MINOT: Modeling of the Intra-cluster medium (Non-)thermal content and Observables prediction Tools

During the last decade, the observations of diffuse radio synchrotron emission towards galaxy clusters have revealed the presence of cosmic ray (CR) electrons and magnetic fields on Mpc scales. However, their origin remains poorly understood to date, and several models have been discussed in the literature. CR protons are also expected to accumulate during the formation of clusters and should contribute to the production of these high energy electrons. In order to understand the physics of CR in clusters, the combining of observations at various wavelengths is particularly relevant. The exploitation of such data requires to use a self-consistent approach including both the thermal and the non-thermal components, capable of predicting observables associated to the multi-wavelength probes at play, in particular in the radio, millimeter, X-ray and gamma-ray bands. We develop and describe such a self-consistent modeling framework named MINOT (Modeling of the Intra-cluster medium (Non-)thermal content and Observables prediction Tools) and make this tool available to the community. The multi-wavelength observables are computed given the relevant physical process, according to the cluster location, and given the sampling defined by the user. We describe the way MINOT is implemented and how to use it. We also discuss the different assumptions and approximations that are involved, and provide various examples regarding the production of output products at different wavelengths. As an illustration, we model the clusters A1795, A2142 and A2255 and compare the MINOT predictions to literature data. MINOT can be used to model the cluster thermal and non-thermal physical processes for a wide variety of datasets in the radio, millimeter, X-ray and gamma-ray bands, as well as the neutrinos emission. [abridged]


Introduction
Galaxy clusters are the largest gravitationally bound structures that are decoupled from the expansion of the Universe, forming peaks in the matter density field. Their assembly has been driven by the gravitational collapse of dark matter (Kravtsov & Borgani 2012), which is believed to dominate the matter content of clusters (about 80% in mass). Clusters are also made of baryonic matter, essentially in the form of hot ionized thermal plasma, called the intra-cluster medium (ICM; about 15%), and galaxies (about 5%). While clusters are used to understand the formation of large scale structures and constrain cosmological models, they are also the place of very rich astrophysical processes and excellent targets to test fundamental physics (see, e.g., Allen et al. 2011, for a review).
Galaxy clusters form through the merging and accretion of other groups and surrounding material (Sarazin 2002), lead-R. Adam, H. Goksu and A. Leingärtner-Goth: Modeling of the ICM (Non-)thermal content and Observables prediction Tools lent reacceleration of seed electrons and/or secondary electrons produced by hadronic interactions. In any case, γ-ray emission is also expected due to the inverse Compton emission arising from the scattering of background photon fields onto relativistic electrons, or the hadronic interaction from cosmic ray protons (CRp) and the ICM (see, e.g., Pinzke & Pfrommer 2010, for the signal expectation based on numerical simulations).
The annihilation or the decay of dark matter particles could also lead to the γ-ray emission from galaxy clusters (see, e.g. Combet 2018) and many searches of such signal have been performed (e.g. Ackermann et al. 2010;Aleksić et al. 2010;Arlen et al. 2012;Abramowski et al. 2012;Combet et al. 2012;Cadena 2017;Acciari et al. 2018). In the case of dark matter decay, galaxy clusters are particularly competitive targets because of linear scaling of the signal to the huge dark matter reservoirs in galaxy clusters. In the case of dark matter annihilation, clusters can be at the same level of flux as dwarfs galaxies when accounting for substructures and they are thus also very relevant targets (Sánchez-Conde et al. 2011;Moliné et al. 2017). However, the limits that one can set on the properties of dark matter depends on the uncertainties associated to the modeling of the background emission, so that accurate CR modeling is also essential for dark matter searches.
Many attempts to detect the cluster γ-ray emission were made using ground-based (e.g., Aharonian et al. 2009;Aleksić et al. 2012;Arlen et al. 2012;Ahnen et al. 2016, at 50 GeV -10 TeV energies) and space-based observations (e.g. Reimer et al. 2003;Huber et al. 2013;Prokhorov & Churazov 2014;Zandanel & Ando 2014;Ackermann et al. 2014. While so far unsuccessful, these searches were in fact very useful to constrain the CR physics and particle acceleration at play in clusters, especially when combined to radio observations (e.g. Vazza et al. 2015;Brunetti et al. 2017). Recently, Xi et al. (2018) claimed the first significant detection of γ-ray signal towards the Coma cluster, using the Fermi-Large Area Telescope (Fermi-LAT) data. However, their results might be confounded by a possible point source due to the limited signal to noise and angular resolution of the observations. While the Fermi-LAT satellite is to continue to take data for several additional years (compared to about the 12 years of data collected so far), major discoveries concerning galaxy clusters are unlikely given the modest increase in statistics that is expected. From the ground, the Cherenkov Telescope Array (CTA, Cherenkov Telescope Array Consortium et al. 2019) should provide a major improvement of the sensitivity accessible in the 100 GeV -100 TeV energy range.
With the construction of such new facility, in order to address the CR physics in galaxy clusters, multi-wavelength observations and analysis are becoming particularly relevant. Indeed, while the presence of cluster CR is accessible essentially in the radio and γ-ray bands, their physics is driven by the continuous interaction with the thermal plasma. When comparing data to modeling, or generating mock observations, the thermal and the non-thermal components should thus be modeled together, in a self-consistent way, in order to account for uncertainties and degeneracies between the two. The thermal emission can be probed in particular in the X-ray and at millimeter wavelengths, thanks to thermal Bremsstrahlung emission (Sarazin 1986;Böhringer & Werner 2010) and via the thermal Sunyaev-Zel'dovich (tSZ) effect (Sunyaev & Zeldovich 1970, 1972. In addition to the primary components, the modeling of the particle interactions in the ICM relies on particle physics data, both from accelerators or sophisticated Monte Carlo code (see e.g. Kafexhiu et al. 2014, for discussions), and it should be accounted for carefully.
Nevertheless, the modeling of clusters is usually performed focusing on individual (or just a few) components and no public self-consistent multi-wavelength software exists in the literature. For instance, Li et al. (2019) and Brüggen & Vazza (2020) recently modeled the diffuse radio synchrotron emission in the case of radio halos and radio relics, respectively, and employed the Press-Schechter formalism to estimate the statistical properties of the corresponding signal.
Here, we present a software dedicated to the self-consistent modeling of the thermal and non-thermal diffuse components of galaxy clusters, for which the main objective is the computation of accurate and well characterized multi-wavelength predictions for the radio, millimeter, X-ray, γ-ray, and neutrinos emission. This software is named MINOT -Modeling of the Intracluster medium (Non-)thermal content and Observables prediction Tools -is based on the Python language, and is available at the following url: https://github.com/remi-adam/ minot. MINOT includes various parametrizations for the radial profiles and spectral properties of the different components of the clusters. The code does not aim at computing the production rate of CR from microphysics considerations (e.g. turbulence, shocks, diffusion), but instead directly models the spatial and spectral distributions of the CR and of the thermal gas. The predictions for associated observables are available in the radio (synchrotron), millimeter (tSZ effect), X-ray (thermal Bremsstrahlung), γ-ray (inverse Compton and hadronic processes), and also for neutrino emissions (hadronic processes). This includes surface brightness profiles or maps, spectra, and integrated flux computed with different options. Regarding the γ-rays, cosmic ray electrons (CRe), and neutrinos from hadronic origin, MINOT includes a state-of-the-art description of the hadronic interactions in the ICM, based on the Naima software (Zabalza 2015). The thermal modeling uses the XSPEC software for X-ray predictions (Arnaud 1996), and includes accurate description of the tSZ signal up to high plasma temperatures.
This article is organized as follows. In Section 2, we provide a general overview of the code and discuss the different interfaces at play. Section 3 discusses the physical modeling of the cluster components. The physical processes related to particle interactions are detailed in Section 4. In Section 5, we discuss the prediction of observables in the relevant energy bands. The use of MINOT is illustrated in Section 6 using three nearby massive well known clusters for which multi-wavelength data are available in the literature. Finally, Section 7 provides a summary and concludes. In the text, equations are given following the international system of units.

General overview and structure of the code
MINOT is a python based code available at https://github. com/remi-adam/minot 1 . It essentially depends on standard python libraries, but some functionalities require specific softwares and packages, as discussed below. In this section, we provide a general overview of the working principle of the code, of its structure, and the interactions between the different modules. The list of the code parameters is also discussed, as well as the available functional forms for the radial and spectral models. Figure 1 highlights how the input modeling is used to generate observables via the different plasma processes considered in MINOT, and the general overview of the code is illustrated in Fig. 2.

Overview of the physical modeling
MINOT was first developed to compute accurate γ-ray prediction for galaxy clusters. As discussed below and as can be seen in Fig. 1, this requires several key ingredients. Because the same ingredients also provide other observable diagnosis at different wavelengths, via various physical processes, MINOT was further developed to account for them. This allows us to provide external constraints to a given input modeling used to generate γ-ray observables, but also to provide further diagnosis on the cluster physical state.
First, the spatial and spectral distribution of primary cosmic ray electrons (CRe 1 ) and protons are crucial. They generate γ-rays via inverse Compton scattering on the Cosmic Microwave Background (CMB), or via hadronic interactions, respectively. The modeling of the thermal gas is also essential because hadronic processes arise from the interaction between CRp and the thermal plasma. As we will see in Section 3, the thermal component is based on the thermal electron pressure and density. Additionally, the normalization of the CR distributions are generally given relative to the thermal energy. The hadronic interactions also generate secondary cosmic ray electrons and positrons (CRe 2 ). Since they are affected by synchrotron losses, they require to account for the magnetic field as another key ingredient of the input modeling (Section 4). These electrons will contribute to the inverse Compton emission (Section 5). In summary, the necessary input modeling ingredients are: the CRe 1 , the magnetic field strength, the CRp, and the thermal electron pressure and density.
With these ingredients at hand, one can model the radio emission that arises from CRe (primary and secondary) moving in the magnetic field. Similarly, the thermal pressure and density allow us to compute the tSZ signal and the thermal bremsstrahlung X-ray emission. They also provide a complete diagnosis of the cluster thermodynamic properties. Neutrinos are also produced during hadronic interactions, and their associated observable is thus available.

