CoCoNuT Meeting 2017

Alejandro Torres-Forné, Pablo Cerdá-Durán, Andrea Passamonti, and J. Antonio Font TOWARDS ASTEROSEISMOLOGY OF CORE- COLLAPSE SUPERNOVAE WITH GRAVITATIONAL-WAVE OBSERVATIONS Asteroseismology of core-collapse supernovae Outline

1. Motivation 2. Introduction to mode analysis 3. Numerical simulation 4. Results • Mode classification • Spectrum comparison with simulations • Gravitational Wave (GW) emission • Imprint of the SASI • Efficiency 5. Conclusions Asteroseismology of core-collapse supernovae Motivation

Parameter estimation for binary black hole mergers. B. P. Abbott et al. (LIGO Scientific Collaboration and Virgo Collaboration) Phys. Rev. Lett. 116, 061102

Template Bayesian Bank Inference

250,000 templates! Asteroseismology of core-collapse supernovae Motivation

Supernova modelling • Sophisticated microphysics • Computational challenges • Progenitor uncertainties • …

Simulation templates

GW observations & data analysis Asteroseismology of core-collapse supernovae Motivation

Supernova modelling • Sophisticated microphysics • Computational challenges • Progenitor uncertainties • … Simulation templates + mode analysis

GW/mode frequency • Surface gravity (M/R2) • Central density • PNS surface temperature • … Phenomenological parameterized GW observations & data analysis templates Asteroseismology of core-collapse supernovae Project steps

1. Identify properties of proto-neutron star

• Study of their normal modes of oscillation. • Compare the mode spectrum with the frequencies of gravitational-wave signals from core-collapse simulations.

2. Find the relation with the physical parameter • Perform numerical simulations.

3. Develop a model

• Calculate a set of phenomelogical templates.

4. Perform statistical parameter estimation

• Include the model and templates in standard codes. Asteroseismology of core-collapse supernovae Introduction

Goal: check if it is possible to infer the properties of PNS based on the identification of mode frequencies in their waveforms.

We model the problem as linear perturbations of a spherical equilibrium background.

