Fast neutrino conversions: Ubiquitous in compact binary merger remnants

The massive neutron star (NS) or black hole (BH) accretion disk resulting from NS–NS or NS–BH mergers is dense in neutrinos. We present the first study on the role of angular distributions in the neutrino flavor conversion above the remnant disk. In particular, we focus on “fast” pairwise conversions whose rate depends on the local angular intensity of the electron lepton number carried by neutrinos. Because of the emission geometry and the flux density of ${\overline{\nu }}_e$ being larger than that of ${\nu }_e$, fast conversions prove to be a generic phenomenon in NS–NS and NS–BH mergers for physically motivated disturbances in the mean field of flavor coherence. Our findings suggest that, differently from the core-collapse supernova case, fast flavor conversions seem to be unavoidable in compact mergers and could have major consequences for the jet dynamics and the synthesis of elements above the remnant disk.

Figure 1

Geometry of ${\nu }_e$ (in red) and ${\overline{\nu }}_e$ (in blue) emitting surfaces with radii $R_{{\nu }_e}$ and $R_{{\overline{\nu }}_e}$, heights $h_{{\nu }_e}$ and $h_{{\overline{\nu }}_e}$. $R_0$ is the innermost stable circular orbit for a BH-disk system ($R_0=0$ for a NS-disk remnant). Inset: Example of crossings of the ELN distribution (${\mathrm{\Phi }}_{{\nu }_e}-{\mathrm{\Phi }}_{{\overline{\nu }}_e}$) as a function of the polar and azimuthal angles $\cos \theta$ and $\varphi$ above the NS–disk. The exact shapes are calculated at $(x,z)=(0.6R_{{\nu }_e},0.35R_{{\nu }_e})$ with $R_{{\overline{\nu }}_e}=0.75R_{{\nu }_e}$ and $h_{{\nu }_e}/R_{{\nu }_e}=h_{{\overline{\nu }}_e}/R_{{\overline{\nu }}_e}=0.25$. The region shaded in red (blue) corresponds to ${\mathrm{\Phi }}_{{\nu }_e}<{\mathrm{\Phi }}_{{\overline{\nu }}_e}$ (${\mathrm{\Phi }}_{{\nu }_e}>{\mathrm{\Phi }}_{{\overline{\nu }}_e}$).

Figure 2

Dispersion relation of $\mathbf{k}=(0,0,k_z)$ for the ELN distribution shown in Fig. 1 with $\alpha ={\mathrm{\Phi }}_{{\overline{\nu }}_e}^0/{\mathrm{\Phi }}_{{\nu }_e}^0=2.4$. For the complex $\omega$ that lead to flavor instability, $\mathrm{Re}(\omega )$ are shown by the red (green) dash-dotted curves and $\mathrm{Re}(\omega )\pm \mathrm{Im}(\omega )$ are shown by the red (green) solid curves for the MS preserving (breaking) solutions. The gray regions are the zone of avoidance for real $(\omega ,k_z)$. The temporal instability exists for a large range of $k_z/{\mu }_0$ and it is, therefore, unavoidable.

Figure 3

Contour plot of $|\mathrm{Im}(\omega )|/{\mu }_0$ in the $(x,z)$ plane above the ${\nu }_e$-surface for $\mathbf{k}=0$ for our benchmark NS-disk model. The mirror symmetry preserving and breaking solutions are shown in panel (a) and (b). Also shown are the MNR locations obtained by adopting the $n_e$ profiles of [12] for neutrinos emitted at $(x,z)=(0,h_{{\nu }_e})$ (solid blue curve) and at $(x,z)=(-R_{{\nu }_e},h_{{\nu }_e})$ (dashed green curve). Fast conversions occur everywhere above the ${\nu }_e$ surface and could alter the otherwise favorable conditions for the MNR.

Figure 4

Growth rate of the flavor instability, $|\mathrm{Im}(\omega )|/{\mu }_0$, as a function of $x$ on the ${\nu }_e$-surface for the same NS disk in Fig. 1 (thick curves) with different $\alpha ={\mathrm{\Phi }}_{{\overline{\nu }}_e}^0/{\mathrm{\Phi }}_{{\nu }_e}^0$ for the mirror symmetry preserving solutions [panel (a)] and the mirror symmetry breaking solutions [panel (b)]. The thin dashed curves show the corresponding solutions of the BH torus with $R_0=0.15R_{{\nu }_e}$. For any $\alpha \ge 1.1$, flavor instabilities exist above the ${\nu }_e$ surface.

