The THREEHUNDRED project: the effect of baryon processes at galaxy cluster scale

The role of baryon models played in hydrodynamic simulations is still unclear. Future surveys that use cluster statistics to precisely constrain cosmology models require a better understanding of that. With the hydro-simulated galaxy clusters from different baryon models (Gadget-MUSIC, Gadget-X and Gizmo-SIMBA) from the THREEHUNDRED project, we can look into more details of this question. We find that the galaxy cluster mass change due to different baryon models is at a few per cent level. However, the mass changes can be positive or negative, which is depending on the baryon models. Such a small mass change leaves a weak influence (slightly larger compared to the mass changes) on both the cumulative halo numbers and the differential halo mass function (HMF) above the mass completeness. Agreed to the halo mass change, the halo mass (or HMF) can be increased or decreased with respect to the dark-matter-only (DMO) run depending on the baryon models.


Introduction
More than a decade before, theoretical studies on structure and galaxy formations are relying N-body DMO simulations, see the well-known Millennium simulations [1] and the Multi-Dark simulations [2], for example. As we can only directly observe the galaxies in the sky and simulations only contains gravitational bound objects -dark matter halos, there is a missing connection between observation -galaxies, and theoretical prediction -dark matter halos. Thus, numerous techniques, such as hydrodynamic simulations, semi-analytic models, empirical forward modelling, subhalo abundance modelling and halo occupation models (from more physical models to more empirical models), are developed to bridging this connection [see 3, for a recent review]. Ideally, we would like to model the baryon process as physical as we could. However, limited to the current computation power, unknown baryon processes or uncompleted baryon models implemented in the simulation codes [see 4, for the current development of baryon models in hydrodynamic simulations] as well as the dependence on the simulation resolution [5], we are still facing difficulties to fully model galaxy formation at the non-linear scales. Nevertheless, the hydrodynamic simulation with baryon evolved simultaneously inside is the only way to understand the difference between these DMO simulations and the effects of baryons on them. Numerous work has studied the effects from different aspects [see 6, for a review]. However, no clear agreement has been reached, especially at the non-linear scale.
Galaxy clusters as the one of the independent constraints on cosmology model parameters, will be able to provide precise values of σ 8 and Ω m with errors at around 0.1 percent from the next-generation space telescopes [see 7, for example], such as EUCLID, CSST. Therefore, theoretically understanding the cluster masses, especially their changes according to different baryon models, is essential to accurately constrain cosmology parameters [see 8, for a detailed discussion]. In this short article, we will probe this question, focusing on the galaxy cluster scale with clusters simulated with different codes from the THREEHUN-DRED project [9]. The outline of this paper is following: the THREEHUNDRED project is introduced at Sect. 2; the effects of baryons on the halo mass and HMF are presented in Sect. 3; we finally list the conclusions and discuss our results in Sect. 4.

The simulated galaxy clusters from the THREEHUNDRED project
The THREEHUNDRED project [9] is a re-simulation of 324 most massive galaxy clusters (M vir > 8 × 10 14 h −1 M ) 1 from the MultiDark simulation (MDPL2, [2], also refers as the DMO run in this paper) which utilises the cosmological parameters form the Planck mission [10], and has a periodic cube of comoving length 1 h −1 Gpc containing 3840 3 DM particles with a mass of 1.5 × 10 9 h −1 M . Each cluster lies in the highest resolution region of a comoving radius of 15 h −1 Mpc (over 5 times R 200 ) for re-simulations with different baryonic models: Gadget-MUSIC [11], Gadget-X [12,13], Gizmo-SIMBA ( [14] and  in prep. for more details).
These re-simulation regions are generated with the parallel GINNUNGAGAP code 2 : the highest resolution Lagrangian regions share the same mass resolution as the original MDPL2 simulation with gas particles (M gas = 2.36 × 10 8 h −1 M ) split from DM particles. The outside regions are degraded in multiple layers (with a shell thickness of ∼ 4 h −1 Mpc) with lower mass resolution particles (mass increased by eight times for each layer) that eventually provide the same tidal fields yet at a much lower computational costs. The halo catalogue used in this paper is generated with AHF [15] and we mainly focusing on halo masses within two interesting overdensities: 200 and 500, at z = 0, in this paper.
Benefited from the large volume of these re-simulated cluster regions, detailed relations between the central cluster and the filaments connecting to it have been studied [16][17][18]. Furthermore, the cluster backsplash galaxies [19,20] and shock radius [21] have also been well addressed. The advanced baryon models in hydrodynamic simulations allow us to perform a detailed investigation on the cluster properties, such as profiles [22,23], substructure and its baryonic content [24][25][26][27], dynamical state and morphology [28,29], cluster (non-)thermalization [30,31], the fundamental plane [32], and the cluster mass biases [33, for hydrostatic-equilibrium assumption], [34, for sigma-mass relation] and [35, for weaklensing]. Lastly, comparing to the void/field region runs in this project allows us to study the effect of environment [36]; including the self-interacting dark matter run allow us to constrain the dark matter cross-section [37]; It further help us to examine the chameleon gravity [38].

