Waveforms

Following previous chapters, we consider GW emission from garden-variety CCSNe (dominated by PNS oscillations excited by convection and the SASI) and more extreme CCSNe originating from rapidly-rotating progenitors (GW emission from collapse, bounce, and ringdown of millisecond PNSs). Fur- ther to these, we consider low frequency emission from GW memory effects originating from aspherical neutrino emission, as well as high frequency emission from the ringdown of BHs formed in collapsar-type systems thought to be associated with long GRBs. We augment our waveform catalogs with new signals from state-of-the-art simulations, which we describe below.

Time after core bounce [ms] 0 2 4 h+ [ 10 − 21 at 10 kpc ] _{GW memory} Y+15-B20ν 0 50 100

Time after core bounce [ms] −8 −4 0 4 h+ [ 10 − 21 at 10 kpc ] BH formation O+11-rot1 0 300 600 900

Time after core bounce [ms] −5 0 5 10 h+ , h× [ 10 − 23 at 10 kpc ]

Convection & SASI A+17-s20

h+ h×

0 50 100

Time after core bounce [ms] −6 −3 0 3 h+ , h× [ 10 − 21 at 10 kpc ] h+ h× Rotating core collapse

K+14-R3

Figure 8.2: GW strain as seen by an equatorial observer at10kpc for GW memory (upper left panel; model Y+15-B20𝜈 [47]), BH formation (upper right panel; modelO+11-rot1[72]), PNS oscillations excited by convection and the SASI (lower left panel; modelA+17-s20[233]), and post-bounce ring- down of millisecond PNS (lower right panel; modelK+14-R3).

GW memory

Thus far we have considered GWs that return spacetime to its original state after propagating through. Some GW emission, however, imprints a perma- nent non-oscillatory offset on spacetime after its passage; a so-called ‘mem- ory’ effect. GW memory (see, e.g, [353,354]) is difficult to detect with ground- based detectors, as the rise time over which this DC offset builds up is of order seconds if not longer. In the context of CCSNe, anisotropic neutrino emission (see, e.g., [45–47,197,355,356]) and aspherical explosive outflows of matter and magnetic stresses (from, for example, jet-like dynamics; see [357–

359]) may source memory effects that produce observables around (1 − 10)Hz.

For the purposes of this study, we draw waveforms from the ab-initio ax- isymmetric CCSN simulations presented by Yakuninet al.[47]. The authors employ theCHIMERAcode to evolve four non-rotating progenitors with ZAMS

mass {12, 15, 20, 25} 𝑀⊙ in Newtonian self-gravity with relativistic correc- tions, multi-frequency neutrino treatment through the ray-by-ray approx- imation with weak-interaction physics, and using the LS220 EOS [198] to close the system of equations. Specifically, we consider the GW signal from aspherical neutrino emission for the12 𝑀_⊙and20 𝑀_⊙progenitors (labelled B12-WH07-neutrino and B20-WH07-neutrino respectively by the authors in [47]), which we hereafter denoteY+15-B12𝜈andY+15-B20𝜈in this chapter. In the upper left panel of Fig.8.2, we show the GW strain as seen by an equatorial observerℎ_+,eqat10kpc forY+15-B20𝜈.

Black hole formation

We have often discussed in this thesis the GW signature from core collapse assuming that the stalled shock is indeed revived, but this is not necessarily the case. For progenitors of ZAMS mass ≲ 40𝑀⊙, BH formation can oc- cur through fallback accretion onto the PNS should the stalled shock not be revived in a timely fashion. The timescale from the initial core collapse to delayed BH formation is dependent on the accretion rate onto the PNS (influ- enced by the properties of the progenitor star), the angular momentum of the PNS, and the nuclear matter EOS, but is typically around∼ (0.5 − 3)s (see, e.g, [49,68–70]). The GW signature of BH formation is a characteristic short burst and ringdown. The peak ringdown frequency is inversely propor- tional to the mass of the nascent BH, with typical ringdown spectra for stellar mass BH formation peaking around several kilohertz [27,49,71,72].