Code structure
In order to model galaxy clusters and predict observables associated to the diffuse thermal and non-thermal components, MINOT is organized in six main parts, each of them being related to specific functions and procedures.
1. The main class, called Cluster, is written in the file model.py and provides an entry point to the user. It allows to define the model and deal with the entanglement between parameters. 2. A sub-class, called Admin allows us to deal with administrative tasks, in particular handling input/output procedures. 3. The Modpar sub-class is dedicated to the model parametrization, gathering a library of available radial and spectral models. 4. The physical modeling of the cluster is performed in the Physics sub-class. It includes many functions to retrieve the desired physical quantities. 5. The Observable sub-class allows us to extract the requested cluster observables based on the inner physics encoded in the model.
6. Finally, the sub-class called Plots is designed for automated plots to provide a cluster diagnostic based on the current modeling.
In addition to these six main parts, MINOT also includes a library called ClusterTools in which numerical tools and astrometric tools are defined. It also includes several classes used to deal with various physical processes relevant for MINOT. In the following Subsections, we highlight the working principle of the different functionalities.

Initialization and parameters
As illustrated in Fig. 2, the user can directly define a cluster object calling the Cluster (main) class of MINOT, as: cluster = minot.Cluster(optional parameters) Optional parameters, such as cluster name, coordinates or redshift, can be passed directly to the initialization call. However, any parameter can be modified on the fly, such as: The entanglement between parameters is dealt with in the code. For instance, changing the cluster redshift will automatically change the cluster's angular diameter distance according to the current cosmological model. Information is provided to the user in the case the 'silent' parameter is set to 'False'. The list of parameters that describe the cluster object is available in Table 1. We note that whenever possible, the code is using Astropy units to deal with quantities 2 . We can distinguish four types of parameters, as can be seen in Table 1. The first type corresponds to administrative-like parameters (e.g. output directory used for generating products), the second one concerns the global properties of the cluster object (e.g. the redshift), the third one is related to the radial and spectral modeling of the cluster physical quantities of interest (e.g. CR number density profile), and the last one allows the user to deal with the sampling of the output observables. In particular, it is possible to set a map header (e.g. obtained for real data) on which the model prediction maps will be projected, which eases the data versus model comparison.

Modeling of the cluster physical state
The parameters describing the cluster can be divided into two kinds: global properties that apply to the entire cluster (e.g. the mass, the redshift, the coordinates), and properties which vary as a function of radius or energy. This separation is highlighted in Table 1. We can see that some parameters are assumed to be constant over the entire cluster volume, such as the hydrostatic mass bias, or the metal abundances.
In addition to the global properties, the primary quantities that are used to define the physical state of the cluster are (see also Section 3 for further details): the thermal electrons gas pressure, the thermal electrons gas number density, the CRp number density profile and spectrum, the CRe 1 profile and spectrum, and the magnetic field strength profile. The CR distributions are normalized according to the ratio between CR and thermal energy enclosed within a given radius. The physical modeling of the radial and spectral properties of the cluster relies on a library of predefined models, in the Modpar sub-class of MINOT. The list  of models that are currently available in the code are given in Tables 2 and 3 for the spectral and spatial component, respectively. Figure 3 provides an illustration of the shape of the different models; they will be further discussed in a more physical context in Section 3. Note that for the moment, the spatial and spectral parts of the modeling are decoupled (e.g., the spectrum of CRp does not change with radius), such that a physical quantity f can be expressed as where E is the particle energy (only relevant for the CR) and r is the physical radius in three dimensions. However, functions that couple the radius and the energy dependence are ready to be implemented in the model library, as any calculations relying on the modeling of f (r, E) are done on 2D grids (energy versus radius) that are ignorant about the underlying parametrization of the distributions. In addition, it is possible to apply some losses, assuming a given scenario, to the input distribution. In this case, f (r, E) is considered as an injection rate and the output distribution will be affected differently for different energy and radii. The implementation of the losses will be discussed in detail in Section 4.2. Setting a new model to a given physical property is done by passing a python dictionary, such as:  It is also possible to automatically set a parametrization of several quantities to a predefined physical states without directly setting the model parameters, e.g. forcing the CRp to follow the radial distribution of the gas density: cluster.set_density_crp_isodens_scal_param () or to define the thermal electron number density based on the thermal electron pressure in the case of an isothermal cluster with a given temperature. These functions are written as part of the Modpar sub-class.

Derived physical properties and observables
Once the desired physical properties of the cluster have been set, functions related to the physical description of the cluster, from the sub-class Physics, can be called to extract the thermodynamic and CR properties of the cluster, or the production rate of non-thermal particles (the physical modeling will be further detailed in Section 3), e.g. extracting the hydrostatic mass profile, or the neutrino emission rate via: r, M = cluster.get_hse_mass_profile() dN_dEdVdt = cluster.get_rate_neutrino() Table 2. List of spectral models.

Model name Function
Dictionary keys PowerLaw User f (E) = anything 'name', 'User', 'energy', 'spectrum' Note: in addition to these models, the parameter cre1 loss model allows to apply an energy loss to the given parametrization, thus modifying its energy distribution (with a radial dependence). In this case, the parametrizations given here correspond to the injection rate q(E, r) and not the actual CR distribution J CR ≡ dN CR dEdV given in Eq. 15. See Section 4.3 for further details, and in particular Eq. 33 for the steady state scenario.   (1, 50 kpc, 0.7) ; the SVM model parameters are (n 0 , r c , β, r s , γ, , α) = (1, 50 kpc, 0.7, 1500 kpc, 3, 4, 0.5) ; the GNFW model parameters are (P 0 , r p , a, b, c) = (1, 200 kpc, 1.5, 4, 0.3) ; the double β-model parameters are (n 01 , r c1 , β 1 , (n 02 , r c2 , β 2 ) = (1, 50 kpc, 0.7, 5, 5 kpc, 2). Right: Illustration of the different spectral models available in the library. The index is set to α = 2.3 for all models, and the cutoff or break energy to E break/cut = 1 GeV. In both cases, the 'User' model is not shown, but allows to pass any arbitrary function that will be interpolated in the code.
The user may also generate observables corresponding to the radio synchrotron emission, the tSZ signal in the millimeter, the thermal Bremsstrahlung in the X-ray, the inverse Compton emission and the hadronic emission in the γ-rays, or the associated neutrino emission (see also Section 5 for more details). This is implemented in the sub-class Observable of MINOT, e.g.: E, dN_dEdSdt = cluster.get_gamma_spectrum() Note that many of the functions or sub-classes related to the physical processes that are called, when running such function, are gathered in the ClusterTools sub-directory, which also includes many numerical tools.

Administrative functions
Once defined, the cluster object also includes various administrative functions, gathered in the sub-class Admin. They can be used to: display the current values of the parameters save the current status of the cluster object, or load a previously saved model generate output observable products automatically (maps, profiles, spectra) get the header of the current map The generation of automatic plots corresponding to the various observables included in MINOT is also available using the subclass Plots.

Baseline model and test clusters
In the following sections, we will use different cluster models to illustrate the behavior of the MINOT code. First, we define a baseline cluster model using parametric functions in order to show how changes in the modeling affect the observables. The baseline properties of the cluster are set using a GNFW thermal electron pressure profile with (P 0 , c 500 , a, b, c) = 2.2 × 10 −2 keVcm −3 , 3.2, 1, 5, 3.1, 0.0 , and a SVM thermal electron number density profile with (n 0 , r c , β, α, r s , γ, ) = 3 × 10 −3 cm −3 , 290 kpc, 0.6, 0.0, 1000 kpc, 3, 1.7 , which correspond to a typical massive merging cluster. The redshift is set to z = 0.02 and the mass to M 500 = 7 × 10 14 M , inspired by the Coma cluster. The CRp follow an exponential cutoff power law spectrum, with spectral index 2.4 and cutoff energy of 100 PeV. The normalization is set to have a CRp to thermal energy ratio within R 500 of 10 −2 , which corresponds to the typical expected values according to Pinzke & Pfrommer (2010). The CRe 1 follow a continuous injection spectrum, with injection spectral index 2.3 and break energy of 5 GeV. The normalization is set to have a CRe 1 to thermal energy ratio within R 500 of 10 −5 , that is about the proton value scaled by the proton to electron mass ratio (i.e. assumes similar Lorentz factor distribution for the two). The spatial profile of both CRp and CRe 1 is set to the same shape as the thermal gas density (see Section 3.2). The magnetic field profile is set to follow the square root of the thermal gas density, and normalized to have an amplitude of 5 µG, assuming similar properties as the one measured for the Coma cluster (Bonafede et al. 2010). These model, referred to as Baseline in the following, will be varied whenever illustrating the impact of relevant quantities to the cluster physical state or observable.
In addition to this baseline model, it is also useful to use real clusters, with the aim of comparing our model predictions to measurements available in the literature. To do so, we need clusters for which the thermal properties have been measured, and are available, over a large range of spatial scales, in order to calibrate our model as best as possible. The sources targeted by the XMM Cluster Outskirt project 3 are perfectly suited for this purpose because the project allowed for the precise measurement of the thermal pressure and density profiles of nearby galaxy clusters from about 10 kpc to the cluster outskirts, thanks to XMM-Newton and Planck data (Tchernin et al. 2016;Eckert et al. 2017;Ghirardini et al. 2019). Because we are interested in the non-thermal component of the ICM, we select from the 12 XCOP clusters those for which a diffuse radio halo have been observed, using the GalaxyCluster database 4 , and for which Fermi-LAT constraints have been obtained by Ackermann et al. (2014). We are left with three objects: 1) Abell 1795, a relaxed cool-core system; 2) Abell 2142, an elongated, dynamically active cluster, but presenting a cool-core; 3) Abell 2255, a merging cluster with a very perturbed core (see also the recent work by

Physical modeling of the primary components
In this section, we discuss the physical modeling of the cluster. First, the global cluster properties are briefly discussed, as well as several assumptions employed in the modeling. Then the properties of the thermal and non-thermal components are detailed. The cluster modeling relies on primary base physical quantities, from which other cluster properties can be derived, in particular in the case of the thermal component. The choice of the base quantities is discussed. Then, the derivation of the secondary quantities that characterize the cluster are developed both for the thermal and non-thermal components.

