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INSTABILITIES OF ROTATING RELATIVISTIC STARS

INSTABILITIES OF ROTATING RELATIVISTIC STARS. John Friedman University of Wisconsin-Milwaukee Center for Gravitation and Cosmology. outline.

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INSTABILITIES OF ROTATING RELATIVISTIC STARS

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  1. INSTABILITIES OF ROTATING RELATIVISTIC STARS John Friedman University of Wisconsin-MilwaukeeCenter for Gravitation and Cosmology

  2. outline I. NONAXISYMMETRIC INSTABILITY II. DYNAMICAL INSTABILITY III. GW-DRIVEN (CFS) INSTABILITY & R-MODES IV. SPIN-DOWN AND GRAVITATIONAL WAVES FROM A NEWBORN NEUTRON STAR V. INSTABIILTY OF OLD NEUTRON STARS SPUN-UP BY ACCRETION VI. DOES THE INSTABILITY SURVIVE THE PHYSICS OF A REAL NEUTRON STAR?(MUCH OF THIS LAST PART TO BE COVERED BY NILS ANDERSSON’S TALK)

  3. NONAXISYMMETRIC INSTABILITY • MINIMIZING ENERGY AT FIXED ANGULAR MOMENTUM: • GRAVITY BUT NO ROTATION: MINIMIZE ENERGY BY MAXIMIZING GRAVITATIONAL BINDING ENERGY

  4. NONAXISYMMETRIC INSTABILITY • MINIMIZING ENERGY AT FIXED ANGULAR MOMENTUM: • ROTATION BUT NO GRAVITY, MINIMIZE KINETIC ENERGYAT FIXED J BY PUSHING FLUID TO BOUNDARY

  5. NONAXISYMMETRIC INSTABILITY • MINIMIZING ENERGY AT FIXED ANGULAR MOMENTUM: • RAPID ROTATION AND GRAVITY:COMPROMISE: SEPARATE FLUID INTO TWO SYMMETRIC PARTS

  6. DYNAMICAL INSTABILITY • GROWS RAPIDLY DYNAMICAL TIMESCALE = TIME FOR SOUND TO CROSS STAR • SECULAR INSTABILITY • REQUIRES DISSIPATION – VISCOSITY OR GRAVITATIONAL RADIATIONSLOWER, DISSIPATIVE TIMESCALE

  7. DYNAMICAL INSTABILITY • CONSERVATION LAWS BLOCK NONAXISYMMETRIC INSTABILITY IN UNIFORMLY ROTATING STARS UNTIL STAR ROTATES FAST ENOUGH THAT • T ( ROTATIONAL KINETIC ENERGY ) .|W| ( GRAVITATIONAL BINDING ENERGY) t= > 0.26 UNIFORMLY ROTATING STARS WITH NS EQUATIONS OF STATE HAVE MAXIMUM ROTATION t < 0.12

  8. BUT A COLLAPSING STAR WITH LARGE DIFFERENTIAL ROTATION MAY BECOME UNSTABLE AS IT CONTRACTS AND SPINS UP Bar-mode instability of rotating disk (Simulation by Kimberly New)

  9. Recent studies of dynamical instability byGondek-Rosinska and GourgoulhonShibata, Karino, Eriguchi, YoshidaWatts, Andersson, Beyer, SchutzCentrella, New, Lowe and BrownImamura, Durisen, PickettNew, Centrella and TohlineShibata, Baumgarte and Shapiro • TWO SURPRISES FOR LARGE DIFFERENTIAL ROTATION • m=2 (BAR MODE) INSTABILITY CAN SET IN FOR SMALL VALUES OF t • m=1 (ONE ARMED SPIRAL) INSTABILITY CAN DOMINATE

  10. SAIJO,YOSHIDA GROWTH OF AN l=m=1 INSTABILITYIN A RAPIDLY DIFFERENTIALLY ROTATATING MODEL

  11. SECULAR INSTABILITY

  12. GRAVITATIONAL-WAVE INSTABILITY Chandrasekhar, F, SchutzOutgoing nonaxisymmetric modes radiate angular momentumto cfs1 If the pattern rotates forwardrelative to , it radiates positive Jto

  13. cfs2 If the pattern rotates backwardrelative to , it radiates negative Jto

  14. That is: A forward mode, with J > 0, radiates positive Jto A backwardmode, with J < 0, radiates negative Jto Radiation damps all modes of a spherical star cfs3

  15. But, a rotating star drags a mode in the direction of thestar's rotation: A mode with behavior that moves cfs4 backward relative to the staris draggedforward relative to , whenmW > sThe mode still has J < 0, because Jstar + J mode < J star . This backwardmode, with J < 0, radiates positive Jto . Thus Jbecomes increasingly negative, and THE AMPLITUDE OF THE MODE GROWS

  16. surprise OBSERVATIONAL SUPRISE: 16 ms pulsar seen in a supernova remnant

  17. surprise2 OBSERVATIONAL SUPRISE: 16 ms pulsar seen in a supernova remnant In a young (5000 yr old) supernova remnant in the Large Magellanic Cloud, Marshall et al found a pulsar with a 16 ms period and a spin-down time ~ lifetime of the remnant This, for the first time, implies: A class of neutron stars have millisecond periods at birth.