PNS + shock system Numerical Simulation

Eigenvalue problem

Modes spectrum Asteroseismology of core-collapse supernovae Introduction

8 H. Andresen et al.

analysed with some care. Since we plot the square of the Fourier coecientsShock one can not add the values of layers A, B, and C to- gether and recover the value for the total signal. In addition, arte- Standing accretion shock facts can ariseHot bubble due to e↵ects at theà boundariesconvection/SASI between layers, as in the case of model s20 (top right panel of Fig. 6). There is an artificially strongPNS surface (stable) peak at 160 Hz, particularly fromà layerg B.-modes We have confirmed that shifting the boundary between layers A and B C inwards reducesPNS interior this peak significantly.à Theconvection exact values of the low- frequency amplitudes are sensitive to the boundary definition, but 10 3 the fact thatInner core (stable) all three layers contribute to emissionà belowg-modes 250 Hz ⇢ =10 g/cm is robust. The high-frequency component is less a↵ected by such max B fm =0.1fm artefacts since the high-frequency emission is mostly confined to A2 fm =0 layer A. The results of this dissection of the contributions to the in- A1 A tegral in Eq. (6) are somewhat unexpected. The high-frequency r=10km emission mostly stems from aspherical mass motions in layer A and there is only a minor contributionShock from layer B, which has been posited as the crucial region for GW emission during the pre- explosion phase in works based onPNS surface 2D simulations (Marek et al. Figure 4. Schematic overview of the regions of hydrodynamical activity. In 2009; Murphy et al. 2009; Müller et al. 2013). Aspherical mass Section 3.4 we investigate the contribution to the total GW signal from three motions in layer C hardly contributeInner core to this component at all. diAndresen et al 2016↵erent layers. The PNS, indicated by the shaded red area, is divided into two layers: Layer A includes the convectively unstable region in the PNS By contrast, all three regions contribute to the low-frequency (layer A1) and the overshooting layer A2 directly above it. The boundary signal (i.e. emission at frequencies lower than 250 Hz) to a sim- between the convective layer and the overshooting layer is indicated by a ilar degree. This is also surprising if the dominant frequency of dashed curve within layer A. The second layer, layer B, extends from the top this component appears to be set by the SASI as speculated before. of the overshooting region and out to the PNS surface, defined by a fiducial In this case, one might expect that the fluid motions responsibleStability criterion 10 3 density of 10 g cm . Layer C extends from the PNS surface to the outer for GW emission are propagating waves in layer C and perhaps• 2 boundary of our simulation volume. Layer C therefore includes the post- layer B, where the conversion of vorticity perturbations into acous- N <0 : unstable shock region, the standing accretion shock (indicated by the blue line), and tic perturbations occurs in the SASI feedback cycle. the pre-shock region. Formal definitions of the boundaries between layers (convection) are given on the right hand side, see Section 3.4 for details. 2 3.5 Origin of High-Frequency Emission • N >0 : stable (g- 1 What do these findings imply about the physical mechanisms that modes) max give rise to GW emission and determine their frequency? Let us fm first address the high-frequency signal. Recent 2D studies have con- 0 nected GW emission at &500 Hz to oscillatory modes (g-modes) 2 excited either in the PNS surface (layer B) from above by down- Brunt Väisälä frequency (N ) flows impinging onto the PNS (Marek et al. 2009; Murphy et al. Overshooting 2009; Müller et al. 2013), or from below by PNS convection layer(A2) (Marek et al. 2009; Müller et al. 2012a, 2013). Prior to shock re- 2 vival, the excitation of oscillations by mass motions in the gain gcm/s] layer was found to be dominant, with PNS convection taking over as the dominant excitation mechanism only after the onset of the 18 explosion (Müller et al. 2012a, 2013). The typical angular fre- 10

[ quency of such processes is roughly given by the Brunt-Väisälä Convective frequency, N, in the convectively stable region between the gain m 4 layer(A1) f region and the PNS convection zone, 1 @ 1 @P @⇢ N2 = , (17) ⇢ @r c2 @r @r " s # where cs is the sound speed. Müller et al. (2013) further investi- 6 gated the dependence of this frequency on the mass M, the radius 051015202530354045 R, and the surface temperature T of the PNS to explain the secu- r[km] lar increase of N during the contraction of the PNS and a tendency towards higher frequencies for more massive neutron stars. Our results confirm that the peak frequency of the high- Figure 5. Turbulent mass flux fm (blue curve) for model s27, calculated frequency GW emission is still set by the Brunt-Väisälä frequency 192 ms after core bounce. The shaded region indicates the convectively in 3D and therefore point to a similar role of buoyancy forces in de- unstable region and the overshooting layer, which are lumped together as termining the spectral structure of the high-frequency component. layer A (see Fig. 4). As shown in Fig. 7 for model s27, we find very good agreement between the peak GW frequency, fpeak, and the Brunt-Väisälä fre- quency, N, calculated at the outer boundary of the overshooting

MNRAS 000, 000–000 (0000) Oscillation modes in CFC

r it ⇠ = ⌘r Ylme , • Perturbations of a spherical background. ✓ 1 it ⇠ = ⌘ @✓Ylme , ? r2 • Cowling approximation.

• Impose boundary conditions at shock location. ⇠ =0 ⌘ =0. r|shock ! r|shock • At the origin (r = 0) it is sufficient to impose regularity. l 1 ⌘r r=0 = l ⌘ r r . | ?| 0 / Linear perturbation analysis

TF et a 2017

• Linear perturbations of a spherical background à 1D average of 2D simulations • Hydrostatic equilibrium à the PNS evolves in time-scales of 100 ms • Cowling approximation • Model 35OC of Cerdá-Durán et al 2013

s: eigenfrequency

B.C. Brunt-Väisälä frequency Lamb frequency ⇠ =0 ⌘ =0. r|shock ! r|shock Asteroseismology of core-collapse supernovae Numerical simulation

We employ the results of the 2D core-collapse simulation using the general-relativistic code CoCoNuT. Dimmelmeier H., Novak J., Font J. A., Ibáñez J. M., Müller E., 2005, Phys. Rev. D, 71, 064023.