Global properties and assumptions
Before modeling the inner structure of the clusters, it is useful to characterize the global cluster properties, as listed in the second block of parameters in Table 1.
The cluster location is defined in terms of redshift and sky coordinates. From the redshift, and given a cosmological model, the angular diameter and luminosity distances are computed and used latter in the code. The default cosmological model is based on Planck Collaboration et al. (2016b), but can be modified if necessary.
Even if it does not play a direct role in the modeling, the characteristic mass of the cluster M 500 5 is part of the global parameters. It can be used to set several internal properties of the cluster, to their universal expectation, according to the fact that clusters are, at first order, self-similar objects (in particular for the thermal pressure, see Arnaud et al. 2010). The value of M 500 also allows us to dispose of a characteristic radius, R 500 (see also Eq. 14).
It is also worth emphasizing one of the global parameters, the truncation radius, which is used in MINOT in order to set a physical boundary to the cluster, beyond which the density drops to zero. This is not only useful for numerical issues when integrating cluster properties, but could be associated to the accretion shock radius at which the kinetic energy from accreting structures is converted into thermal energy (see, e.g. Hurier et al. 2019, for the observation of such accretion shock).
In the modeling, the plasma is assumed to be fully ionized and to follow the ideal gas law. The ions and electrons are assumed to be in thermal equilibrium (see Fox & Loeb 1997, for discussions about the temperatures of electrons and ions). While it could in principle depend on radius, the hydrostatic mass bias, the helium mass fraction, and the metallicity of the cluster are assumed to be constant (see, e.g. Leccardi & Molendi 2008;Nelson et al. 2014, for measured cluster metallicity profiles and simulations of the non-thermal radial profile). Some of these parameters, related to the global properties of the cluster, will be further discussed in the following subsections.

Thermal component
The base thermal properties are the electron number density and the electron pressure profiles. This choice is motivated by the fact the X-ray emission is directly sensitive to the electron number density, while the tSZ effect probes the electron pressure, but other choices could have been made (e.g. density and temperature). Generic literature parametric models are available, such as the β-model (Cavaliere & Fusco-Femiano 1978) or one of its extension the Simplified Vikhlinin model (SVM, Vikhlinin et al. 2006) generally used to describe the thermal density cluster profiles. The generalized Navaro-Frenk-White (Nagai et al. 2007) profile is also available, and is generally used to describe the thermal pressure profile (Arnaud et al. 2010;Planck Collaboration et al. 2013). See Table 3 for the parametrization of these models. In all cases, the different parameters can be used to control the amplitude, the characteristic/transition radius and the slopes at different radii. In Fig. 3, we show examples of these profiles for a given set of parameters.
With the electron pressure, P e (r), and electron number density, n e (r), profiles at hand, it is possible to compute the total gas pressure P gas (r) = µ e µ gas P e (r), and the thermal proton number density profile as n p (r) = µ e µ p n e (r).
The mean molecular weights, µ gas , µ e , µ p , µ He , are computed from the helium primordial abundance and the ICM metallicity, as where Y 0.27 is the helium mass fraction and Z 0.005 is the heavy elements mass fraction (defined via the solar reference metallicity multiplied by the metal abundance, see Table 1). Here, we have used the approximation that N charge +1 N nucleon 1/2 for all metals, with N charge the number of charge and N nucleon the number of nucleons.
It is also straightforward to compute the temperature assuming the ideal gas law, as k B T e (r) = P e (r)/n e (r) ≡ k B T gas (r).
Similarly, the electron entropy index, which records the thermal history of the cluster (Voit 2005), can be defined as Both the temperature and the entropy are useful diagnostics of the ICM. They can show the presence of a cool-core (e.g. Cavagnolo et al. 2009), itself related to the central AGN activity and possibly to its CR feedback onto the surrounding gas (e.g. Ruszkowski et al. 2017). They provide information on the dynamical state and accretion history of the cluster, which are connected to its CR content (e.g., radio emission that switches on during mergers, Rossetti et al. 2011). The thermal energy density stored in the gas is given by and can be integrated over the volume, to get the total thermal energy up to radius R. Such quantity will be very useful when comparing to the amount of energy stored in the CR. The cluster total mass within radius r, under the approximation of hydrostatic equilibrium, is given by The hydrostatic mass is known to be biased with respect to the actual total mass (see e.g. Pratt et al. 2019, for a review on the cluster mass scale). The two can be related via where b HSE is the hydrostatic mass bias (see Table 1), which is assumed to be constant (see Planck Collaboration et al. 2014, for detailed discussions about the value of the bias, expected to be b HSE ∼ 0.2). Based on the electron number density, the gas mass within radius R can be computed as and provides a measurement of the available target mass for the interaction with CRp. The gas fraction can be derived using  Table 4, as computed based on the modeling of the thermal electron pressure and density (i.e. the base quantities used to derive the other ones). Note that the truncation radius can be seen at r = 5 Mpc, where all distributions drop, except for the integrated ones that remain constant afterwards. For the entropy profile, we also show the expectation for purely gravitational collapse (Voit 2005). For the gas fraction, the ratio between the mean baryon density and the mean matter density is shown as a dashed line. We also report the radius at which a density contrast of 500 (i.e. R 500 ) is reached on the over-density profile.
The over-density profile is computed using ρ c (z), the critical density of the Universe, via which allows us to extract the value of the characteristic radius, R ∆ , within which the density of the cluster is ∆ times the critical density of the Universe at the cluster redshift. The value of ∆ is generally taken to 500. The enclosed mass within R ∆ is then All the quantities defined here can be extracted as a function of radius from MINOT, according to a given cluster model, using the dedicated functions that are located in the Physics subclass. In Fig. 4, we provide an illustration of the main thermodynamic properties of our baseline cluster model and the three Abell cluster models discussed in Section 2.7. We show the thermal electron pressure, electron number density, gas temperature, entropy, enclosed thermal energy, enclosed gas mass, enclosed hydrostatic mass, gas fraction, and over-density contrast.
We can see that depending on the dynamical state and the presence or not of a cool-core, the profiles are different. For instance, A1795 clearly presents a high density cool-core given its temperature and entropy profiles. Its large scale electron pressure and density fall quickly, consistent with a compact, relaxed morphology. On the contrary, A2255 and our Baseline model show disturbed cores with a high entropy floor, and their pressure and density profiles are much flatter on large scales consistent with a redistribution of the thermal energy due to a merging event. A2142 is an intermediate case. It presents a peaked density profile (showing the presence of a compact core), but its pressure profile is relatively flat on large scales, typical of disturbed clus-ters. Because particle acceleration is expected to depend on the cluster dynamical state, these thermodynamic diagnosis are useful to characterize individual clusters in the context of understanding cluster CR physics.
The enclosed thermal energy is directly related to the pressure profile. It is particularly relevant here because it will provide a normalization for the amount of CR (see Section 3.3). Given its high pressure profile, and thus thermal energy, and its large density (which implies a high gas mass), A2142 would thus be the best target to search for γ-rays from proton-proton interaction in our sample, assuming the same CR distribution for all clusters.
The hydrostatic mass provides a direct way to measure the cluster total mass profile (given a hydrostatic bias, Eq. 10). This can be particularly relevant to model the γ-ray signal associated to the decay or annihilation of dark matter particles (usually done assuming a NFW dark matter density profile with a given concentration and normalization). In addition, the gas fraction gives the ratio between the amount of dark matter and the amount of gas, which is expected to provide a proxy for the dark matter signal to CR background when performing indirect dark matter searches using clusters, and thus an indication for the best targets. The over-density contrast allows us to measure the radius R 500 (or R 200 ), and thus the corresponding mass.
For further discussions about the thermodynamic properties of galaxy clusters using a similar framework, we refer to the recent work by Tchernin et al. (2016)

