2023-06-09T16:41:40,221 Created temporary directory: /tmp/pip-build-tracker-xb7qpta8
2023-06-09T16:41:40,224 Initialized build tracking at /tmp/pip-build-tracker-xb7qpta8
2023-06-09T16:41:40,225 Created build tracker: /tmp/pip-build-tracker-xb7qpta8
2023-06-09T16:41:40,225 Entered build tracker: /tmp/pip-build-tracker-xb7qpta8
2023-06-09T16:41:40,226 Created temporary directory: /tmp/pip-wheel-ewux3z91
2023-06-09T16:41:40,234 Created temporary directory: /tmp/pip-ephem-wheel-cache-tmlsv2xz
2023-06-09T16:41:40,287 Looking in indexes: https://pypi.org/simple, https://www.piwheels.org/simple
2023-06-09T16:41:40,295 2 location(s) to search for versions of pyspk:
2023-06-09T16:41:40,295 * https://pypi.org/simple/pyspk/
2023-06-09T16:41:40,295 * https://www.piwheels.org/simple/pyspk/
2023-06-09T16:41:40,296 Fetching project page and analyzing links: https://pypi.org/simple/pyspk/
2023-06-09T16:41:40,297 Getting page https://pypi.org/simple/pyspk/
2023-06-09T16:41:40,301 Found index url https://pypi.org/simple/
2023-06-09T16:41:40,494 Fetched page https://pypi.org/simple/pyspk/ as application/vnd.pypi.simple.v1+json
2023-06-09T16:41:40,501   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/)
2023-06-09T16:41:40,502   Found link https://files.pythonhosted.org/packages/a8/d2/0734e1e3790826d866e4d99bdc646fba69430f90883d2ba783b2ec83ec06/pyspk-1.0.tar.gz (from https://pypi.org/simple/pyspk/), version: 1.0
2023-06-09T16:41:40,502   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/)
2023-06-09T16:41:40,503   Found link https://files.pythonhosted.org/packages/61/93/710ef3373d68aa7569f17af7a78e4dc9cb7f07aafb4cbcc56155120846f7/pyspk-1.1.tar.gz (from https://pypi.org/simple/pyspk/), version: 1.1
2023-06-09T16:41:40,504   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/)
2023-06-09T16:41:40,504   Found link https://files.pythonhosted.org/packages/ba/6d/e1283dfc400ad9f9eceacc38e56c49b7614fdb996001ab298678bd394e90/pyspk-1.2.tar.gz (from https://pypi.org/simple/pyspk/), version: 1.2
2023-06-09T16:41:40,505   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/)
2023-06-09T16:41:40,505   Found link https://files.pythonhosted.org/packages/5a/7f/3b4c6ab139cf3771fcb53c4cdd65e8c36cf86ba024e132aa3a38a0db5929/pyspk-1.3.tar.gz (from https://pypi.org/simple/pyspk/), version: 1.3
2023-06-09T16:41:40,506   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/)
2023-06-09T16:41:40,506   Found link https://files.pythonhosted.org/packages/40/f4/170424c88049316ddccc683d5caae03e9e598e4b9bfc5b855e5c12a84e42/pyspk-1.4.tar.gz (from https://pypi.org/simple/pyspk/), version: 1.4
2023-06-09T16:41:40,507 Fetching project page and analyzing links: https://www.piwheels.org/simple/pyspk/
2023-06-09T16:41:40,508 Getting page https://www.piwheels.org/simple/pyspk/
2023-06-09T16:41:40,510 Found index url https://www.piwheels.org/simple/
2023-06-09T16:41:40,728 Fetched page https://www.piwheels.org/simple/pyspk/ as text/html
2023-06-09T16:41:40,733   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/)
2023-06-09T16:41:40,733   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/)
2023-06-09T16:41:40,734   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/)
2023-06-09T16:41:40,734   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/)
2023-06-09T16:41:40,735 Skipping link: not a file: https://www.piwheels.org/simple/pyspk/
2023-06-09T16:41:40,736 Skipping link: not a file: https://pypi.org/simple/pyspk/
2023-06-09T16:41:40,770 Given no hashes to check 1 links for project 'pyspk': discarding no candidates
2023-06-09T16:41:40,801 Collecting pyspk==1.4
2023-06-09T16:41:40,805   Created temporary directory: /tmp/pip-unpack-keaqu9bv
2023-06-09T16:41:40,995   Downloading pyspk-1.4.tar.gz (148 kB)
2023-06-09T16:41:41,200   Added pyspk==1.4 from https://files.pythonhosted.org/packages/40/f4/170424c88049316ddccc683d5caae03e9e598e4b9bfc5b855e5c12a84e42/pyspk-1.4.tar.gz to build tracker '/tmp/pip-build-tracker-xb7qpta8'
2023-06-09T16:41:41,204   Running setup.py (path:/tmp/pip-wheel-ewux3z91/pyspk_f3fdd3df54d74c42a70567ac0b9a4252/setup.py) egg_info for package pyspk
2023-06-09T16:41:41,205   Created temporary directory: /tmp/pip-pip-egg-info-mx8rozr2
2023-06-09T16:41:41,206   Preparing metadata (setup.py): started
2023-06-09T16:41:41,208   Running command python setup.py egg_info
2023-06-09T16:41:42,285   # py-SP(k) - A hydrodynamical simulation-based model for the impact of baryon physics on the non-linear matter power spectrum
2023-06-09T16:41:42,286                             _____ ____   ____   _
2023-06-09T16:41:42,287           ____  __  __     / ___// __ \_/_/ /__| |
2023-06-09T16:41:42,287          / __ \/ / / /_____\__ \/ /_/ / // //_// /
2023-06-09T16:41:42,288         / /_/ / /_/ /_____/__/ / ____/ // ,<  / /
2023-06-09T16:41:42,288        / .___/\__, /     /____/_/   / //_/|_|/_/
2023-06-09T16:41:42,288       /_/    /____/                 |_|    /_/

