https://github.com/jmsull/sigma_b
Compute pesky normalization factor in super-sample covariance w/ trapz rule
https://github.com/jmsull/sigma_b
Last synced: about 2 months ago
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Compute pesky normalization factor in super-sample covariance w/ trapz rule
- Host: GitHub
- URL: https://github.com/jmsull/sigma_b
- Owner: jmsull
- License: mit
- Created: 2023-02-08T23:36:48.000Z (over 2 years ago)
- Default Branch: main
- Last Pushed: 2023-02-09T04:51:09.000Z (over 2 years ago)
- Last Synced: 2025-02-07T09:43:25.783Z (3 months ago)
- Language: Julia
- Size: 31.3 KB
- Stars: 0
- Watchers: 1
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
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README
# sigma_b
*Very* simple code to compute the pesky normalization factor in super-sample covariance w/ trapz rule for a simulation box
$\sigma_{b}^{2} = \int \frac{d^{3}\mathbf{k}}{(2\pi)^3} |W(\mathbf{k})|^{2} P_{L}(k)$
where
$W^{2}(\mathbf{k}) = j_{0}^{2}(k_{x}L/2)j_{0}^{2}(k_{y}L/2)j_{0}^{2}(k_{z}L/2)$
which is appropriately normalized to $1/V = L^{-3}$.
[Li, Hu, & Takada 2014](https://arxiv.org/abs/1401.0385)
# Notes:
Run this code with ``julia sigmab.jl``
The integration range and number of points appear to be decent at a $<3$% level (using window error as a guide) but are actually much better than this for estimating the window integral for a typical cosmology - that integral peaks at very low k, whereas the window integral doesn't converge quickly b/c at high k we've entered the wiggle zone. If we you want a more accurate estimate you can increase kmax or N (at your own runtime risk).
Default ouput on my machine is:
``Is the window close to 1? true``
``Power spectrum variance in a cubic box of side length 625.0 Mpc/h is 6.756502209257932e-5.``
This is in close agreement with directly computing the variance of linear field on a grid but has the benefit of being faster and not requiring seed averaging.