Fisher relationship In 1977, Tully and Fisher found that the width of the 21cm emission line from a galaxy, was broader when the galaxy was brighter. wavelength flux 21cm x (1+z)

1B11 Tully-Fisher relationship They suggested that this is a fundamental physical property, because: More stars => more mass => higher rotation + brighter The stars and gas in the galaxy are in orbit, so: Centrifugal force = gravitational force M(star)v 2 /R = GM(galaxy)m(star)/R 2 M(galaxy) = v 2 R/G (G=Gravitational constant) And since luminosity is (probably) proportional to M(galaxy), Luminosity(galaxy) would be proportional to v 2

1B11 Tully-Fisher relationship The trouble is – It’s not yet clearly understood why the relation works so well. It works really well over at least 7 magnitudes (a factor of 600 in luminosity terms). It implies a cross-talk between the bulge and the disk components in galaxies… we don’t know how the bulge and the disk ”conspire” to produce the same mass to light ratios for such a range of luminosities.

1B11 Hubble’s Law In 1929, Edwin Hubble discovered that all galaxies (beyond our local group) were moving away from us, and that their recession speed was proportional to their distance. v = H 0 d Where v is the recessional velocity, measured from the redshift, d is the distance to the galaxy and H 0 is Hubble’s constant. This general expansion of the Universe demonstrated to Einstein that it was not static as he had thought. H 0 is hard to measure, Hubble thought it should be ~500 km s -1, Mpc -1 – current observations indicate km s -1 Mpc -1. The best measurements indicate ~65 km s -1 Mpc -1

1B11 The age of the Universe Once the Hubble constant has been measured, if we can assume that the rate of the expansion of the Universe has not changed, then we can calculate the age of the Universe, Hubble’s law: v = H 0 d And in general, d = vt, so t = d/v Substituting for Hubble’s law, then t = d/(H 0 d) So t = 1/H 0 And if H 0 = 65 km s -1 Mpc -1, then t = 1.3x10 10 years. Maybe expansion was faster in the early stages of the Universe, but there is evidence for a “dark energy” in the Universe which is increasing the expansion rate now.