Non-thermal component
The base non-thermal properties of the cluster are the magnetic field strength, the spectra and profile of the CRp, and the CRe 1 . The CRe 1 differ from the CRe 2 as they correspond to a population that have been accelerated from the plasma microphysics (e.g., shocks, or turbulences, as for CRp), while the secondaries are the product of hadronic interactions (see Section 4 for further details). The radial models available for the non-thermal component are the same as for the thermal one (see Table 3). Regarding the spectral distributions, current available models are listed in Table 2. While all these models could in principle be attributed to either the CRp or the CRe 1 , the initial injection (Jaffe & Perola 1973) and continuous injection (Pacholczyk 1970) models are expected to account for electron losses and are thus not well suited for CRp (see Turner et al. 2018, for discussions about the parametrization). We note that the minimal and maximal energy of the CR are part of the parameters and it is possible to use this parameters to truncate the spectra. By default, the minimal energy of CRp and CRe 1 correspond to the energy threshold of the proton-proton interaction, and the rest mass of the electrons, respectively. Finally, it is also possible to use these parametric function for the injection of CRe 1 , and apply losses (see Section 4.2 for details) to obtain the actual electron population. In Fig. 3, example spectra are shown for the CRe 1 . The implication of these spectra on the observables will be shown in Section 5.
At the moment, the radial and spectral distributions of the CR are decoupled, and we can express the CR distribution (i.e. the CR number density per unit energy) as where A CR is the normalization, and f 1 (E) and f 2 (r) are the spectral and radial distributions, respectively (see Table 2 and 3 for available models). In principle, the functions f 1 and f 2 could be merged into f 1,2 (r, E) to include a radial dependence of the spectral component, but such function has not been implemented yet.
In the case of applying losses to the input distribution, there is however a radial dependence that affects the spectrum, because losses themselves depend on the radius (see Section 4.2 for details).
In order to normalize the CR distribution, we compute the energy density stored between energy E 1 and E 2 , which can be expressed by integrating over the energy as and is related to the CR pressure, P CR . Here we assume that the CR are ultra-relativistic particles, with adiabatic index Γ = 4/3. The result is not very sensitive to the upper bound, E 2 = E max,CRp/e , as the CR spectrum generally vanishes rapidly, for a spectral index larger than 2. The default lower bound is set to the minimum proton energy necessary to trigger the pion production, E 1 ≡ E th p , for protons, and to the electron rest mass, for the electrons. The total energy stored in CR enclosed within the radius R can then be computed as The CR to thermal energy density ratio is then given by or similarly, when integrated over the volume up to the radius R.
In practice, the normalization of the CR distribution, A CR , is obtained by setting the value of X CR (R), at a given radius (e.g., R 500 ). Note that this fraction is defined relative to the enclosed energy here, while it is also common to find this definition in terms of pressure in the literature. The two differ by a factor of 2 because the thermal gas is non-relativistic, while the CR are in the relativistic regime.
The CR distributions can be integrated over the energy, as or the radius, as to compute the number density profile within E 1 and E 2 , or the spectrum enclosed within R, respectively. In Fig. 5, we provide an illustration of the integrated CR number density profiles and spectra for the baseline cluster model. As we can see, the CRe 1 and CRp follow the same profile, because they are calibrated to follow the thermal electron number density. The amount of electrons and protons is nearly the same given the chosen normalization. We can see that the number of CR drastically decreases when applying a cut in energy. The spectra show different shapes for the electrons and protons, reflecting our baseline choice (power law for the protons, and continuous injection with a break at 1 GeV for the electrons) and the minimum energy is also different for the two populations. The number of enclosed CR naturally increases with ) CRe1, R < 10 kpc CRe1, R < 1000 kpc CRp, R < 10 kpc CRp, R < 1000 kpc Figure 5. Left: CR number density profile (i.e. CR distribution integrated between E min and E max , as indicated in the legend) for the CRe 1 , and the CRp. Right: CR spectrum integrated over the radius up to a maximal radius, as given in the legend, for both CRe 1 and CRp.

XCR/XCR(Rnorm)
Isobaric scaling (nCR Pgas) Isodensity scaling (nCR n 0.5 gas ) Flat CRp profile (nCR = constant) Baseline + XCOP (color), with nCR ngas Figure 6. Left: magnetic field profile obtained by assuming a fixed magnetic field strength of 5 µG at 100 kpc, and a scaling relative to the thermal density as B ∝ n 0.5 e . Right: CRp to thermal energy profile for different models of the CRp distribution. The color lines are for each real cluster, using the same colors as in the left panel, and with n CRp ∝ n gas . The black lines correspond to variation of the CRp scaling with respect to the thermal gas, in the case baseline cluster model, as indicated in the legend.
increasing radius. Note that the figure would be very similar for the real cluster models because the underlying CR modeling is the same.
In Fig. 6, we show the magnetic field profiles of our cluster models on the left panel, and the ratio between the CRp energy and the thermal energy on the right panel. The magnetic field has been calibrated on the thermal density profile, as B ∝ n 0.5 e , and normalized to 5 µG (at the peak for the baseline model, and at 100 kpc for the real clusters). For the CR to thermal energy, we also vary the CR number density profiles using different scaling relations with respect to the thermal density and pressure to show how the resulting profiles change. However, we note that the exact shape also depends on the shape of the thermal pressure which is kept fixed here. Because the pressure profile is decreasing with radius, setting the CR distribution to a flatter profile leads to a deficit in the center and an increase in the outskirt for the energy ratio X CR . For cool-core clusters, if the CR number density profile follows the thermal density profile, the CR to thermal energy will be boosted in the center since the thermal pressure is low relative to the thermal density in the core (see e.g., the case of A1795). In all cases, the ratio is set to X CR (R 500 ) = 10 −2 .

Particle interactions in the ICM
The physical properties of the ICM, both for its thermal and nonthermal components, have been defined in Section 3. In this section, we can now model the hadronic interactions, which take place in the plasma, generating secondary particles (see also Fig. 1). We also discuss the loss processes that affect them, in particular the electrons.

Production rate of secondary particles from hadronic interactions
The collision between high energy CRp and the thermal ambient gas, produces γ-rays, electrons, positrons, and neutrinos. This is mainly due to the production of pions, via the following interaction chains: When considering the thermal plasma at rest with respect to the CR, the CRp -thermal proton collision rate per unit energy 10 2 10 1 10 0 10 1 10 2 10 3 10 4 10 5 10 6 10 7 Energy ( 10 2 10 1 10 0 10 1 10 2 10 3 10 4 10 5 10 6 10 7 Energy (GeV) With He, with metals With He, no metals 10 2 10 1 10 0 10 1 10 2 10 3 10 4 10 5 10 6 10 7 Energy (GeV) of CRp is given by where σ pp is the proton-proton interaction cross section, v CRp c the speed of CRp, n p the number density of thermal protons, and J CRp the number density per unit energy of CRp. The production rate of secondary particles X per unit volume, unit energy and unit time, can then be expressed as Two ingredients are thus necessary: 1) the total inelastic crosssection of the proton-proton interaction and its evolution as a function of energy, σ pp (E CRp ) ; 2) the number of secondary particles produced in a collision, per unit energy of the produced particle, as a function of the initial energy of the CRp, namely F X (E X , E CRp ). These ingredients are usually obtained by fitting parametric functions to accelerator data, together with Monte Carlo simulations performed with sophisticated codes (e.g. Kelner et al. 2006;Kamae et al. 2006;Kafexhiu et al. 2014).
The Kafexhiu et al. (2014) parametrization was implemented in Naima (Zabalza 2015), a publicly available Python package dedicated to the computation of non-thermal radiation from relativistic particle populations. The work presented here is based on Naima, to which the radial dimension was added, and thus, we also use the work by Kafexhiu et al. (2014) as our baseline.
As we will see below, heavy elements will also have an important contribution to the particle production rate. Such contribution is only available in the work by Kafexhiu et al. (2014), which is also expected to be the most up-to-date, in particular at the highest energies. However, Kafexhiu et al. (2014) only focuses on the γ-ray production rate, while Kelner et al. (2006) also provides a parametrization for the leptons (electrons, positrons and neutrinos), but does not include heavy elements. Therefore, we employ a hybrid approach. We use the parametrization by Kafexhiu et al. (2014) for the γ-ray production and the one from Kelner et al. (2006) for the leptons. To account for heavy elements in the case of leptons, we apply a rescaling of the production rate given by Kelner et al. (2006). To do so, we assume that the ratio between the production rate of leptons and the one of γ-rays does not depend on the inclusion of heavy elements. This is motivated by the fact that Kafexhiu et al. (2014) accounts for heavy elements by using a multiplicative correction to the cross section. In the end, the production rate of leptons is given by While this approach allows us to compute the electron, positron and neutrino production rate in the presence of helium and non-zero metallicity of the ICM, it uses the so-called δapproximation for the ratio of leptons to γ-rays in the high energy regime (see Kelner et al. 2006), which is expected to be a relatively crude approximation (see Kafexhiu et al. 2014). Nevertheless, the accuracy of the lepton to γ-ray ratio should be much better as biases in the spectra are expected to cancel.
In Fig. 7, we provide an illustration of the computation of the secondary particle production rate in the case of our baseline cluster model (see Section 3), with a power-law model with index 2.4 for the CRp.
The left panel shows the relative difference between the Kafexhiu et al. (2014) and Kelner et al. (2006) parametrizations for the γ-ray production rate, when the helium and metals abundances have been set to zero. We use the Pythia8 parametrization from Kafexhiu et al. (2014) as a reference. In practice, the Kelner et al. (2006) parametrization is the combining of a calculation at low energy, and the use of the δ-approximation at high energy, which are both shown as dashed lines. The agreement between Pythia8 and Kelner et al. (2006) is relatively good over most of the energy range (less than 25% for most of it, but with a peak reaching more than 100% around 100 MeV). The different high energy parametrizations available in the work by Kafexhiu et al. (2014), namely using the Monte Carlo codes Pythia8, SIBYLL, QGSJET or Geant4, are also shown. As expected, the difference with respect to Pythia8 is only important at high energy. It remains below 25% for energies below 1 TeV, and increases to more than 50% above 100 TeV (see Kafexhiu et al. 2014, for further discussions). Given the comparison of the top panels of 10 2 10 1 10 0 10 1 10 2 10 3 Energy (GeV)  The middle panel quantifies the impact of accounting for helium and metals in the ICM. The helium mass fraction has been chosen to 0.27 and the metallicity is set to the the solar value. We can see that the helium can boost the signal by more than 50%, especially at low energies, but has an important effect over the full energy range where its contribution remains larger than 40%. The metals, on the other hand, only account for percent level changes in the spectrum. Note that the ratio µ e /µ p depends on the ICM composition, which affects the value of n p for fixed n e , and explains why the γ-ray production rate can get lower in the case of including metals compared to the helium only case, visible around 100 MeV. Given these results, we expect that ignoring the helium contribution will lead to an important systematic effect in the model amplitude, underestimating the signal by about 40-50%.
Finally, the right panel of Fig. 7 provides the particle injection rate for γ-rays, electrons and positrons, and both muonic and electronic neutrinos. The high energy cutoff is due to the maximal energy of the CRp, being set to 10 PeV, while the decrease below 1 GeV is due to the kinematic production threshold of the proton-proton interaction, of about 1.2 GeV. Between these energies, the slope of the secondary particle production rate nearly follows that of the injected CRp, as shown by the black dotted line.

