Why is it worth to spend 1.5 million CPU-hours on Relativistic Astrophysics? Miguel Ángel Aloy Torás Departamento de Astronomía y Astrofísica Universidad de Valencia Collaborators: Petar Mimica, Javier Vargas SciComp09 Barcelona, 19-05-09 1
The topic in a nutshell We have employed a numerical approach in order to understand the actual physics happening in relativistic, astrophysical sources. Over the last 2 years, we have used ~10 6 CPU hours/year of computer time in RES-facilities. In this period we have accomplished several tasks in the field of relativistic (magneto-)hydrodynamics. Tasks: 1.Calculation of the early phases of propagation of ultrarelativistic shells of plasma. These calculations are addressed to model the so-called afterglow phase of gamma-ray bursts (GRBs), which find themselves among the most energetic events in our Universe. 2.Study of the physical parameters of blazars by comparing synthetic- emission models with observations. 3.Influence of the cooling on the collimation properties of relativistic outflows. Common link: Relativistic (Resistive) (Magneto-)Hydrodynamics RHD, RMHD, RRMHD 2
5 equations Equations of RHD Special Relativistic Hydrodynamics (SRHD): Equations 5 unknowns + p( , ) � D � t + � · ( D v ) = 0 ( mass conservation ) � S � t + � · ( S ⊗ v + p I ) = 0 ( momentum conservation ) �� � t + � · ( S − D v ) = 0 ( energy conservation ) The state vector and the flux vectors are: U = ( D , S 1 , S 2 , S 3 , � ) , F i = ( Dv i , S 1 v i + � 1 i , S 2 v i + � 2 i , S 3 v i + � 3 i , S i − Dv i ) D = � W : relativistic rest-mass density. � : rest-mass density. S = � hW 2 v : relativistic momentum density. h = 1 + � / c 2 + p / � c 2 : specific enthalpy. � = � hW 2 c 2 − p − � Wc 2 : relativistic � : specific internal energy. p : pressure. energy density. v : flow velocity. Relativistic Effects � 1 − v 2 / c 2 : Lorentz factor. W = 1 / h ≥ 1 ( � ≥ c 2 ) , W ≥ 1 ( v → c ) 3
8 equations Equations of RMHD 8 unknowns + p( , ) Requires 3 more variables than RHD. ∂ t + ∂ F x ( U ) + ∂ F y ( U ) + ∂ F z ( U ) ∂ U = 0 , RMHD differs substantially from RHD at the ∂ x ∂ y ∂ z numerical level. There is a mixture of volume average (v, p, etc.) and surface average ∇ · B = 0 , variables ( B ). The volumetric variables follow the same ρ u 0 numerical scheme as in RHD. ( ρ h + b 2 ) u 0 u x − b 0 b x ( ρ h + b 2 ) u 0 u y − b 0 b y ( ρ h + b 2 ) u 0 u z − b 0 b z Magnetic field components evolved using U = , � � ( ρ h + b 2 )( u 0 ) 2 − p + b 2 − ( b 0 ) 2 constraint transport to account for the 2 B x numerical preservation of B . B y B z ρ u x ρ u y ρ u z ( ρ h + b 2 ) u x u x + � � ( ρ h + b 2 ) u x u y − b x b y p + b 2 ( ρ h + b 2 ) u x u z − b x b z − b x b x 2 ( ρ h + b 2 ) u y u y + � � p + b 2 ( ρ h + b 2 ) u y u z − b y b z − b y b y ( ρ h + b 2 ) u x u y − b x b y 2 ( ρ h + b 2 ) u z u z + � � p + b 2 ( ρ h + b 2 ) u x u z − b x b z − b z b z ( ρ h + b 2 ) u y u z − b y b z F x ( U ) = F y ( U ) = F z ( U ) = , 2 . ( ρ h + b 2 ) u 0 u x − b 0 b x ( ρ h + b 2 ) u 0 u y − b 0 b y ( ρ h + b 2 ) u 0 u z − b 0 b z B x v y − B y v x 0 B x v z − B z v x B y v x − B x v y 0 B y v z − B y v z B z v x − B x v z B z v y − B y v z 0 4
14 equations Equations of RRMHD 14 unknowns + p( , ) + ∂ F m ( P ) ∂ Q ( P ) RRMHD is treated in a way very similar to = S ( P ) , (55) ∂ x m ∂ t RHD (Komissarov 2007), e.g., no constraint where transport since all variables are volumetric. � � − κ� B i B i 0 i Drawback: need 2 extra scalar fields ( , ). � � q − κ� E i E i − J i Stiffness: Semi-analytic integration of the Q = , P = , S = source terms involving resistivity and/or scalar q q 0 fields. ργ ρ 0 e p 0 P i u i 0 i are the vectors of conserved quantities, primitive quantities and y sources, respectively, and 0 − κ� B m L x e imk E k + � g im 0 i 0 i q − κ� E j B 0 − q v i − J i − e imk B k + � g im 2L y c F m = S a ( P ) = and S b ( P ) = , 0 0 J m x 0 0 ρ u m 0 0 S m L 0 i 0 i � im computational domain where i i J c = σγ [ E + v × B − ( E · v ) v ] From Komissarov (2007) is the conductivity current. The source term S is potentially stiff (in 5
