2023-06-21T13:06:03,675 Created temporary directory: /tmp/pip-build-tracker-eund0byu 2023-06-21T13:06:03,678 Initialized build tracking at /tmp/pip-build-tracker-eund0byu 2023-06-21T13:06:03,678 Created build tracker: /tmp/pip-build-tracker-eund0byu 2023-06-21T13:06:03,679 Entered build tracker: /tmp/pip-build-tracker-eund0byu 2023-06-21T13:06:03,680 Created temporary directory: /tmp/pip-wheel-t1ni1p4r 2023-06-21T13:06:03,688 Created temporary directory: /tmp/pip-ephem-wheel-cache-_kudzyyw 2023-06-21T13:06:03,740 Looking in indexes: https://pypi.org/simple, https://www.piwheels.org/simple 2023-06-21T13:06:03,748 2 location(s) to search for versions of pyspk: 2023-06-21T13:06:03,748 * https://pypi.org/simple/pyspk/ 2023-06-21T13:06:03,748 * https://www.piwheels.org/simple/pyspk/ 2023-06-21T13:06:03,749 Fetching project page and analyzing links: https://pypi.org/simple/pyspk/ 2023-06-21T13:06:03,751 Getting page https://pypi.org/simple/pyspk/ 2023-06-21T13:06:03,755 Found index url https://pypi.org/simple/ 2023-06-21T13:06:03,967 Fetched page https://pypi.org/simple/pyspk/ as application/vnd.pypi.simple.v1+json 2023-06-21T13:06:03,975 Skipping link: No binaries permitted for pyspk: https://files.pythonhosted.org/packages/5e/28/45cc983684e34adf374c2d114a24861d4d9e1c2250a56078fa251ecde3fa/pyspk-1.0-py3-none-any.whl (from https://pypi.org/simple/pyspk/) 2023-06-21T13:06:03,975 Found link https://files.pythonhosted.org/packages/a8/d2/0734e1e3790826d866e4d99bdc646fba69430f90883d2ba783b2ec83ec06/pyspk-1.0.tar.gz (from https://pypi.org/simple/pyspk/), version: 1.0 2023-06-21T13:06:03,976 Skipping link: No binaries permitted for pyspk: https://files.pythonhosted.org/packages/b1/c7/ee2389a93f921f2c51aac240ab5039aa4d26a5ffcb617b68cbe0e469b4b7/pyspk-1.1-py3-none-any.whl (from https://pypi.org/simple/pyspk/) 2023-06-21T13:06:03,977 Found link https://files.pythonhosted.org/packages/61/93/710ef3373d68aa7569f17af7a78e4dc9cb7f07aafb4cbcc56155120846f7/pyspk-1.1.tar.gz (from https://pypi.org/simple/pyspk/), version: 1.1 2023-06-21T13:06:03,977 Skipping link: No binaries permitted for pyspk: https://files.pythonhosted.org/packages/c2/6b/7271ba22fe0d78e89f627a570997ae4a369fecda22088c350bfe8b9f9b9f/pyspk-1.2-py3-none-any.whl (from https://pypi.org/simple/pyspk/) 2023-06-21T13:06:03,978 Found link https://files.pythonhosted.org/packages/ba/6d/e1283dfc400ad9f9eceacc38e56c49b7614fdb996001ab298678bd394e90/pyspk-1.2.tar.gz (from https://pypi.org/simple/pyspk/), version: 1.2 2023-06-21T13:06:03,979 Skipping link: No binaries permitted for pyspk: https://files.pythonhosted.org/packages/e1/72/d87a0c6679f43fb1d299509860e44bf7437d3108ba7816e0213a9f4479d2/pyspk-1.3-py3-none-any.whl (from https://pypi.org/simple/pyspk/) 2023-06-21T13:06:03,979 Found link https://files.pythonhosted.org/packages/5a/7f/3b4c6ab139cf3771fcb53c4cdd65e8c36cf86ba024e132aa3a38a0db5929/pyspk-1.3.tar.gz (from https://pypi.org/simple/pyspk/), version: 1.3 2023-06-21T13:06:03,980 Skipping link: No binaries permitted for pyspk: https://files.pythonhosted.org/packages/ba/f2/06c887225a955a4c2022e3835bba85543421172d03236e6ad2a7c650d31f/pyspk-1.4-py3-none-any.whl (from https://pypi.org/simple/pyspk/) 2023-06-21T13:06:03,981 Found link https://files.pythonhosted.org/packages/40/f4/170424c88049316ddccc683d5caae03e9e598e4b9bfc5b855e5c12a84e42/pyspk-1.4.tar.gz (from https://pypi.org/simple/pyspk/), version: 1.4 2023-06-21T13:06:03,981 Skipping link: No binaries permitted for pyspk: https://files.pythonhosted.org/packages/f0/e2/5bac0d5d344b818eab812410cd125093c1013075c4c02683a978fd5ab6a7/pyspk-1.5-py3-none-any.whl (from https://pypi.org/simple/pyspk/) 2023-06-21T13:06:03,982 Found link https://files.pythonhosted.org/packages/de/42/7fc705db4a4cc3f762a58788ed3e9e2bafb87eb5ffa06ac12fda19ef0c90/pyspk-1.5.tar.gz (from https://pypi.org/simple/pyspk/), version: 1.5 2023-06-21T13:06:03,982 Skipping link: No binaries permitted for pyspk: https://files.pythonhosted.org/packages/13/8a/c893bf21c365de202210bc167bbf597c1e0ca11dfacfd08d594318ffdfe9/pyspk-1.6-py3-none-any.whl (from https://pypi.org/simple/pyspk/) 2023-06-21T13:06:03,983 Found link https://files.pythonhosted.org/packages/8c/56/7390a102e9ffc123a7c98ce38a01df97a66f31cd6d3bc27c6109b4194913/pyspk-1.6.tar.gz (from https://pypi.org/simple/pyspk/), version: 1.6 2023-06-21T13:06:03,984 Fetching project page and analyzing links: https://www.piwheels.org/simple/pyspk/ 2023-06-21T13:06:03,985 Getting page https://www.piwheels.org/simple/pyspk/ 2023-06-21T13:06:03,987 Found index url https://www.piwheels.org/simple/ 2023-06-21T13:06:04,259 Fetched page https://www.piwheels.org/simple/pyspk/ as text/html 2023-06-21T13:06:04,266 Skipping link: No binaries permitted for pyspk: https://www.piwheels.org/simple/pyspk/pyspk-1.5-py3-none-any.whl#sha256=93305fb0b22ddc50cd6b6f015ba94f8a7a76d3d68323707388b4d03718c46854 (from https://www.piwheels.org/simple/pyspk/) 2023-06-21T13:06:04,267 Skipping link: No binaries permitted for pyspk: https://www.piwheels.org/simple/pyspk/pyspk-1.4-py3-none-any.whl#sha256=dea174bb5bfae84e6b0cc9e4565f70dc0182a66c20f3065689e23598401574a3 (from https://www.piwheels.org/simple/pyspk/) 2023-06-21T13:06:04,267 Skipping link: No binaries permitted for pyspk: https://www.piwheels.org/simple/pyspk/pyspk-1.3-py3-none-any.whl#sha256=9a5918d4a9524a9e7ae6cbb9fa78f638bf79250975d3a6df402bb9451aeea281 (from https://www.piwheels.org/simple/pyspk/) 2023-06-21T13:06:04,268 Skipping link: No binaries permitted for pyspk: https://www.piwheels.org/simple/pyspk/pyspk-1.2-py3-none-any.whl#sha256=83010a88648bf4bbe2dffd0eb64c5a1892d598c03297cd19ce0d785f28662c28 (from https://www.piwheels.org/simple/pyspk/) 2023-06-21T13:06:04,268 Skipping link: No binaries permitted for pyspk: https://www.piwheels.org/simple/pyspk/pyspk-1.1-py3-none-any.whl#sha256=2c787ef97d85f7abf4348ac04aa1b05fc7f6dc20af7fb5e0dd1551349d6446ac (from https://www.piwheels.org/simple/pyspk/) 2023-06-21T13:06:04,268 Skipping link: No binaries permitted for pyspk: https://www.piwheels.org/simple/pyspk/pyspk-1.0-py3-none-any.whl#sha256=cfc057fd75e4214b94b5938b6e9840b03b3933ac7e44d0c84e2ce139ee2f42da (from https://www.piwheels.org/simple/pyspk/) 2023-06-21T13:06:04,269 Skipping link: not a file: https://www.piwheels.org/simple/pyspk/ 2023-06-21T13:06:04,269 Skipping link: not a file: https://pypi.org/simple/pyspk/ 2023-06-21T13:06:04,304 Given no hashes to check 1 links for project 'pyspk': discarding no candidates 2023-06-21T13:06:04,335 Collecting pyspk==1.6 2023-06-21T13:06:04,340 Created temporary directory: /tmp/pip-unpack-wbjicrxo 2023-06-21T13:06:04,528 Downloading pyspk-1.6.tar.gz (153 kB) 2023-06-21T13:06:04,747 Added pyspk==1.6 from https://files.pythonhosted.org/packages/8c/56/7390a102e9ffc123a7c98ce38a01df97a66f31cd6d3bc27c6109b4194913/pyspk-1.6.tar.gz to build tracker '/tmp/pip-build-tracker-eund0byu' 2023-06-21T13:06:04,751 Running setup.py (path:/tmp/pip-wheel-t1ni1p4r/pyspk_d42cf08a75c745d5ba0e907c1a7d8d3c/setup.py) egg_info for package pyspk 2023-06-21T13:06:04,752 Created temporary directory: /tmp/pip-pip-egg-info-qk6k6em7 2023-06-21T13:06:04,753 Preparing metadata (setup.py): started 2023-06-21T13:06:04,755 Running command python setup.py egg_info 2023-06-21T13:06:05,881 # py-SP(k) - A hydrodynamical simulation-based model for the impact of baryon physics on the non-linear matter power spectrum 2023-06-21T13:06:05,882 _____ ____ ____ _ 2023-06-21T13:06:05,882 ____ __ __ / ___// __ \_/_/ /__| | 2023-06-21T13:06:05,883 / __ \/ / / /_____\__ \/ /_/ / // //_// / 2023-06-21T13:06:05,883 / /_/ / /_/ /_____/__/ / ____/ // ,< / / 2023-06-21T13:06:05,883 / .___/\__, / /____/_/ / //_/|_|/_/ 2023-06-21T13:06:05,884 /_/ /____/ |_| /_/ 2023-06-21T13:06:05,884 py-SP(k) [(Salcido et al. 2023)](https://academic.oup.com/mnras/article/523/2/2247/7165765) is a python package aimed at predicting the suppression of the total matter power spectrum due to baryonic physics as a function of the baryon fraction of haloes and redshift. 2023-06-21T13:06:05,885 ## Requirements 2023-06-21T13:06:05,886 The module requires the following: 2023-06-21T13:06:05,887 - numpy 2023-06-21T13:06:05,887 - scipy 2023-06-21T13:06:05,888 ## Installation 2023-06-21T13:06:05,888 The easiest way to install py-SP(k) is using pip: 2023-06-21T13:06:05,889 ``` 2023-06-21T13:06:05,889 pip install pyspk [--user] 2023-06-21T13:06:05,889 ``` 2023-06-21T13:06:05,890 The --user flag may be required if you do not have root privileges. 2023-06-21T13:06:05,891 ## Usage 2023-06-21T13:06:05,891 py-SP(k) is not restrictive to a particular shape of the baryon fraction – halo mass relation. In order to provide flexibility to the user, we have implemented 3 different methods to provide py-SP(k) with the required $f_b$ - $M_\mathrm{halo}$ relation. In the following sections we describe these implementations. A jupyter notebook with more detailed examples can be found within this [repository](https://github.com/jemme07/pyspk/blob/main/examples/pySPk_Examples.ipynb). 2023-06-21T13:06:05,892 ### Method 1: Using a power-law fit to the $f_b$ - $M_\mathrm{halo}$ relation 2023-06-21T13:06:05,893 py-SP(k) can be provided with power-law fitted parameters to the $f_b$ - $M_\mathrm{halo}$ relation using the functional form: 2023-06-21T13:06:05,893 $$f_b/(\Omega_b/\Omega_m)=a\left(\frac{M_{SO}}{M_{\mathrm{pivot}}}\right)^{b},$$ 2023-06-21T13:06:05,894 where $M_{SO}$ could be either $M_{200c}$ or $M_{500c}$ in $\mathrm{M}_ \odot$, $a$ is the normalisation of the $f_b$ - $M_\mathrm{halo}$ relation at $M_\mathrm{pivot}$, and $b$ is the power-law slope. The power-law can be normalised at any pivot point in units of $\mathrm{M}_ {\odot}$. If a pivot point is not given, `spk.sup_model()` uses a default pivot point of $M_{\mathrm{pivot}} = 1 \mathrm{M}_ \odot$. $a$, $b$ and $M_\mathrm{pivot}$ can be specified at each redshift independently. 