• Low-metallicity Cerdá-Durán P., DeBrye N., Aloy M. A., Font J. A., Obergaulinger M., 2013, ApJ, 779, L18. • 35 M star at zero-age main-sequence • High rotation rate • Usually regarded as a progenitor of long-duration gamma-ray bursts (GRBs). Asteroseismology of core-collapse supernovae Numerical simulation Gravitational-wave emission

Bounce Accretion onto PNS BH formation Asteroseismology of core-collapse supernovae Gravitational wave signal (Supernovae)

The Astrophysical Journal,766:43(21pp),2013March20 Muller,¨ Janka, & Marek

Figure 10. Comparison of the wavelet spectra (identical to those in Figures 2 and 3, respectively) of model G11.2 (left) and G15 (right) and the prediction of Murphy et al 2009 Equation (17) for the typical GWMüller et al 2013 frequency in terms of the PNS mass and radius and the mean energyYakunin of electron antineutrinoset al 2015 measured by an observer at infinity. Equation (17) describes the evolution of the typical frequency fairly well and only overestimates fpeak somewhat at late times.

4.4. Explosion Phase—Proto-neutron Star 5 Convection and Late-time Bursts G15 G11.2 4 As established by Murphy et al. (2009)andYakuninetal. ]

(2010), the emission of high-frequency GWs subsides to a g

er 3

reduced level once the shock accelerates outward because 45 the excitation of oscillations in the PNS surface by violent [10 convective motions in the hot-bubble region largely ceases. 2 GW This is well reflected in the GW signals of models G11.2 and E G15 (Figures 2 and 3)intheinitial phase of the explosion, as 1 the GW amplitude drops noticeably after 400 ms and 600 ms, respectively. However, the surface g-mode oscillations remain 0 the dominant source of high-frequency GWs during this phase: 0 0.2 0.4 0.6 0.8 1 the wavelet spectra clearly show that the late-time signal comes time after bounce [s] from the same emission band as the signal from the accretion Figure 11. Energy EGW radiated in GWs as a function of time for the explosion phase (which shifts continuously to higher frequencies as the models G11.2 (black solid line) and G15 (red dashed line) for the entire duration neutron star contracts). An analysis of the integrand ψ in of the simulation. For model G15, most of the energy is radiated around the the quadrupole formula (1)asinSection4.2.1alsoconfirms onset of the explosion between 400 ms and 600 ms after bounce. By contrast, Kuroda et al 2016 late-time GW bursts carry a sizable fraction of the radiated energy in the case that aspherical motions in the PNS surface region are still theAndresen et al 2017of model G11.2. dominant source of GWs. PNS convection now provides an (A color version of this figure is available in the online journal.) excitation mechanism for the oscillations (Muller¨ & Janka 1997; Marek et al. 2009;Murphyetal.2009;Muller¨ et al. 2012c), but due to the subsonic character (with Mach numbers !0.05) of PNS in a similar manner in a weak explosion in 3D (cf. some 3D E2 the convective motions, the GW amplitude A20 remains rather results of Muller¨ et al. 2012c,wherelong-lastingaccretionaf- small. ter the explosion was associated with time-dependent accretion However, model G11.2 contradicts the established picture of downdrafts). Given the fact that Takiwaki et al. (2012) do not subsiding GW emission during the explosion. For this progeni- obtain faster shock propagation in 3D than in 2D for this par- tor, we observe several “bursts” of stronger GW emission later in ticular progenitor in their simulations using the IDSA scheme, the explosion phase on at least three occasions (630 ms, 790 ms, it is not unlikely that the explosion energies will remain low and 820 ms), during which the amplitude can become compa- as in our 2D model (a few 1049 erg; see Muller¨ et al. 2012b) rable to that coming from the phase of hot-bubble convection. and that late-time bursts seen in our simulations will survive in About 40% of the GW energy is emitted later than 600 ms after 3D. Without detailed 3D simulations of this sort, however, it is bounce (Figure 11), which is in stark contrast to the more vigor- unclear how massive the downdrafts can become and what GW ous explosion in model G15 with faster shock expansion. These burst amplitudes they can cause. bursts occur when matter falls back onto the PNS through a Several interesting features of these late-time bursts should be newly developing downflow, which excites g-mode oscillations noted: between the few instances where new accretion downflow in the PNS surface region (Figure 12). The formation of new develops, aspherical mass motions above the PNS surface are downflows in the explosion phase is a consequence of the small apparently not strong enough to produce significant noise in explosion energy of model G11.2 (see Paper II), and one could the GW signal, and the g-mode frequency therefore emerges speculate that low-energy fallback supernovae may generally much more cleanly from the spectrum during the late-time GW reveal themselves through such multiple GW burst episodes. bursts than in the accretion phase. The narrowband character While the development of such an accretion downflow may be of the spectrum (see Figure 2 and the red curve in Figure 14) facilitated by the constraint of axisymmetry, it is conceivable is potentially helpful both for the detection of the GW signal that funnel- or plume-shaped downdrafts may impinge on the and for the interpretation of the data (e.g., by allowing for

