Distance Scales

Additional details about the distance scale and lookback time are provided below in a more detailed addendum to these instructions, but for now you need to know that the distances shown in Partiview are called ``comoving'' distances. A helpful description of the idea is in the paper ``A Map of the Universe'' by J. Richard Gott, III, a link to which is on our class web site [1]. There is also a brief discussion in the text ``Galaxies in the Universe'' [2]. comoving coordinates provide a way to interpret distances without having to worry that we are looking back in time as we observe out to high $z$. They are defined by a conformal time scaled by the changing size of the universe. The relationship between $z$ and a comoving $d$ depends on the history of the universe, that is, it depends on cosmological parameters such as the Hubble Constant $H_0$ at the present epoch.

If the redshift is interpreted as a Doppler shift,

$$1+z = \lambda/\lambda_0$$

where $\lambda_0$ is the rest wavelength and

$$\lambda/\lambda_0 = \sqrt{(c+v)/(c-v)}$$

While the Hubble Law

$$v = H_0 \cdot d$$

is useful when $v$ is small compared to $c$, many of the galaxies and all of the quasars in the Sloan Survey are at such large $z$ that this relationship gives a misleading picture of distance.

The comoving distance in the Partiview database has been calculated with cosmological parameters derived from the Wilkinson Microwave Anisotropy Probe (WMAP) data on the cosmic background radiation. To see how this is done mathematically, and for a fuller explanation of the distance scales, look at Section 5 in this document.