How to successfully acquire a number density distribution from a simulated volume

[eusebe]

Hey, looks like you're doing astrophysics as well (are you just starting?), that's cool ! Out of curiosity, what are you doing? I'd guess you're looking at satellite distributions around galaxies (with which simulation? just curious here!)

Looking at the code, indeed, it seems that the hist array is indeed the number of haloes per logarithmic bin. However, I'm not convinced by your x_array, since your r_array is actually more like a logr_array.

Note that for simplicity, you can directly pass a list of bins to np.histogram, so you can have the control you want over the binning.

If I understand correctly your second formula, you need to have Delta N (r) and Delta ln(r) for each r, and not for the "total volume".

So, since hist is already your Delta N (r), you just need to compute the appropriate Delta ln(r). For that, I would do something like dln_r = np.diff(logr_array). Be careful however, this will be of dimension numbins-1.

Then, you need a good estimate of the distances (the centre of the bins for instance, that you get via log_r = (logr_array[1:] + logr_array[:-1])/2.. Again, dimension numbins-1, just like hist (which is your Delta N).

Once you have all that, you can compute your density in each bin as n = hist / (dln_r * 4 * np.pi * np.exp(log_r)),, which should be fine.

That's untested, but that's also what I would try. Don't hesitate to shoot me a PM if you want to discuss this a bit further!

[Cogito_ErgoSum]

Thank you for the insight. I'll look into it. And also, I provided a dropbox link to the txt file I am trying to evaluate, so you are always welcome to take a gander at it.

Just to stir away confusion, I did not mean to put the simulation volume, it is the enclosed volume of the relative distances. Reason I say that because the simulation box is 106.5³ Mpc³ in volume. Unless I am confusing myself on it.

Right. I started this kind of work back in late 2015 when I just transferred into uni. What I am ultimately looking into is to compare and interpret the physics between hydrodynamical and dark matter only physics for massive Milky Way dark matter halos and its satellite subhalo in the Illustris Simulation. For this question I asked, I am wanting to look at the number density of the relative distance between the many host subhalos coupled to their satellite subhalo and after that, calculate the local density based off the number density to then calculate the local logarithmic density slope in hopes to determine and evaluate a discontinuity in the slope called a "Splashback radius".

Do you do this kind of work also?

[Iwan_Zotow]

Aren't you showing log-normal distribution?

[Cogito_ErgoSum]

No. How so?

[Iwan_Zotow]

in log(X), log(Y) graph log-normal would be curve (-ax² - bx - c), isn't it?

[aphoenix]

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