Helicity coherence in binary neutron star mergers and nonlinear feedback

Neutrino flavor conversion studies based on astrophysical environments usually implement neutrino mixings, neutrino interactions with matter, and neutrino self-interactions. In anisotropic media, the most general mean-field treatment includes neutrino mass contributions as well, which introduce a coupling between neutrinos and antineutrinos termed helicity or spin coherence. We discuss resonance conditions for helicity coherence for Dirac and Majorana neutrinos. We explore the role of these mean-field contributions on flavor evolution in the context of a binary neutron star merger remnant. We find that resonance conditions can be satisfied in neutron star merger scenarios while adiabaticity is not sufficient for efficient flavor conversion. We analyze our numerical findings by discussing general conditions to have multiple Mikheyev-Smirnov-Wolfenstein-like resonances, in the presence of nonlinear feedback, in astrophysical environments.

Figure 1

Geometry of our model. The blue surface shows the neutrinospheres, which we will approximate later on as infinitely thin disks. We chose the emission point $(x_0,z_0)$ of our test neutrino ${\nu }_q$ on this surface, while the angle ${\theta }_q$ fixes the direction of its momentum $\widehat{q}$ (${\varphi }_q$ is set to zero). The quantity ${\overrightarrow{J}}_{\mathrm{mat}}^{\perp }$ indicates the perpendicular matter current. The momentum $\widehat{p}$ of the background neutrino ${\nu }_p$ also has a component $p^{\perp }$ perpendicular to the test neutrino, creating a neutrino current perpendicular to the test neutrino trajectory.

Figure 2

Geometrical factors for neutrinos (upper) and antineutrinos (lower figure), as a function of distance, in our schematic model based on binary star mergers. The two curves correspond to $G_{\nu }$ (43) (solid line) and $G_{\nu }^{\perp }$ (46) (dashed line) in the self-interaction Hamiltonian Eq. (42) and Eq. (45) respectively. Results correspond to Model C (Table 2).

Figure 3

Same as Fig. 2 for Model A (see Table 2).

Figure 4

Matrix elements appearing in the MNR (50) and helicity resonance conditions (52) for Model A (Table 2). The values correspond to the matter and to the unoscillated self-interaction potentials (30) and (49), respectively. The green pentagon shows the location of the beginning of the MNR, while the blue dot shows the location of the helicity coherence resonance.

Figure 5

Model A: Electron neutrino (upper) and antineutrino (middle) survival probabilities for different energies, in the presence of a MNR starting at 40 km (see Fig. 4). The averaged probability is also presented. The lower panel shows the locally averaged cosine of the angle between the effective isospin and magnetic field.

Figure 6

Same as Fig. 4 but for Model B (Table 2).

Figure 7

Model B: Resonance condition (52) (upper) as well as the off-diagonal matrix element $h_{\mathcal{G},13}$ (lower) which is nonzero in the presence of the neutrino mass. The helicity coherence resonance can be seen at 34 km. The different colors correspond to different neutrino energies. The solid lines are the results for $m_0=0.1\mathrm{eV}$, while the dotted lines are for the unrealistic value of $m_0=100\mathrm{eV}$.

Figure 8

Model B: Electron neutrino survival probability (upper) and adiabaticity (lower). The results for different energies are indistinguishable.

Figure 9

Same as Fig. 4 but for Model C (Table 2).

Figure 10

Model C: Electron neutrino (upper) and antineutrino (lower) survival probabilities for different energies, in the presence of a symmetric MNR at 59 km (see Fig. 9) and a helicity coherence resonance around 103 km. The averaged probabilities are also shown.

Figure 11

Model C: Resonance condition (52) and the off-diagonal matrix element $h_{\mathcal{G},13}$ for two different values of the absolute mass $m_0$.

Figure 12

Matter profile $\lambda Y_e$ for Model A (solid line), and the right-hand side of Eq. (61) for neutrinos (dashed line) and antineutrinos (dotted line). The pentagons show the multiple crossing where MNR condition (61) is fulfilled.

Figure 13

Side view of the accretion disk, with the central object located at the center. The radius of the disk is flavor dependent and is denoted $R_{{\nu }_{\alpha }}$. A neutrino is emitted near the disk at the point ${\mathbf{Q}}_{\mathbf{0}}$, and then leaves it with a momentum $\overrightarrow{q}$ located by its spherical coordinates $(q,{\theta }_q,{\varphi }_q)$. The coordinate $r$ is the distance between the location of the neutrino at time $t$ and its emission point, with the corresponding Cartesian coordinates $(x,0,z)$.

Figure 14

Bird’s eye view of the accretion disk. The emission point of the neutrino is located by its polar coordinates $(r_d,\phi )$.