- Email: [email protected]
Merging clusters and the formation of radio haloes
Computer Physics Communications 169 (2005) 378–381 www.elsevier.com/locate/cpc
Merging clusters and the formation of radio haloes Claudio Gheller a,∗ , Gianfranco Brunetti b a Via Magnanelli 6/3, Casalecchio di Reno, Bologna, CINECA, Italy b Via P.Gobetti 101, Bologna, IRA-INAF, Italy
Available online 11 May 2005
Abstract In this paper we present the preliminary result obtained from a set of cosmological numerical simulations run with the goal of describing self-consistently the evolution of the gas diffused in clusters of galaxies (Intra-Cluster Medium—ICM), including hydrodynamical and gravitational processes, in a cosmological framework. We have followed the details of the physical evolution of the ICM with particular attention to shock processes and merging events and their possible feedbacks the relativistic plasma. Furthermore, we have analyzed the details of the ICM dynamics in the most massive clusters, using tracers particles which follows the fluid in its motion. 2005 Elsevier B.V. All rights reserved. Keywords: Cosmology; Numerics; Fluid dynamics
1. Introduction It is now well established that the intracluster medium (ICM) is a mixture of hot gas, magnetic fields and relativistic particles. While the hot gas results in thermal bremsstrahlung X-ray emission, relativistic electrons and positrons generate non-thermal radio (synchrotron) and hard X-ray radiation (inverse Compton). The observed radio emission implies magnetic fields of the order of ∼ 0.1–1 µG, relativistic particles with Lorentz factor γ 1000 and energy density of 10−14 –10−13 erg cm−3 . * Corresponding author.
E-mail address: [email protected] (C. Gheller). 0010-4655/$ – see front matter 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.cpc.2005.03.084
The most important observational evidence for relativistic electrons in clusters of galaxies comes from the large scale diffuse synchrotron radio emission observed in a growing number of massive clusters (e.g., [1]). The diffuse emissions are referred to as radio halos or radio mini-halos, when they appear confined to the center of the cluster, while they are called radio relics when they are found in the cluster periphery. Relativistic electrons and hadrons are injected in the ICM by cluster galaxies and AGN. Further secondary leptons are continuously generated by relativistic hadrons due to collisions with thermal protons. However the injection process of relativistic electrons cannot explain the radio features of galaxy clusters. In fact diffused radio sources have ∼ Mpc size and the diffusion time necessary to these electrons to cover
C. Gheller, G. Brunetti / Computer Physics Communications 169 (2005) 378–381
such distances is orders of magnitude larger than their radiative lifetime (about 108 yrs). Some other mechanisms must act to re-accelerate electrons, leading the observed properties. Interestingly, there is a correlation between the nonthermal diffuse radio emission and the presence of merger activity in the host clusters of galaxies ([1] and references therein): this suggests a link between the process of formation of galaxy clusters and the origin of the non-thermal activity. Merger shocks, which characterize the dynamical evolution of galaxy clusters, may represent a natural acceleration mechanism for the relativistic electrons in galaxy clusters. Mergers may produce also a significant level of turbulence in the ICM. In this case Alfven waves and/or some other Fermi-like processes could reaccelerate γ ∼ 100–300 relativistic electrons to the higher energies required to explain radio halos (e.g., [2]). Several theoretical studies have focused on these processes. Various models of particle acceleration due to MHD waves in the ICM have been recently successfully developed (see [3] for a review). However the simplifications and approximations adopted in these models, pose severe limits on their possible applications. First, the cosmological evolution of the physical conditions in the ICM is not taken into account (the evolution of relativistic particles depends on these conditions). Furthermore the injection of turbulence during mergers in galaxy clusters is assumed. Finally these models are time-independent, i.e. the injection rate of energy in turbulence waves is assumed to be constant during each merger. Numerical simulations help to overcome many of these limits and to clarify some of the proposed issues. We have simulated the evolution of the ICM in a cosmological framework in several different realization of a standard Λ model. The simulations have been performed using the Eulerian, N -body + hydrodynamics, shock capturing HYDROPAD code [4]. We focused on two basic aspects. First, the characterization of clusters shock waves, due both to primary infall of matter and to secondary merger events. To this aim, moderate spatial resolution and high statistics are required. Therefore we run three different simulations of a box of 50 Mpc and a spatial resolution of 125 kpc. Second, a detailed analysis of the ICM dynamics, with the introduction of fluid tracers (see Section 2), and the analysis of the presence of turbulent motion in
379
the intracluster fluid. In this case, the highest possible resolution (with respect to computational resources) is necessary. A single run with a box of 30 kpc and 58 kpc of spatial resolution was performed. All the simulations were performed on the IBM-SP4 system of CINECA, partially supported by the resources provided by the INAF-CINECA agreement.
