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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)