2023-06-21T13:06:05,895 Next, we show a simple example using power-law fit parameters: 2023-06-21T13:06:05,895 ``` 2023-06-21T13:06:05,896 import pyspk as spk 2023-06-21T13:06:05,896 z = 0.125 2023-06-21T13:06:05,897 fb_a = 0.4 2023-06-21T13:06:05,897 fb_pow = 0.3 2023-06-21T13:06:05,897 fb_pivot = 10 ** 13.5 2023-06-21T13:06:05,898 k, sup = spk.sup_model(SO=200, z=z, fb_a=fb_a, fb_pow=fb_pow, fb_pivot=fb_pivot) 2023-06-21T13:06:05,898 ``` 2023-06-21T13:06:05,899 ### Method 2: Redshift-dependent power-law fit to the $f_b$ - $M_\mathrm{halo}$ relation. 2023-06-21T13:06:05,899 For the mass range that can be relatively well probed in current X-ray and Sunyaev-Zel'dovich effect observations (roughly $10^{13} \leq M_{500c} [\mathrm{M}_ \odot] \leq 10^{15}$), the total baryon fraction of haloes can be roughly approximated by a power-law with constant slope (e.g. Mulroy et al. 2019; Akino et al. 2022). Akino et al. (2022) determined the of the baryon budget for X-ray-selected galaxy groups and clusters using weak-lensing mass measurements. They provide a parametric redshift-dependent power-law fit to the gas mass - halo mass and stellar mass - halo mass relations, finding very little redshift evolution. 2023-06-21T13:06:05,900 We implemented a modified version of the functional form presented in Akino et al. (2022), to fit the total $f_b$ - $M_\mathrm{halo}$ relation as follows: 2023-06-21T13:06:05,901 $$f_b/(\Omega_b/\Omega_m)= \left(\frac{0.1658}{\Omega_b/\Omega_m}\right) \left(\frac{e^\alpha}{100}\right) \left(\frac{M_{500c}}{10^{14} \mathrm{M}_ \odot}\right)^{\beta - 1} \left(\frac{E(z)}{E(0.3)}\right)^{\gamma},$$ 2023-06-21T13:06:05,902 where $\alpha$ sets the power-law normalisation, $\beta$ sets power-law slope, $\gamma$ provides the redshift dependence and $E(z)$ is the usual dimensionless Hubble parameter. For simplicity, we use the cosmology implementation of `astropy` to specify the cosmological parameters in py-SP(k). 2023-06-21T13:06:05,902 Note that this power-law has a normalisation that is redshift dependent, while the the slope is constant in redshift. While this provides a less flexible approach compared with Methods 1 (simple power-law) and Method 3 (binned data), we find that this parametrisation provides a reasonable agreement with our simulations up to redshift $z=1$, which is the redshift range proved by Akino et al. (2022). For higher redshifts, we find that simulations require a mass-dependent slope, especially at the lower mass range required to predict the suppression of the total matter power spectrum at such redshifts. 2023-06-21T13:06:05,903 In the following example we use the redshift-dependent power-law fit parameters with a flat LambdaCDM cosmology. Note that any `astropy` cosmology could be used instead. 2023-06-21T13:06:05,904 ``` 2023-06-21T13:06:05,904 import pyspk.model as spk 2023-06-21T13:06:05,904 from astropy.cosmology import FlatLambdaCDM 2023-06-21T13:06:05,905 H0 = 70 2023-06-21T13:06:05,905 Omega_b = 0.0463 2023-06-21T13:06:05,906 Omega_m = 0.2793 2023-06-21T13:06:05,906 cosmo = FlatLambdaCDM(H0=H0, Om0=Omega_m, Ob0=Omega_b) 2023-06-21T13:06:05,907 alpha = 4.189 2023-06-21T13:06:05,907 beta = 1.273 2023-06-21T13:06:05,907 gamma = 0.298 2023-06-21T13:06:05,908 z = 0.5 2023-06-21T13:06:05,908 k, sup = spk.sup_model(SO=500, z=z, alpha=alpha, beta=beta, gamma=gamma, cosmo=cosmo) 2023-06-21T13:06:05,909 ``` 2023-06-21T13:06:05,909 ### Method 3: Binned data for the $f_b$ - $M_\mathrm{halo}$ relation. 2023-06-21T13:06:05,910 The final, and most flexible method is to provide py-SP(k) with the baryon fraction binned in bins of halo mass. This could be, for example, obtained from observational constraints, measured directly form simulations, or sampled from a predefined distribution or functional form. For an example using data obtained from the BAHAMAS simulations (McCarthy et al. 2017), please refer to the [examples](https://github.com/jemme07/pyspk/blob/main/examples/pySPk_Examples.ipynb) provided. 2023-06-21T13:06:05,911 ## Priors 2023-06-21T13:06:05,911 While py-SP(k) was calibrated using a wide range of sub-grid feedback parameters, some applications may require a more limited range of baryon fractions that encompass current observational constraints. For such applications, we used the gas mass - halo mass and stellar mass - halo mass constraints from the fits in Table 5 in Akino et al. (2022), and find the subset of simulations from our 400 models that agree to within $\pm 2$ or $3 \times \sigma$ of the inferred baryon budget at redshift $z=0.1$. We note that for our simulations, we include all stellar and gas particles within a spherical overdensity radius. Hence, in order to make reasonable comparisons with the fits in Akino et al. (2022), we included an additional 15\% contribution to the total stellar masses from the contribution of blue galaxies, and 30\% additional stellar mass to the brightest cluster galaxies (BCGs) to account for the diffuse intracluster light (ICL, see Akino et al. 2022). 