2. The simulations The simulations have been performed using the HYDROPAD numerical code [4]. The HYDROPAD code describes the ICM with a hydrodynamical approach based on the Eulerian version of the shock capturing Piecewise Parabolic Method (PPM; [5]), which ensures at least second-order (up to the fourth-order, in the case of smooth flows and small timesteps) accuracy in space and second-order accuracy in time. The basic PPM technique has been modified to include the gravitational interaction and the expansion of the universe. The hydrodynamical part has been coupled to a Particle Mesh (PM) N -body code [6] that describes the evolution of the dark component. The N -body numerical schema describes the collisionless matter as a set of massive particles which interact gravitationally with themselves and with the baryonic gas. The dynamics of the particle is determined solving their equations of motion using a second-order two-step Lax–Wendroff method, which allows to work with non-constant timesteps equal to those used for the integration of the hydrodynamics equations. The gravitational field, due to both the baryons and the dark matter, is calculated using a standard FFT based procedure. The code is fully parallelized using the standard MPI library, which make it portable on any parallel architecture. In the HYDROPAD code fluid variables are calculated on the cells of a fixed mesh. Therefore, it is not possible to follow the fluid elements in their motion in the computational volume. However this is required for our analysis. To this goal, we have introduced a set of tracer particles which move together with the fluid. Tracers do not affect the dynamics of the system and moves with the velocity of the cell in which they are located, already calculated in the previous hydrodynamics integration steps. The trac-
380
C. Gheller, G. Brunetti / Computer Physics Communications 169 (2005) 378–381
ers are initially distributed homogeneously. The data of the cell in which a tracer falls can be local to the processor on which also the tracer data are stored, or they can be remote. In this last case, the processor which owns the particle must access asynchronously a remote memory. The MPI2 Remote Memory Access (RMA) paradigm has been adopted for this purpose. This one-side communication technique permits to retrieve data located on remote processors easily. However it can lead to a strong performance penalty due to the necessary synchronization which follows each of the RMA access. In order to limit this synchronization time overhead the number of tracer particles that can be used must be kept low. For this reason, the code allows the user to select only interesting subregions (e.g., around the clusters) on which define and activate the tracers. We have performed four runs of the same cosmological model starting from different realization of the initial conditions. We have adopted the socalled Concordance Model with Ω = 1, ΩΛ = 0.73, ΩDM = 0.226, ΩBM = 0.044, h = 0.71 and the initial spectrum normalization and spectral index, σ8 = 0.94 and n = 1, respectively. In the first run (RUN1) the number of computational cells and particles and the physical box size have been set in order to meet two basic requirements. High spatial resolution, to follow the details of ICM evolution, and a large computational box to have a meaningful cosmological sample and to adopt safely periodic boundary conditions. At the same time the request of computational resources (memory, disk, CPU time) must be kept reasonable. We have used 5123 computational cells and the same number of dark matter particles. The number of tracers was limited to 32 178 for each of three selected clusters. In fact, the usage of one-side atomic communication in the implementation of the tracers part of the code rises dramatically the execution time, preventing us from using a larger number of particles. However this number is sufficient for our purposes. The simulation required about 40 GBytes of memory and about 25 000 CPU hours on 32 processors of the IBM SP4 system of CINECA. In the other three runs (RUN2–4) we have used 4003 cells and particles on boxes of 50 Mpc. These lower resolution runs allowed us to have more data and larger statistics. In these simulations we have
Fig. 1. Distribution of the Dark Matter at z = 0.0 (upper panel), with tracers in the initial positions (middle) and with tracers in their final configurations (bottom).
focused on the analysis of the details of clusters shock waves formation and evolution and the characterization of their morphology and properties. The three simulations required about 15 000 hours of CPU time and each needed about 20 GBytes of memory.