11 Asteroseismology of core-collapse supernovae Mode classification

For each time step of the numerical simulation, we obtain the frequencies of the modes that solve the equations.

We also perform a automatic classification based on the number of nodes (n) and on their origin, namely gravity modes (g-modes) and acoustic modes (p-modes).

Modes with increasing n with frequency

Fundamental mode

Modes with decreasing n with frequency Asteroseismology of core-collapse supernovae Mode classification: origin

Mode name Restoring force Approximation

p modes Pressure Remove buoyancy

g modes Buoyancy Neglect sounds waves

Classification by number of nodes Mode origin approximation Asteroseismology of core-collapse supernovae Mode classification: origin

Mode name Restoring force Approximation

p modes Pressure Remove buoyancy

g modes Buoyancy Neglect sounds waves

p-modes

Modes with increasing n with frequency

Fundamental mode

g-modes Modes with decreasing n with frequency Asteroseismology of core-collapse supernovae Mode classification Linear oscillation of proto-neutron stars Comparison with the simulation

We study the relationship between the post-bounce oscillation spectrum of the PNS- shock system and the characteristic frequencies observed in gravitational-wave signals from core-collapse simulations. Linear oscillation of proto-neutron stars Comparison with the simulation

We study the relationship between the post-bounce oscillation spectrum of the PNS- shock system and the characteristic frequencies observed in gravitational-wave signals from core-collapse simulations. Asteroseismology of core-collapse supernovae GW emission Asteroseismology of core-collapse supernovae Imprint of the SASI

The features associated with the p-modes were identified as SASI modes by Cerdá-Durán et al. (2013) because their frequencies trace the sloshing motions of the shock.

Radial position of the shock p-modes rescaled by number of nodes (n)

• Oscillations of the shock (SASI) trace the p-mode frequencies • Two low frequency bellow the lowest frequency p-mode à integer fractions of p-modes • SASI theory (Foglizzo et al 2007): advective-acoustic cycle (acoustic = p-mode) Asteroseismology of core-collapse supernovae GW emission timescale

TF et a 2017 Less efficient emitters

More efficient emitters

• p-modes emit much more efficiently than g-modes àexplains why we see many p-modes but not high order g-modes • l=4 highly suppressed because we consider a spherical background Asteroseismology of core-collapse supernovae Conclusions • We have obtained a remarkably close correspondence with the time- frequency distribution of the gravitational-wave modes.

• GW emission in core-collapse SNe can be explained to a large degree by the excitation of PNS modes

• This will allow in the future to do parameter estimation (M, R, …) from GW observations

• We need accurate methods to compute the eigenfrequencies and estimate the systematic uncertainties of the model

• Future work: • Remove cowling approximation • Deformated background • Quasi-radial oscillations (l=0)