Imprints of neutrino-pair flavor conversions on nucleosynthesis in ejecta from neutron-star merger remnants

The remnant of neutron star mergers is dense in neutrinos. By employing inputs from one hydrodynamical simulation of a binary neutron star merger remnant with a black hole of $3M_{\odot }$ in the center, dimensionless spin parameter 0.8 and an accretion torus of $0.3M_{\odot }$, the neutrino emission properties are investigated as the merger remnant evolves. Initially, the local number density of ${\overline{\nu }}_e$ is larger than that of ${\nu }_e$ everywhere above the remnant. Then, as the torus approaches self-regulated equilibrium, the local abundance of neutrinos overcomes that of antineutrinos in a funnel around the polar region. The region where the fast pairwise flavor conversions can occur shrinks accordingly as time evolves. Still, we find that fast flavor conversions do affect most of the neutrino-driven ejecta. Assuming that fast flavor conversions lead to flavor equilibration, a significant enhancement of nuclei with mass numbers $A>130$ is found as well as a change of the lanthanide mass fraction by more than a factor of a thousand. Our findings hint towards a potentially relevant role of neutrino flavor oscillations for the prediction of the kilonova (macronova) light curves and motivate further work in this direction.

Figure 1

Schematic representation of a BH-torus remnant and its ejecta resulting from a NS-NS or a NS-BH merger. The dynamical ejecta (“dyn,” violet-shaded area) is the earliest matter outflow, followed by the neutrino-driven component (“$\nu$-driven,” green-shaded area) and finally the viscously driven ejecta (“visc,” orange-shaded area). For each of the aforementioned outflow components, characteristic values are reported for the ejecta mass and velocity. Neutrino-driven winds may dominate the ejecta in a cone centered at the polar axis with half-opening angle of about 10–40°. The picture sketched here for a BH-torus remnant is qualitatively similar to the case of a NS-torus system that may form after a NS-NS merger, except that more massive neutrino-driven winds are expected with a central NS.

Figure 2

Evolution of ${\nu }_e$ and ${\overline{\nu }}_e$ energy luminosities (top panel) and average energies (middle) as functions of time for the model M3A8m3a5. The neutrino properties have been extracted at a radius of 500 km. The bottom panel shows the ratio of the number luminosities of ${\nu }_e$ and ${\overline{\nu }}_e$, which indicates that the torus on average protonizes (apart from the first $\sim 2\mathrm{ms}$) until neutrino emission becomes inefficient. The vertical lines approximately mark the three different stages of the torus evolution; see text for more details.

Figure 3

BH-tours remnant properties for model M3A8m3a5 around the $z$ axis at 20, 35 and 50 ms (from left to right) as functions of $x$ and $z$ (assuming cylindrical symmetry around the $z$ axis). First row: Baryon mass density $\rho$. Second row: Temperature $T$. Third row: Degeneracy parameter ${\mu }_e/T$ of electrons with ${\mu }_e$ being the electron chemical potential. Fourth row: Relative electron neutrino lepton number $(n_{{\nu }_e}-n_{{\overline{\nu }}_e})/n_{{\nu }_e}$. The degeneracy parameter in the innermost torus region slightly increases over time as the torus evolves (see text for details). The BH-torus evolves from a configuration where $n_{{\overline{\nu }}_e}>n_{{\nu }_e}$ to a configuration where $n_{{\overline{\nu }}_e}<n_{{\nu }_e}$ around the polar axis. Also shown are the emitting surfaces of $n_{{\nu }_e}$ and $n_{{\overline{\nu }}_e}$ which are computed as described in Sec. 2c and are marked in red and blue, respectively.

Figure 4

BH-torus remnant properties for model M3A8m3a5 at 20, 35 and 50 ms (from left to right) as functions of $x$ and $z$ (assuming cylindrical symmetry around the $z$ axis). First row: Relative ELN, $(n_{{\nu }_e}-n_{{\overline{\nu }}_e})/n_{{\nu }_e}$. Second row: Relative ELN flux density $(F_{{\nu }_e}^z-F_{{\overline{\nu }}_e}^z)/F_{{\nu }_e}^z$ along the $z$ direction [see Eq. (1) for the definition]. Third row: Local protonization rate $d{Y}_e/dt$. The reduced protonization rate as the torus evolves and the different emission geometry of the $n_{{\nu }_e}$ and $n_{{\overline{\nu }}_e}$ surfaces (red and blue curves) lead to the growing excess of ${\nu }_e$ compared to ${\overline{\nu }}_e$ around the $z$ axis.