  18. th_surprise A nearly simultaneous THEORETICAL SURPRISE:A new variant of a gravitational-wave driven instability of relativistic stars may limit the spin of newly formed pulsars and of old neutron stars spun up by accretion. The newly discovered instability may set the initial spin of pulsars in the newly discovered class.

  19. Andersson JF, Morsink Kojima Lindblom,Owen, Morsink Owen, Lindblom, Cutler, Andersson, Kokkotas,Schutz Schutz, Vecchio, Andersson Madsen Andersson, Kokkotas, Stergioulas Levin Bildsten Ipser, Lindblom JF, Lockitch Beyer, Kokkotas Kojima, Hosonuma Hiscock Lindblom Brady, Creighton Owen Rezzolla, Shibata, Asada, Lindblom, Mendell, Owen Baumgarte, Shapiro Flanagan Rezzola,Lamb, Shapiro Spruit Levin Ferrari, Matarrese,Schneider Lockitch Rezania Prior work on axial modes: Chandrasekhar & Ferrari These surprises led to an explosion of interest:

  20. STILL MORE RECENT Stergioulas, Font, Kokkotas Kojima, Hosonuma Yoshida, Lee Rezania, Jahan-Miri Yoshida, Karino, Yoshida, Eriguchi Rezania, Maartens Andersson, Lockitch, JF Lindblom, Mendell Andersson, Kokkotas, Stergioulas AnderssonUshomirsky, Cutler, Bildsten Bildsten, Ushomirsky Andersson, Jones, Kokkotas, Brown, Ushomirsky Stergioulas Lindblom,Owen,Ushomirsky Rieutord Wu, Matzner, Arras Ho, Lai Levin, Ushomirsky Madsen Lindblom, Tohline, Vallisneri Stergioulas, Font Arras, Flanagan, Schenk, JF, Lockitch Sa Teukolsky,Wasserman Morsink Jones Lindblom,Owen Ruoff, Kokkotas, Andersson,Lockitch,JF

  21. AND MORE Karino, Yoshida, Eriguchi Hosonuma Watts, Andersson Rezzolla,Lamb,Markovic,Arras, Flanagan, Morsink, ShapiroWagoner, Hennawi, Liu Shenk, Teukolsky, Wasserman Morsink Jones, Andersson, Stergioulas Haensel, Lockitch, Andersson Prix, Comer, Andersson Hehl Gressman, Lin, Suen, Stergioulas, JF Lin, SuenXiaoping, Xuewen, Miao, Shuhua, NanaReisnegger, Bonacic Yoon, LangerDrago, Lavagno, Pagliara Drago, Pagliara, BerezhianiGondek-Rosinska, Gourgoulhon, HaenselBrink, Teukolsky, Wasserman

  22. GRAVITATIONAL RADIATION MASS QUADRUPOLE MASSQUADRUPOLE ENERGY RADIATED

  23. AXIAL GRAVITATIONAL RADIATION MASS QUADRUPOLE CURRENT QUADRUPOLE ENERGY RADIATED

  24. AXIAL GRAVITATIONAL RADIATION MASS QUADRUPOLE CURRENT QUADRUPOLE ENERGY RADIATED

  25. PERTURBATIONS WITH ODINARY (POLAR) PARITY

  26. P = 1 l = 1 P = -1 l = 2 P = 1 l = 0

  27. P = 1 l = 1 P = -1 l = 2 P = 1 l = 0

  28. PERTURBATIONS WITH AXIAL PARITY BECAUSE ANY SCALAR IS A SUPERPOSITION OF Ylm AND Ylm HAS, BY DEFINITION, POLAR PARITY, EVERY SCALAR HAS AXIAL PARITY: BUT VECTORS (& TENSORS) CAN HAVE AXIAL PARITY

  29. P = 1 l = 0 NONE l = 1

  30. l = m = 2 View from pole View from equator

  31. P = 1 P = -1 Above equator l = 0 NONE l = 1 l = 2 Below equator

  32. GROWTH TIME:ENERGY PUMPED INTO MODE = ENERGY RADIATED TO I+

  33. INSTABILITY OF POLAR MODES THE QUADRUPOLE POLAR MODE (f-mode ) HAS FREQUENCY s OF ORDER THE MAXIMUM ANGULAR VELOCITY WMAX OF A STAR.

