Simulating Binary Star Systems. Kaitlin M. Kratter Hubble Fellow, JILA/ CU Boulder

Transcription

1 Simulating Binary Star Systems Kaitlin M. Kratter Hubble Fellow, JILA/ CU Boulder

2 Outline Why bother with binaries? How do they form? What challenges do binaries pose from a numerical perspective? Example Calculations

3 Binaries Matter Type Ia Runaway supernovae / Escape darkof Ionizing energy OB Stars and the Radiation from High Redshift Galaxies 5 Gallo et al enhancement in fesc Vary dust 25% smaller 8 fiducial 6 LMC no dust Mhalo (MO ) Mhalo (MO ) 30 MO frun=0.2 4 Vary Q LF fiducial model 80 km/s 60 km/s POW binary model km/s Mhalo (MO ) S91 frun=0.4 8 Mhalo (MO ) 8 frun=0.3 7 Vary Vrun Confirmed BH Vary frun enhancement in fesc 60 MO 6 25% larger 10 GW signal Vary Mmin, Mmax 8 SMC 2 GR confirmation Mhalo (MO ) Exoplanet characterization Mhalo (MO ) 1010 Reionization (Conroy & Kratter 2012) F IG. 3. The effect of various model parameters and assumptions on the derived enhancement in fesc. The solid line in each panel is our fiducial model where runaways are produced by dynamical encounters. Top Left: Variation in the normalization of the galaxy size-mass relation by ±25% (dotted lines). A model with a β density profile for the gas is included (green line). Top Middle: Variation in the treatment of dust. Top Right: Variation in the minimum and maximum stellar masses. Bottom Left: Variation in the fraction of runaways, frun. The dependence of fesc on frun is approximately linear over the range considered. Bottom Middle: Variation in the treatment of the runaway velocities, Vrun. A fixed Vrun is varied from km s 1. In addition, we consider a power-law distribution of Vrun (labelled POW in the figure), and a Maxwellian distribution of Vrun as advocated in Stone (1991, labelled S91 in the figure). In this last case frun = 0.46,

4 What we (theorists) know : Multiple systems help solve the angular momentum problem (R. Larson) There are multiple pathways to form binaries The cluster population should be distinct from the field population The formation mechanism should leave an imprint on the population

5 Binary Formation Three modes Offner, Kratter et al 2010 Capture /ejection Turbulent Fragmentation Disk Fragmentation 276 MOECKEL & BALLY Vol. 656 Kratter et al 2010 Moeckel & Bally 2007 Fig. 1. Example of an encounter with m ¼ 3:0 M, rp ¼ 175 AU, and i ¼ 45. Plotted is the logarithm of the gas column density. Left:Impactorhasnotyetpassed through the disk, which is in its relaxed, initial state. Right: Passage through the disk is completed, and spiral features are visible. formation of binaries and the destruction of the disks around The temperature profile is

6 What observations show us: For solar type stars, the distribution is log-flat from AU with no apparent break in slope or frequency Lower mass stars have separations typically < 200 AU (except the wide ones) Higher mass stars are incomplete but high multiplicity. May show a preference for more equal mass ratio at smaller separation, and a correlation between mass ratio and separation For solar type and lower mass stars, all companions masses are equally probable Separation in field is log normal, and the frequency is lower Kraus et al 2011, Raghavan et al 2010, Sana & Evans 2011

7 Multiplicity is Mass Dependent 30 RAGHAVA Figure 12. Multiplicity statistics by spectral type. The thin solid lines represent Raghavan et al 2010

8 Pre-Main Sequence stars have a higher multiple fraction Mathieu 1994 Goodwin et al 2007

9 Two Right Answers Fisher 2004: less controversial ICs, no physics, right (field) distribution gure 17. Bate 2012: controversial ICs, right (field) distribution

10 Current Binary Star Problems Binary Formation and Early Evolution: Large Scale - collapse from GMCs Mid Scale - formation from individual core Small Scale - formation within / interaction with protostellar disks Evolved Binaries Common Envelope Phases Supernovae / Tidal Disruptions

11 Simulating Binaries: What we want Robust hydrodynamic scheme (shock capturing, *low numerical diffusion) Dynamic Range AMR Sink Particles (Self) Gravity No enforced axisymmetry MHD? Radiation? Cooling / complex EOS?

12 What we get with...cartesian Grid Codes PRO: AMR Sink Particles (Self) Gravity (FFT / multigrid) Shock capturing hydro (Reimann solvers) (non-ideal) MHD, radiation, EOS, etc CON: linear vs angular momentum conservation high Mach number problem resolving spheres with cubes some dynamic range limitations (courant, alfven speed) (somewhat) flexible w.r.t symmetry Kratter et al 2010

13 Example 1: Binaries via disk fragmentation Numerical Experiments: star + disk r Rc ORION: Parallel, Adaptive Mesh Refinement, hydro + SG + sink particles, isothermal limit (Klein 99, Truelove 98, Krumholz 2004) Goals core study role of rapid infall and fragmentation caused by self gravity Understand conditions for binary and multiple formation Conduct resolution study Kratter et al 2010

