2.1.2. NS Crust Crack Model

During the inspiral of the NS binary, tidal interactions can distort the NS, inducing ellipticities. Once the ellipticity becomes large enough that after the crystalline structure of the NS crust cannot respond linearly, a crust failure may be induced [40,64]. It has been suggested that the crust breaking strain is around 0.1 [74], which corresponds to a critical ellipticity of *<sup>e</sup><sup>c</sup>* <sup>≈</sup> *<sup>δ</sup>R*/*<sup>R</sup>* <sup>≈</sup> <sup>4</sup> <sup>×</sup> <sup>10</sup>−<sup>6</sup> , where *R* + *δR* is the elongated NS radius. This can be easily reached by the tidally-induced f-mode oscillation in the last seconds before the merger [65] (see also Figure 3 of Reference [75]). Recent works show that the g-mode can also lead to the breaking of the NS crust [66].

If the energy is dissipated into heat, the crust can be heated up to *T*<sup>c</sup> = *E*cc/*C* ≈ 27.2*E* 1/2 cc,46 keV with *<sup>C</sup>* <sup>≈</sup> <sup>10</sup>29*T*<sup>c</sup> erg/K [76] and *<sup>E</sup>*cc <sup>=</sup> *<sup>E</sup>*cc,4610<sup>46</sup> erg. The corresponding thermal luminosity from the crust surface with *<sup>R</sup>*<sup>∗</sup> <sup>≈</sup> <sup>10</sup><sup>6</sup> cm is then [69],

$$L\_{\infty} \approx 4 \pi R\_\*^2 a\_{\rm S} T\_{\rm c}^4 \sim 4.5 \times 10^{42} E\_{\rm cc,46}^2 \text{ erg s}^{-1},\tag{5}$$

where *a*<sup>S</sup> is the Stefan–Boltzmann constant. This is too faint to be observed at an extragalactic distance.

It has also been proposed that, if the NS is highly magnetized, i.e., being a magnetar with *<sup>B</sup>* <sup>10</sup><sup>13</sup> G, the crust failure may trigger a violent reconstruction of magnetic fields, leading to a magnetar-giant-flare-like event (e.g., [40,66]). However, it should be noted that for magnetar giant flares, the crust failure is believed to be caused by the sudden rearrangement of magnetic field [77]. It is unclear whether a crust failure could lead to the amplification and rearrangement of magnetar magnetic field. Nevertheless, in this case, the luminosity may be estimated as

$$L\_{\rm Flare} = E\_{\rm cc}/t\_f = 10^{46} E\_{\rm cc,46}/t\_f \text{ erg s}^{-1} \text{ }^{\prime} \tag{6}$$

where *t<sup>f</sup>* is the duration of the flare. The SED and opening angle in this case would be similar to observed giant flares.