Energy losses
While the neutrinos and the γ-rays can escape the cluster and be detected by ground and space based instruments, the electrons will evolve in the ICM, being affected by several sources of energy loss. Here, we will consider the main sources of energy loss: synchrotron radiation, inverse Compton interaction, Coulomb losses, and Bremsstrahlung radiation.
Let's first define the Lorentz factor of the electrons γ = E m e c 2 , and the reduced speed of the electrons, β = 1 − 1/γ 2 . The synchrotron radiation loss is given (in S.I. units) by Longair (2011) with σ T the Thomson cross section and µ 0 the vacuum permeability. It is proportional to the amplitude of the magnetic field squared, B 2 . Thus, we expect it to be most efficient in the cluster central regions. Given the γ 2 dependency, the synchrotron loss will be more important at high energy. Inverse Compton losses can be expressed in a very similar way (Longair 2011), as where the magnetic field dependence has been replaced by the ambient photon field, assumed to be dominated by the CMB, whose energy density is given by The inverse Compton energy losses do not depend on the cluster location, but increases with redshift due to the CMB dependence.
The Coulomb losses are computed as (Gould 1972) where ω p = e 2 n e m e 0 is the plasma frequency. The Coulomb losses are proportional to the thermal electron number density, thus more effective in the cluster core and are nearly energy independent. Finally, the Bremsstrahlung losses are computed as (Blumenthal & Gould 1970) dE dt Brem.
= −8αcr 2 0 E(n p + 3n He ) ln (2γ) + 1 3 where α = e 2 4π 0h c is the fine structure constant and r 0 = e 2 4π 0 m e c 2 is the classical electron radius. Here, we have neglected elements heavier than helium and used the completely unscreened limit that is appropriate for low density plasma. As for the Coulomb losses, the Bremsstrahlung losses depend on the thermal nuclei number density, however they increase with energy.
In Fig. 8, we provide the loss function for the synchrotron, inverse Compton, Bremsstrahlung, and Coulomb contributions for two different radii, 10 and 1000 kpc, from the center, in the case of our baseline model. We can see that at low energy, the Coulomb losses are expected to dominate, while at high energy, the synchrotron and the inverse Compton will dominate, depending of the relative value of the magnetic field and the CMB photon field. The Bremsstrahlung contribution is always subdominant.

Secondary electrons in the steady state approximation
Once injected in the ICM, the evolution of CRe is expected to follow the diffusion-loss equation (Berezinskii et al. 1990), where n(E, r, t) ≡ dN CRe dEdV is the number of CRe per unit volume and energy, q(E, r, t) is the injection rate, v is the ICM velocity, D(E) is the diffusion coefficient, and where the loss function, (E, r) is given by Assuming that the CRe do not significantly diffuse, and assuming steady state condition, we write the number density of CRe at equilibrium as where q( , r) is computed as the output of Eq. 25. We note that here we do not account explicitly for the possible re-acceleration of seed electrons by ICM turbulences (e.g. Brunetti et al. 2017, and references therein). However, since we are not modeling the details of the microphysics here, such population could be included in the CRe 1 , which is modeled independently as discussed in Section 3.3. By doing so, we would assume implicitly that the re-acceleration process, which would effectively contribute to a loss for our secondary electron population (i.e. a population transfer) is subdominant with respect to the losses. In this case the physical consistency between the different CR populations will not necessarily be verified. While re-acceleration models are beyond the scope of the current work, we leave room for implementing re-acceleration options in the MINOT code in the future.
In Fig. 9, we present the radial profile and the spectra of the CRe 2 in the steady state approximation, with no diffusion. As we can see, the profile gets steeper at higher energy because inverse Compton and synchrotron losses get more important in this regime, relative to the Coulomb loss that is more efficient in the core. We can also see that electrons accumulate around 100 MeV, as lower energy electrons quickly disappear because of Coulomb losses, and higher energy electrons are more affected by inverse Compton and synchrotron losses. We also provide the same profiles and spectra in the case of boosting the magnetic field and the thermal density by a factor of 10. In the latter case, we also decrease the amount of CRp by a factor of 10 so that the rate of proton-proton collision is conserved. We can see that increasing the thermal plasma density leads to a much flatter profile because Coulomb losses are much more important in the core where the density is large. Increasing the magnetic field also flattens the profile, albeit less drastically, since the magnetic field profile is itself flatter. On the spectrum, we see that the magnetic field has a larger impact at high energy, while the increase of the thermal plasma density leads to more losses at low energy. The peak of the secondary electron spectrum will thus depend on the competition between the energy losses in magnetic field and in thermal plasma.

Multi-wavelenght observables
In this section, the physical properties of the cluster (Section 3) and the production of secondary particles in the ICM (Section 4) are used to compute the observables of galaxy clusters related to the diffuse gas component. This includes the tSZ effect, the thermal X-ray emission, the radio synchrotron emission, the inverse Compton emission, and the γ and neutrino emission from hadronic processes. We focus here on the illustration of the implication of the model changes to the observables, using our baseline cluster model.

General considerations
In general, the cluster observables are associated to physical processes at play in the ICM, which can be described in terms of production rate (note that this does not strictly apply to the tSZ signal because it is a spectral distortion, as it will be discussed in Section 5.3). Let's define Q(r, E) ≡ dN dEdVdt , the emission rate associated with the physical process considered. For instance, in the case of X-ray emission, Q would be the number of X-ray photons emitted per unit volume, per unit of time, and per unit energy in the ICM.
The surface brightness (or flux per solid angle), at a projected distance R from the center, is therefore given by integrating Q(r, E) over the line-of-sight, as where the factor D 2 A accounts for the conversion from physical area to solid angle, and the normalization by 4πD 2 L assumes that the emission is isotropic. Note that Eq. 34 is valid in the small angle approximation (i.e. assumes the cluster size to be small against the distance to the observer), which is expected to be accurate for our purpose since the extent of clusters never exceeds a few degrees. It also neglects the redshift extent of the cluster.
From Eq. 34, we now want to compute several quantities accessible from observations: 1) the surface brightness profile ; 2) the spectrum, by integrating the signal over the cluster volume or the solid angle ; 3) the total flux, by integrating over both the volume and the energy (or at fixed energy) ; 4) the map of the signal, which in our case is equivalent to the surface brightness profile because of azimuthal symmetry, but allows us to generate spatial templates for dedicated analysis.
The surface brightness profiles (and maps, respectively), are computed by log-log integration of the quantity dN dEdS dtdΩ (R, E) over the requested energy range, or simply by fixing the energy to the one required by the observation (as done for example in the radio and millimeter domain). In the case of the map, the signal is projected on a grid corresponding to the header (or sampling properties) set by the user. An option allows the user to normalized the map to the total flux so that the map only accounts for the spatial dependence of the signal, in unit proportional to inverse solid angle. This proves useful, e.g., for γ-ray analysis in which image templates are needed.
The spectra are computed in a similar way, by log-log integration over the volume. In this case, two possibilities are available. 1) Integration over the solid angle within a circle of radius R max , so that the total integration volume is a cylinder. 2) The emission rate Q(r, E) can be integrated spherically up to R max before normalization by 4πD 2 L . The two quantities only differ by the definition of the integration volume, and should converge when all the cluster emission is accounted for with increasing R max . The cylindrical integration resembles more what would be accessible directly from observations, while the spherical integration is more natural from a physical point of view since it returns a quantity computed in a single physical (3D) radius.
In order to compute the flux, one should integrate both over the cluster volume and the energy, or fixing the energy, as discussed above. By definition, the luminosity of a given source, within the energy band ∆E ≡ [E 1 , E 2 ], is given by Note that we also apply the redshift stretching to the energy of the photons, even if this can be switched off by the user.

