Gravitational Waves from Supernova Core Collapse Outline Max Planck Institute for Astrophysics, Garching, Germany

Harald Dimmelmeier [email protected]

Gravitational Waves from Supernova Core Collapse: What could the Signal tell us?

Work done at the MPA in Garching

Dimmelmeier, Font, M¨uller, Astron. Astrophys., 388, 917–935 (2002), astro-ph/0204288 Dimmelmeier, Font, M¨uller, Astron. Astrophys., 393, 523–542 (2002), astro-ph/0204289

Source Simulation Focus Session, Center for Gravitational Wave Physics, Penn State University, 2002 Gravitational Waves from Supernova Core Collapse

Max Planck Institute for Astrophysics, Garching, Germany Motivation

Physics of Core Collapse Supernovæ

Physical model of core collapse supernova:

Massive progenitor star (Mprogenitor 10 30M ) develops an iron core (Mcore 1.5M ). • ≈ − ≈ This approximate 4/3-polytrope becomes unstable and collapses (Tcollapse 100 ms). • ≈ During collapse, neutrinos are practically trapped and core contracts adiabatically. • At supernuclear density, hot proto-neutron star forms (EoS of matter stiﬀens bounce). • ⇒ During bounce, gravitational waves are emitted; they are unimportant for collapse dynamics. • Hydrodynamic shock propagates from sonic sphere outward, but stalls at Rstall 300 km. • ≈ Collapse energy is released by emission of neutrinos (Tν 1 s). • ≈ Proto-neutron subsequently cools, possibly accretes matter, and shrinks to ﬁnal neutron star. • Neutrinos deposit energy behind stalled shock and revive it (delayed explosion mechanism). • Shock wave propagates through stellar envelope and disrupts rest of star (visible explosion). • Neutron star might develop triaxial instabilities due to gravitational wave backreaction. •

Source Simulation Focus Session, Center for Gravitational Wave Physics, Penn State University, 2002 Gravitational Waves from Supernova Core Collapse

Max Planck Institute for Astrophysics, Garching, Germany Motivation

Gravitational Waves from Core Collapse Supernovæ

Diﬃculties with observing core collapse supernova: So far we only see optical light emission (light curve) of the explosion (hours after collapse – envelope optically thick).

Gravitational waves are direct means of observation of stellar core collapse!

Challenge: Such burst signals are very complex! We need realistic prediction of signal from relativistic numerical simulations! ⇒

Our contribution:

Relativistic simulations of rotational core collapse to a neutron star in axisymmetry, and publicly available gravitational wave signal catalogue from a parameter study.

Source Simulation Focus Session, Center for Gravitational Wave Physics, Penn State University, 2002 Gravitational Waves from Supernova Core Collapse

Max Planck Institute for Astrophysics, Garching, Germany Motivation

Gravitational Waves from Core Collapse Supernovæ

During the various evolution stages, simulations of core collapse face many challenges:

Physical complexity: • Many and complicated aspects of physics involved. Some of the physics like supernuclear EoS uncertain. Initial rotation state of iron core not well known. Numerical diﬃculties: • Many diﬀerent time and length scales (comoving coordinates, FMR, AMR). Multidimensional treatment might be crucial (convection in proto-neutron star and neutrino heating region, triaxial instabilities, Rayleigh–Taylor instabilities in envelope, rotation, magnetic ﬁelds, . . . ). Solution of Boltzmann transport equations for consistent treatment of neutrinos.

Numerical simulations are very complicated, many approximations necessary. ⇒ But: Measurement of signal waveform will reveal new physics!

Gravitational waves will put constraints on rotation states of iron core and neutron star, supernuclear EoS, degree of convection,...

Max Planck Institute for Astrophysics, Garching, Germany Motivation

Gravitational Waves from Core Collapse Supernovæ

Example:

Development of triaxial instabilities on dynamic or secular timescales can be an important source of gravitational waves.

Signal amplitude is comparable to core collapse signal.

This process will yield particular waveform structure. Waveform reveals information about supernuclear EoS.

Such simulations can only be done in 3d codes.

Max Planck Institute for Astrophysics, Garching, Germany Motivation

Gravitational Waves from Core Collapse Supernovæ

During the various evolution stages, simulations of core collapse face many challenges:

Physical complexity: • Many and complicated aspects of physics involved. Some of the physics like supernuclear EoS uncertain. Initial rotation state of iron core not well known. Numerical diﬃculties: • Many diﬀerent time and length scales (comoving coordinates, FMR, AMR). Multidimensional treatment might be crucial (convection in proto-neutron star and neutrino heating region, triaxial instabilities Rayleigh–Taylor instabilities in envelope, rotation, magnetic ﬁelds, . . . ). Solution of Boltzmann transport equations for consistent treatment of neutrinos.

Numerical simulations are very complicated, many approximations necessary. ⇒ But: Measurement of signal waveform will reveal new physics!

Gravitational waves will put constraints on rotation states of iron core and neutron star, supernuclear EoS, degree of convection,...