2023-06-09T16:41:42,289   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.

2023-06-09T16:41:42,290   ## Requirements

2023-06-09T16:41:42,291   The module requires the following:

2023-06-09T16:41:42,291   - numpy
2023-06-09T16:41:42,292   - scipy

2023-06-09T16:41:42,292   ## Installation

2023-06-09T16:41:42,293   The easiest way to install py-SP(k) is using pip:

2023-06-09T16:41:42,294   ```
2023-06-09T16:41:42,294   pip install pyspk [--user]
2023-06-09T16:41:42,295   ```

2023-06-09T16:41:42,296   The --user flag may be required if you do not have root privileges.

2023-06-09T16:41:42,296   ## Usage

2023-06-09T16:41:42,297   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).

2023-06-09T16:41:42,298   ### Method 1: Using a power-law fit to the $f_b$ - $M_\mathrm{halo}$ relation

2023-06-09T16:41:42,299   py-SP(k) can be provided with power-law fitted parameters to the $f_b$ - $M_\mathrm{halo}$ relation using the functional form:

2023-06-09T16:41:42,299   $$f_b/(\Omega_b/\Omega_m)=a\left(\frac{M_{SO}}{M_{\mathrm{pivot}}}\right)^{b},$$

2023-06-09T16:41:42,300   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.

2023-06-09T16:41:42,301   Next, we show a simple example using power-law fit parameters:

2023-06-09T16:41:42,302   ```
2023-06-09T16:41:42,303   import pyspk as spk

2023-06-09T16:41:42,303   z = 0.125
2023-06-09T16:41:42,304   fb_a = 0.4
2023-06-09T16:41:42,304   fb_pow = 0.3
2023-06-09T16:41:42,304   fb_pivot = 10 ** 13.5

2023-06-09T16:41:42,305   k, sup = spk.sup_model(SO=200, z=z, fb_a=fb_a, fb_pow=fb_pow, fb_pivot=fb_pivot)
2023-06-09T16:41:42,306   ```

2023-06-09T16:41:42,306   ### Method 2: Redshift-dependent power-law fit to the $f_b$ - $M_\mathrm{halo}$ relation.

2023-06-09T16:41:42,307   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.

2023-06-09T16:41:42,308   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:

2023-06-09T16:41:42,310   $$f_b/(\Omega_b/\Omega_m)= \left(\frac{0.1658}{\Omega_b/\Omega_m}\right) \left(\frac{e^\alpha}{100}\right) \left(\frac{M_{500c}}{10^{14} \mathrm{M}_ \odot}\right)^{\beta - 1} \left(\frac{E(z)}{E(0.3)}\right)^{\gamma},$$

2023-06-09T16:41:42,311   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).

2023-06-09T16:41:42,312   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.

2023-06-09T16:41:42,312   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.