2023-06-21T13:06:05,912 We utilised the simulations satisfying these restrictions to determine the redshift-dependent power-law parameters for the $f_b$ - $M_\mathrm{halo}$ relation up to redshift $z=1$ (Method 2), and then utilised these parameters to infer suitable priors. We limited the fitting range to $6 \times 10^{12} \leq M_{500c} [\mathrm{M}_ \odot] \leq 10^{14}$. 2023-06-21T13:06:05,913 Priors inferred from simulations that fall within $\pm 2 \times \sigma$ of the inferred baryon budget: 2023-06-21T13:06:05,913 | Parameter | Description | Prior | 2023-06-21T13:06:05,914 | ----------- | ------------------ | --------------- | 2023-06-21T13:06:05,914 | $\alpha$ | Normaliasation | $\mathcal{N}$(4.16, 0.07) | 2023-06-21T13:06:05,914 | $\beta$ | Slope | $\mathcal{N}$(1.20, 0.05) | 2023-06-21T13:06:05,915 | $\gamma$ | Redshift evolution | $\mathcal{N}$(0.39, 0.09) | 2023-06-21T13:06:05,915 where $\mathcal{N}(\mu,\sigma)$ is a Gaussian distribution with mean $\mu$ and standard deviation $\sigma$. 2023-06-21T13:06:05,916 Priors inferred from simulations that fall within $\pm 3 \times \sigma$ of the inferred baryon budget: 2023-06-21T13:06:05,917 | Parameter | Description | Prior | 2023-06-21T13:06:05,917 | ----------- | ------------------ | --------------- | 2023-06-21T13:06:05,917 | $\alpha$ | Normaliasation | $\mathcal{N}$(4.18, 0.12) | 2023-06-21T13:06:05,918 | $\beta$ | Slope | $\mathcal{N}$(1.26, 0.08) | 2023-06-21T13:06:05,918 | $\gamma$ | Redshift evolution | $\mathcal{N}$(0.42, 0.10) | 2023-06-21T13:06:05,918 where $\mathcal{N}(\mu,\sigma)$ is a Gaussian distribution with mean $\mu$ and standard deviation $\sigma$. 2023-06-21T13:06:05,919 ## Acknowledging the code 2023-06-21T13:06:05,920 Please cite py-SP(k) using: 2023-06-21T13:06:05,920 ``` 2023-06-21T13:06:05,921 @ARTICLE{SPK_Salcido_2023, 2023-06-21T13:06:05,921 author = {Salcido, Jaime and McCarthy, Ian G and Kwan, Juliana and Upadhye, Amol and Font, Andreea S}, 2023-06-21T13:06:05,922 title = "{SP(k) – a hydrodynamical simulation-based model for the impact of baryon physics on the non-linear matter power spectrum}", 2023-06-21T13:06:05,922 journal = {Monthly Notices of the Royal Astronomical Society}, 2023-06-21T13:06:05,922 volume = {523}, 2023-06-21T13:06:05,923 number = {2}, 2023-06-21T13:06:05,923 pages = {2247-2262}, 2023-06-21T13:06:05,923 year = {2023}, 2023-06-21T13:06:05,924 month = {05}, 2023-06-21T13:06:05,924 issn = {0035-8711}, 2023-06-21T13:06:05,924 doi = {10.1093/mnras/stad1474}, 2023-06-21T13:06:05,924 url = {https://doi.org/10.1093/mnras/stad1474}, 2023-06-21T13:06:05,925 eprint = {https://academic.oup.com/mnras/article-pdf/523/2/2247/50512773/stad1474.pdf}, 2023-06-21T13:06:05,925 } 2023-06-21T13:06:05,925 ``` 2023-06-21T13:06:05,926 For any questions and enquires please contact me via email at *j.salcidonegrete@ljmu.ac.uk* 2023-06-21T13:06:06,303 running egg_info 2023-06-21T13:06:06,306 creating /tmp/pip-pip-egg-info-qk6k6em7/pyspk.egg-info 2023-06-21T13:06:06,380 writing /tmp/pip-pip-egg-info-qk6k6em7/pyspk.egg-info/PKG-INFO 2023-06-21T13:06:06,385 writing dependency_links to /tmp/pip-pip-egg-info-qk6k6em7/pyspk.egg-info/dependency_links.txt 2023-06-21T13:06:06,390 writing requirements to /tmp/pip-pip-egg-info-qk6k6em7/pyspk.egg-info/requires.txt 2023-06-21T13:06:06,392 writing top-level names to /tmp/pip-pip-egg-info-qk6k6em7/pyspk.egg-info/top_level.txt 2023-06-21T13:06:06,395 writing manifest file '/tmp/pip-pip-egg-info-qk6k6em7/pyspk.egg-info/SOURCES.txt' 2023-06-21T13:06:06,597 reading manifest file '/tmp/pip-pip-egg-info-qk6k6em7/pyspk.egg-info/SOURCES.txt' 2023-06-21T13:06:06,600 reading manifest template 'MANIFEST.in' 2023-06-21T13:06:06,612 adding license file 'LICENSE.md' 2023-06-21T13:06:06,617 writing manifest file '/tmp/pip-pip-egg-info-qk6k6em7/pyspk.egg-info/SOURCES.txt' 2023-06-21T13:06:06,736 Preparing metadata (setup.py): finished with status 'done' 2023-06-21T13:06:06,750 Source in /tmp/pip-wheel-t1ni1p4r/pyspk_d42cf08a75c745d5ba0e907c1a7d8d3c has version 1.6, which satisfies requirement pyspk==1.6 from https://files.pythonhosted.org/packages/8c/56/7390a102e9ffc123a7c98ce38a01df97a66f31cd6d3bc27c6109b4194913/pyspk-1.6.tar.gz 2023-06-21T13:06:06,752 Removed pyspk==1.6 from