The Cosmic Distance Ladder (Mário Santos)
What is it? A way to calculate distances to objects very far away based on the measured distances to nearby objects: 1. Start with the distance to the Sun (1 AU) 2. Measure the distance to nearby stars in terms of the distance to the Sun 3. Calculate the distance to other galaxies using the measurements to nearby stars 4. Measure the size of the Universe!
Example: using parallax Change in apparent position of an object relative to background Knowing the angle of this change and the distance between the 2 viewpoints we can calculate the distance to the object It allows humans to see depth and perspective!
Measuring distances to nearby stars Measure apparent movement (angle) of nearby stars against the background of more distant stars But nearby stars are far away! Need large distances to observe the angle Cannot use 2 points on Earth - make observations as the Earth moves around the Sun (say July and January) parallax angle Small angle: So, for 1 : sin(p) = 1AU d d 1AU p [radians] distance to star 206265 AU p [arcsec] d 206265 AU 1 parsec [pc]
Measuring distances to nearby stars But need to know distance to the Sun (AU) Determine relative distance of planets to the Sun (e.g. Kepler) Measure distance of Earth to planets (e.g. parallax during transit of Venus) Modern values use direct radar measurements 1 AU = 149,597,870,700 metres
Distance to nearby stars: examples Ground based parallaxes up to ~ 0.01 out to 100 pc ~ 1000 stars First measurement: 61 Cygni ~ 3.5 pc (Friedrich Bessel - 1838) Nearest star: Proxima Centauri - 0.762 ~ 1.31 pc Hipparcos satellite ~ 0.001 up to 1000 pc ~ 100,000 stars GAIA (2013) ~ 0.00002 up to 50 Kpc ~ 1 billion stars
Note: Luminosity distances Indirect distance estimate: Measure the object s Flux (apparent brightness), F Assume the object s Luminosity (absolute brightness), L Apply inverse square law of brightness to determine distance, d L F = L 4 d 2 L =) d L = r L 4 F Assume Measure Need to know L beforehand! Use Standard Candles
Next step: spectroscopic parallax Measure the apparent brightness of a nearby star Determine distance using the parallax method Determine the Luminosity Analyse the spectrum of the star Construct the Hertzprung- Russell diagram: Luminosity (absolute brightness) versus spectral type (color)
Next step: spectroscopic parallax Use diagram to measure distances to stars farther away: From the spectra, determine the position of the star on the H-R diagram Read off the Luminosity (absolute brightness) From the measured apparent brightness determine the distance to the star Good up to ~ 100 Kpc
Going one step further in the ladder: Distance to other galaxies A certain class of stars (Cepheids) were observed to oscillate in brightness periodically Knowing the distance to these stars (using spectroscopic parallax) we can calculate its absolute brightness Found precise relationship between Luminosity and period! Get L and calculate d L! Measure period Henrietta Swan Leavitt, 1912
Cepheids Up to 100,000 times more luminous than the Sun Distance Limit: 30-40 Megaparsecs (Hubble Space Telescope) Crucial for measuring distances to galaxies
Distance to galaxies farther away: Supernovae Type Ia supernovae are great standard candles Basically the same (constant Luminosity) Very bright ~ 100,000 times brighter than Cepheids -> can see to large distances! Most distant: SN 1997ff - distance ~ 5 Gpc!
Final step: the Universe Measure a galaxy doppler shift - z (fractional change in the wavelength of light) Radial speed of the galaxy: v=c z (c - speed of light) Measure distance to galaxies - d (using Cepheids) Hubble law: v=h d (Edwin Hubble) Galaxies are receding from us - the Universe is expanding! Current value: H 71 Km/s/Mpc (using the Hubble satellite with Cepheids) NASA
Final step: the Universe We can use Hubble s law to calculate distances to galaxies very far away: Measure redshift z - velocity d=cz/h (for large z need to include General Relativity effects) Radius of the visible Universe ~ 14 Gpc Comparison of the expected distance to a Galaxy from the redshift to the measured distance using supernovae Ia told us that the Universe is accelerating - dark energy! Hubble deep field, NASA