Max Planck Institute for Astrophysics, Garching, Germany Motivation

Gravitational Waves from Core Collapse Supernovæ

Another example:

Convection in both the proto-neutron star, • the remainder of the iron core, and • the stellar envelope • can have important consequences on dynamics of supernova explosion.

In inner, dense regions, convection can produce considerable amount of gravitational radiation.

Now concentrate on gravitational waves from core bounce.

Source Simulation Focus Session, Center for Gravitational Wave Physics, Penn State University, 2002 Gravitational Waves from Supernova Core Collapse Model Assumptions Max Planck Institute for Astrophysics, Garching, Germany

Model Assumptions

To reduce complexity of problem, we have assumed axisymmetry and equatorial symmetry, • rotating γ = 4/3 polytropes in equilibrium as initial models, • 10 3 with ρc ini = 10 gm cm , Rcore 1 500 km, and various rotation proﬁles and rates, − ≈ simpliﬁed ideal ﬂuid equation of state, P (ρ, ) = Ppoly + Pth (neglect complicated microphysics), • constrained system of Einstein equations (assume conformal ﬂatness for 3-metric). •

Goals

We have built an axisymmetric GR hydro code and performed parameter study of 26 models to extend research on Newtonian rotational core collapse by Zwerger and M¨ullerto GR, • obtain more realistic waveforms as “wave templates” for interferometer data analysis, • (wave templates are important and actually being used in data analysis: VIRGO data analysis group has used Zwerger’s catalogue (Pradier et al., 2000), and already uses our results (Chassande-Mottin, 2002)), have 2d GR hydro code for comparison with future simulations and as basis for extension. •

Max Planck Institute for Astrophysics, Garching, Germany Results

Regular Collapse

Model A: Slow, almost uniform rotation, fast collapse ( 40 ms), soft supernuclear EoS. ≈ 10.0 500.0 Relativistic ]

-3 8.0 bounce Newtonian g cm

0.0 [cm] 14 20 ring down E2

6.0 A

[10 oscillations c

ρ ring down signal 4.0 -500.0

2.0 ρ signal amplitude central density nuc signal maximum

0.0 -1000.0 35.0 40.0 45.0 50.0 35.0 40.0 45.0 50.0 time t [ms] time t [ms] Deep dive into potential, high supernuclear densities, single bounce, subsequent ring down. • GR simulation: Higher central density and signal frequency, but lower signal amplitude. • Explanation: GW signal is determined by accelation of extended mass distribution: 2 E2 d A = Q¨ Z dV ρ r2 . weight factor! 20 ∝ dt2 ← In relativistic gravity core is more compact. Gravitational waves can have smaller amplitude! ⇒

Max Planck Institute for Astrophysics, Garching, Germany Results

Typical Features of Gravitational Wave Signals

Every waveform shares some or all of several more or less clearly identiﬁable features.

500.0 positive peak (can be the signal maximum) positive signal rise ring down (except in multiple 250.0 bounce collapse) [cm] 20 E2 0.0 A

-250.0 flank to local minimum is missing negative peak (except in multiple with bend bounce collapse) -500.0 signal amplitude in slope

-750.0 negative peak (usually the signal maximum)

45.0 50.0 55.0 time t [ms]

Our waveform catalogue shows dependence of these features on the parameters. These features can be used to train ﬁlters and search algorithms (together with information about signal amplitude and frequency). Conversely, in detected signal, these features allow for conclusions about physics of core collapse.

Max Planck Institute for Astrophysics, Garching, Germany Results

Change of Collapse Dynamics

Model B: Slow, almost uniform rotation, slow collapse ( 90 ms). ≈ 4.0 1000.0 regular bounce Relativistic ring down signal ]

-3 Newtonian 3.0 0.0 g cm [cm] 14 20 E2 A [10

c multiple bounce ρ 2.0 ρ -1000.0 nuc

multiple bounce signal 1.0 bounce interval -2000.0 signal amplitude central density

0.0 -3000.0 80.0 90.0 100.0 110.0 120.0 80.0 90.0 100.0 110.0 120.0 time t [ms] time t [ms] Rotation increases strongly during collapse (angular momentum conservation!). • Newtonian: Nuclear density hardly reached, multiple centrifugal bounce with re-expansion. • GR: Nuclear density easily reached, regular single bounce. • Relativistic simulations show multiple bounces only for few extreme models. • Strong qualitative diﬀerence in collapse dynamics and thus in signal form.

Max Planck Institute for Astrophysics, Garching, Germany Results

Change of Collapse Dynamics

A change in collapse dynamics is clearly visible in energy spectrum.