https://files.pythonhosted.org/packages/8c/56/7390a102e9ffc123a7c98ce38a01df97a66f31cd6d3bc27c6109b4194913/pyspk-1.6.tar.gz from build tracker '/tmp/pip-build-tracker-eund0byu' 2023-06-21T13:06:06,764 Created temporary directory: /tmp/pip-unpack-xaadt7hl 2023-06-21T13:06:06,765 Building wheels for collected packages: pyspk 2023-06-21T13:06:06,774 Created temporary directory: /tmp/pip-wheel-bsyk3n4z 2023-06-21T13:06:06,774 Building wheel for pyspk (setup.py): started 2023-06-21T13:06:06,777 Destination directory: /tmp/pip-wheel-bsyk3n4z 2023-06-21T13:06:06,777 Running command python setup.py bdist_wheel 2023-06-21T13:06:07,837 # py-SP(k) - A hydrodynamical simulation-based model for the impact of baryon physics on the non-linear matter power spectrum 2023-06-21T13:06:07,839 _____ ____ ____ _ 2023-06-21T13:06:07,839 ____ __ __ / ___// __ \_/_/ /__| | 2023-06-21T13:06:07,840 / __ \/ / / /_____\__ \/ /_/ / // //_// / 2023-06-21T13:06:07,840 / /_/ / /_/ /_____/__/ / ____/ // ,< / / 2023-06-21T13:06:07,840 / .___/\__, / /____/_/ / //_/|_|/_/ 2023-06-21T13:06:07,841 /_/ /____/ |_| /_/ 2023-06-21T13:06:07,841 py-SP(k) [(Salcido et al. 2023)](https://academic.oup.com/mnras/article/523/2/2247/7165765) is a python package aimed at predicting the suppression of the total matter power spectrum due to baryonic physics as a function of the baryon fraction of haloes and redshift. 2023-06-21T13:06:07,842 ## Requirements 2023-06-21T13:06:07,843 The module requires the following: 2023-06-21T13:06:07,843 - numpy 2023-06-21T13:06:07,844 - scipy 2023-06-21T13:06:07,844 ## Installation 2023-06-21T13:06:07,845 The easiest way to install py-SP(k) is using pip: 2023-06-21T13:06:07,846 ``` 2023-06-21T13:06:07,846 pip install pyspk [--user] 2023-06-21T13:06:07,846 ``` 2023-06-21T13:06:07,847 The --user flag may be required if you do not have root privileges. 2023-06-21T13:06:07,848 ## Usage 2023-06-21T13:06:07,848 py-SP(k) is not restrictive to a particular shape of the baryon fraction – halo mass relation. In order to provide flexibility to the user, we have implemented 3 different methods to provide py-SP(k) with the required $f_b$ - $M_\mathrm{halo}$ relation. In the following sections we describe these implementations. A jupyter notebook with more detailed examples can be found within this [repository](https://github.com/jemme07/pyspk/blob/main/examples/pySPk_Examples.ipynb). 2023-06-21T13:06:07,849 ### Method 1: Using a power-law fit to the $f_b$ - $M_\mathrm{halo}$ relation 2023-06-21T13:06:07,850 py-SP(k) can be provided with power-law fitted parameters to the $f_b$ - $M_\mathrm{halo}$ relation using the functional form: 2023-06-21T13:06:07,850 $$f_b/(\Omega_b/\Omega_m)=a\left(\frac{M_{SO}}{M_{\mathrm{pivot}}}\right)^{b},$$ 2023-06-21T13:06:07,851 where $M_{SO}$ could be either $M_{200c}$ or $M_{500c}$ in $\mathrm{M}_ \odot$, $a$ is the normalisation of the $f_b$ - $M_\mathrm{halo}$ relation at $M_\mathrm{pivot}$, and $b$ is the power-law slope. The power-law can be normalised at any pivot point in units of $\mathrm{M}_ {\odot}$. If a pivot point is not given, `spk.sup_model()` uses a default pivot point of $M_{\mathrm{pivot}} = 1 \mathrm{M}_ \odot$. $a$, $b$ and $M_\mathrm{pivot}$ can be specified at each redshift independently. 2023-06-21T13:06:07,852 Next, we show a simple example using power-law fit parameters: 2023-06-21T13:06:07,852 ``` 2023-06-21T13:06:07,853 import pyspk as spk 2023-06-21T13:06:07,853 z = 0.125 2023-06-21T13:06:07,854 fb_a = 0.4 2023-06-21T13:06:07,854 fb_pow = 0.3 2023-06-21T13:06:07,854 fb_pivot = 10 ** 13.5 2023-06-21T13:06:07,855 k, sup = spk.sup_model(SO=200, z=z, fb_a=fb_a, fb_pow=fb_pow, fb_pivot=fb_pivot) 2023-06-21T13:06:07,855 ``` 2023-06-21T13:06:07,856 ### Method 2: Redshift-dependent power-law fit to the $f_b$ - $M_\mathrm{halo}$ relation. 2023-06-21T13:06:07,857 For the mass range that can be relatively well probed in current X-ray and Sunyaev-Zel'dovich effect observations (roughly $10^{13} \leq M_{500c} [\mathrm{M}_ \odot] \leq 10^{15}$), the total baryon fraction of haloes can be roughly approximated by a power-law with constant slope (e.g. Mulroy et al. 2019; Akino et al. 2022). Akino et al. (2022) determined the of the baryon budget for X-ray-selected galaxy groups and clusters using weak-lensing mass measurements. They provide a parametric redshift-dependent power-law fit to the gas mass - halo mass and stellar mass - halo mass relations, finding very little redshift evolution. 