2023-06-09T16:41:42,313   ```
2023-06-09T16:41:42,313   import pyspk.model as spk
2023-06-09T16:41:42,314   from astropy.cosmology import FlatLambdaCDM

2023-06-09T16:41:42,315   H0 = 70
2023-06-09T16:41:42,315   Omega_b = 0.0463
2023-06-09T16:41:42,315   Omega_m = 0.2793

2023-06-09T16:41:42,316   cosmo = FlatLambdaCDM(H0=H0, Om0=Omega_m, Ob0=Omega_b)

2023-06-09T16:41:42,317   alpha = 4.189
2023-06-09T16:41:42,317   beta = 1.273
2023-06-09T16:41:42,318   gamma = 0.298
2023-06-09T16:41:42,318   z = 0.5

2023-06-09T16:41:42,319   k, sup = spk.sup_model(SO=500, z=z, alpha=alpha, beta=beta, gamma=gamma, cosmo=cosmo)
2023-06-09T16:41:42,319   ```

2023-06-09T16:41:42,320   ### Method 3: Binned data for the $f_b$ - $M_\mathrm{halo}$ relation.

2023-06-09T16:41:42,320   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.


2023-06-09T16:41:42,322   ## Priors

2023-06-09T16:41:42,322   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).

2023-06-09T16:41:42,323   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 $6 \times 10^{12} \leq M_{500c} [\mathrm{M}_ \odot] \leq 10^{14}$.

2023-06-09T16:41:42,324   Priors inferred from simulations that fall within $\pm 2 \times \sigma$ of the inferred baryon budget:

2023-06-09T16:41:42,325   | Parameter   | Description        | Prior           |
2023-06-09T16:41:42,325   | ----------- | ------------------ | --------------- |
2023-06-09T16:41:42,325   | $\alpha$    | Normaliasation     | $\mathcal{N}$(4.16, 0.07) |
2023-06-09T16:41:42,326   | $\beta$     | Slope              | $\mathcal{N}$(1.20, 0.05) |
2023-06-09T16:41:42,326   | $\gamma$    | Redshift evolution | $\mathcal{N}$(0.39, 0.09) |

2023-06-09T16:41:42,327   where $\mathcal{N}(\mu,\sigma)$ is a Gaussian distribution with mean $\mu$ and standard deviation $\sigma$.

2023-06-09T16:41:42,327   Priors inferred from simulations that fall within $\pm 3 \times \sigma$ of the inferred baryon budget:

2023-06-09T16:41:42,328   | Parameter   | Description        | Prior           |
2023-06-09T16:41:42,328   | ----------- | ------------------ | --------------- |
2023-06-09T16:41:42,329   | $\alpha$    | Normaliasation     | $\mathcal{N}$(4.18, 0.12) |
2023-06-09T16:41:42,329   | $\beta$     | Slope              | $\mathcal{N}$(1.26, 0.08) |
2023-06-09T16:41:42,329   | $\gamma$    | Redshift evolution | $\mathcal{N}$(0.42, 0.10) |

2023-06-09T16:41:42,330   where $\mathcal{N}(\mu,\sigma)$ is a Gaussian distribution with mean $\mu$ and standard deviation $\sigma$.

2023-06-09T16:41:42,331   ## Acknowledging the code

2023-06-09T16:41:42,331   Please cite py-SP(k) using:

2023-06-09T16:41:42,332   ```
2023-06-09T16:41:42,333   @ARTICLE{SPK_Salcido_2023,
2023-06-09T16:41:42,333       author = {Salcido, Jaime and McCarthy, Ian G and Kwan, Juliana and Upadhye, Amol and Font, Andreea S},
2023-06-09T16:41:42,333       title = "{SP(k) – a hydrodynamical simulation-based model for the impact of baryon physics on the non-linear matter power spectrum}",
2023-06-09T16:41:42,334       journal = {Monthly Notices of the Royal Astronomical Society},
2023-06-09T16:41:42,334       volume = {523},
2023-06-09T16:41:42,334       number = {2},
2023-06-09T16:41:42,335       pages = {2247-2262},
2023-06-09T16:41:42,335       year = {2023},
2023-06-09T16:41:42,335       month = {05},
2023-06-09T16:41:42,336       issn = {0035-8711},
2023-06-09T16:41:42,336       doi = {10.1093/mnras/stad1474},
2023-06-09T16:41:42,336       url = {https://doi.org/10.1093/mnras/stad1474},
2023-06-09T16:41:42,337       eprint = {https://academic.oup.com/mnras/article-pdf/523/2/2247/50512773/stad1474.pdf},
2023-06-09T16:41:42,337   }
2023-06-09T16:41:42,337   ```
2023-06-09T16:41:42,338   For any questions and enquires please contact me via email at *j.salcidonegrete@ljmu.ac.uk*