Thermal X-ray emission
Given the gas temperature (a few keV), the density (typically 10 −3 − 10 −5 cm −3 ), the leading emission process at X-ray energies is thermal bremsstrahlung (see Sarazin 1986;Böhringer & Werner 2010, for reviews). The X-ray emission is thus a direct probe for the thermal gas density. It presents a characteristic exponential cutoff at high energies, determined by the gas temperature. The presence of heavy elements also induces a large number of spectral lines. The X-ray surface brightness is generally expressed as where Λ(T e , Z) is the cooling function, which varies with temperature.
In practice, MINOT use the XSPEC software (Arnaud 1996) to compute directly the counts using either the MEKAL or APEC X-ray plasma spectral models. These models require the ICM abundance, the redshift, the temperature, the energy range, and a normalization defined as norm = 10 −14 4π D A 1 cm (1 + z) 2 n e 1 cm 3 n H 1 cm 3 dV. (37) MINOT also account for the foreground photoelectric absorption using the value of hydrogen column density at the cluster location. The XSPEC outputs are then normalized to compute the emission rate (counts or energy) per unit volume and time. It is also possible to account for the response function of X-ray satellites, so that the outputs are normalized by the effective area of the observation. The spectrum, surface brightness profile and maps, and flux, are then extracted as discussed in Section 5.1. In Fig. 10, we provide an illustration of these X-ray observables in the case of our baseline cluster. The two models MEKAL and APEC are in good agreement. The blue dashed spectrum shows the impact of the photoelectric absorption from the foreground, leading to low energy cuts. At high energy, the exponential cutoff is clearly visible and the spectral lines are also visible below 10 keV. The raw signal associated to the inverse Compton emission is also shown, but will be discussed in Section 5.6. We note that it is well below the thermal X-ray emission, but could become significant with increasing energy. The surface brightness profile, computed between 0.1 keV and 2.4 keV drops very rapidly in the outskirt as the signal is proportional to the density squared. The integrated flux reaches about 1 ph cm −2 s −1 at large radii.

Thermal Sunyaev-Zeldovich signal
The tSZ effect results in a distortion of the CMB black-body spectrum due to the inverse Compton scattering onto energetic thermal electrons (see Birkinshaw 1999; Mroczkowski et al. 2019, for reviews). Because it is a spectral distortion, it does not suffer from redshift dimming and the general considerations of Section 5.1 do not strictly apply here. The change in surface brightness, is expressed as with respect to the CMB, I 0 = 2(k B T CMB ) 3 (hc) 2 270.1 MJy sr −1 . The parameter y is the so-called Compton parameter, which gives the normalization of the tSZ effect. It provides a measurement of the thermal electron pressure integrated along the line-of-sight, as The frequency dependence of the tSZ effect is given by where x = hν k B T CMB . The term δ tSZ (x, T e ) is a relativistic correction, which introduces a small temperature dependence to the tSZ effect, and becomes important when the temperature gets larger than about 10 keV, depending on the frequency. The relativistic correction are implemented following the work by Itoh & Nozawa (2003), which is expected to be accurate at the percent level up to 50 keV. When neglecting relativistic corrections, the tSZ spectrum is null at 217 GHz, negative below (with a minimum around 150 GHz), and positive above (peaking at about 350 GHz).  Figure 10. Illustration of the observables associated with the X-ray emission. Left: X-ray spectrum within R 500 shown for both MEKAL and APEC models, as well as with and without galactic photoelectric absorption. Not that the MEKAL model is difficult to distinguish because it coincides very well with the APEC one. Right: surface brightness profile in the band 0.1-2.4 keV. Note that the dynamical range of the profile amplitude has been set to the same value for all observables.  Figure 11. Illustration of the observables associated with the tSZ effect. Left: tSZ spectrum within R 500 . We also provide the spectrum in the case relativistic corrections are neglected for illustration. Right: Compton parameter profile. Note that the dynamical range of the profile amplitude has been set to the same value for all observables.
The tSZ integrated flux, often used to track the cluster mass, can be expressed as in the case of cylindrical integration, or for the spherically integrated flux. Both integrated flux, Y cyl,sph , can be expressed in units of surface, or normalized by D 2 A , to be homogeneous to solid angle as usually done in the literature.
In Fig. 11, we provide an illustration of the spectrum and profile (shown in terms of the Compton parameter) of our reference cluster. The tSZ flux can be significant down to a few GHz, and could thus affect radio synchrotron observations. On the other hand, the synchrotron emission is not shown here, but is much smaller than the tSZ signal in the considered frequency range. Given the linear sensitivity of the tSZ signal to the pressure, the profile is relatively flat (e.g. compared to the X-ray surface brightness).

γ-ray hadronic emission
In the case of high energy photons, one needs to account for the absorption by the extra-galactic background light (EBL, Dwek & Krennrich 2013), thought to have been produced by the sum of all light contributions (e.g., starlight, dust reemission) at all epochs in the Universe. Indeed, while traveling from the cluster to the Earth, γ-rays may interact with the EBL via electronpositron pair production, and thus be effectively absorbed along the way, as with τ(E) the optical depth. EBL absorption depends on redshift and on the energy of the γ-rays. To account for EBL absorption, we use the ebltable Python package 6 , which read in and interpolate tables for the photon density of the EBL and the resulting opacity for high energy γ-rays. This package provide different models for the EBL based on the work by Franceschini et al.  Figure 12. Effect of the EBL on the normalized spectra of a baseline model cluster at z = 0.02. All the available models are shown as indicated in the legend. Note also that because of the redshift stretching, the shape of the γ-ray spectrum slightly changes even in the case of no EBL absorption ('none').
the EBL for various models available in Fig. 12, in the case of redshift z = 0.02 clusters. While it is crucial to account for the EBL, especially at very high energies, the uncertainties associated with the EBL models are expected to be small. The intergalactic magnetic fields should also affect the predictions for the γ-ray observables (e.g., Neronov & Semikoz 2009). However, given the current uncertainties in the properties of the magnetic field, its impact remains uncertain. While such effect is not implemented yet, it is being considered for future improvement of the MINOT code.
The γ-ray production rate resulting from hadronic interaction is computed following Kafexhiu et al. (2014), as described in Section 4.1. We compute the spectrum (within R 500 , using spherical integration) and profile as detailed in Section 5.1. These quantities are displayed in Fig. 13 for our baseline cluster model. As we can see, the spectrum peaks at GeV energies, quickly vanishes at lower energies and is affected by a cutoff at high energy due to the EBL. We also show how the change in the CRp slope affects the γ-ray spectrum, for a fixed normalization X CRp . In the case of a flatter CRp profile, the amplitude of the spectrum is reduced because the amount of proton proton collision is reduced due to a smaller spatial coincidence between thermal and CRp. The inverse Compton signal computed for our baseline model is also shown for comparison, and is below the hadronic emission except at low energy. The profile presents a compact signal because it arises from the product of the thermal electron number density and the CR density. In the case of flattening the CR number density profile, we see that the γ-ray signal gets itself flatter. Nevertheless, it still decreases with radius even in the case of a completely flat CR number density profile because the thermal density profile remains peaked. The inverse Compton signal is expected to be flatter than the one of the hadronic emission, but also lower in amplitude, in our baseline model. The integrated spectrum between 1 GeV and 1 TeV nearly reaches 10 −9 photon cm −2 s −1 in the case of this baseline model.

Neutrinos (hadronic) emission
In contrast to the γ-rays, the neutrinos are not affected by the EBL absorption. Except for the EBL, their observables are com-puted in the same way as the γ-rays associated to hadronic interactions (Section 5.4), with the production rate computed following a combination of the work by Kelner et al. (2006) and Kafexhiu et al. (2014), as described in Section 4.1. Figure 14 provide an illustration of the neutrinos observable, both for the muonic and electronic neutrinos in the case of the spectrum and the profile, and the sum of the two for the flux. In practice, due to neutrino oscillation, one would expect a mixing between the ratio of neutrinos of different flavors. Because the processes associated to the neutrino is the same as the γ-rays, their observables are very close to one another, except for a small difference in the normalization.

Inverse Compton emission
The inverse Compton emission is also affected by the EBL absorption in the high energy limit, and we refer the reader to Section 5.4 and Fig. 13 for this effect.
We use the analytical approximation for the treatment of inverse Compton scattering of relativistic electrons in the CMB blackbody radiation field, given by Khangulyan et al. (2014), expected to be accurate within 1% uncertainty over all the range of application. In particular their Eq. 14 gives us the number of inverse Compton photons produced per unit energy and time, per CRe, as a function of the CRe energy, dN IC dEdt , which we express as with G IC (E IC , E CRe ) an analytical function computed following Khangulyan et al. (2014), using the approximation given by their Eq. 24. We thus integrate this quantity over the electron energy, accounting for the amount of CRe in the ICM. The emissivity is expressed as where J e (E CRe ) ≡ dN CRe dE CRe dV is the CRe number density, summing the contributions from primary and secondary electrons.
In Fig. 15, we provide the illustration of the observables associated to inverse Compton emission for our baseline cluster model. The shape of the spectrum reflects the complex processing of secondary electrons via their production rate in hadronic interaction, their losses in the ICM, and the production of inverse Compton after having also summed the CRe 1 . In particular, we can see that changing the distribution of CRe 1 to an initial injection model removes relativistic electrons with energy larger than E break , and thus no removes the inverse Compton emission at energies above ∼ E break /100. In contrast, when using a power law model, more CRe are present at low energy, which increases the inverse Compton emission in this regime. Regarding the secondary electrons, we can see that the slope of the inverse Compton emission changes according to the slope of the CRp. In addition, as in the case of hadronic emission, flattening the CRp profile decrease the production of secondary particles, and thus that of inverse Compton associated to secondary electrons. The inverse Compton profile is relatively flat for primary electrons, because the signal depends linearly on the CRe spatial distribution. For the secondary electrons, the profile is more compact because the secondary electron are produced proportionally to the product of the thermal gas and the CRp number density. For both populations, we also show the effect of flattening the profiles of either the CRe 1 , or the CRp. The integrated flux reaches 10 2 10 1 10 0 10 1 10 2 10 3 10 4 10 5 10 6 Energy (GeV)  Figure 13. Illustration of the observables associated with the γ-ray hadronic emission. The signal coming from inverse Compton interactions is also shown for comparison. Left: γ-ray spectrum within R 500 . Right: γ-ray profile integrated between 1 GeV and 1 TeV. Note that the dynamical range of the profile amplitude has been set to the same value for all observables.  Figure 14. Illustration of the observables associated with the neutrinos hadronic emission. Left: neutrino spectrum within R 500 . Right: neutrino profile integrated between 1 GeV and 1 TeV. Note that the dynamical range of the profile amplitude has been set to the same value for all observables. more than 10 −11 ph cm −2 s −1 between 1 GeV and 100 TeV, with our baseline model.