Figure 5

Dispersion relation of $(\omega ,\mathbf{k})=(\omega ,0,0,k_z)$ [panel(a)] and $(\omega ,k_x,0,0)$ [panel(b)] for the ELN distribution at $(x,z)=(0,0.25R_{{\nu }_e})$ with $\alpha ={\mathrm{\Phi }}_{{\overline{\nu }}_e}^0/{\mathrm{\Phi }}_{{\nu }_e}^0=2.4$ (see top left panel of Fig. 9). For the complex $k_{z,x}$ that lead to the spatial flavor instability, $\mathrm{Re}(k_{z,x})$ are shown by the red (green) dash-dotted curves and $\mathrm{Re}(k_{z,x})\pm \mathrm{Im}(k_{z,x})$ are shown by the red (green) solid curves for the MS preserving (breaking) solutions. The gray regions are zone of avoidance for real $(\omega ,k_{z,x})$.

Figure 6

Contour plot of the mirror symmetry preserving solution of $|\mathrm{Im}(k_z)|/{\mu }_0$ [panel(a)] and $|\mathrm{Im}(k_x)|/{\mu }_0$ [panel(b)] in the $(x,z)$ plane above the ${\nu }_e$-surface for $\omega =k_x=k_y=0$ and $\omega =k_z=k_y=0$ for the NS-disk model with $\alpha =2.4$, using the $n_e$ profiles of [12] at 60 ms post merger. Also shown are the MNR locations for neutrinos emitted at $(x,z)=(0,h_{{\nu }_e})$ (solid blue curve) and at $(x,z)=(-R_{{\nu }_e},h_{{\nu }_e})$ (dashed green curve). The spatial instabilities exist inside the low-density funnel where ${\lambda }_0\lesssim |{\epsilon }_0|$ and are largely suppressed outside the funnel where ${\lambda }_0\gg |{\epsilon }_0|$.

Figure 7

Symmetry preserving solution of $|\mathrm{Im}(\omega )|/{\mu }_0$ in the $(x,z)$ plane above the ${\nu }_e$-surface for $\mathbf{k}=0$ for the same NS-disk model as in Fig. 3 except for that $h_{{\nu }_e}=h_{{\overline{\nu }}_e}=0.25R_{{\nu }_e}$. The temporal instability in the central part right above the disk is suppressed, see Fig. 3 for comparison.

Figure 8

Angular projections for neutrinos emitted from the disk surface. Top panel: The neutrino distribution at a point $P$ at a certain distance from the NS-disk surface is restricted within the angles ${\theta }_{\min }$ and ${\theta }_{\max }$ for a certain $\varphi$ [see Eq. (a2)]. Middle panel: Same as above but for a BH-disk surface. The neutrino distribution at $P$ also depend on $\varphi$. In this example, neutrinos can only reach $P$ from ${\theta }_{\min }\le \theta \le {\theta }_{\mathrm{near}}$ and ${\theta }_{\mathrm{far}}\le \theta \le {\theta }_{\max }$, see Eq. (a3). Bottom panel: Angular projections for the BH-disk viewed from above; see text for details.

Figure 9

Electron neutrino lepton number distribution, ${\mathrm{\Phi }}_{{\nu }_e}-{\mathrm{\Phi }}_{{\overline{\nu }}_e}$, as a function of $\cos \theta$ and $\varphi$ and different $(x,z)$ points above the ${\nu }_e$ surface. The top three rows [panel (a)] refer to our benchmark NS–disk model ($R_{{\overline{\nu }}_e}=0.75R_{{\nu }_e}$ $h_{{\nu }_e}/R_{{\nu }_e}=h_{{\overline{\nu }}_e}/R_{{\overline{\nu }}_e}=0.25$, and $\alpha \equiv {\mathrm{\Phi }}_{{\overline{\nu }}_e}^0/{\mathrm{\Phi }}_{{\nu }_e}^0>1$). In the red (blue) shaded area, ${\mathrm{\Phi }}_{{\nu }_e}-{\mathrm{\Phi }}_{{\overline{\nu }}_e}<0$ (${\mathrm{\Phi }}_{{\nu }_e}-{\mathrm{\Phi }}_{{\overline{\nu }}_e}>0$). Null electron neutrino lepton number is shown in white. The bottom three rows [panel (b)] refer to the BH–torus case with $R_0=0.15R_{{\nu }_e}$ and the orange shaded area marks regions where ${\mathrm{\Phi }}_{{\nu }_e}=0$. In both cases, as one moves away from the surface center, the ${\overline{\nu }}_e$ contribution is significantly reduced.