Can a Dehnen-type dark matter halo affect the neutrino flavor oscillations?

TL;DR

The paper investigates how a Dehnen-type dark matter halo surrounding a Schwarzschild black hole influences gravitationally lensed neutrino flavor oscillations. It develops analytic expressions for the oscillation phase in radial and non-radial propagation, and computes oscillation probabilities using a two-flavor toy model, highlighting halo-induced modifications to the phase and damping. The study also analyzes decoherence by modeling neutrinos as Gaussian wave packets and showing that halo parameters can enlarge the decoherence length, reducing oscillation visibility. While current experiments cannot test these effects, the work suggests neutrino oscillations could, in principle, serve as a probe of dark matter distributions around compact objects.

Abstract

The gravitational weak lensing of neutrinos in the presence of a Schwarzschild black hole surrounded by a Dehnen-type dark matter halo is investigated. The event horizon structure is explored, and the existence of the BH is studied in two different slices of the parameter space. Additionally, we derive analytic expressions for the oscillation phase and transition probabilities for both radial and non-radial neutrino propagation. Finally, we use a two-flavor toy model, and numerically analyze how the dark matter halo parameters as density and scale radius, affect oscillation probabilities and examine the role of decoherence. The results show that the presence of a dark matter halo modifies the oscillation phase and damping factor, leading to measurable deviations from the standard Schwarzschild BH case. These findings suggest that neutrino oscillations could, in principle, serve as a probe for dark matter distributions around compact astrophysical objects.

Figures (8)

• Figure 1: Left panel: The phase diagram demonstrates the existence of the Schwarzschild BH surrounded by a Dehnen-type DM halo region in the $(\rho_a,r)$ plane. The black region represents the slice of the parameter space where $f(r,\rho_a) \leq 0$, pointing to the presence of the Schwarzschild BH surrounded by a Dehnen-type DM halo. Right panel: The phase diagram illustrates the existence of the Schwarzschild BH surrounded by a Dehnen-type DM halo region in the $(r_a,r)$ plane. The black region represents the slice of the parameter space where $f(r,r_a) \leq 0$, pointing to the presence of the Schwarzschild BH surrounded by a Dehnen-type DM halo. The boundary lines separate the BH and No-BH regions.
• Figure 2: The plot shows the event horizon radius of the Schwarzschild BH surrounded by a Dehnen-type DM halo as a function of $\rho_a$ for the different values of the $r_a$.
• Figure 3: The plot demonstrates the schematic diagram of the gravitational weak lensing of neutrinos in the spacetime of the Schwarzschild BH surrounded by a Dehnen-type DM halo.
• Figure 4: The plot demonstrates the probability of neutrino oscillation as a function of azimuthal angle $\varphi$. From top to bottom, the densities of the central halo are $\rho_a=0$, $\rho_a=0.005$, and $\rho_a=0.01$, respectively. Blue and red-dashed lines correspond to the normal hierarchy $\Delta m^2 >0$ and inverted hierarchy $\Delta m^2 <0$, respectively. The other parameters are as follows: the mixing angle $\alpha=\pi/6$, $r_a=0.2$, $M=1M_{\odot}$, $\Delta m^2=10^{-3} eV^2$. Here, we consider that the lightest neutrino is massless.
• Figure 5: The plot shows the neutrino oscillation probability as a function of azimuthal angle $\varphi$ for different values of the density of the DM halo. Top and bottom panels correspond to normal hierarchy $\Delta m^2>0$ and inverted hierarchy $\Delta m^2<0$, respectively. The other parameters are as follows: the mixing angle $\alpha=\pi/6$, $r_a=0.2$, $M=1M_{\odot}$, $\Delta m^2=10^{-3} eV^2$. Here, we consider that the lightest neutrino is massless.