14 Example 2: Binary Orbital Evolution with MHD 7 Logarithm of Column Density (g/cm 2 ) Evolution of binary orbits with a misaligned magnetic field and core rotation axis (Enzo) Time= kyr, Length= 3.00e+16 cm Logarithm of Column Density (g/cm 2 ) Binary Separation (cm) AU Time (kyr) 0 Fig. 2. Evolution of binary separation with time for λ = 4caseswithdifferent tilt angles: 0 (black solid), 45 (blue dash-dotted), and 90 (red dashed). Time= kyr, Length= 3.00e+16 cm Zhao, Li, & Kratter, in prep

15 What we get with...cylindrical / Spherical Grid Codes PRO: aligned flows and grids (disks / spheres) Sink Particles (Self) Gravity CON: high Mach number problem constrained axis of symmetry some dynamic range limitations (courant, alfven speed) Shock capturing hydro (non-ideal) MHD, radiation, EOS, etc angular momentum conservation FARGO type algorithm P. Armitage

16 Example 1: Binary - disk interaction with Binary offgrid Live binary at the center, but not on the grid Pierens & Nelson, 2008

17 What we get with...sph PRO: Lagrangian solution to dynamic range problems Sink Particles (Self) Gravity (tree) angular momentum conservation CON: complexities in addressing numerical diffusion some dynamic range limitations (courant, alfven speed) some shock capturing challenges some uncertainties in convergence No imposed symmetries / domain geometry N. Moeckel

18 M. Bate, 2011

19 What we get with...moving Mesh PRO: Lagrangian solution to dynamic range problems Sink Particles (Self) Gravity (tree) No imposed symmetries / domain geometry Reimann solver hydro CON: complexities in addressing numerical diffusion and conservation slower due to tesselation requirements complex boundary conditions grid sampling noise no high-mach number flows across the mesh

20 Moving Mesh Codes (e.g. AREPO, Springel 2009) 8 Mun oz et al. Mesh is made every timestep to track the motion of the cell center of mass Reimann problem is solved in the cell face frame (boosted) Planet-disk interaction on a moving mesh 3 Figure 6. Zoomed-in projected gas density in units of M AU fortunately, non of these approximations is a good substitute for radiation hydrodynamics. The implementation of an optically thin cooling function as we have done in this work Figure 1. Evolution of a Voronoi mesh under differential rotation supported by a Keplerian potential (time increases left-to-right and top-to-bottom). The mesh-generating points are initially positioned in a polar distribution (logarithmic spacing in radius), which is roughly maintained. The color-filled cells correspond to set of cells tagged according to ID number at time= 0(top left panel) and subsequently followed in time. The spatial distribution of the4.2.1 taggedclump Identification cells highlights the quasi-lagrangian nature (Vogelsberger et al. 2012) of the moving-mesh approach in the case of Keplerian shear. The identification of over-dense regions in circumstellar disk sim- 2 at six different times around pericenter for configuration Q1. Our clump-finding method consists of four stages: (1) a smoothed density field is obtained at each mesh-generating point by averaging over 128 neighbors; (2) over-dense regions are identified as those exceeding the smooth background by a factor of 5-10; (3) over-dense cells are grouped into collections of clumps by means of a friends-of-friends algorithm; and (4) the self-gravitating character of these clumps is addressed by computing the ratio of thermal to gravitational potential energy. Diego Munoz, 2013

21 Diego Muñoz - Harvard University example: density wake in a small mass ratio binary AAS Winter Meeting - Long Beach, CA - 01/08/13

22 Moving-mesh techniques for Astrophysical Gas Dynamics How to construct the Voronoi mesh Diego Muñoz -- NBI Talk 8/14/12

23 Moving-mesh techniques for Astrophysical Gas Dynamics How to construct the Voronoi mesh Each Voronoi cell contains the space closest to its generating point The Delaunay triangulation contains only triangles with an empty circumcircle. The Delaunay tiangulation maximizes the minimum angle occurring among all triangles. The centres of the circumcircles of the Delaunay triangles are the vertices of the Voronoi mesh. In fact, the two tessellations are the topological dual graph to each other. Diego Muñoz -- NBI Talk 8/14/12

24 Moving-mesh techniques for Astrophysical Gas Dynamics How to construct the Voronoi mesh Each Voronoi cell contains the space closest to its generating point The Delaunay triangulation contains only triangles with an empty circumcircle. The Delaunay tiangulation maximizes the minimum angle occurring among all triangles. The centres of the circumcircles of the Delaunay triangles are the vertices of the Voronoi mesh. In fact, the two tessellations are the topological dual graph to each other. Diego Muñoz -- NBI Talk 8/14/12

25 Moving-mesh techniques for Astrophysical Gas Dynamics The fluxes are calculated with an exact Riemann solver in the frame of the moving cell boundary SKETCH OF THE FLUX CALCULATION The motion of the mesh generators uniquely determines the motion of all cell boundaries State left of cell face State right of cell face Riemann solver (in frame of cell face) Diego Muñoz -- NBI Talk 8/14/12

26 Another kind of n-body After the hydrodynamics is mostly done, we need to worry about dynamics For planetary dynamics, precision requires direct integration of the equations of motion Easy: 4th order Runge-Kutta Efficient: Symplectic Methods, e.g. Wisdom-Holman Mapping Robust: Bulirsch-Stoer Many dynamics problems are Embarrassingly Parallel

27 U of A: Not just telescopes! Gurtina Besla: Galaxy Formation / Dynamics me! Travis Barman (LPL): planetary atmospheres Andrew Youdin: Planet / solar system formation YOU?! New Theory Fellowship, coming this fall...