Cosmology: what is a quantity that is called "$h$" in regard to angular size of a galaxy?

I am trying to solve a Cosmology problem, but a certain quantity $h$ appears in it, of which I do not know the definition (I have never seen it mentioned anywhere before). So I thought maybe someone here could tell me what this $h$ is?

The problem goes as follows:

If $a$ is the scale factor in a FLRW-universe and $1+z=1/a$ is the redshift, then the luminosity distance of a far away object that is emitting light is given by $d_L=a_0r(1+z)$ (where $a_0$ is the scale factor today and can be scaled to $a_0=1$). Knowing the luminosity distance, we can get the angular diameter distance $d_A=l/\theta=d_L/(1+z)^2$, where $l$ is the proper size of the source and $\theta$ the apparent size. Knowing $l$, what is the minimum angular size of the radiating object? Be sure to first express your finding in terms of $h$, and then use $h=0.7$ to get a numerical value.

So, the problem asks to find the minimum angular size (which is $\theta$ I assume), and I can do that. But I have no idea what $h$ is supposed to be! Can someone clarify? Thanks for any suggestion!

This goes back to the history of the Hubble constant. It's easy enough to write most cosmological formulas in terms of this value, but measuring it was something of a challenge for a while.

For several decades, we were confident it was between $50$ and $100\ \mathrm{km/s/Mpc}$. Many results scale with this value (to some power), so what people did was write $$H_0 = h \times 100\ \mathrm{km/s/Mpc}.$$ This way, you could put any value of $h$ you personally believed into the final result, but since this factor is of order unity you can also remove it from the result (replace it with $1$) to get a quick sense of what the answer is. Today we know $h = 0.7$ well enough that this practice of leaving $h$ in equations is disappearing... slowly. It's still a useful exercise, though, if you are comparing results that assume different values of $H_0$, in order to see how the change in $H_0$ affects the results.

• I do know of $H_0$ but did not suspect a connection between $H_0$ and $h$. Maybe I should have guessed, since $H_0\approx 68 \frac{km}{Mpc\cdot s}$. Anyway, now I know. Thank you! Commented Feb 9, 2015 at 23:05

This is explained in the Wikipedia article on Hubble's Law: http://en.wikipedia.org/wiki/Hubble%27s_law

In particular,

"Dimensionless Hubble parameter

Instead of working with Hubble's constant, a common practice is to introduce the dimensionless Hubble parameter, usually denoted by h, and to write the Hubble's parameter $H_0$ as 100 h km s −1 Mpc−1, all the uncertainty relative of the value of $H_0$ being then relegated on h."