2023-06-09T16:41:42,682   running egg_info
2023-06-09T16:41:42,685   creating /tmp/pip-pip-egg-info-mx8rozr2/pyspk.egg-info
2023-06-09T16:41:42,747   writing /tmp/pip-pip-egg-info-mx8rozr2/pyspk.egg-info/PKG-INFO
2023-06-09T16:41:42,752   writing dependency_links to /tmp/pip-pip-egg-info-mx8rozr2/pyspk.egg-info/dependency_links.txt
2023-06-09T16:41:42,757   writing requirements to /tmp/pip-pip-egg-info-mx8rozr2/pyspk.egg-info/requires.txt
2023-06-09T16:41:42,759   writing top-level names to /tmp/pip-pip-egg-info-mx8rozr2/pyspk.egg-info/top_level.txt
2023-06-09T16:41:42,762   writing manifest file '/tmp/pip-pip-egg-info-mx8rozr2/pyspk.egg-info/SOURCES.txt'
2023-06-09T16:41:42,956   reading manifest file '/tmp/pip-pip-egg-info-mx8rozr2/pyspk.egg-info/SOURCES.txt'
2023-06-09T16:41:42,960   reading manifest template 'MANIFEST.in'
2023-06-09T16:41:42,968   adding license file 'LICENSE.md'
2023-06-09T16:41:42,974   writing manifest file '/tmp/pip-pip-egg-info-mx8rozr2/pyspk.egg-info/SOURCES.txt'
2023-06-09T16:41:43,094   Preparing metadata (setup.py): finished with status 'done'
2023-06-09T16:41:43,108   Source in /tmp/pip-wheel-ewux3z91/pyspk_f3fdd3df54d74c42a70567ac0b9a4252 has version 1.4, which satisfies requirement pyspk==1.4 from https://files.pythonhosted.org/packages/40/f4/170424c88049316ddccc683d5caae03e9e598e4b9bfc5b855e5c12a84e42/pyspk-1.4.tar.gz
2023-06-09T16:41:43,110   Removed pyspk==1.4 from https://files.pythonhosted.org/packages/40/f4/170424c88049316ddccc683d5caae03e9e598e4b9bfc5b855e5c12a84e42/pyspk-1.4.tar.gz from build tracker '/tmp/pip-build-tracker-xb7qpta8'
2023-06-09T16:41:43,121 Created temporary directory: /tmp/pip-unpack-2jydemni
2023-06-09T16:41:43,123 Building wheels for collected packages: pyspk
2023-06-09T16:41:43,132   Created temporary directory: /tmp/pip-wheel-bwz228lp
2023-06-09T16:41:43,133   Building wheel for pyspk (setup.py): started
2023-06-09T16:41:43,135   Destination directory: /tmp/pip-wheel-bwz228lp
2023-06-09T16:41:43,135   Running command python setup.py bdist_wheel
2023-06-09T16:41:44,217   # py-SP(k) - A hydrodynamical simulation-based model for the impact of baryon physics on the non-linear matter power spectrum
2023-06-09T16:41:44,218                             _____ ____   ____   _
2023-06-09T16:41:44,219           ____  __  __     / ___// __ \_/_/ /__| |
2023-06-09T16:41:44,219          / __ \/ / / /_____\__ \/ /_/ / // //_// /
2023-06-09T16:41:44,219         / /_/ / /_/ /_____/__/ / ____/ // ,<  / /
2023-06-09T16:41:44,220        / .___/\__, /     /____/_/   / //_/|_|/_/
2023-06-09T16:41:44,220       /_/    /____/                 |_|    /_/

2023-06-09T16:41:44,221   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.

2023-06-09T16:41:44,222   ## Requirements

2023-06-09T16:41:44,222   The module requires the following:

2023-06-09T16:41:44,223   - numpy
2023-06-09T16:41:44,224   - scipy

2023-06-09T16:41:44,224   ## Installation

2023-06-09T16:41:44,225   The easiest way to install py-SP(k) is using pip:

2023-06-09T16:41:44,226   ```
2023-06-09T16:41:44,226   pip install pyspk [--user]
2023-06-09T16:41:44,227   ```

2023-06-09T16:41:44,227   The --user flag may be required if you do not have root privileges.