1.0e-08 Relativistic ]

-1 frequency shift 1.0e-09 Newtonian Hz 2 c . O

M 1.0e-10 multiple bounce [

ν collapse /d

gw 1.0e-11 dE

1.0e-12 regular collapse

1.0e-13 energy spectrum

1.0e-14 100.0 1000.0

ν [Hz] Multiple bounce collapse has broad round spectrum which peaks at relatively low frequency. • Regular collapse has steeper spectrum with pronounced peak at higher frequency. •

Max Planck Institute for Astrophysics, Garching, Germany Results

Rapidly Rotating Models

Model C: Fast and extremely diﬀerential rotation, rapid collapse ( 30 ms). ≈

Initial model has toroidal density shape; torus becomes more pronounced during contraction. • Proto-neutron star is surrounded by disc-like structure, which is accreted. • After bounce, strongly anisotropic shock front forms. • Bar instabilities are likely to develop on dynamical timescale (particularly in GR and • with diﬀerential rotation (cf. Shibata et al., 2002)); they will produce characteristic signal!

Max Planck Institute for Astrophysics, Garching, Germany Results

Gravitational Wave Signals

Just as in Newtonian gravity, in our relativistic simulations we observe three normal collapse types, • regular collapse (signal shows one large negative peak, and clear ring down), multiple bounce collapse (signal shows distinct multiple large negative peaks, and no ring down), rapid collapse (signal shows one small positive maximum peak, and low-amplitude ring down), a separate class of rapidly and diﬀerentially rotating models (which form torus). •

10.0 400.0 Regular collapse

] 200.0 -3 8.0 Multiple bounce collapse Rapid collapse g cm

0.0 [cm] 14 20 E2

6.0 A [10 c

ρ -200.0 4.0 -400.0

2.0 ρ signal amplitude central density nuc -600.0

0.0 -800.0 -5.0 0.0 5.0 10.0 15.0 -5.0 0.0 5.0 10.0 15.0 time after bounce t [ms] time after bounce t [ms] These collapse types can be identiﬁed both in density evolution and in signal waveform.

Max Planck Institute for Astrophysics, Garching, Germany Results

Gravitational Wave Signals

Inﬂuence of relativistic eﬀects on signals: Investigate amplitude–frequency diagram.

1.0e-19 4.0

3.0

detector 2.0

1.0e-20 first LIGO

sensitivity (at 10 kpc) TT h (arbitrary scaling)

1.0 TT 0.9 h

advanced LIGO a frequency 0.8 1.0e-21 (and amplitude) 0.7 shift 0.6 b

signal strength 0.5

0.4 signal strength

1.0e-22 0.3 10.0 100.0 1000.0 10000.0 100.0 1000.0 frequency ν [Hz] frequency ν [Hz] Spread of the 26 models does not change much. Signal of galactic supernova detectable. • ⇒ On average: Amplitude remains at hTT 10 23 10 Mpc/R, frequency increases to ν 1000 Hz. • ≈ − · ≈ If close to detection threshold: Signal could leave sensitivity window in relativistic gravity!

Max Planck Institute for Astrophysics, Garching, Germany Future Directions

Future Directions

Further developments of our axisymmetric CFC code: Include more accurate approximation of spacetime metric (CFC Plus) • (get closer to formation of rotating black hole). Extend code to 3d, and investigate dynamic development of triaxial instabilities. • Add more realistic microphysics and check robustness of wave signal • (simple extension of supernuclear EoS, tabulated EoS (Lattimer–Swesty), neutrino eﬀects). Use better extraction method for gravitational waves (currently quadrupole formula is used). •

Ongoing or planned other projects: Assess quality of CFC approximation by comparison to fully relativistic simulations • (Cartoon method used by Shibata – Problems with wave extraction!). Use AEI Cactus Code to simulate axisymmetric and fully 3-dimensional core collapse. • Make AMR work with multidimensional hydrodynamic core collapse codes. • Extract gravitational waves from existing multidimensional Newtonian simulations. • Add (full or approximate) relativistic gravity to existing Newtonian codes. • Extend existing spherical Newtonian codes with sophisticated microphysics to multidimensions. •

Source Simulation Focus Session, Center for Gravitational Wave Physics, Penn State University, 2002 Gravitational Waves from Supernova Core Collapse Summary Max Planck Institute for Astrophysics, Garching, Germany

Summary

We have obtained the ﬁrst gravitational wave templates from simulations of rotational supernova core collapse in general relativity.

Our simulations show: We can identify same three collapse types as in Newtonian simulations. • Remnants are more compact with higher central densities compared to Newtonian gravity. • Many previous multiple bounce models collapse to supernuclear densities in relativity. • On average, signal amplitude does not change • (we still ﬁnd hTT 10 23 10 Mpc/R for axisymmetric supernova core collapse). ≈ − · However, frequency increases to ν 1000 Hz • ≈ (particularly due to suppression of multiple bounce collapse). Relativistic eﬀects increase rotation rate; many models could develop triaxial instabilities. • Our wave templates replace Zwerger catalogue; we have made them publicly available: http://www.mpa-garching.mpg.de/Hydro/RGRAV/.

This area of research is currently very active and exciting. The emerging interaction between numerical relativity and hydrodynamics, and data analysis is stimulating on both sides.

Source Simulation Focus Session, Center for Gravitational Wave Physics, Penn State University, 2002