  34. W = WMAX ROTATION ENERGY AT INSTABILITY 1014 1015 CENTRAL DENSITY THAT MEANS A BACKWARD MOVING POLAR MODE IS DRAGGED FORWARD, ONLY WHEN A STAR ROTATES NEAR ITS MAXIMUM ANGULAR VELOCITY,WMAX Stergioulas

  35. BECAUSE AN AXIAL PERTURBATION OF A SPHERICAL STAR HAS NO RESTORING FORCE – ITS FREQUENCY VANISHES. IN A ROTATING STAR IT HAS A CORIOLIS-LIKE RESTORING FORCE, PROPORTIONAL TO W

  36. Frequency relative to an inertial observer:fR= f - Wtdv = r2 r [ sin2 qei(2f - 4/3 Wt)]sR = - 2/3 WCOROTATING THE UNSTABLE l = m = 2 r-MODE Newtonian: Papaloizou & Pringle, Provost et al, Saio et al, Lee, Strohmayer The mode is a current that is odd under paritydv = r2 r [ sin2 q ei(2f + 2/3 Wt) ]Frequency relative to a rotating observer:sR = 2/3 W COUNTERROTATING R

  37. FLOW PATTERN OF THE l = m = 2 r-MODE

  38. Rotating Frame • Animation shows backward (clockwise) motion of patternand motion of fluid elements Ben Owen’s animation

  39. Inertial Frame Pattern moves forward(counterclockwise) Star and fluid elements rotate forward more rapidly

  40. VISCOUSDAMPING ep n Above 1010K, beta decay and inverse beta decay n produce neutrinos that carry off the energy of the mode:bulk viscositytBULK = CT6 Below 109K, shear viscosity (free e-e scattering) dissipates the mode’s energy in heat tSHEAR = CT-2

  41. Star is unstable only whenWis larger than critical frequency set by bulk and shear viscosity Bulk viscosity kills instability at high temperature Shear viscosity kills instability atlow temperature Wcrit/Wmax 1 0.5 0.1 Star spins down as it radiates its angular momentum in gravitational waves 105 107 109 1011(From Lindblom-Owen-Morsink Figure)Temperature (K)

  42. GRAVITATIONAL WAVES FROM SPIN-DOWN hc = h[t(f)] / f2/|df/dt| hc= 1024 (W/WK)3 (20 Mpc/D) a AMPLITUDE, dv/RW Owen, Lindblom, Cutler, Schutz, Vecchio, Andersson Brady, Creighton Owen Lindblom

  43. hc 10-20 10-21 10-22 10-23 LIGO I hc LIGO II 100 Hz 1000 Hz GRAVITATIONAL WAVES FROM SPIN-DOWN hc= 1024 (W/WK)3 (20 Mpc/D) a AMPLITUDE, dv/RW IF ONE HAD A PRECISE TEMPLATE, SIGNAL/NOISE WOULD LOOK LIKE THISFOR WAVES FROM A GALAXY 20 Mpc AWAY:

  44. INSTABILITY OFOLD ACCRETING STARS:LMXBs

  45. BINARIES WITH A NEUTRON STAR AND A SOLAR-MASS COMPANION CAN BE OBSERVED AS LOW-MASS X-RAY BINARIES (LMXBs), WHEN MATTER FROM THE COMPANION ACCRETES ONTO THE NEUTRON STAR.MYSTERY: THE MAXIMUM PERIODS CLUSTER BELOW 642 HZ, WITH THE FASTEST 3 WITHIN 4%

  46. From Chakrabarty, Bildsten FASTEST 3: 619 Hz, 622 Hz, 642 Hz VERY DIFFERENT MAGNETIC FIELDS – IMPLIES SPIN NOT LIMITED BY MAGNETIC FIELD

  47. PAPALOIZOU & PRINGLE, AND WAGONER (80s)ACCRETION MIGHT SPIN UP A STAR UNTIL J LOST IN GW = J GAINED IN ACCRETION FOR POLAR MODES, VISCOSITY OF SUPERFLUID DAMPS THE INSTABILITY AND RULES THIS OUT BUT AXIAL MODES CAN BE UNSTABLE Andersson, Kokkotas, Stergioulas Bildsten Levin Wagoner Heyl Owen Reisenegger & Bonacic R-MODE INSTABILITY IS NOW A LEADING CANDIDATE FOR LIMIT ON SPIN OF OLD NSs

  48. CAN GW FROM LMXBs BE OBSERVED? IF WAGONER’S PICTURE IS RIGHT, R-MODES ARE AN ATTRACTIVE TARGET FOR OBSERVATORIES WITH THE SENSITIVITY OF ADVANCED LIGO WITH NARROW BANDING BUT YURI LEVIN POINTED OUT THAT IF THE VISCOSITY DECREASES AS THE UNSTABIILITY HEATS UP THE STAR, A RUNAWAY GROWTH IN AMPLITUDE RADIATES WAVE TOO QUICKLY TO HOPE TO SEE A STAR WHEN IT’S UNSTABLE

  49. 4 months! 5x106 yr LEVIN’S CYCLE Wcritical.Wmax T 108 109 107 SPIN DOWN TIME < 1/106 SPIN UP TIME IS A STAR YOU NOW OBSERVE SPINNING DOWN? PROBABILITY < 1/106

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