HMF Lightcone

I want to check that the HMF recovered from the lightcone looks right.

HMF from Snapshots

If I calculate the HMF from individual snapshots, and compare to theory, I get the following:

HMF from Lightcone

Now I want to calculate for redshift slices in my light cone.

One correction I have to make is for the volume. The survey volume is a pyramid with an angle $\theta$. At redshift, $z_i$ (with corresponding comoving distance, $d_i$), the sides of the pyrimid are $d_i \sin(\theta)$, and therefore the volume is $d_i^3 \sin(\theta)^2/3$. Therefore redshift slices between $z_i$ and $z_{i+1}$ have volumes $\sin(\theta)^2 (d_{i+1}^3 - d_i^3)/3$.

Here is the recovered HMFs (where I have taken the theory curve to be at the center of the redshift range):

They don’t agree completely, which is probably partially due to the redshift ranges… here is another visualization:

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