Gravitational Wave Signals from Core-Collapse Supernovae

Bernhard MüllerQueen's University Belfast

Monash

H. Andresen, E. Müller, H.-Th. Janka (MPA Garching)

core-collapsesupernovae

massive star

heavy elements

neutron stars & supernova remnants

gravitational waves neutrinos

h~2G

c4 r

d 2 I

dt 2~ 2G

c4 rM R2 f 2

dimensionless strain distance

mass quadrupole moment (transverse-

trace free component)

mass involved

radius typical frequency

Gravitational Waves from Core-Collapse Supernovae

Rotational collapse Convection & SASI

Scheidegger et al. (2010)

Other triaxial instabilities (low T/W, r-mode)

Asymmetry parameter

Rotational Collapse

Bounce signal (Dimmelmeier et al. 2008): very regular shape, amenable to template-based searches, frequency of fundamental quadrupole mode of proto-neutron star (~750 Hz)

Characteristic strain & frequency for different progenitors, EoS & rotation rates (Dimmelmeier et al. 2008)

Detectability limit: of order ~40kpc for Advanced LIGO for initial core

rotation periods of ~seconds (see, e.g., Logue et al. 2012, Hayama et al. 2015,

Gossan et al. 2016)

At ~10kpc, the initial period can be constrained to within ~20% (Abdikamalov et al. 2014)

10kpc

15Mpc

800kpc

Rotational Collapse

Characteristic strain & frequency for different progenitors, EoS & rotation rates (Dimmelmeier et al. 2008)

10kpc

15Mpc

800kpc

Abdikamlov et al. (2014): Inferred=T/W in progenitor coe from prospective signal

Rapid Rotation & Non-axisymmetric Instabilities

● For initial rotation periods <1s: core subject to low-T/W triaxial instability

● GW emission around ~1kHz (Ott et al. 2007, Scheidegger 2010, Kuroda et al. 2014) with long life-time

● Long coherence time & large amplitudes increase detectability limit (~100kpc with AdvLIGO/Kagra, Gossan et al. 2016)

● Triaxial instabilities could also be excited at later times (Piro & Thrane 2012: fallback), but simulations are lacking

@10kpc

from Scheidegger et al. (2010)

Gravitational Wave Emission in Neutrino-Driven Supernovae

● Shock pushed outward to ~150km as matter piles up on the neutron star, then recedes again

● Heating or gain region develops some tens of ms after bounce

● Convective overturn & shock oscillations (“SASI”) enhance the efficiency of -heating, which finally revives the shock

● Instabilities imply time-varying quadrupole moment → GW emission

convection

shock oscillations

(“SASI”)

shock

heat

ing

co

olin

g

shock

gravitational

wave emission

Explosion of 20M⊙ progenitor aided by standing accretion shock instability (Melson et al. 2015)

rotating 15M8 model of Heger, Woosley & Spruit (2005)(2D simulation)

peak from rotational collapse

Most cores of massive stars expected to rotate slowly!

Bounce signal subdominant for the “typical” slowly rotating SN progenitor

8.1 M8, Z=10-

4Z8

9.6 M8, Z=0 11.2 M8

15 M8 27 M825 M8

(no explosion!)

“onset” of explosion

The Post-Bounce & Explosion Phase

Müller, Janka & Marek (2013)General trends from 2D models:

● Emission stronger for more massive progenitors (massive Si and O shells)● Peak activity around onset of explosion (weaker emission w/o explosion)

11

Structure of the GW Spectrum

time-integrated spectrum, 15M8

Signal seems to contain a lot of broad-band noise, but there is a well-defined and sharp frequency structure underneath:

● Better time-frequency analysis helps!

● Normalized wavelet spectrogram clearly shows evolution of typical frequency

zooming in on an exemplary time interval...

12

Structure of the GW Spectrum

“prompt convection”

Increasing PNS surface g-mode

frequency

time-integrated spectrum, 15M8

normalized wavelet spectrogram, 15M8

23zooming in on an exemplary

time interval...

