PALABRAS CLAVE Maltrato técnico;

Rapidly-rotating CCSNe are highly energetic, and may be associated with high energy events, such as hypernovae and gamma ray bursts. Rapid-rotation is only expected in a small number (_{≤ 10%) of progenitor stars [106, 107]. Theory and} simulations have shown that magnetorotational processes could extract rotational energy and drive a jet-driven bipolar explosion [108, 109]. When core-collapse to a proto-neutron star occurs, it may result in spin-up of the stellar core by a factor of ∼ 1000 [110]. The rapidly-rotating pre-collapse core results in a millisecond period proto-neutron star, which if combined with a magnetar strength magnetic field could power a strong CCSN explosion. For the magnetorotational mechanism to work, simulations suggest that the pre-collapse core needs a spin period of . 4−5 s, and a magnetic field of order 1015_{G [109]. This value is larger than predicted by}

stellar evolution models [106]. Therefore, some magnetic field amplification may be necessary after core bounce, which could be created by rotational winding of the magnetic field, or through magnetorotational instabilities [111, 112].

Some example rapidly-rotating CCSN GW signals, hereafter referred to as the RotCC model, are shown in Figure 4.1. Rapidly-rotating CCSN signals are domi- nated by the bounce and subsequent ring down of the proto-neutron star. Typically, the peak GW strain from rotating core-collapse is_{∼ 10}−21_{− 10}−20, for a source at 10 kpc, and emitted energy in GWs (EGW) is ∼ 10−10− 10−8M. The GW energy

spectrum is more narrowband than for non-rotating core-collapse, with most power emitted between 500_{− 800 Hz, over timescales of a few tens of ms. For pre-collapse} cores with an initial spin period less than _{∼ 0.5 − 1 s, core bounce occurs slowly at} subnuclear densities, dynamics are dominated by centrifugal effects, and most en- ergy in GWs is emitted around_{∼ 200 Hz [40, 113]. In the remainder of this section,} we describe the rotating core-collapse waveforms used in this thesis chapter.

The Dimmelmeier et al. [113] waveform catalogue contains 128 two-dimensional waveforms, with progenitor star ZAMS mass values of 12 M, 15 M, 20 M, and

40 M, varying angular momentum distributions, and two different nuclear matter

−10 0 10 20 30 40 50 t − tbounce[ms] −8 −6 −4 −2 0 2 4 h+ [10 − 21at 10 kpc ] Dimmelmeier et al. 2008 Model s15a2o09 shen

0 50 100 150 200 t − tbounce[ms] −10 −5 0 5 h+ [10 − 21at 10 kpc ] Scheidegger et al. 2010 Model R3E1ACL −5 0 5 10 15 20 25 t − tbounce[ms] −10 −5 0 5 h+ [10 − 21at 10 kpc ] Abdikamalov et al. 2014 Model A3O09

Figure 4.1: Time series GW h+ strain for representative models of GWs from rotating core- collapse, as seen by an equatorial observer at 10 kpc. The top left is a representative 2D waveform from the Dimmelmeier et al. [113] waveform catalogue. The top right is a representative 3D waveform from the Scheidegger et al. [114] waveform catalogue. The bottom sub-figure is a repre- sentative 2D waveform from Abdikamalov et al. [115]. All examples have a 15 Mprogenitor star. The GW strain from rotating core-collapse is an order of magnitude larger than the typical GW strain from neutrino-driven explosions. Figure reproduced from [3].

initial angular momentum distribution of the pre-collapse core is imposed through an angular velocity profile, Ωi(¯ω), defined as,

Ωi(¯ω) =

Ωc,i

1 + (¯ω/A)2 , (4.1)

where ¯ω is the cylindrical radius, Ωc,i is the central angular velocity, and A is

the differential rotation length scale. Simulations are performed across the angu- lar momentum distribution space, considering strongly differential rotation (A = 500 km) to almost uniform rotation (A = 50000 km); and slowly-rotating (Ωc,i =

0.45 rad s−1) to rapidly-rotating (Ωc,i = 13.31 rad s−1) pre-collapse cores. As the

simulations are axisymmetric, the waveforms are linearly polarized. A representa- tive waveform from the Dimmelmeier et al. catalogue is shown in the top left panel of Figure 4.1. As the main feature of the Dimmelmeier waveforms is the spike at core bounce, they are still a good approximation of a three-dimensional CCSN sig-

nal, as any rotating three-dimensional model stays sufficiently close to axisymmetry around the bounce signal and non-axisymmetric features only start to appear a few milliseconds after the bounce [114].

Abdikamalov et al. [115] performed two-dimensional, general-relativistic, hydro- dynamic, rotating core-collapse simulations. They use a 15 M progenitor star,

and the Lattimer-Swesty EOS [116]. A typical waveform from the Abdikamalov catalogue is shown in the bottom panel of Figure 4.1. The Abdikamalov wave- forms are very similar in duration, amplitude and time series morphology to the Dimmelmeier waveforms. In this chapter, we use waveforms A1O14 (A = 300 km; Ωc = 14 rad s−1), A3O09 (A = 634 km; Ωc= 9 rad s−1), and A4O01 (A = 1268 km;

Ωc = 1 rad s−1), referred to as abd1, abd2, and abd3, respectively.

Scheidegger et al. [114] performed three-dimensional magnetohydrodynamical simulations of 25 GW signals, using a leakage scheme for neutrino transport. They use a 15 M progenitor star, and the Lattimer-Swesty EOS [116]. Due to the

three-dimensional nature of the simulations, the Scheidegger et al. waveforms have two GW polarizations. The waveforms contain only h+ around the spike at core

bounce, and the h×polarisation starts a few ms later. In this chapter, we use wave-

form models R3E1ACL(moderate pre-collapse rotation, toroidal/poloidal magnetic

field strength of 106_G/109_{G), shown in the top right panel of Figure 4.1, and}

R4E1F CL (rapid pre-collapse rotation, toroidal/poloidal magnetic field strength of

1012G/109G). We hereafter refer to these waveforms as sch1 and sch2, respec- tively. The Scheidegger waveforms are much longer than the Abdikamalov and Dimmelmeier waveforms, but are similar in amplitude.