2023-06-21T13:06:07,857 We implemented a modified version of the functional form presented in Akino et al. (2022), to fit the total $f_b$ - $M_\mathrm{halo}$ relation as follows: 2023-06-21T13:06:07,858 $$f_b/(\Omega_b/\Omega_m)= \left(\frac{0.1658}{\Omega_b/\Omega_m}\right) \left(\frac{e^\alpha}{100}\right) \left(\frac{M_{500c}}{10^{14} \mathrm{M}_ \odot}\right)^{\beta - 1} \left(\frac{E(z)}{E(0.3)}\right)^{\gamma},$$ 2023-06-21T13:06:07,859 where $\alpha$ sets the power-law normalisation, $\beta$ sets power-law slope, $\gamma$ provides the redshift dependence and $E(z)$ is the usual dimensionless Hubble parameter. For simplicity, we use the cosmology implementation of `astropy` to specify the cosmological parameters in py-SP(k). 2023-06-21T13:06:07,859 Note that this power-law has a normalisation that is redshift dependent, while the the slope is constant in redshift. While this provides a less flexible approach compared with Methods 1 (simple power-law) and Method 3 (binned data), we find that this parametrisation provides a reasonable agreement with our simulations up to redshift $z=1$, which is the redshift range proved by Akino et al. (2022). For higher redshifts, we find that simulations require a mass-dependent slope, especially at the lower mass range required to predict the suppression of the total matter power spectrum at such redshifts. 2023-06-21T13:06:07,860 In the following example we use the redshift-dependent power-law fit parameters with a flat LambdaCDM cosmology. Note that any `astropy` cosmology could be used instead. 2023-06-21T13:06:07,861 ``` 2023-06-21T13:06:07,861 import pyspk.model as spk 2023-06-21T13:06:07,861 from astropy.cosmology import FlatLambdaCDM 2023-06-21T13:06:07,862 H0 = 70 2023-06-21T13:06:07,862 Omega_b = 0.0463 2023-06-21T13:06:07,862 Omega_m = 0.2793 2023-06-21T13:06:07,863 cosmo = FlatLambdaCDM(H0=H0, Om0=Omega_m, Ob0=Omega_b) 2023-06-21T13:06:07,864 alpha = 4.189 2023-06-21T13:06:07,864 beta = 1.273 2023-06-21T13:06:07,864 gamma = 0.298 2023-06-21T13:06:07,864 z = 0.5 2023-06-21T13:06:07,865 k, sup = spk.sup_model(SO=500, z=z, alpha=alpha, beta=beta, gamma=gamma, cosmo=cosmo) 2023-06-21T13:06:07,865 ``` 2023-06-21T13:06:07,866 ### Method 3: Binned data for the $f_b$ - $M_\mathrm{halo}$ relation. 2023-06-21T13:06:07,867 The final, and most flexible method is to provide py-SP(k) with the baryon fraction binned in bins of halo mass. This could be, for example, obtained from observational constraints, measured directly form simulations, or sampled from a predefined distribution or functional form. For an example using data obtained from the BAHAMAS simulations (McCarthy et al. 2017), please refer to the [examples](https://github.com/jemme07/pyspk/blob/main/examples/pySPk_Examples.ipynb) provided. 2023-06-21T13:06:07,868 ## Priors 2023-06-21T13:06:07,868 While py-SP(k) was calibrated using a wide range of sub-grid feedback parameters, some applications may require a more limited range of baryon fractions that encompass current observational constraints. For such applications, we used the gas mass - halo mass and stellar mass - halo mass constraints from the fits in Table 5 in Akino et al. (2022), and find the subset of simulations from our 400 models that agree to within $\pm 2$ or $3 \times \sigma$ of the inferred baryon budget at redshift $z=0.1$. We note that for our simulations, we include all stellar and gas particles within a spherical overdensity radius. Hence, in order to make reasonable comparisons with the fits in Akino et al. (2022), we included an additional 15\% contribution to the total stellar masses from the contribution of blue galaxies, and 30\% additional stellar mass to the brightest cluster galaxies (BCGs) to account for the diffuse intracluster light (ICL, see Akino et al. 2022). 2023-06-21T13:06:07,869 We utilised the simulations satisfying these restrictions to determine the redshift-dependent power-law parameters for the $f_b$ - $M_\mathrm{halo}$ relation up to redshift $z=1$ (Method 2), and then utilised these parameters to infer suitable priors. We limited the fitting range to $6 \times 10^{12} \leq M_{500c} [\mathrm{M}_ \odot] \leq 10^{14}$. 2023-06-21T13:06:07,870 Priors inferred from simulations that fall within $\pm 2 \times \sigma$ of the inferred baryon budget: 2023-06-21T13:06:07,870 | Parameter | Description | Prior | 2023-06-21T13:06:07,871 | ----------- | ------------------ | --------------- | 2023-06-21T13:06:07,871 | $\alpha$ | Normaliasation | $\mathcal{N}$(4.16, 0.07) | 2023-06-21T13:06:07,871 | $\beta$ | Slope | $\mathcal{N}$(1.20, 0.05) | 2023-06-21T13:06:07,872 | $\gamma$ | Redshift evolution | $\mathcal{N}$(0.39, 0.09) | 2023-06-21T13:06:07,872 where $\mathcal{N}(\mu,\sigma)$ is a Gaussian distribution with mean $\mu$ and standard deviation $\sigma$. 2023-06-21T13:06:07,873 Priors inferred from simulations that fall within $\pm 3 \times \sigma$ of the inferred baryon budget: 2023-06-21T13:06:07,874 | Parameter | Description | Prior | 2023-06-21T13:06:07,874 | ----------- | ------------------ | --------------- | 2023-06-21T13:06:07,874 | $\alpha$ | Normaliasation | $\mathcal{N}$(4.18, 0.12) | 2023-06-21T13:06:07,874 | $\beta$ | Slope | $\mathcal{N}$(1.26, 0.08) | 2023-06-21T13:06:07,875 | $\gamma$ | Redshift evolution | $\mathcal{N}$(0.42, 0.10) | 2023-06-21T13:06:07,875 where $\mathcal{N}(\mu,\sigma)$ is a Gaussian distribution with mean $\mu$ and standard deviation $\sigma$. 