2023-06-09T16:41:44,228   ## Usage

2023-06-09T16:41:44,229   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).

2023-06-09T16:41:44,230   ### Method 1: Using a power-law fit to the $f_b$ - $M_\mathrm{halo}$ relation

2023-06-09T16:41:44,231   py-SP(k) can be provided with power-law fitted parameters to the $f_b$ - $M_\mathrm{halo}$ relation using the functional form:

2023-06-09T16:41:44,231   $$f_b/(\Omega_b/\Omega_m)=a\left(\frac{M_{SO}}{M_{\mathrm{pivot}}}\right)^{b},$$

2023-06-09T16:41:44,232   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.

2023-06-09T16:41:44,233   Next, we show a simple example using power-law fit parameters:

2023-06-09T16:41:44,234   ```
2023-06-09T16:41:44,234   import pyspk as spk

2023-06-09T16:41:44,235   z = 0.125
2023-06-09T16:41:44,235   fb_a = 0.4
2023-06-09T16:41:44,235   fb_pow = 0.3
2023-06-09T16:41:44,236   fb_pivot = 10 ** 13.5

2023-06-09T16:41:44,236   k, sup = spk.sup_model(SO=200, z=z, fb_a=fb_a, fb_pow=fb_pow, fb_pivot=fb_pivot)
2023-06-09T16:41:44,237   ```

2023-06-09T16:41:44,237   ### Method 2: Redshift-dependent power-law fit to the $f_b$ - $M_\mathrm{halo}$ relation.

2023-06-09T16:41:44,238   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.

2023-06-09T16:41:44,239   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:

2023-06-09T16:41:44,239   $$f_b/(\Omega_b/\Omega_m)= \left(\frac{0.1658}{\Omega_b/\Omega_m}\right) \left(\frac{e^\alpha}{100}\right) \left(\frac{M_{500c}}{10^{14} \mathrm{M}_ \odot}\right)^{\beta - 1} \left(\frac{E(z)}{E(0.3)}\right)^{\gamma},$$

2023-06-09T16:41:44,240   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).

2023-06-09T16:41:44,241   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.

2023-06-09T16:41:44,241   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.

2023-06-09T16:41:44,242   ```
2023-06-09T16:41:44,243   import pyspk.model as spk
2023-06-09T16:41:44,243   from astropy.cosmology import FlatLambdaCDM

2023-06-09T16:41:44,244   H0 = 70
2023-06-09T16:41:44,244   Omega_b = 0.0463
2023-06-09T16:41:44,244   Omega_m = 0.2793

2023-06-09T16:41:44,245   cosmo = FlatLambdaCDM(H0=H0, Om0=Omega_m, Ob0=Omega_b)

2023-06-09T16:41:44,246   alpha = 4.189
2023-06-09T16:41:44,246   beta = 1.273
2023-06-09T16:41:44,246   gamma = 0.298
2023-06-09T16:41:44,247   z = 0.5

2023-06-09T16:41:44,248   k, sup = spk.sup_model(SO=500, z=z, alpha=alpha, beta=beta, gamma=gamma, cosmo=cosmo)
2023-06-09T16:41:44,248   ```

2023-06-09T16:41:44,248   ### Method 3: Binned data for the $f_b$ - $M_\mathrm{halo}$ relation.

2023-06-09T16:41:44,249   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.


2023-06-09T16:41:44,250   ## Priors

2023-06-09T16:41:44,251   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).

2023-06-09T16:41:44,252   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 $6 \times 10^{12} \leq M_{500c} [\mathrm{M}_ \odot] \leq 10^{14}$.

2023-06-09T16:41:44,253   Priors inferred from simulations that fall within $\pm 2 \times \sigma$ of the inferred baryon budget:

2023-06-09T16:41:44,253   | Parameter   | Description        | Prior           |
2023-06-09T16:41:44,254   | ----------- | ------------------ | --------------- |
2023-06-09T16:41:44,254   | $\alpha$    | Normaliasation     | $\mathcal{N}$(4.16, 0.07) |
2023-06-09T16:41:44,255   | $\beta$     | Slope              | $\mathcal{N}$(1.20, 0.05) |
2023-06-09T16:41:44,255   | $\gamma$    | Redshift evolution | $\mathcal{N}$(0.39, 0.09) |

2023-06-09T16:41:44,256   where $\mathcal{N}(\mu,\sigma)$ is a Gaussian distribution with mean $\mu$ and standard deviation $\sigma$.