In very massive progenitors (𝑀ZAMS ≳ (60 − 70) 𝑀⊙), a BH will be formed within timescales of a few hundred milliseconds, even if the progenitor core possesses significant angular momentum. Such systems have oft been dis- cussed in connection to the collapsar model for LGRBs (see, e.g. [206,360] for original literature), in which a nascent BH surrounded by an accretion disk formed from fallback material powers jet-like, bipolar outflows. GW emis- sion may arise in a number of different ways from collapsar-type systems (see, e.g., [63, 72, 207, 361, 362]), a couple of which have already been dis- cussed in Chap.4in the context of prospects for observational model exclu- sion for CCSNe within a few Mpc. Here, we consider two models from the general-relativistic axisymmetric study of Ottet al.[72], in which the collapse and evolution of a75 𝑀_⊙progenitor with several different rotation profiles

imposed is followed using theZelmaniCCSN code [21]. Specifically, we em- ploy two waveforms from simulations in which the progenitor has an initial central velocity of1rad/s and2rad/s, which we hereafter denoteO+11-rot1 and O+11-rot2, respectively. In the upper right panel of Fig.8.2, we show the GW strain as seen by an equatorial observer at10kpc for theO+11-rot1 model.

Convection & SASI

As discussed previously (see Chap. 3, Chap. 4, and Chap. 5), for CCSNe borne of precollapse cores with periods exceeding a few tens of seconds, GW emission is dominated by oscillations of the nascent PNS, excited by convective plumes and hydrodynamic waves striking the PNS and causing it to ring up. The peak frequency of emission naturally follows the dom- inant PNS surface g-mode frequency, which increases quasi-linearly with time from∼ (100 − 200)Hz to over1kHz as the PNS accretes fallback ma- terial, contracts, and deleptonises, although it has been shown that a broad and complex spectrum of oscillations is typically excited (see, e.g., [44, 48,

233,344]). Strong fluid downflows from development of the SASI can mod- ify the accretion rate at the PNS, inducing quadrupolar oscillations around (100 − 200)Hz at later times (after a few hundred milliseconds), where the emission frequency is related to the characteristic frequency of the advective- acoustic cavity in which the SASI develops (see, e.g., [25,42]).

We sample here broadly from the literature, choosing six waveforms from

three different studies. In addition to themüller1,müller2, andmüller3waveforms introduced in Chap.4, we draw models from the three-dimensional general-

relativistic studies presented by Andresenet al.[233] and Kurodaet al.[230]. From Andresen et al. [233], who treat neutrino transport through a multi- group ray-by-ray approximation, we choose model s20 (hereafter denoted A+17-s20), which follows the core collapse and post-bounce evolution of a progenitor with 𝑀_ZAMS = 20 𝑀_⊙ and the LS220 EOS. From Kuroda et al.[230], who employ an M1 closure approximation to account for neutrino effects, we choose models SFHx and TM1 (hereafter denotedK+16-SFHxand K+16-TM1, respectively), which evolve a progenitor star with𝑀ZAMS = 15 𝑀⊙ and either the SFHx EOS [363] or TM1 EOS [364]. In the lower left panel of Fig.8.2, we show the GW strain as seen by an equatorial observer at10kpc

for theA+17-s20model.

Rapidly-rotating core collapse

As explored extensively throughout this thesis (see, e.g., Chap. 3, Chap.4, Chap.5, and Chap.6), rotating progenitors yield CCSNe in which GW emis- sion is dominated by collapse, bounce, and ringdown of the core. Centrifu- gal affects cause oblate deformation of the PNS, which produces a large quadrupole moment. For precollapse cores characterised by extremely rapid rotation and/or strongly differential rotation profiles, non-axisymmetric dy- namics may develop at later times due to development of co-rotation, secu- lar, or dynamic fluid instabilities (see, e.g., [65,66]).

In addition to thesch1and sch2waveforms introduced in Chap. 4, we em- ploy a rapidly rotating model from the three-dimensional general-relativistic simulations with approximate neutrino treatement of a15𝑀⊙progenitor car- ried out by Kurodaet al.[66]. Specifically, we consider the R3 model (here- after denotedK+14-R3), which evolves the aforementioned progenitor with a cylindrical rotation profile characterised by central angular velocity𝜋rad/s imposed. In the lower right panel of Fig. 8.2, we show the GW strain for K+14-R3as seen by an equatorial observer at10kpc .