Beamed super-Eddington emission from a weakly magnetized neutron star - an ultraluminous X-ray source (ULX) David Abarca⋆1, Kyle Parfrey2 & Włodek Kluźniak1 1Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences 2School of Mathematics, Trinity College Dublin, Dublin 2, Ireland ⋆dabarca@camk.edu.pl Abstract We model an ultraluminous X-ray source using a global 2D axisymmetric general relativistic radiation magnetohydrodynamic simulation of super-Eddington accretion onto a neutron star with a 10 billion Gauss dipolar magnetic ﬁeld. We found that the magnetic conﬁnement of the gas into accretion columns along with the interaction of the gas with the neutron star surface produce a total luminosity of a few times the Eddington limit. Furthermore, this radiation is beamed by outﬂows from the accretion disk causing the apparent isotropic luminosity to exceed 1040 erg s−1, showing that low-magnetic ﬁeld neutron stars can be good candidates for the central engines of ULXs. Neutron stars power ULXs What is a ULX? • Bright, extragalactic object with X-ray luminosities L ≳1039 erg s−1. • Not observed in the central region of galaxies, i.e., not an active galactic nucleus/supermassive black hole. The Eddington luminosity LEdd = 4πGMmpc σT , for a 1 M⊙object is approximately 1040 erg s−1. Bachetti et al. (2014) observed a ULX along with ∼1 s coherent pulsations, indicating a neutron star accretor with a super-Eddington luminosity. About a dozen such objects have been found, and there is evidence that even non-pulsating ULXs may be powered by neutron stars (King et al. 2017; Wiktorowicz et al. 2017). GRRMHD simulations Super-Eddington accreting neutron stars are excellent systems for applying general-relativistic radiation magne- tohydrodynamics (GRRMHD). • Strong gravity from the neutron star requires general relativity. • Super-Eddington accretion mean radiation pressure becomes dynamically important which requires radiation hydrodynamics. • Accretion is inherently a magnetoturbulent phenomenon, which requires magnetohydrodynamics to describe properly. GRRMHD Equations ∇µ(ρuµ) = 0 Conservation of mass ∇µT µν = Gν Conservation of matter momentum-energy ∇µRµν = −Gν Conservation of radiation momentum-energy ∇µF ∗µν = 0 Source-free Maxwell’s equations 20 10 0 10 20 r[GM/c2] 14 15 16 17 18 19 log10 c E, [ergcm−3] 5 4 3 2 1 log10 ρ[gcm−3] Figure: Snapshot (upper) and time-averaged (lower) plots of the radiation energy density, left, and the gas rest-mass density, right. We plot equispaced contours of Aφ, the φ component of the vector potential, which correspond to poloidal ﬁeld lines due to the axisymmetric nature of the problem. A bold contour shows the remnant of a torus loop which had just reconnected with the neutron star’s dipole. Simulation details • We run the simulation using the Koral code (Sądowski et al., 2013, 2015) which solves the GRRMHD equations on a static grid for a ﬁxed metric. • Radiation is evolved using the M1 closure scheme (Levermore 1984). • We implement the method from Parfrey & Tchekhovskoy (2017) in order to handle large magnetizations. • We use a 2D axisymmetric grid with resolution in r and θ corresponding to [512, 510] cells. • We initialize the simulation from an equilibrium torus threaded by a weak magnetic ﬁeld. The neutron star magnetic ﬁeld is initialized to a dipole with a maximum ﬁeld strength of 2 × 1010 G. • The boundary condition is set to return a fraction (75%) of the inﬂowing energy as outﬂowing radiation. • The simulation is run for 80,000 GMc−3. Simulation Result As the simulation evolves, the magnetorotational instabil- ity develops in the disk driving accretion. The infalling gas hits the neutron star magnetic ﬁeld and is forced to accrete along magnetic ﬁeld lines, forming accretion columns. Gas hits the the neutron star surface and becomes shocked. Ra- diation escapes through the sides of the accretion column and reaches the observer through the optically thin funnel regions along t