4.4 Neutrinos

Up until now, we have focused on the GWs from a changing quadrupole moment of the baryonic matter. Anisotropic neutrino emission may also produce GWs. Although less studied than baryonic motions, GW emission from aniostropic neutrino emission [76, 317] has been investigated in proto neutron star convection, convection above the proto neutron star, and in asymmetric collapse (caused either by asymmetries in the collapse or by rotation).

Müller et al. [209Jump To The Next Citation Point] have modeled the emission of GWs from anisotropic neutrino emission from convection both inside and above the proto neutron star for non-rotating models. The signal from the proto neutron star is shown in Figure 26View Image. Note that although the quadrupole amplitude for the neutrino emission is much higher, it varies slower than the mass motions. Hence, it only dominates the signal at low frequencies. This model is of a cooling, isolated proto neutron star that developed much stronger convection than is seen in proto neutron star models of full systems. As such, it represents an upper limit for the GW signal of non-rotating proto neutron stars. Figure 26View Image shows the signal for the convection above the proto neutron star. Like in the case of neutrino emission for proto neutron star convection, anisotropic neutrino emission from convection above the proto neutron star dominates the low-frequency part of the signal.

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Figure 26: The GW signal from convection in a proto neutron star. The top panel shows the GW quadrupole amplitude AE220 as a function of time for both the convective mass flow (thick line) and anisotropic neutrino emission (thin line). The combined spectral energy distribution of the quadrupole radiation for both sources is shown in the middle figure, with just the neutrino component alone in the bottom panel. Note that although the quadrupole amplitude for the neutrino emission is much higher, it varies slower than the mass motions. Hence, it only dominates the signal at low frequencies. (Figures from [209]; used with permission.)

For mass motions, rotation strongly increases the signal at bounce and during the convective phase. But the neutrino signal does not increase as dramatically. Kotake et al. [166Jump To The Next Citation Point] found that the signal from a rotating collapse is dominated at nearly all frequencies by the matter contribution (Figure 27View Image). This is because the neutrino signal is axially symmetric and the variation in the quadrupole moment is fairly weak. However, within the SASI paradigm, Kotake et al. [165] found that the amplitude of the GW signal is two orders of magnitude larger than those from convective matter motions outside the proto neutron star. This result has been confirmed by several groups [195, 228Jump To The Next Citation Point].

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Figure 27: Detection limits of TAMA, first LIGO, advanced LIGO, and Large-scale Cryogenic Gravitational wave Telescope (LCGT) with the expected GW spectrum obtained from the numerical simulations. The left panel shows the GW spectrum contributed from neutrinos (solid) and from the matter (dashed) in a rotating model with − 1 Ω = 4 rad s imposed initially on a 15M ⊙ progenitor model. In the right panel, the open circles and the pluses represent the amplitudes of hν,eq with the characteristic frequencies of νeq for the models with the cylindrical and the shell-type rotation profiles, respectively. Under the frequency of ν eq, the GWs from the neutrinos dominate over those from the matter contributions. From the panel, it is seen that the GWs from neutrinos dominate over the ones from the matter in a lower frequency (f ≤ 100 Hz). Note that the source is assumed to be located at the distance of 10 kpc. (Figures from [166]; used with permission.)

The asymmetric collapse simulations discussed in Section 4.2 are one way to increase the GW signal from anisotropic neutrino emission. Recall from Figure 17View Image that Burrows & Hayes found that the neutrino-induced term dominated the GW signal for their asymmetric collapse simulations. Fryer et al. [107Jump To The Next Citation Point] found the same result. The GW amplitude is dominated by the neutrino component and can exceed − 24 hpk ∼ 6 × 10, for a source located at 10 Mpc in Fryer’s most extreme example. A caveat in this result is that Fryer et al. were artificially increasing the level of the asymmetry in the collapse in an attempt to obtain strong neutron star kicks and it is unlikely that any stellar system will have such large asymmetries in nature. This signal estimate should be seen as an extreme upper limit.

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Figure 28: The gravitational waveform for neutrino contributions from the asymmetric collapse simulations of Fryer et al. [107Jump To The Next Citation Point]. The curves plot the product of the GW amplitude to the source as a function of time. (Figures from [107Jump To The Next Citation Point]; used with permission.)

Anisotropic neutrino emission has several distinguishing features that will allow us to differentiate it from a matter-driven GW signal. It has much less variation in the time structure and will produce a stronger signal at lower frequencies. But much more work must be done to understand fully the neutrino-driven GW signal. For example, GWs can be produced by asymmetric neutrino emission from the core (e.g., from oscillations with sterile neutrinos [187]). If magnetic fields induce asymmetries in this oscillation and the neutron star is rotating, the sterile neutrino emission can produce a neutrino-driven GW signature that is very different from what was shown here.

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