Radio synchrotron emission
The MINOT code focuses on the diffuse galaxy cluster emission associated with the bulk of the X-ray emitting ICM. Therefore, in the case of the diffuse synchrotron emission, we focus on the emission associated to radio halos and leave radio shocks (or relics, see van Weeren et al. 2019) aside. As the orientation of the magnetic field is expected to be chaotic in the bulk ICM regions of galaxy cluster, we need to average the standard energy distribution of the synchrotron emission over directions of the orientation of the field. To do so, we follow the results of Aharonian et al. (2010), appendix D, in which the orientation of the magnetic field is assumed to be randomized. This provides a convenient approximation with an accuracy better than 0.2% over the entire energy range (see Aharonian et al. 2010, for more details in the approximation and its accuracy).
As in the case of inverse Compton emission, we express where dN sync dE sync dt = 3e 3 B 8π 2 0 m e chE syncG (E sync /E c ).
The quantity E c = 3eBhγ 2 2m e is the synchrotron characteristic energy andG(x) the emissivity function of synchrotron radiation, which quickly increases from x = 0 to x 0.23 and smoothly vanished for increasing x (see Aharonian et al. 2010).
In Fig. 16, we provide the illustration of the observables associated to synchrotron emission, including both the contribution from primary and secondary electrons. As for the inverse Compton case, the emission reflects the complex processing of secondary electrons, while it is more direct for the primary electrons. In particular, the curvature in the synchrotron emission is due to the losses of CRe at high energies. We can see that when changing the CRe 1 population model to an initial injection scenario, the high frequency curvature is significantly enhanced due to the lack of very high energy electrons. In the case of a power law CRe population, extending to lower energy, the spectrum is enhanced at low frequency. Regarding the secondary electrons, we note that the slope of the CRp directly reflects in the synchrotron spectrum slope. Similarly as in the case of hadronic γray emission, flattening the CRp profile decreases the amount of synchrotron emission because less secondary electrons are pro-   Figure 16. Illustration of the observables associated with the synchrotron emission. Left: synchrotron spectrum within R 500 , with the contribution from both primary and secondary electrons are given. Right: synchrotron emission profile at 100 MHz. Note that the dynamical range of the profile amplitude has been set to the same value for all observables.
duced. As highlighted in the figure, we note that the tSZ contribution is potentially important at high frequencies, and could mimic a curved synchrotron spectrum if not accounted for. The synchrotron profile is more compact than that of the inverse Compton emission because it is also depends on the magnetic field, which decreases with radius. As for the inverse Compton emission, the profile is more compact for secondary electrons due to the dependence on the product of the thermal density and the CRp number density. We also show how the flattening of the CR population reflects in the synchrotron profile. The flux, at 100 MHz, reaches typical values of 10 Jy, in our baseline model.

Comparison to the literature
In order to verify the validity of the modeling and to further illustrate the use of the MINOT code, we compare the model predictions to results obtained in the literature and existing data. To do so, we use the models of the XCOP clusters defined in Section 2.7 and Table 4. We focus on millimeter and X-ray data for the thermal part, and γ-rays and radio data for the non thermal component. Given the current limited sensitivity of neutrino telescopes, and because of the typical predicted fluxes, we leave the neutrino emission model predictions aside.

Thermal gas
First we compare the measured X-ray luminosity given by Eckert et al. (2017) to the one we recover, integrated within R 500 . We use the same values of R 500 and set the MINOT cosmological model to the one used in Eckert et al. (2017) to mitigate differences. The comparison of the obtained rest frame luminosity are given in Table 5. As we can see, we obtain comparable luminosities, with differences of a few percent for A1795 and A2142, but up to 19% for A2255. As our model is based on the interpolation of the results by the XCOP project, we expect consistency between the two. However, our model has been defined by extrapolation of the thermal plasma density profiles down to small radii. While these profile were measured down to about 10 kpc, or even less, for A1795 and A2142, it was only measured down to about 30 kpc for A2255. Thus, uncertainties coming from the extrapolation are likely to be more important for this cluster. The differences that we observe in Table 5 are thus likely due to extrapolation uncertainties.
We also compare the tSZ flux computed using MINOT to the one given in the Planck PSZ2 catalog (Planck Collaboration et al. 2016a). Again, our model is based on the XCOP outputs, themselves obtained using Planck data, so that we expect consistency. As we can see, in Table 6, the total integrated Compton pa-R. Adam, H. Goksu and A. Leingärtner-Goth: Modeling of the ICM (Non-)thermal content and Observables prediction Tools  rameter (i.e. computed within 5R 500 ), are in good agreement for A1795 and A2142, and differ by 2.3 σ for A2255. As A2255 is a strongly merging cluster, the flux arising from the cluster outskirt is likely to be more important than for A1795 and A2142, and the truncation radius involved in MINOT (set at 5 Mpc) may not be enough to account for all the tSZ flux. Indeed, increasing the truncation radius to 10R 500 brings the flux to nearly 18×10 −3 arcmin 2 , in better agreement with the PSZ2 value. As in the case of the X-ray luminosity, the differences that we observe are thus likely due to the interpolation and assumption that we have made in the definition of the clusters. In addition to the fluxes, we also compare directly the X-ray and tSZ images to existing data. We use the publicly available ROSAT (Truemper 1993) X-ray pointed data 7 obtained for our three targets to produce maps in the [0.1, 2.4] keV energy band. The maps are subtracted from the background and normalized by the exposure. The ROSAT PSPC response matrices are accounted for in MINOT via the use of XSPEC, as well as the hydrogen column density taken at the location of each cluster, as obtained by the LAB survey (Kalberla et al. 2005). The model is projected on the same header as the original ROSAT data and accounts for the ROSAT effective area, in units of counts per unit of time and solid angle. We account for the PSF by smoothing our model with a mean effective gaussian function with full width half maximum (FWHM) of 30 arcsec, which is the typical number expected for ROSAT pointed observations. While the detailed analysis of the X-ray data, including all instrumental effects is beyond the scope of this work, this comparison already provides a useful qualitative comparison to our modeling. The data, model, and residual images are displayed on the left panel of Fig. 17. The data and the model are shown on a log scale, while the residual is shown on a linear scale. While the overall agreement is good for all three clusters, we can see several features. First, many point sources, that are not accounted for here, affect the residual. Then, the real clusters are not perfectly azimuthally symmetric, as we see on the residual with a positive/negative butterfly shape in the core of all targets. Finally, we note that the model of A2255 slightly over-predicts the signal, in agreement with its model luminosity being too high, as discussed above.
We also use the MILCA (Hurier et al. 2013) Compton parameter map obtained from Planck (Planck Collaboration et al. 2016c) to compare our tSZ model to real data. We extract a 1 degree × 1 degree sky patch centered on the individual clusters, and project the MINOT Compton parameter map on the same grid for comparison. We smooth the model with a 10 arcmin FWHM Flux above E (s 1 cm 2 ) A2255 Hadronic emission Inverse Compton A2142 A1795 A2255 upper limit A2142 upper limit A1795 upper limit Figure 18. Comparison between the cluster models flux predictions and the Fermi-LAT upper limit from Ackermann et al. (2014). gaussian beam to account for the Planck angular resolution. In the right panel of Fig. 17, we show the data, the model and the residual. The data and the model are shown on a log scale, while the residual is shown on a linear scale. As we can see, the model and the data are in good agreement for all three clusters. Nevertheless, we can still note a small excess in the central part of the A2142 model, which can be explained by the fact that this cluster is slightly elongated, as also seen in the ROSAT image.
In conclusion, we have compared the prediction from MINOT to the X-ray luminosity and tSZ fluxes, finding overall good consistency between the two, with differences being likely explained by uncertainties in the model extrapolation. Similarly, MINOT is able, with dedicated functions, to predict the X-ray and tSZ images associated to a cluster model. The comparison to ROSAT and Planck maps has shown overall good consistency for the targets tested here. In the context of the modeling of the nonthermal component of galaxy clusters, it is thus possible to use MINOT together with X-ray or tSZ data, to calibrate the thermal part of the model.