The effects on halo mass and HMF
The effect of baryons on HMF is simply a consequence of the halo mass change. Therefore, we need to firstly investigate the halo mass changes due to the effects of baryon models. This requires a match of the galaxy cluster between different runs. For each DMO cluster, we     to find its corresponding ones. Figure 1 shows the relative mass differences between the hydro-simulated clusters and their DMO counterparts. As there are many clusters, we simply bin them in the DMO cluster mass and show the median values with errorbars. At M 200 , both Gadget-MUSIC and Gadget-X tend to have slightly (at about 1 percent) higher mass than Gizmo-SIMBA which seems about 1 percent lower than the DMO halo mass. Gadget-X shows weak dependence on halo mass, while Gizmo-SIMBA does not within this mass-complete range. At M 500 , all the three hydro runs tends to deviate from the DMO halo mass larger towards opposite directions, besides the highest halo mass end. It also worth to note that the errorbars are slightly larger compared to the ones in the left panel.
At lower halo mass M halo 10 14 h −1 M , the hydro-simulated halo tends to gain mass without AGN feedback [see 39, for example]. However, it is well-known that it is very hard to cease the star formation in galaxies without AGN feedback which will result in unrealistic galaxy properties compared to observation. Including AGN feedback, the hydro-simulated halo tends to lose mass compared to the DMO run [see 40, 41, for example]. At more massive end, this requires a very large volume simulation or zoomed-in simulations like the THREE-HUNDRED to provide statistical information. It seems that the baryon models leave a weak influence (∼ a few percents) on changing these massive cluster masses.
We continue to show the cumulative HMFs in figure 2 for these different runs. The mass completeness of our cluster sample is shown by vertical dashed lines, which is determined by the crossing point between the Gizmo-SIMBA and MDPL2 lines. More details about the mass-complete sample can be found in table 1. Note that these values are slightly different to [9] which used the crossing point between Gadget-X and MDPL2. It is clear that the difference between these cumulative HMFs is very small for the mass-complete sample.
Lastly, in figure 3, the relative differences of these differential HMFs with respective to the DMO run seem to wiggle around 1 with no clear discrepancy within this limited mass range. Calculating the median raitos for all the mass bins with more than 8 clusters, we notice a few to about 10 percent changes depending on the simulations with lower values from Gizmo-SIMBA and higher values for Gadget-X . Similar to the halo mass changes, different baryon models can also change the HMF towards the same opposite directions.

Conclusion and discussion
Use the hydro-simulated galaxy clusters from the THREEHUNDRED project, which was performed using different simulation codes, we investigate the effects of baryon models on the halo mass and HMF by comparing to their DMO counterparts. Limited to our masscomplete sample, we can only statistically present the results at the massive cluster mass scale. We find that the cluster mass changes due to different baryon models is at few percent level. There is a slightly larger deviation for ∆ M 500 than ∆ M 200 . The cluster mass can be increased or decreased with respect to the DMO run and that is model dependent. Such a small change in mass leaves weak influence on the HMF (although slightly higher fractions compared to mass changes). However, different models can alter the changes into different directions of increase or decease, the same as the mass changes.
The effect of baryons on halo mass is tightly connect with the halo mass definition. In this paper, we adopt the commonly used halo masses M 200 and M 500 which are based on the critical density of the universe. Within a fixed radius (not very large), we can expect that baryons condensed in the centre of the cluster will result in a high concentration, thus an increase in mass. While this may result a steep slope and the 200, 500 ×ρ crit can be reached at a shorter distance. Hence, maybe a lower M 200,500 . Therefore, it is also not surprising to see that there is less mass change for M 200 than M 500 as shown in figure 1 [see also 39,40]. We note here that the FoF (Friend-of-Friend) halo definition seems to have a similar problem [see 40, for example]. Furthermore, the effect of baryons may change the centre of the halo [42]. Although this may not happen very frequently, the change due to this mis-centring problem is generally believed to bias towards a lower halo mass.

Acknowledgement
The author would like to thank the amazing organisers of the NIKA2 conference and the THREEHUNDRED project for contribution and collaboration. This work can not be finished without them. WC is supported by the STFC AGP Grant ST/V000594/1 and the science research grants from the China Manned Space Project with NO. CMS-CSST-2021-A01 and CMS-CSST-2021-B01.