Signal seems to contain a lot of broad-band noise, but there is a well-defined and sharp frequency structure underneath:

● Better time-frequency analysis helps!

● Normalized wavelet spectrogram clearly shows evolution of typical frequency

GR : f B2=d c2

dr

h4c s2

dS r dr

Newtonian : f B2=d dr

1

cs2

dS r dr

downflow

● Gravitational wave emission due to “ringing” in the neutron star surface region (Murphy et al. 2009, Müller et 2013)

● Typical frequency ~ buoyancy-frequency fb (l=2 g-mode) in convectively stable layer below the gain region

● GR correction factors matter!

● Relation to neutron star properties:

Gradient of potential

density

Schwarzschild discriminant

sound speed

f peak≈1

2GM

R2 1.1mn⟨E⟩ 1−GMRc2

2

The GW Spectrum

neutron mass

electron antineutrino mean energy ~ neutron

star surface temperature

neutron star mass

neutron star radius

Gravitational Waves from SASI & Convection in 3D

downflow Forcing by downflows in 2D is unphysically strong & impulsive (broad spectrum) → weaker excitation of surface g-mode in 3D

SASI (probably dipole+quadrupole components)

PNS interior

PNS “surface”

gain region

Total spectrum

High-frequency signal excited by PNS convection

Andresen, Müller, Janka & Müller (to be submitted)

Amplitudes lower by factor ~10 than in 2D

Gravitational Waves from SASI & Convection in 3D

Dominant source of high-frequency GW emission in 3D

SASI (probably dipole+quadrupole components)

PNS interior

PNS “surface”

gain region

Total spectrum

High-frequency signal excited by PNS convection

Andresen, Müller, Janka & Müller (to be submitted)

Amplitudes lower by factor ~10 than in 2D

GW Spectrograms from 3D Models

SASI episodes

PNS convection (+ surface g-mode as “frequency stabilizer”)

non-

expl

odi

ngex

plod

ing

Enhanced emission after explosion

What will gravitational wave detectors actually hear?

Signal from convection/SASI

In this region

Signal with simulated noise● Strain in 3D lower by a factor of ~10

than 2D (but: exploding models will have stronger signals)

● How much does this restrict the detectability of the signal?

Core-collapse supernovae in this

region√S/N in wavelet spectrogram, distance of Crab supernova

(Einstein Telescope)

=70°, =210°

What will gravitational wave detectors actually hear?

Effective SNR for broad-band excess power (need >11..15 to be measurable)

● Strain in 3D lower by a factor of ~10 than 2D (but: exploding models will have stronger signals)

● How much does this restrict the detectability of the signal?

● Advanced LIGO: Signal detectable as excess power only out to a few kpc

● Future instruments: Excess power detectable to ~20...50kpc with Einstein Telescope

● At smaller distances: “color” of signal and timing may reveal physics (SASI-dominated models are “redder”)

● Detailed time-frequency information with Einstein telescope at ~2kpc (Crab) → PNS radius, surface gravity

Simulated neutrino signal in IceCube (with noise)

f SASI∝r shock3/2 ln

r shockrPNS

Non-exploding 25 M8 model

f peak≈1

2GM

R2 1.1mn⟨E⟩

M ∝⟨E e⟩

GWs: Neutrinos:

and a bit moreHuge potential of combined neutrino & GW observations

from close supernova with 3rd generation detectors.

Müller& Janka (2014)

Conclusions

Cerda-Duran et al. (2013): 2D models of BH forming collapse

100kpc

10Mpc

● Bounce signal: promising quantitative diagnostic for rapid rotation in nearby supernovae

● GW signal from convection & SASI:● Weaker in 3D – can only hope for mere detection of nearby event

with Advanced LIGO● Different with 3D generation instruments: detection out to LMC,

extract physics in Milky Way (especially combined with neutrinos)● Stronger signal connected to

a) SASI activity and b) shock revival

● Scenarios for stronger signals:● Triaxial instabilities with long life-time?● BH formation (long signal, more violent

SASI & convection, Cerda-Duranet al. 2013)