Comparison to Fermi-LAT constraints
γ-ray constraints have been obtained by Ackermann et al. (2014) for A1795, A2142 and A2255, as part of a larger sample, using Fermi-LAT data (Atwood et al. 2009). For all clusters, they predict the expected fraction of CRp pressure over the thermal pressure based on the work by Pinzke & Pfrommer (2010) and Pinzke et al. (2011), given the mass of the clusters. They use these predictions, together with a model for the spatial distribution of the CR, to compute flux prediction for these clusters. In order to compare our predictions to theirs, we first set the value of X CRp (R 200 ) to that of Ackermann et al. (2014), taking into account the fact that the pressure ratio is twice the energy ratio (which we use for our parametrization). Our baseline CRp density model already matches well their baseline (based on simulations, Pinzke & Pfrommer 2010), because the CR are tied to the gas, as they neglect CR transport.
As we can see in Table 7, our predictions are lower than that of Ackermann et al. (2014) by a factor of about 3. However, we note that the masses of our selected clusters used in Ackermann et al. (2014), and which are taken from Chen et al. (2007), are larger by a factor of 1.5-2.1 to ours. Therefore, in order to account for this differences, we rescale our thermal energy accord-ing to self-similarity expectations, as U th → U th M 500, this work M 500, Ackermann 2014 After applying this rescaling, our fluxes are in much better agreement, within 20%. The differences may arise from the γ-ray production rate modeling, scatter in the thermal pressure, or differences in the thermal gas distribution that are not necessarily the same. To check, the effect of the latter, we also compute our fluxes changing our density profiles to the best fit β-model of the true density. We find that this change leads to differences in the γ-ray flux of up to 7% in the case of these clusters, which is significant.
In Fig. 18, we compute the energy integrated flux as a function of energy in the case of our reference model (Section 2.7) and compare it to the upper limit set by (Ackermann et al. 2014). While the predictions are relatively close to the upper limit, they remain below for all three clusters.
In conclusion, we have shown that our model gives comparable predictions for the γ-ray flux as compared to what is used in the literature. However, significant differences may arise due to the inner structure modeling of the clusters, which is generally ignored when using large samples.

Comparison to radio observations
In this section, we aim at comparing qualitatively the radio predictions of our model to measurements available in the literature. To do so, we use the database from https: //galaxyclusters.hs.uni-hamburg.de/, which reference available radio data for many cluster. All of our target clusters present diffuse radio emission: a radio mini-halo for A1795 (Giacintucci et al. 2014), a giant radio halo for A2142 (Giovannini & Feretti 2000;Venturi et al. 2017), and a giant radio halo plus a relic for A2255 (Kempner & Sarazin 2001;Govoni et al. 2005). In the case of A2142, we note that two components were distinguished in Venturi et al. (2017), and they are likely two arise from different physical processes. However, in this qualitative comparison, we only consider the global emission and sum the contribution from the two components.
In Fig. 19, we present the comparison of our models (defined in Section 2.7) to the flux measured in the literature. In order to compute the model flux emission, we use an aperture radius that matches the signal from the respective articles (100, 500 and 930 kpc, for A1795, A2142 and A2255, respectively) and perform cylindrical integration of the synchrotron emission. For each cluster, we illustrate how it is possible to qualitatively change our model parameters to match the radio data, and also show how these changes translate into the γ-ray prediction and its comparison to the Ackermann et al. (2014) upper limits.
In the case of A1795, our default model underpredicts the radio flux by a factor of about 50%. As we can see, boosting the magnetic field by a factor of 1.4 would solve the difference without affecting the γ-ray prediction. Alternatively, one could boost the amount of CRp by a factor of about 1.5, but a the cost of increasing the γ-ray prediction by a similar amount and get closer to the Fermi-LAT limit. Finally, increasing the amount of CRe 1 by a factor of 3 would also solve the difference, with changes in the γ-ray prediction only at energies below 0.1 GeV and thus barely accessible for Fermi-LAT.
In the case of A2142, our default model overpredicts the radio emission by almost an order of magnitude, and our spectrum appears too flat compared to the data. First, we consider a pure Table 7. Comparison of the γ-ray (hadronic) flux prediction obtained by Ackermann et al. (2014), and this work, using the same value for the CR to thermal energy ratio. Note that we have converted the pressure ratio to an energy ratio as defined in this work. Fluxes are given for energies E > 500 MeV, in units of s −1 cm −2 . The integration radius was set to the truncation radius (total volume). The rescaling of U th was done using Eq. 48.  Flux above E (s 1 cm 2 ) A2255 -Gamma-ray No CRe1, CRp index + 0.5, XCRp × 10 No CRp, CRe1 index + 0.8, XCRe1 × 500 Fermi upper limit Figure 19. Comparison of our model prediction and the radio flux observed in our three clusters (left), and the implication of the radio models on the γ-ray constraints (right). Top: A1795. Middle: A2142. Bottom: A2255. hadronic scenario (i.e. no CRe 1 ), for which a slope of the CRp spectrum needs to be set to about 2.9, and the amplitude reduced by a factor of two, in order to match the data. Another option is to consider only CRe 1 , in which case the spectrum slope should be set to about 3.3 and the normalization increased by a factor of 500, to match the data. A combination of the two scenario could also be used, especially since the radio emission presents two distinct components (see Venturi et al. 2017, for discussions). In both scenario, the predicted γ-ray emission also decreases, and thus remains in agreement with the Fermi-LAT limit.
In the case of A2255, we observe a disagreement between the 1400 GHz flux from Kempner & Sarazin (2001) and Govoni et al. (2005). For our purpose, we choose to use the value of Govoni et al. (2005) as a reference (flux of the halo only, excluding the relic). As we can see, the amplitude of our default model is in broad agreement with the observation, but our spectral index is too small. In the purely hadronic scenario, increasing the slope of the CRp spectrum to 2.9 together with increasing its normalization by a factor of 10, would bring agreement between the model and the data. Alternatively, in a model with only CRe 1 , we need to increase the CR spectrum slope to 3.1 and multiply the normalization by 500 in order to reach agreements. In the two cases, the γ-ray flux remains below the Fermi-LAT upper limit.
In this section, we have seen how we can change the model parameters to match the radio data in a qualitative way. We focused on the slope and normalization of the CR content of the cluster, but opening the parameter space to spatial distributions or functional form of the spectra could also play an important role. In all the considered cases, it is not possible to rule out any model using γ-ray data because the limits remain too high. However, purely hadronic models predictions are just a factor of a few below the Fermi-LAT limits, in the case of these clusters.

Conclusions and summary
In this paper, we have provided an exhaustive description of MINOT, a new software dedicated to the modeling of the nonthermal components of galaxy clusters and the prediction of associated observables. While the software was originally developed to describe the γ-ray emission from galaxy clusters, MINOT also accounts for most of the emission associated with the diffuse ICM component: X-ray from thermal bremsstrahlung, tSZ signal in the millimeter band, γ-rays and neutrino emission form hadronic processes, γ-rays from inverse Compton emission, and radio synchrotron emission. As the γ-ray emission is connected to the same underlying cluster physical properties as these other observables, MNOS provides a useful self-consistent modeling of the signal and these extra observables can be used, for example, to calibrate a γ-ray model. However, MINOT can also be used to model observables in the different bands independently.
The software is made publicly available at https:// github.com/remi-adam/minot, and this paper aims at providing a reference for any user of the code. To this aim, we have discussed the structure of the code and the interdependencies of the different modules in Section 2, while Sections 3, 4 and 5 provided details about the physical processes considered, how they are accounted for, and the way observables are computed. The different functions were illustrated with the use of a reference cluster model. It allowed us to show the dependence of each wavelength on the physical properties of the cluster. In Section 6, we also compared the predictions from MINOT to data available in the literature, in order to show how the code could be used to model real data. We used Planck and ROSAT data for the ther-mal component, and Fermi-LAT plus various radio data for the non-thermal component. Finally, we note that the MINOT code is well documented and many examples are provided in the public repository.
The different assumptions made in the code have been discussed. In particular, the modeling relies on primary base quantities, that are used to derive secondary properties of the cluster, and generate observables under the assumption of spherical symmetry. The primary quantities are the thermal electron pressure and density profiles, the CRe 1 and the CRp profiles and spectra, and the magnetic field strength profile. Regarding the CRe 2 , they are processed assuming no diffusion in a steady state scenario. However, other electron populations can be accounted for using the CRe 1 . In order to set the base physical properties of the cluster, several predefined models are available, but it is also possible to provide any user defined quantity.
The accuracy of the modeling has been addressed. Regarding the thermal component, modeling uncertainties associated with X-ray are below the percent level, and that of the tSZ signal are at the percent level when considering relativistic correction at high temperature and much smaller otherwise. The hadronic processes (γ-rays, neutrinos, secondary electrons), on the other hand, present uncertainties at a level of typically 25% over the considered energy range, when considering the latest models available in the literature. In addition, we stress that the impact of helium is of the order of 50% of the signal, and should be accounted for (as done in MINOT). The computation of inverse Compton and synchrotron emission is based on analytical approximations, for which the precision is expected to remain within 1% and 0.2%, respectively. Nevertheless, we stress that the main limitations of the modeling is not the accuracy of the computation but the underlying assumptions discussed above. In particular the use of spherical symmetry and the assumption of stationarity to compute the distribution of secondary electrons are likely to be the dominant sources of mismodeling.
The MINOT software could be used for a wide variety of operations and we list just a few examples here: -The joint modeling of the non-thermal emission in galaxy clusters for which detailed multi-wavelength data are available. The parameters of the model could be fit jointly to such data to constrain different scenarios, while accounting for uncertainties in the different components. -The prediction of the expected signal, based on ancillary data, for observation proposals. For instance, it would be possible to make prediction for the tSZ emission associated with that of an X-ray observed cluster, assuming that the pressure follow a universal profile. -The prediction of the background CR induced γ-rays in the context of dark matter searches. Indeed, MINOT provides an easy way to model the CR background, which needs to be marginalized over to obtain constraints on the nature of dark matter. -The simulation of sky maps associated to the observables considered here, given a halo catalog. -Pedagogical purposes. Because it includes most of the ICM associated processes, MINOT could be used to understand the impact of some given parameters on the observable.
Historically, the understanding of the physical properties of galaxy clusters have strongly benefited from multi-wavelength observations and analysis. With the current and upcoming facilities aiming at exploring the non-thermal component of galaxy clusters, in particular in the radio and γ-ray bands, it has become very useful to dispose of an easy-to-use self-consistent modeling software allowing us to predict the expected signal given some assumptions. The MINOT software provides such a tool.