2023-06-09T16:41:44,256   Priors inferred from simulations that fall within $\pm 3 \times \sigma$ of the inferred baryon budget:

2023-06-09T16:41:44,257   | Parameter   | Description        | Prior           |
2023-06-09T16:41:44,257   | ----------- | ------------------ | --------------- |
2023-06-09T16:41:44,258   | $\alpha$    | Normaliasation     | $\mathcal{N}$(4.18, 0.12) |
2023-06-09T16:41:44,258   | $\beta$     | Slope              | $\mathcal{N}$(1.26, 0.08) |
2023-06-09T16:41:44,258   | $\gamma$    | Redshift evolution | $\mathcal{N}$(0.42, 0.10) |

2023-06-09T16:41:44,259   where $\mathcal{N}(\mu,\sigma)$ is a Gaussian distribution with mean $\mu$ and standard deviation $\sigma$.

2023-06-09T16:41:44,260   ## Acknowledging the code

2023-06-09T16:41:44,260   Please cite py-SP(k) using:

2023-06-09T16:41:44,261   ```
2023-06-09T16:41:44,261   @ARTICLE{SPK_Salcido_2023,
2023-06-09T16:41:44,262       author = {Salcido, Jaime and McCarthy, Ian G and Kwan, Juliana and Upadhye, Amol and Font, Andreea S},
2023-06-09T16:41:44,262       title = "{SP(k) – a hydrodynamical simulation-based model for the impact of baryon physics on the non-linear matter power spectrum}",
2023-06-09T16:41:44,263       journal = {Monthly Notices of the Royal Astronomical Society},
2023-06-09T16:41:44,263       volume = {523},
2023-06-09T16:41:44,263       number = {2},
2023-06-09T16:41:44,264       pages = {2247-2262},
2023-06-09T16:41:44,264       year = {2023},
2023-06-09T16:41:44,264       month = {05},
2023-06-09T16:41:44,265       issn = {0035-8711},
2023-06-09T16:41:44,265       doi = {10.1093/mnras/stad1474},
2023-06-09T16:41:44,266       url = {https://doi.org/10.1093/mnras/stad1474},
2023-06-09T16:41:44,266       eprint = {https://academic.oup.com/mnras/article-pdf/523/2/2247/50512773/stad1474.pdf},
2023-06-09T16:41:44,266   }
2023-06-09T16:41:44,267   ```
2023-06-09T16:41:44,267   For any questions and enquires please contact me via email at *j.salcidonegrete@ljmu.ac.uk*



2023-06-09T16:41:44,681   running bdist_wheel
2023-06-09T16:41:45,369   running build
2023-06-09T16:41:45,370   running build_py
2023-06-09T16:41:45,441   creating build
2023-06-09T16:41:45,442   creating build/lib
2023-06-09T16:41:45,444   creating build/lib/pyspk
2023-06-09T16:41:45,446   copying pyspk/model.py -> build/lib/pyspk
2023-06-09T16:41:45,450   copying pyspk/__init__.py -> build/lib/pyspk
2023-06-09T16:41:45,454   copying pyspk/fit_vals.py -> build/lib/pyspk
2023-06-09T16:41:45,457   running egg_info
2023-06-09T16:41:45,599   writing pyspk.egg-info/PKG-INFO
2023-06-09T16:41:45,603   writing dependency_links to pyspk.egg-info/dependency_links.txt
2023-06-09T16:41:45,607   writing requirements to pyspk.egg-info/requires.txt
2023-06-09T16:41:45,610   writing top-level names to pyspk.egg-info/top_level.txt
2023-06-09T16:41:45,676   reading manifest file 'pyspk.egg-info/SOURCES.txt'
2023-06-09T16:41:45,679   reading manifest template 'MANIFEST.in'
2023-06-09T16:41:45,686   adding license file 'LICENSE.md'
2023-06-09T16:41:45,691   writing manifest file 'pyspk.egg-info/SOURCES.txt'
2023-06-09T16:41:45,695   copying pyspk/stat_errors_200.csv -> build/lib/pyspk
2023-06-09T16:41:45,710   copying pyspk/stat_errors_500.csv -> build/lib/pyspk
2023-06-09T16:41:45,793   /usr/local/lib/python3.7/dist-packages/setuptools/_distutils/cmd.py:66: SetuptoolsDeprecationWarning: setup.py install is deprecated.
2023-06-09T16:41:45,794   !!