C. Gheller, G. Brunetti / Computer Physics Communications 169 (2005) 378–381
381
Fig. 2. Gas density isocontours (solid lines) and the velocity field of the largest cluster of RUN1 (left panel). Tracers velocity projections along coordinate directions (right panel).
3. Results Fig. 1 shows the final distribution of the dark matter with and without the tracers. Fig. 2 presents the results obtained in the preliminary analysis phase. The upper panel shows a 2D cutting plane of the computational box of RUN1 in the region where the most massive galaxy cluster forms. Solid lines represents isodensity contours, while vectors are the velocities projected on the cutting plane. It is interesting to notice how shock waves are clearly marked by the velocity field and the cluster core is completely thermalized. Furthermore turbulence motions driven by plasma instabilities develop inside the virial radius where plasma with different physical properties interact. These numerical simulations are a unique tool to establish the injection and spatial transport of cluster-turbulence eddies and the results can be coupled with particle acceleration models to better understand the origin of the non-thermal phenomena. The lower panel shows the tracers velocity projection along orthogonal line of sight for the most massive RUN1 cluster. Tracers are concentrated around the cluster core. The curves reveal a rotation of the gas, with velocities (highest than 400 km/s) which could be detected by spectroscopic observations. The
profiles of the spectral lines emitted by the hot gas (e.g., the iron line at 6.4 keV) should be broadened by random motions and blueshifted (and redshifted) by cluster rotation. Given the velocities measured in our simulated clusters, the expected distorsions of the profiles of the lines should be detected by future X-ray satellites (e.g., ASTRO-E2, Next).
Acknowledgements We thank the INAF/CINECA agreement for the CPU time that has allowed us to perform this work.
References [1] L. Feretti, ASP Conf. Ser. 301 (2003) 143–157. [2] G. Brunetti, G. Setti, L. Feretti, G. Giovannini, MNRAS 320 (2001) 365–375. [3] G. Brunetti, ASP Conf. Ser. 301 (2002) 349–361. [4] C. Gheller, L. Moscardini, O. Pantano, MNRAS 296 (1998) 519–535. [5] P. Colella, P. Woodward, J. Comp. Phys. 54 (1984) 174–201. [6] R. Hockney, J. Eastwood, Computer Simulations Using Particles, McGraw-Hill, New York, 1981.
Merging clusters and the formation of radio haloes Claudio Gheller a,∗ , Gianfranco Brunetti b a Via Magnanelli 6/3, Casalecchio di Reno, Bologna, CINECA, Italy b Via P.Gobetti 101, Bologna, IRA-INAF, Italy
Available online 11 May 2005
Abstract In this paper we present the preliminary result obtained from a set of cosmological numerical simulations run with the goal of describing self-consistently the evolution of the gas diffused in clusters of galaxies (Intra-Cluster Medium—ICM), including hydrodynamical and gravitational processes, in a cosmological framework. We have followed the details of the physical evolution of the ICM with particular attention to shock processes and merging events and their possible feedbacks the relativistic plasma. Furthermore, we have analyzed the details of the ICM dynamics in the most massive clusters, using tracers particles which follows the fluid in its motion. 2005 Elsevier B.V. All rights reserved. Keywords: Cosmology; Numerics; Fluid dynamics
1. Introduction It is now well established that the intracluster medium (ICM) is a mixture of hot gas, magnetic fields and relativistic particles. While the hot gas results in thermal bremsstrahlung X-ray emission, relativistic electrons and positrons generate non-thermal radio (synchrotron) and hard X-ray radiation (inverse Compton). The observed radio emission implies magnetic fields of the order of ∼ 0.1–1 µG, relativistic particles with Lorentz factor γ 1000 and energy density of 10−14 –10−13 erg cm−3 . * Corresponding author.
