Cosmic Distance Ladder
For ages our obsession with the heavens means that we can measure distances with greater rigour and precision, from gnomons and sundials to standard candles and gravitational lensing; such are the rungs of the cosmic distance ladder.
Its is a hierarchy of rather clever (yet surprisingly elementary) mathematical methods that astronomers use to indirectly measure very large distances, such as the distance to planets, nearby stars, or distant stars.It’s a great testament to the power of indirect measurement, and to the use of mathematics to cleverly augment observation.
Each rung of the ladder provides information that can be used to determine the distances at the next higher rung.
So in the lecture on cosmic distance ladder Alankar discussed the various methods used for calculting distances starting from distances within our solar system. The primary unit used for them is Astronomical Unit or AU, which is equal to the distance between earth and sun.
Distances within solar system can be measured using direct measurement, kepler's laws and parallax method.
Astronomical unit can be measured using venus transits.
Within solar system, using baselines on earth, distances can be measured using parallax method. The earth-sun mean distance provides scale for fundamental baseline from which we can step outside solar system. It enables us to measure the distances of nearer stars by measuring their parallax after six months using distant stars as background.
The smallest parallax that can be measured depends on resolving power of the largest telescopes, and this limits us to stars closer than about 30 pc.
Going higher up the ladder, distances can be measured using velocity measurements. Velocities can be resolved in two components-radial and transverse. Radial velocities can be easily measured using doppler shifts. Now transverse velocity, Vt=Dw where D is the distance and w the angular velocity. This w can be measured directly. But these information are not sufficient to determine D, except in two special cases-
1. For cluster of stars-In a cluster, all stars have approximately the same velocity and this parallel motion can be recognised by the convergence of proper motions on a point(direction) in sky. The angle between this direction and line of sight to cluster is ratio of radial velocity component and velocity which gives us the distance.
2. Statistical parallax-In second limiting case, it is assumed that group of stars have random motion and it is isotropic and therefore (2*(Vr)^2)average = ((Vt)^2)average, otherwise we would be in a privileged position relative to group. From here we can get distance.
These methods take us out to several 100 pc but still within our galaxy.
Higher up, distances measured from apparent luminosity-
From relation between absolute and apparent luminosities, D can be found out. Now apparent luminosity can be measured and for some special objects absolute luminosity is approximately known. These are called standard candles.
These luminosities are measured on a logarithmic scale where 'm' is the apparent magnitude and 'M' is the absolute magnitude defined as apparent magnitude that object would have at a distance of 10 pc. We have some knowledge of M for some classes of objects-main sequence stars, cepheid variables, novae and brightest galaxies in clusters.
1. Main sequence - In 1910, from nearby stars distances, Hertzsprung and Russell found M and spectral type for many stars are strongly correlated. Thus if we know a star is main sequence then from it's m and spectral class measurement, M can be obtained and hence D.
2. Cepheid variables - Many stars vary regularly in brightness with period P. It was found by Leavitt in 1912, M and P are related for these stars and since stars with same M have same P, then these can be employed as standard candles. This relation is caliberated using distances smaller in hierarchy and then can be used to measure distances upto about 10^6 pc i.e. within local cluster of galaxies.
3. Type 1A supernova - When in a binary system, one star is a white dwarf and other a massive star, white dwarf begins to get more mass and after a limit it collapses resulting in supernova of characteristic brightness. Thus can be employed as standard candles.
Extreme distances on cosmological scales can be measured using Hubble law i.e. distance and velocity are linearly related by hubble constant H.
Here are the slides used in the lecture.