MRGENESIS: a common framework for RHD, RMHD & RRMHD MRGENESIS is a multidimensional (1D, 2D or 3D), parallel (MPI) code which allows one to compute problems where RHD or RMHD are relevant. In the newest development, not fully integrated with RMHD-branch, RRMHD is also included. Employs: • Finite Volume approach. • Method of lines: separate semi-discretization of space and time. • Time advance: TVD Runge Kutta methods of 2nd and 3rd order. • High-resolution Shock Capturing schemes. • Inter-cell reconstruction: Up to 3rd order using PPM algorithm. • In RMHD: constraint transport. • In RRMHD: Munz’s method (=Lagrange Multipliers) to conserve B and charge. • Several orthogonal coordinate systems (Cartesian, Cylindrical, Spherical). • SPEV for problems where the non-thermal emission of R(M)HD models is sought. 6
Parallel performance Small and multicore systems iMac Intel Core 2 Duo 2.8 GHz (Uni. Valencia) wall clock time [normalized] 10 iMac Intel Core 2 Duo 2.8 GHz, ifort 11.0 (Uni. Valencia) Intel Xeon 5140 2.33 GHz (Uni. Valencia) Intel Xeon E6405 2.0 GHz (HYBRID cluster, Uni. Split) AMD Opteron 8350 2.9 GHz (Uni. Valencia) 1 0,1 0,01 0,001 1 10 100 1000 number of threads 7
Parallel performance Small and multicore systems best performance: different threads on different processors. iMac Intel Core 2 Duo 2.8 GHz (Uni. Valencia) wall clock time [normalized] 10 iMac Intel Core 2 Duo 2.8 GHz, ifort 11.0 (Uni. Valencia) worst performance: Intel Xeon 5140 2.33 GHz (Uni. Valencia) Intel Xeon E6405 2.0 GHz (HYBRID cluster, Uni. Split) different threads on same AMD Opteron 8350 2.9 GHz (Uni. Valencia) processor but different cores 1 0,1 0,01 0,001 1 10 100 1000 number of threads 7
Parallel performance Large multiprocessor systems SiCortex SC072 (Megware Computer GmbH) wall clock time [normalized] 10 Tirant (Uni. Valencia) MareNostrum (BSC) 1 0,1 0,01 0,001 1 10 100 1000 number of threads 8
Parallel performance All systems iMac Intel Core 2 Duo 2.8 GHz (Uni. Valencia) wall clock time [normalized] 10 iMac Intel Core 2 Duo 2.8 GHz, ifort 11.0 (Uni. Valencia) Intel Xeon 5140 2.33 GHz (Uni. Valencia) SiCortex SC072 (Megware Computer GmbH) Intel Xeon E6405 2.0 GHz (HYBRID cluster, Uni. Split) Tirant (Uni. Valencia) MareNostrum (BSC) AMD Opteron 8350 2.9 GHz (Uni. Valencia) 1 0,1 0,01 0,001 1 10 100 1000 number of threads 9
Early afterglow The use of a cutting-edge facility as Mare Nostrum (also Cesvima and Tirant) has allowed us to simulate with unprecedented resolution the early phase of the afterglow associated to one of the most luminous events in the Universe: GRBs. Because of the ultrarelativistic character of the ejecta flow, we have to use huge numerical resolution, i.e., enormous computational resources. Long standing issue: do afterglows result from 10 � rel =1.04 magnetized or unmagnetized ejecta sweeping � rel =1.1 the interstellar medium (ISM)?. Weak/No Reverse Shock Dissipation � rel =1.25 Our simulations have quantified which is the � eq Substantial Reverse Shock Dissipation approximate magnetization of the ejecta ( o ) to 1 allow for the production of a reverse shock in the ejecta, which may accelerate particles, whose optical emission ( optical flash ) is envisioned to be the signature of such shock. 0,1 E 1 / 6 B 2 0,001 0,01 0,1 1 10 100 0 53 ξ = 0 . 73 σ 0 := � � n 1 / 6 ∆ 1 / 2 12 γ 4 / 3 4 πγ 0 ρ 0 c 2 2 . 5 0 Mimica, Giannios, Aloy (2009) 10
Evolution of magnetized and non-magnetized afterglows 1 light-day = 2.6x10 15 cm = 174 AU Earth surface magnetic field strength = 0.03 - 0.06 mT 11
Evolution of magnetized and non-magnetized afterglows 1 light-day = 2.6x10 15 cm = 174 AU Earth surface magnetic field strength = 0.03 - 0.06 mT 12
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