E-mail address: [email protected] (C. Gheller). 0010-4655/$ – see front matter 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.cpc.2005.03.084
The most important observational evidence for relativistic electrons in clusters of galaxies comes from the large scale diffuse synchrotron radio emission observed in a growing number of massive clusters (e.g., [1]). The diffuse emissions are referred to as radio halos or radio mini-halos, when they appear confined to the center of the cluster, while they are called radio relics when they are found in the cluster periphery. Relativistic electrons and hadrons are injected in the ICM by cluster galaxies and AGN. Further secondary leptons are continuously generated by relativistic hadrons due to collisions with thermal protons. However the injection process of relativistic electrons cannot explain the radio features of galaxy clusters. In fact diffused radio sources have ∼ Mpc size and the diffusion time necessary to these electrons to cover
C. Gheller, G. Brunetti / Computer Physics Communications 169 (2005) 378–381
such distances is orders of magnitude larger than their radiative lifetime (about 108 yrs). Some other mechanisms must act to re-accelerate electrons, leading the observed properties. Interestingly, there is a correlation between the nonthermal diffuse radio emission and the presence of merger activity in the host clusters of galaxies ([1] and references therein): this suggests a link between the process of formation of galaxy clusters and the origin of the non-thermal activity. Merger shocks, which characterize the dynamical evolution of galaxy clusters, may represent a natural acceleration mechanism for the relativistic electrons in galaxy clusters. Mergers may produce also a significant level of turbulence in the ICM. In this case Alfven waves and/or some other Fermi-like processes could reaccelerate γ ∼ 100–300 relativistic electrons to the higher energies required to explain radio halos (e.g., [2]). Several theoretical studies have focused on these processes. Various models of particle acceleration due to MHD waves in the ICM have been recently successfully developed (see [3] for a review). However the simplifications and approximations adopted in these models, pose severe limits on their possible applications. First, the cosmological evolution of the physical conditions in the ICM is not taken into account (the evolution of relativistic particles depends on these conditions). Furthermore the injection of turbulence during mergers in galaxy clusters is assumed. Finally these models are time-independent, i.e. the injection rate of energy in turbulence waves is assumed to be constant during each merger. Numerical simulations help to overcome many of these limits and to clarify some of the proposed issues. We have simulated the evolution of the ICM in a cosmological framework in several different realization of a standard Λ model. The simulations have been performed using the Eulerian, N -body + hydrodynamics, shock capturing HYDROPAD code [4]. We focused on two basic aspects. First, the characterization of clusters shock waves, due both to primary infall of matter and to secondary merger events. To this aim, moderate spatial resolution and high statistics are required. Therefore we run three different simulations of a box of 50 Mpc and a spatial resolution of 125 kpc. Second, a detailed analysis of the ICM dynamics, with the introduction of fluid tracers (see Section 2), and the analysis of the presence of turbulent motion in
379
the intracluster fluid. In this case, the highest possible resolution (with respect to computational resources) is necessary. A single run with a box of 30 kpc and 58 kpc of spatial resolution was performed. All the simulations were performed on the IBM-SP4 system of CINECA, partially supported by the resources provided by the INAF-CINECA agreement.
2. The simulations The simulations have been performed using the HYDROPAD numerical code [4]. The HYDROPAD code describes the ICM with a hydrodynamical approach based on the Eulerian version of the shock capturing Piecewise Parabolic Method (PPM; [5]), which ensures at least second-order (up to the fourth-order, in the case of smooth flows and small timesteps) accuracy in space and second-order accuracy in time. The basic PPM technique has been modified to include the gravitational interaction and the expansion of the universe. The hydrodynamical part has been coupled to a Particle Mesh (PM) N -body code [6] that describes the evolution of the dark component. The N -body numerical schema describes the collisionless matter as a set of massive particles which interact gravitationally with themselves and with the baryonic gas. The dynamics of the particle is determined solving their equations of motion using a second-order two-step Lax–Wendroff method, which allows to work with non-constant timesteps equal to those used for the integration of the hydrodynamics equations. The gravitational field, due to both the baryons and the dark matter, is calculated using a standard FFT based procedure. The code is fully parallelized using the standard MPI library, which make it portable on any parallel architecture. In the HYDROPAD code fluid variables are calculated on the cells of a fixed mesh. Therefore, it is not possible to follow the fluid elements in their motion in the computational volume. However this is required for our analysis. To this goal, we have introduced a set of tracer particles which move together with the fluid. Tracers do not affect the dynamics of the system and moves with the velocity of the cell in which they are located, already calculated in the previous hydrodynamics integration steps. The trac-
