Can we ignore the time dependence in matter neutrino resonance?

TL;DR

This work questions the validity of the common time-independent (steady-state) treatment of matter–neutrino resonance (MNR) in dense astrophysical environments, focusing on a multi-angle MNR setup relevant to neutron star mergers. By performing reproducible simulations in both time-dependent and time-independent formalisms, the authors demonstrate that steady-state solutions are unstable or non-unique and yield flavor survival probabilities that qualitatively differ from fully time-dependent dynamics, often overestimating flavor conversion and inducing artificial angular structure. These findings imply that prior insights derived from steady-state analyses, including neutrino-bulb models, must be re-evaluated and that fully time-dependent modeling is essential for accurate predictions of neutrino flavor evolution in dense media. The paper highlights the need to extend such analyses to more realistic geometries, like accretion disks, using time-dependent simulations to capture the true dynamics of neutrino self-interactions.

Abstract

In the vicinity of neutron star mergers (NSMs), it is possible for the neutrino self-interaction potential to cancel with the matter potential leading to matter neutrino resonance (MNR). MNR is one of the most interesting mechanisms by which neutrino flavor evolution can occur in dense astrophysical environments. Previous studies have typically assumed that the neutrino flavor field evolves to a steady state -- a simplification also used in other self-interaction models such as the neutrino-bulb model. Here, we perform reproducible calculations of MNR using both time-independent and time-dependent formalisms and show that they yield qualitatively different flavor survival probabilities. The time-independent approach produces unstable steady-state solutions that differ fundamentally from the dynamical behavior captured in time-dependent simulations. These results demonstrate that the steady-state assumption is generally invalid, and physical interpretations based on time-independent calculations of dense neutrino systems require re-evaluation.

Figures (8)

• Figure 1: Left: Comparison between neutrino flavor evolution for normal mass odering in identical systems obtained using time-dependent formalism (red) and time-independent formalism (blue) The top, middle, and bottom panels are for $\Delta \theta = 1^{\circ}, 2^{\circ}$, and $4^{\circ}$, respectively. Right: Same as that in the left column but for inverted mass ordering.
• Figure 2: Left: Angular distribution of electron neutrinos (green) and electron antineutrinos (purple) at 60 km obtained using time-independent formalism and assuming normal mass ordering. One can see that the angular distribution has significant structure, and hence, a large number of angular bins is required. The results in this panel have been obtained with 100 angular bins, which is sufficient in this case, as seen in \ref{['AppendixA']}. Right: Angular distribution of electron neutrinos (green) and electron antineutrinos (purple) at 60 km obtained using time-dependent formalism. The angular distribution does not have too much structure, and hence, the number of angular bins required is not large. The results in this panel have been obtained using 50 angular bins, which is more than what is necessary for convergence.
• Figure 3: Left: Real (solid) and imaginary (dashed) parts of the off-diagonal component of the density matrix for a neutrino at two different times (140 km/c in blue and 150 km/c in red). It is not possible to see the red lines because they are perfectly behind the blue lines, implying that the flavor evolution with respect to time has stopped. The numerical simulation was carried out using the time-dependent formalism in normal mass ordering and assuming $\Delta \theta = 1^{\circ}$. Right: The same as the left panel, but for antineutrinos.
• Figure 4: Top: The blue lines show the initial spatial dependence of the real (solid) and imaginary (dashed) parts of the off-diagonal components of the density matrix for neutrinos (left) and antineutrinos (right). The spatial dependence used for the initial state is obtained from the solution of the time-independent formalism. The red lines show the real and imaginary parts of the final state obtained using the time-dependent formalism. Note that red lines are identical to those in Fig. \ref{['offdiag']}, implying that the solution is not sensitive to the initial conditions used in the time-dependent formalism. The numerical calculation was performed assuming $\Delta \theta = 1^{\circ}$ and normal mass ordering with 100 angular bins. Bottom: The same as the top panels, but shows the evolution of the diagonal components of the density matrix. The solid lines are used to denote neutrinos, whereas the dashed lines are used to denote antineutrinos.
• Figure 5: Left: Survival probability of electron neutrinos and electron antineutrinos as a function of $r$, with $\Delta \theta = 1^{\circ}$ and normal mass ordering calculated using the time-independent formalism. The survival probability has been calculated using 100 (blue) and 300 (purple) angular bins in the time-independent formalism. The two evolve identically up to $\approx 60$ km, after which they diverge from each other. This implies that 100 angular bins are sufficient if the system is evolved up to 60 km. Right: Same as the left pane,l but for $\Delta \theta = 4^{\circ}$ and the number of angular bins has been changed to 500 (blue) and 1000 (purple).