Astronomers often calculate the distance to a galaxy assuming that
distance = f(z,Ωm) / H0 |
h = H0 / (100 km s-1 Mpc-1) |
The following table compares these approaches with some examples for various observational quantities (tables in both directions here):
Value assuming h=0.7 | Value with h dependence | |
line-of-sight distance, and transverse distance from distance times angular separation | 1.00 Mpc | 0.70 h-1 Mpc |
volume from distance cubed | 1.00 Mpc3 | 0.343 h-3 Mpc3 |
luminosity that is proportional to distance squared | 1.00 L☉ | 0.49 h-2 L☉ |
number density of galaxies from inverse volume | 1.00 Mpc-3 | 2.92 h3 Mpc-3 |
luminosity density from combining previous two | 1.00 L☉ Mpc-3 | 1.43 h L☉ Mpc-3 |
absolute magnitude from -2.5 log luminosity | -20.00 | -19.23 + 5 log h |
mass from scaled luminosity | 1.00 M☉ | 0.49 h-2 M☉ |
mass from velocity squared times transverse distance | 1.00 M☉ | 0.70 h-1 M☉ |
Other h dependencies:
Value assuming h=0.7 | Value with h dependence | |
critical density of the universe from dynamical equations | 1.36 x 1011 M☉ Mpc-3 | 2.775 x 1011 h2 M☉ Mpc-3 |
Hubble time from inverse H0 | 13.97 Gyr | 9.78 h-1 Gyr |
mass in N-body gravitational simulations, allowed scaling | 1.00 M☉ | 0.70 h-1 M☉ |
And now it can get slightly confusing. The h dependence can be defined by adjusting a variable, or by placing the dependence after the variable's value or in front of the units. The following table shows examples of these variations in style.
Adjusting variable | After value | In front of units | |
Tabulating number density values | φ h-3 / Mpc-3 = 0.1 | φ / Mpc-3 = 0.1 h3 | φ / (h3 Mpc-3) = 0.1 |
Assigning absolute magnitude values | M - 5 log h = -20 | M = -20 + 5 log h | |
Physical baryon density measurement using density parameter | Ωb h2 = 0.022 | Ωb = 0.022 h-2 |
Written by Ivan Baldry, 2015 November.
Links: - return to my home page; return to my research page.