Spin oscillations of neutrinos scattered by the supermassive black hole in the galactic center

TL;DR

This paper addresses how ultra-relativistic neutrinos undergo spin oscillations while gravitationally scattered by a rotating supermassive black hole surrounded by a thick, toroidally magnetized accretion disk. It develops a quasiclassical framework combining BMT-type spin evolution with curved-spacetime Kerr geodesics and a Polish doughnut disk model to capture electromagnetic and electroweak interactions along many trajectories. The authors show that toroidal magnetic fields alone can induce sizable spin flips, and they reveal symmetry properties that depend on BH spin and disk rotation, offering a potential observational handle on disk geometry in the Galactic center. Overall, the work provides a path to using astrophysical neutrinos as probes of strong gravity and disk magnetization, with implications for multimessenger observations and Galactic-center plasma conditions.

Abstract

In this work, we study the propagation and spin oscillations of neutrinos in their scattering by a supermassive black hole (SMBH) surrounded by a realistic accretion disk. We review various descriptions of the fermion spin evolution in a curved spacetime under the influence of external fields. The overview of the test particle motion in the gravitational field of a rotating SMBH is also present. The external fields which a neutrino spin interacts with are the electroweak forces in plasma and the toroidal magnetic field in the accretion disk surrounding SMBH. Spin precession of neutrinos, which are supposed to be Dirac particles, is caused by the interaction of the neutrino magnetic moment with the magnetic field in the disk. We use a semi-analytical model of a thick accretion disk and review its characteristics. The cases of co-rotating and counter-rotating disks with respect to BH are discussed. We consider the incoming flux of neutrinos having an arbitrary angle with respect to the BH spin since the recent results of the Event Horizon Telescope indicate that the BH spin in the galactic center is not always perpendicular to the galactic plane. For our study, we consider a large number of incoming test neutrinos. We briefly discuss our results and their applications in the observations of astrophysical neutrinos.

Figures (9)

• Figure 1: Schematic diagrams showing neutrino trajectories. (a) A beam of neutrinos coming from $\infty$ at an angle $\theta_i$ with respect to the BH spin. (b) Neutrinos crossing the equatorial plane through the accretion disk. The toroidal magnetic field is perpendicular to their momenta.
• Figure 2: Figures showing the dimensionless values of the integrals of motion, $y$ and $w$, together with the BH shadow. The points are spherically distributed in $y$ and $w$. They represent neutrino beams either coming out of or going into the page. We consider three different values of $\mathfrak{\tilde{t}}_i = \cos\theta_i$, namely $\mathfrak{\tilde{t}}_i = 0.01, 0.50$ and $0.90$ for each of the BH spins (a) $a = 0.02 M$ and (b) $a = 0.98M$. The beam or the point that falls in the shadow area is captured. For $\mathfrak{\tilde{t}}_i = 0.01$, only the neutrinos marked by light blue points are scattered. Similarly for $\mathfrak{\tilde{t}}_i = 0.50$ and $\mathfrak{\tilde{t}}_i = 0.90$, only the neutrinos marked by green and red points, respectively are scattered. In our computation, we consider only the scattered beams.
• Figure 3: Figure showing the screen coordinates $\alpha$ and $\beta$. The observer is at an angle, $\theta_0$.
• Figure 4: Figures showing BH shadows in screen coordinates for two different BH spins, (a) $a = 0.50M$ and (b) $a = 0.98M$. For each BH spin, these figures represent different values of $\mathfrak{\tilde{t}}_i$, namely $\mathfrak{\tilde{t}}_i = 0.01, 0.50$ and $0.90$. The points represent neutrino beams either coming out of or going into the page. The gray colored beams (points) as well as the beams that are inside the BH shadow area are discarded from our computation.
• Figure 5: Figures showing $r$ vs $\cos\theta$ for the trajectories of a few upper and lower neutrinos. (a) $a = 0.02 M$ and (b) $a = 0.98M$. In both figures, the angle of incidence of the neutrino beam is $\theta_i = 45^{\circ}$, i.e. $\cos\theta_i = 0.707$. We can see that while approaching the BH, the neutrinos travel in straight line for most of the part. Only near the turn point, the beam separates into upper and lower neutrinos and start oscillating in $\cos\theta$. The $\cos\theta$ behavour is dictated by the Eqs. \ref{['eq:thetabtp_north']}, \ref{['eq:thetaatp_north']}, \ref{['eq:thetabtp_south']} and \ref{['eq:thetaatp_south']}. We see that the values of $\cos\theta$ experience changes in signs. This implies crossing of neutrinos from above the equatorial plane to below and vice versa.