380
C. Gheller, G. Brunetti / Computer Physics Communications 169 (2005) 378–381
ers are initially distributed homogeneously. The data of the cell in which a tracer falls can be local to the processor on which also the tracer data are stored, or they can be remote. In this last case, the processor which owns the particle must access asynchronously a remote memory. The MPI2 Remote Memory Access (RMA) paradigm has been adopted for this purpose. This one-side communication technique permits to retrieve data located on remote processors easily. However it can lead to a strong performance penalty due to the necessary synchronization which follows each of the RMA access. In order to limit this synchronization time overhead the number of tracer particles that can be used must be kept low. For this reason, the code allows the user to select only interesting subregions (e.g., around the clusters) on which define and activate the tracers. We have performed four runs of the same cosmological model starting from different realization of the initial conditions. We have adopted the socalled Concordance Model with Ω = 1, ΩΛ = 0.73, ΩDM = 0.226, ΩBM = 0.044, h = 0.71 and the initial spectrum normalization and spectral index, σ8 = 0.94 and n = 1, respectively. In the first run (RUN1) the number of computational cells and particles and the physical box size have been set in order to meet two basic requirements. High spatial resolution, to follow the details of ICM evolution, and a large computational box to have a meaningful cosmological sample and to adopt safely periodic boundary conditions. At the same time the request of computational resources (memory, disk, CPU time) must be kept reasonable. We have used 5123 computational cells and the same number of dark matter particles. The number of tracers was limited to 32 178 for each of three selected clusters. In fact, the usage of one-side atomic communication in the implementation of the tracers part of the code rises dramatically the execution time, preventing us from using a larger number of particles. However this number is sufficient for our purposes. The simulation required about 40 GBytes of memory and about 25 000 CPU hours on 32 processors of the IBM SP4 system of CINECA. In the other three runs (RUN2–4) we have used 4003 cells and particles on boxes of 50 Mpc. These lower resolution runs allowed us to have more data and larger statistics. In these simulations we have
Fig. 1. Distribution of the Dark Matter at z = 0.0 (upper panel), with tracers in the initial positions (middle) and with tracers in their final configurations (bottom).
focused on the analysis of the details of clusters shock waves formation and evolution and the characterization of their morphology and properties. The three simulations required about 15 000 hours of CPU time and each needed about 20 GBytes of memory.
C. Gheller, G. Brunetti / Computer Physics Communications 169 (2005) 378–381
381
Fig. 2. Gas density isocontours (solid lines) and the velocity field of the largest cluster of RUN1 (left panel). Tracers velocity projections along coordinate directions (right panel).
3. Results Fig. 1 shows the final distribution of the dark matter with and without the tracers. Fig. 2 presents the results obtained in the preliminary analysis phase. The upper panel shows a 2D cutting plane of the computational box of RUN1 in the region where the most massive galaxy cluster forms. Solid lines represents isodensity contours, while vectors are the velocities projected on the cutting plane. It is interesting to notice how shock waves are clearly marked by the velocity field and the cluster core is completely thermalized. Furthermore turbulence motions driven by plasma instabilities develop inside the virial radius where plasma with different physical properties interact. These numerical simulations are a unique tool to establish the injection and spatial transport of cluster-turbulence eddies and the results can be coupled with particle acceleration models to better understand the origin of the non-thermal phenomena. The lower panel shows the tracers velocity projection along orthogonal line of sight for the most massive RUN1 cluster. Tracers are concentrated around the cluster core. The curves reveal a rotation of the gas, with velocities (highest than 400 km/s) which could be detected by spectroscopic observations. The
profiles of the spectral lines emitted by the hot gas (e.g., the iron line at 6.4 keV) should be broadened by random motions and blueshifted (and redshifted) by cluster rotation. Given the velocities measured in our simulated clusters, the expected distorsions of the profiles of the lines should be detected by future X-ray satellites (e.g., ASTRO-E2, Next).
Acknowledgements We thank the INAF/CINECA agreement for the CPU time that has allowed us to perform this work.
References [1] L. Feretti, ASP Conf. Ser. 301 (2003) 143–157. [2] G. Brunetti, G. Setti, L. Feretti, G. Giovannini, MNRAS 320 (2001) 365–375. [3] G. Brunetti, ASP Conf. Ser. 301 (2002) 349–361. [4] C. Gheller, L. Moscardini, O. Pantano, MNRAS 296 (1998) 519–535. [5] P. Colella, P. Woodward, J. Comp. Phys. 54 (1984) 174–201. [6] R. Hockney, J. Eastwood, Computer Simulations Using Particles, McGraw-Hill, New York, 1981.