# Testing Screening Mechanisms with Mass Profiles of Galaxy Clusters

## Abstract

**:**

## 1. Introduction

## 2. Theoretical Background

## 3. The MG-MAMPOSSt Method

## 4. Results

#### 4.1. Synthetic Halo Catalogue

#### 4.2. Vainsthein Screening

#### 4.3. Chameleon Screening

## 5. Discussion and Conclusions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Notes

1 | https://github.com/Pizzuti92/MG-MAMPOSSt. (accessed on 25 January 2022), see [13] for the basic usage of the code. |

2 | In the literature the coupling constant is often indicated by $\beta $. However, as $\beta \left(r\right)$ also denotes the velocity anisotropy profile in kinematic analyses of galaxy clusters, we adopt $\mathcal{Q}$ for the coupling to avoid confusion. |

3 | The public version of MAMPOSSt can be found at https://gitlab.com/gmamon/MAMPOSSt, accessed on 25 January 2022. |

4 | Note that ${r}_{\nu}$ is in general different from ${r}_{\mathrm{s}}$ as the distribution of galaxies in clusters may not follow the distribution of the total matter (e.g., [28]). |

5 | In principle ClusterGEN can be used to produce mock clusters adopting different modified gravity setups and matter density distributions. In the exercise presented here we focus only on an NFW profile in GR as our fiducial model. |

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**Figure 1.**Results for the MG-MAMPOSSt and lensing forecast in VS for one halo in the sample. (

**Bottom-left plot**): confidence regions in the space (${Y}_{1},{Y}_{2}$). Dark and light red areas and green and black contours represent the $1\sigma $ and $2\sigma $ regions for the internal kinematic and lensing analysis with 600 tracers and for the lensing simulation only, respectively. (

**Upper and bottom-right plots**): marginal posteriors of ${Y}_{1}$ and ${Y}_{2}$. Red lines are for the lensing and kinematics analysis with $N=600$ tracers, blue dashed curves are for the case with $N=100$ tracers and green dash-dotted curves show the lensing-only distributions. The GR expectation (i.e., ${Y}_{1}={Y}_{2}=0$) is indicated by the black vertical dashed lines. From [22].

**Figure 2.**Results for the joint lensing and internal kinematics analysis of the synthetic haloes in our sample. The shaded areas show the allowed regions in the plane $({\mathcal{Q}}_{2},{\varphi}_{2})$ at $3\sigma $ (outer region) and $2\sigma $ (innermost region). (

**Left panel**): 100 tracers in the MG-MAMPOSSt fit. (

**Central panel**): 600 tracers in the MG-MAMPOSSt fit. (

**Right panel**): combination of 10 clusters, 600 tracers considered in each halo. The black dashed curves are lines of constant $\varphi /\mathcal{Q}$ while the vertical brown dash-dotted lines indicate value of the coupling $\mathcal{Q}=1/\sqrt{6}$ corresponding to $f\left(\mathcal{R}\right)$ gravity. From [22].

**Table 1.**Constraints at 95% C.L obtained for the parameters of the two modified gravity models presented in this work applying the MG-MAMPOSSt fit with additional lensing information over the mock catalogue of synthetic halos with ${r}_{200}=2.0\phantom{\rule{0.166667em}{0ex}}\mathrm{Mpc}$ and ${r}_{\mathrm{s}}=0.3\phantom{\rule{0.166667em}{0ex}}\mathrm{Mpc}$. From column two to column six: Vainshtein screening. Column seven and eight: scalaron field in general chameleon $f\left(\mathcal{R}\right)$ gravity, related to chameleon field ${\varphi}_{\infty}$ through Equation (13). For both models we show the results when using ∼600 and ∼100 cluster members in the MG-MAMPOSSt fit.

Vainshtein Screening | $\mathit{f}\left(\mathcal{R}\right)$ Gravity | |||||
---|---|---|---|---|---|---|

$\mathit{N}=\mathbf{600}$ | $\mathit{N}=\mathbf{100}$ | $\mathit{N}=\mathbf{600}$ | $\mathit{N}=\mathbf{100}$ | |||

${\mathit{N}}_{\mathrm{h}}$Clusters | ${\mathit{Y}}_{\mathbf{1}}$ | ${\mathit{Y}}_{\mathbf{2}}$ | ${\mathit{Y}}_{\mathbf{1}}$ | ${\mathit{Y}}_{\mathbf{2}}$ | $|{\mathit{f}}_{\mathcal{R}\mathbf{0}}|$ | $|{\mathit{f}}_{\mathcal{R}\mathbf{0}}|$ |

1 | ≲2.75 | $0.{08}_{-0.28}^{+0.32}$ | ≲$3.56$ | $0.{10}_{-0.40}^{+0.44}$ | – | – |

5 | ≲1.65 | $0.{06}_{-0.18}^{+0.20}$ | ≲$1.87$ | $-0.{08}_{-0.20}^{+0.31}$ | ≲$3.37\times {10}^{-5}$ | ≲$5.13\times {10}^{-5}$ |

10 | ≲$1.24$ | $-0.{05}_{-0.13}^{+0.17}$ | ≲$1.65$ | $0.{01}_{-0.17}^{+0.24}$ | ≲$1.12\times {10}^{-5}$ | ≲$3.24\times {10}^{-5}$ |

15 | $0.{04}_{-0.39}^{+1.00}$ | $0.{01}_{-0.09}^{+0.12}$ | ≲$1.20$ | $-0.{01}_{-0.16}^{+0.19}$ | ≲$9.51\times {10}^{-6}$ | ≲$2.43\times {10}^{-5}$ |

20 | $0.{08}_{-0.34}^{+0.77}$ | $0.{01}_{-0.08}^{+0.09}$ | ≲$1.02$ | $0.{01}_{-0.14}^{+0.16}$ | ≲$7.11\times {10}^{-6}$ | ≲$1.79\times {10}^{-5}$ |

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**MDPI and ACS Style**

Pizzuti, L.
Testing Screening Mechanisms with Mass Profiles of Galaxy Clusters. *Universe* **2022**, *8*, 157.
https://doi.org/10.3390/universe8030157

**AMA Style**

Pizzuti L.
Testing Screening Mechanisms with Mass Profiles of Galaxy Clusters. *Universe*. 2022; 8(3):157.
https://doi.org/10.3390/universe8030157

**Chicago/Turabian Style**

Pizzuti, Lorenzo.
2022. "Testing Screening Mechanisms with Mass Profiles of Galaxy Clusters" *Universe* 8, no. 3: 157.
https://doi.org/10.3390/universe8030157