2023-06-09T16:41:45,794           ********************************************************************************
2023-06-09T16:41:45,795           Please avoid running ``setup.py`` directly.
2023-06-09T16:41:45,795           Instead, use pypa/build, pypa/installer, pypa/build or
2023-06-09T16:41:45,795           other standards-based tools.

2023-06-09T16:41:45,796           See https://blog.ganssle.io/articles/2021/10/setup-py-deprecated.html for details.
2023-06-09T16:41:45,796           ********************************************************************************

2023-06-09T16:41:45,797   !!
2023-06-09T16:41:45,798     self.initialize_options()
2023-06-09T16:41:45,858   installing to build/bdist.linux-armv7l/wheel
2023-06-09T16:41:45,859   running install
2023-06-09T16:41:45,924   running install_lib
2023-06-09T16:41:45,993   creating build/bdist.linux-armv7l
2023-06-09T16:41:45,994   creating build/bdist.linux-armv7l/wheel
2023-06-09T16:41:45,997   creating build/bdist.linux-armv7l/wheel/pyspk
2023-06-09T16:41:45,999   copying build/lib/pyspk/stat_errors_200.csv -> build/bdist.linux-armv7l/wheel/pyspk
2023-06-09T16:41:46,014   copying build/lib/pyspk/model.py -> build/bdist.linux-armv7l/wheel/pyspk
2023-06-09T16:41:46,019   copying build/lib/pyspk/__init__.py -> build/bdist.linux-armv7l/wheel/pyspk
2023-06-09T16:41:46,022   copying build/lib/pyspk/stat_errors_500.csv -> build/bdist.linux-armv7l/wheel/pyspk
2023-06-09T16:41:46,037   copying build/lib/pyspk/fit_vals.py -> build/bdist.linux-armv7l/wheel/pyspk
2023-06-09T16:41:46,041   running install_egg_info
2023-06-09T16:41:46,115   Copying pyspk.egg-info to build/bdist.linux-armv7l/wheel/pyspk-1.4-py3.7.egg-info
2023-06-09T16:41:46,136   running install_scripts
2023-06-09T16:41:46,167   creating build/bdist.linux-armv7l/wheel/pyspk-1.4.dist-info/WHEEL
2023-06-09T16:41:46,173   creating '/tmp/pip-wheel-bwz228lp/pyspk-1.4-py3-none-any.whl' and adding 'build/bdist.linux-armv7l/wheel' to it
2023-06-09T16:41:46,178   adding 'pyspk/__init__.py'
2023-06-09T16:41:46,181   adding 'pyspk/fit_vals.py'
2023-06-09T16:41:46,186   adding 'pyspk/model.py'
2023-06-09T16:41:46,278   adding 'pyspk/stat_errors_200.csv'
2023-06-09T16:41:46,373   adding 'pyspk/stat_errors_500.csv'
2023-06-09T16:41:46,382   adding 'pyspk-1.4.dist-info/LICENSE.md'
2023-06-09T16:41:46,386   adding 'pyspk-1.4.dist-info/METADATA'
2023-06-09T16:41:46,389   adding 'pyspk-1.4.dist-info/WHEEL'
2023-06-09T16:41:46,391   adding 'pyspk-1.4.dist-info/top_level.txt'
2023-06-09T16:41:46,393   adding 'pyspk-1.4.dist-info/RECORD'
2023-06-09T16:41:46,402   removing build/bdist.linux-armv7l/wheel
2023-06-09T16:41:46,564   Building wheel for pyspk (setup.py): finished with status 'done'
2023-06-09T16:41:46,576   Created wheel for pyspk: filename=pyspk-1.4-py3-none-any.whl size=146354 sha256=dea174bb5bfae84e6b0cc9e4565f70dc0182a66c20f3065689e23598401574a3
2023-06-09T16:41:46,578   Stored in directory: /tmp/pip-ephem-wheel-cache-tmlsv2xz/wheels/a5/22/c5/03201a4d3016d09f5d9a870a5a952bda4dbecf4c3ce173454c
2023-06-09T16:41:46,605 Successfully built pyspk
2023-06-09T16:41:46,624 Removed build tracker: '/tmp/pip-build-tracker-xb7qpta8'