2023-06-21T13:06:07,876 ## Acknowledging the code 2023-06-21T13:06:07,877 Please cite py-SP(k) using: 2023-06-21T13:06:07,877 ``` 2023-06-21T13:06:07,877 @ARTICLE{SPK_Salcido_2023, 2023-06-21T13:06:07,878 author = {Salcido, Jaime and McCarthy, Ian G and Kwan, Juliana and Upadhye, Amol and Font, Andreea S}, 2023-06-21T13:06:07,878 title = "{SP(k) – a hydrodynamical simulation-based model for the impact of baryon physics on the non-linear matter power spectrum}", 2023-06-21T13:06:07,879 journal = {Monthly Notices of the Royal Astronomical Society}, 2023-06-21T13:06:07,879 volume = {523}, 2023-06-21T13:06:07,879 number = {2}, 2023-06-21T13:06:07,880 pages = {2247-2262}, 2023-06-21T13:06:07,880 year = {2023}, 2023-06-21T13:06:07,880 month = {05}, 2023-06-21T13:06:07,881 issn = {0035-8711}, 2023-06-21T13:06:07,881 doi = {10.1093/mnras/stad1474}, 2023-06-21T13:06:07,881 url = {https://doi.org/10.1093/mnras/stad1474}, 2023-06-21T13:06:07,882 eprint = {https://academic.oup.com/mnras/article-pdf/523/2/2247/50512773/stad1474.pdf}, 2023-06-21T13:06:07,882 } 2023-06-21T13:06:07,882 ``` 2023-06-21T13:06:07,882 For any questions and enquires please contact me via email at *j.salcidonegrete@ljmu.ac.uk* 2023-06-21T13:06:08,540 running bdist_wheel 2023-06-21T13:06:09,245 running build 2023-06-21T13:06:09,245 running build_py 2023-06-21T13:06:09,325 creating build 2023-06-21T13:06:09,326 creating build/lib 2023-06-21T13:06:09,328 creating build/lib/pyspk 2023-06-21T13:06:09,330 copying pyspk/__init__.py -> build/lib/pyspk 2023-06-21T13:06:09,334 copying pyspk/fit_vals.py -> build/lib/pyspk 2023-06-21T13:06:09,338 copying pyspk/model.py -> build/lib/pyspk 2023-06-21T13:06:09,342 running egg_info 2023-06-21T13:06:09,493 writing pyspk.egg-info/PKG-INFO 2023-06-21T13:06:09,498 writing dependency_links to pyspk.egg-info/dependency_links.txt 2023-06-21T13:06:09,502 writing requirements to pyspk.egg-info/requires.txt 2023-06-21T13:06:09,505 writing top-level names to pyspk.egg-info/top_level.txt 2023-06-21T13:06:09,575 reading manifest file 'pyspk.egg-info/SOURCES.txt' 2023-06-21T13:06:09,579 reading manifest template 'MANIFEST.in' 2023-06-21T13:06:09,589 adding license file 'LICENSE.md' 2023-06-21T13:06:09,595 writing manifest file 'pyspk.egg-info/SOURCES.txt' 2023-06-21T13:06:09,600 /home/piwheels/.local/lib/python3.7/site-packages/setuptools/command/build_py.py:201: _Warning: Package 'pyspk.__pycache__' is absent from the `packages` configuration. 2023-06-21T13:06:09,601 !! 2023-06-21T13:06:09,601 ******************************************************************************** 2023-06-21T13:06:09,602 ############################ 2023-06-21T13:06:09,602 # Package would be ignored # 2023-06-21T13:06:09,602 ############################ 2023-06-21T13:06:09,603 Python recognizes 'pyspk.__pycache__' as an importable package[^1], 2023-06-21T13:06:09,603 but it is absent from setuptools' `packages` configuration. 2023-06-21T13:06:09,604 This leads to an ambiguous overall configuration. If you want to distribute this 2023-06-21T13:06:09,604 package, please make sure that 'pyspk.__pycache__' is explicitly added 2023-06-21T13:06:09,604 to the `packages` configuration field. 2023-06-21T13:06:09,605 Alternatively, you can also rely on setuptools' discovery methods 2023-06-21T13:06:09,605 (for example by using `find_namespace_packages(...)`/`find_namespace:` 2023-06-21T13:06:09,606 instead of `find_packages(...)`/`find:`). 2023-06-21T13:06:09,606 You can read more about "package discovery" on setuptools documentation page: 2023-06-21T13:06:09,610 - https://setuptools.pypa.io/en/latest/userguide/package_discovery.html 2023-06-21T13:06:09,616 If you don't want 'pyspk.__pycache__' to be distributed and are 2023-06-21T13:06:09,616 already explicitly excluding 'pyspk.__pycache__' via 2023-06-21T13:06:09,616 `find_namespace_packages(...)/find_namespace` or `find_packages(...)/find`, 2023-06-21T13:06:09,617 you can try to use `exclude_package_data`, or `include-package-data=False` in 2023-06-21T13:06:09,617 combination with a more fine grained `package-data` configuration. 2023-06-21T13:06:09,618 You can read more about "package data files" on setuptools documentation page: 2023-06-21T13:06:09,618 - https://setuptools.pypa.io/en/latest/userguide/datafiles.html 2023-06-21T13:06:09,619 [^1]: For Python, any directory (with suitable naming) can be imported, 2023-06-21T13:06:09,620 even if it does not contain any `.py` files. 