Numerical Astrophysics

1. Numerical Astrophysics Jongsoo Kim Korea Astronomy and Space Science Institute • Contents • Why are numerical simulations for astrophysical flows challenging? • B-fields in the interstellar medium • TVD MHD code, PC cluster, and AMR simulation • SF in the turbulent interstellar medium • Conclusions

2. Radiative Transfer and (M)HD

3. N-body simulations

4. Why are numerical simulations for astrophysical flows challenging? • Interaction between matter and radiation • - ultimate goal of numerical experiments is to provide information what can be compared with observations. • - 6-D (3D in space, 2D in direction, 1D in frequency) problem • Huge dynamic range • - for example, need more than 20 orders-of-magnitude density dynamic range from a MC to stars. • Multi-physics • - self-gravity, magnetic field, relativistic effect, etc … • Indeed, numerical simulations are challenging. However, they provide us with a unique laboratory for astrophysical experiments. •  Due to the rapid development of the computer technology and algorithm, numerical simulations are now quite successful.

5. Topics covered in this workshop • B-Fields and Star Formation (Jongsoo Kim) • MHD instabilities (Seung Soo Hong) • MHD turbulence (Jungyeon Cho) • Cosmology (Juhan Kim)

6. How do astronomers measure magnetic fields in the interstellar medium? • Starlight (due to dust absorption) and IR (dust emission) polarizations • Faraday rotation • Synchrotron radiation (for external gals.) • Zeeman splitting

7. Dust Polarization magnetic field line dust grain dust emission dust absorption

8. Heiles & Crutcher 2005 Starlight polarization • The magnetic field is generally parallel to the plane of the Galaxy. • Polarization directions point to l~80 deg and l~260 deg, which is the orientation of the local spiral arm. • Bu/Br ~ 0.7 – 1.0

9. Crutcher et al. 2004 IR polarization • B=80mG estimated based a C-F method

10. Are magnetic fields dynamically important? Yes. • Sun: Most active phenomena are due to a • B-field in the Sun. • Stars: Magnetically controlled star formation; compact objects (neutron stars and accretion disks ...) • The ISM:Energy density of the B-field is comparable to those in other energy forms. (large-scale structure, CR generation, etc…) • The Galaxy: Dynamo vs. Primordial • Cosmology: Origin of the B-field

11. (Isothermal) MHD equations • Slow time variation • Small drift velocities between electrons and • ions • Ohm’s law; • Non-relativistic transform between the ion and the lab. rest frames

12. (Kim et al. 1999) MHD Shock Tube Test

13. The MHD code was parallelized using basic eight MPI routines. Eight Basics routines MPI_INIT : initialization MPI_FINALIZE : termination MPI_COMM_SIZE : define number of processors MPI_COMM_RANK : give a rank on each processor MPI_SEND : send messages MPI_RECV : receive messages MPI_BCAST : send messages to all processors MPI_REDUCE : reduce values on all the processors to a single value

14. Domain decomposition communication PE0 PE1 PE2 PE3

15. KASI-ARCSEC CLUSTER • The cluster was built bythe fund from KASI and ARCSEC. • A dedicate cluster for astronomers in Korea. • 5 SCI papers / year

16. Test problem for a benchmark for the PC cluster

17. Speed-up of the IMHD code

18. Myers et al. 1986 • CO 2.6m, 150micron, 250micron, • 6cm radio continuum, • H 110alpha recombination • inner Galaxy, -1 deg < b <1 deg, • 12 deg < l < 60deg • 54 molecular cloud complexes • mean SFE = mean Ms/(Ms+Mc)=2%

19. Observed SFEs • Observed SFE = Ms/(Ms+Mc) is - 2-3% for the molecular cloud complexes in the inner Galaxy (e.g., Myers et al. 1986) - 10-30% for cluster-forming cores (e.g., Lada & Lada 2003) • SF theories should explain the low SFEs (Zuckerman & Evans 1974).

20. Two SF Theories ion neutral SF regulated by AD SF regulated by turbulence magnetically supercritical cloud. (B-field is not important ingredient.) magnetically subcritical cloud

21. 10 no 30 n0 100 n0 dt_frame = 0.04Myr Magnetically subcritical case, m=0.9 • Most density peaks are transient with lifetimes at most 1.5Myr. • The AD timescale is comparable to the lifetimes of longest-lived clumps.  The cores may undergo AD-mediated evolution if AD is included even in a strongly turbulent, subcritical flow.

22. 10 no 100 n0 1000 n0 dt_frame = 0.04Myr Magnetically supercritical case, m=2.8 • A few collapsing cores are formed. • First collapsing object goes from first appearance to a fully collapsed state in less than 1 Myr, twice of the local free-fall time.

23. Core Formation Efficiency (SFE) 0.12 0.04 M (n>500n0) 0.05 2.8 8.8 0.025 lifetime of cloud: 4Myr (e.g, Hartmann et al. 2001) • CFE is dependent on the seed for random driving • velocity fields (Heitsch et al 2001). • CFEs are lower than 10 % in most cases.

24. Conclusions • Even though numerical simulations for astronomical flows are challenging, some of them are quite successful due to rapid development of the computer technology and algorithms. • B-fields are important in almost everywhere in the Universe. • A medium-size cluster based on the Gigabit interconnect is fairly good for MHD simulations. • A SF theory based on turbulence is gaining its momentum.