Redshift, Hubble’s Law and Quasars

An identifiable line shifted to a longer wavelength is redshifted; a shorter wavelength is blueshifted. The low-speed Doppler approximation relates the fractional wavelength shift to recession speed. The frequency shift has the opposite sign: a receding source has a lower observed frequency.

Only the radial component of motion shifts the spectrum. For a binary viewed edge-on, one component alternates between approach and recession, producing periodic shifts. At the transverse parts of its orbit the radial velocity can be zero despite the star still moving.

For sufficiently nearby galaxies in the overall expansion, recession speed is approximately proportional to distance. Hubble’s constant is often quoted in km s⁻¹ Mpc⁻¹. Dividing a speed in km s⁻¹ by a constant in those units gives a distance in Mpc.

The inverse of a Hubble constant in s⁻¹ gives a timescale for expansion. Calling this the age assumes a constant expansion rate in the simple extrapolation. Gravity and accelerated expansion change the history, and local peculiar velocities make the approximation poor for some nearby objects.

The redshift–distance trend supports expansion. The cosmic microwave background is radiation from an early hot phase, now cooled by expansion; its near-black-body spectrum is strong evidence for a hot early Universe. The relative abundances of hydrogen and helium are another test of early-universe nuclear processes.

Quasars were first identified as compact bright radio sources with surprisingly large optical redshifts. Their luminosity comes from accretion around active supermassive black holes. They can greatly outshine their host galaxies. Large redshifts require cosmological models rather than extending the low-speed Doppler formula to speeds greater than light.

Try each problem before opening the worked solution. State the physical model, show substitutions with consistent units, and explain what your answer means.