2023-06-21T13:06:09,620 On the other hand, currently there is no concept of package data 2023-06-21T13:06:09,620 directory, all directories are treated like packages. 2023-06-21T13:06:09,621 ******************************************************************************** 2023-06-21T13:06:09,621 !! 2023-06-21T13:06:09,626 check.warn(importable) 2023-06-21T13:06:09,628 copying pyspk/stat_errors_200.csv -> build/lib/pyspk 2023-06-21T13:06:09,629 copying pyspk/stat_errors_500.csv -> build/lib/pyspk 2023-06-21T13:06:09,631 creating build/lib/pyspk/__pycache__ 2023-06-21T13:06:09,633 copying pyspk/__pycache__/__init__.cpython-38.pyc -> build/lib/pyspk/__pycache__ 2023-06-21T13:06:09,638 copying pyspk/__pycache__/fit_vals.cpython-38.pyc -> build/lib/pyspk/__pycache__ 2023-06-21T13:06:09,642 copying pyspk/__pycache__/model.cpython-38.pyc -> build/lib/pyspk/__pycache__ 2023-06-21T13:06:09,722 /home/piwheels/.local/lib/python3.7/site-packages/setuptools/_distutils/cmd.py:66: SetuptoolsDeprecationWarning: setup.py install is deprecated. 2023-06-21T13:06:09,722 !! 2023-06-21T13:06:09,723 ******************************************************************************** 2023-06-21T13:06:09,724 Please avoid running ``setup.py`` directly. 2023-06-21T13:06:09,724 Instead, use pypa/build, pypa/installer, pypa/build or 2023-06-21T13:06:09,724 other standards-based tools. 2023-06-21T13:06:09,725 See https://blog.ganssle.io/articles/2021/10/setup-py-deprecated.html for details. 2023-06-21T13:06:09,725 ******************************************************************************** 2023-06-21T13:06:09,726 !! 2023-06-21T13:06:09,726 self.initialize_options() 2023-06-21T13:06:09,789 installing to build/bdist.linux-armv7l/wheel 2023-06-21T13:06:09,790 running install 2023-06-21T13:06:09,852 running install_lib 2023-06-21T13:06:09,923 creating build/bdist.linux-armv7l 2023-06-21T13:06:09,924 creating build/bdist.linux-armv7l/wheel 2023-06-21T13:06:09,927 creating build/bdist.linux-armv7l/wheel/pyspk 2023-06-21T13:06:09,931 creating build/bdist.linux-armv7l/wheel/pyspk/__pycache__ 2023-06-21T13:06:09,933 copying build/lib/pyspk/__pycache__/model.cpython-38.pyc -> build/bdist.linux-armv7l/wheel/pyspk/__pycache__ 2023-06-21T13:06:09,938 copying build/lib/pyspk/__pycache__/__init__.cpython-38.pyc -> build/bdist.linux-armv7l/wheel/pyspk/__pycache__ 2023-06-21T13:06:09,942 copying build/lib/pyspk/__pycache__/fit_vals.cpython-38.pyc -> build/bdist.linux-armv7l/wheel/pyspk/__pycache__ 2023-06-21T13:06:09,946 copying build/lib/pyspk/__init__.py -> build/bdist.linux-armv7l/wheel/pyspk 2023-06-21T13:06:09,950 copying build/lib/pyspk/fit_vals.py -> build/bdist.linux-armv7l/wheel/pyspk 2023-06-21T13:06:09,954 copying build/lib/pyspk/model.py -> build/bdist.linux-armv7l/wheel/pyspk 2023-06-21T13:06:09,959 copying build/lib/pyspk/stat_errors_200.csv -> build/bdist.linux-armv7l/wheel/pyspk 2023-06-21T13:06:09,973 copying build/lib/pyspk/stat_errors_500.csv -> build/bdist.linux-armv7l/wheel/pyspk 2023-06-21T13:06:09,987 running install_egg_info 2023-06-21T13:06:10,063 Copying pyspk.egg-info to build/bdist.linux-armv7l/wheel/pyspk-1.6-py3.7.egg-info 2023-06-21T13:06:10,083 running install_scripts 2023-06-21T13:06:10,115 creating build/bdist.linux-armv7l/wheel/pyspk-1.6.dist-info/WHEEL 2023-06-21T13:06:10,120 creating '/tmp/pip-wheel-bsyk3n4z/pyspk-1.6-py3-none-any.whl' and adding 'build/bdist.linux-armv7l/wheel' to it 2023-06-21T13:06:10,125 adding 'pyspk/__init__.py' 2023-06-21T13:06:10,128 adding 'pyspk/fit_vals.py' 2023-06-21T13:06:10,134 adding 'pyspk/model.py' 2023-06-21T13:06:10,224 adding 'pyspk/stat_errors_200.csv' 2023-06-21T13:06:10,318 adding 'pyspk/stat_errors_500.csv' 2023-06-21T13:06:10,325 adding 'pyspk/__pycache__/__init__.cpython-38.pyc' 2023-06-21T13:06:10,328 adding 'pyspk/__pycache__/fit_vals.cpython-38.pyc' 2023-06-21T13:06:10,333 adding 'pyspk/__pycache__/model.cpython-38.pyc' 2023-06-21T13:06:10,339 adding 'pyspk-1.6.dist-info/LICENSE.md' 2023-06-21T13:06:10,343 adding 'pyspk-1.6.dist-info/METADATA' 2023-06-21T13:06:10,345 adding 'pyspk-1.6.dist-info/WHEEL' 2023-06-21T13:06:10,347 adding 'pyspk-1.6.dist-info/top_level.txt' 2023-06-21T13:06:10,349 adding 'pyspk-1.6.dist-info/RECORD' 2023-06-21T13:06:10,357 removing build/bdist.linux-armv7l/wheel 2023-06-21T13:06:10,520 Building wheel for pyspk (setup.py): finished with status 'done' 2023-06-21T13:06:10,532 Created wheel for pyspk: filename=pyspk-1.6-py3-none-any.whl size=154075 sha256=bf980607caf0e2261fcddc053db216d0a957c2cd7efefca370986f9f119729f5 2023-06-21T13:06:10,534 Stored in directory: /tmp/pip-ephem-wheel-cache-_kudzyyw/wheels/57/28/b5/33aa6ff4b7459fcbce8b50d40b3f5e93442dc0f82176876ccb 2023-06-21T13:06:10,562 Successfully built pyspk 2023-06-21T13:06:10,581 Removed build tracker: '/tmp/pip-build-tracker-eund0byu'