Figure 5

Number density of ${\nu }_e$ and ${\overline{\nu }}_e$ on their respective emitting surfaces at $t=20$ [panel (a)], 35 [panel (b)] and 50 ms [panel (c)]. As the remnant evolves, the inner torus emits more ${\nu }_e$ than ${\overline{\nu }}_e$ despite protonizing as a whole. The ratio of $n_{{\overline{\nu }}_e}/n_{{\nu }_e}$ (green curves) is also plotted so that this transition is more clearly visible. The black dotted line denotes $n_{{\overline{\nu }}_e}/n_{{\nu }_e}=1$ to guide the eye.

Figure 6

Electron neutrino lepton number distribution as a function of $\cos \theta$ and $\varphi$ for different $(x,z)$ points above the ${\nu }_e$ surface for the model M3A8m3a5 at 20 [panels (a)–(c)], 35 [panels (d)–(f)] and 50 ms [panels (g)–(i)]. In the blue (red) shaded areas, ${\mathrm{\Phi }}_{{\nu }_e}-{\mathrm{\Phi }}_{{\overline{\nu }}_e}<0$ (${\mathrm{\Phi }}_{{\nu }_e}-{\mathrm{\Phi }}_{{\overline{\nu }}_e}>0$). The white regions mark the angular directions that do not cross the neutrino emitting surfaces and therefore the electron lepton number is zero.

Figure 7

Contour plot of $|\mathrm{Im}(\omega )|/\mu$ with $\mu =\sqrt{2}{G}_F{n}_{{\nu }_e}$ in the $(x,z)$ plane above the ${\nu }_e$ surface for $k_x=k_y=k_z=0$ for $t=20$, 35 and 50 ms from top to bottom respectively. The ${\nu }_e$ (${\overline{\nu }}_e$) neutrinosphere is marked in red (blue). At early times, fast conversions occur almost everywhere above the ${\nu }_e$ surface. As the local ${\nu }_e$ abundance starts to be larger than the ${\overline{\nu }}_e$ one, the regions above the torus where $|\mathrm{Im}(\omega )|/\mu \ne 0$ shrink considerably. The growth rates of the flavor instability shown in all three panels range from $10{\mathrm{ns}}^{-1}\lesssim |\mathrm{Im}(\omega )|\lesssim 1\mu {\mathrm{s}}^{-1}$.

Figure 8

Panel (a): Neutrino-driven mass ejecta as a function of the weak-interaction freeze-out time $t_{\mathrm{FO}}$ for the M3A8m3a5 model. The freeze-out time is approximately equal to the time where $Y_e$ reaches the asymptotic value $Y_{\mathrm{e},\mathrm{asym}}$ before neutron capture starts. The largest amount of neutrino-driven ejecta is emitted for $t<35\mathrm{ms}$ when the disk is strongly protonizing. Panel (b): Trajectories of the neutrino-driven ejecta in the M3A8m3a5 model in the $(x,z)$ plane. The ${\nu }_e$ emission surface at 20 ms is also plotted to guide the eye. The color coding of the trajectories indicates the corresponding $t_{\mathrm{FO}}$ shown in panel (a). The trajectories ejected at early times originate closer to the polar region while the later ejecta come from the outer edges of the torus next to the equatorial plane.

Figure 9

Panel (a): Three selected neutrino-driven trajectories in the $(x,z)$ plane, labeled by their respective $t_{\mathrm{FO}}$. The ${\nu }_e$ emission surface at 20 ms is also plotted to guide the eye. Panel (b): Electron fraction $Y_e$ along the three selected trajectories as a function of time; $Y_e$ in the cases with (without) flavor equilibration is plotted with the thick (thin) line.

Figure 10

Final nucleosynthesis outcome shown by mass fraction as a function of the nuclear mass number for the same three selected trajectories shown in Fig. 9. The cases with (without) flavor equilibration are plotted with the thick (thin) lines. Flavor equilibration results in the production of elements with larger $A$.

Figure 11

Top panel: $Y_e^{\mathrm{asym}}$ distribution with (black thick-solid) and without (orange thin-dashed) flavor equilibration. Bottom panel: The corresponding mass fraction $X(A)$ as a function of mass number $A$ for the whole neutrino-driven ejecta. Because of flavor conversions, the element production shifts towards elements with heavier mass number.

Figure 12

Dispersion relation of $\mathbf{k}=(0,0,k_z)$ for the ELN distribution of $t=20$, 50 ms of the model M3A8m3a5. For the complex $\omega$ solutions that lead to flavor instability, $\mathrm{Re}(\omega )$ are plotted with red dash-dotted curves and $\mathrm{Re}(\omega )\pm \mathrm{Im}(\omega )$ are plotted with red solid curves. The gray region indicates the zone of avoidance for real $(\omega ,k_z)$. The system is unstable to fast conversions for a large range of $k_z/{\mu }_0$ and it is therefore unavoidable that fast pairwise conversions would occur.