SPH simulations of irradiation-driven warped accretion discs and the long periods in X-ray binaries

We present three dimensional smoothed particle hydrodynamics (SPH) calculations of irradiation-driven warping of accretion discs. Initially unwarped planar discs are unstable to the radiation reaction when the disc is illuminated by a central radiation source. The disc warps and tilts and precesses slowly in a retrograde direction; its shape continuously flexes in response to the changing orientation of the Roche poten-tial. We simulate ten systems: eight X-ray binaries, one cataclysmic variable (CV), and a ‘generic’ low mass X-ray binary (LMXB). We adopt system parameters from observations and tune our model X-ray luminosity (LX) to reproduce the observed or inferred super-orbital periods. Without exception, across a wide range of parameter space, we find an astonishingly good match between the observed LX and the model LX. We conclude irradiation-driven warping is the mechanism underlying the long periods in X-ray binaries. Our HerX-1 simulation reproduces the observed “main-” and “short-high” X-ray states for realistic orbital inclinations. Our simulations of SS 433 give a maximum warp angle of 18.6◦, a good match to the cone traced by the jets, but this angle is reached only in the outer disc. In all cases, the overall disc tilt is less than 13◦ and the maximum disc warp is less than and or equal to 21◦. In particular, the disc warp in 4U1626-67 cannot explain the observed torque reversals. Taking our results at face value, ignoring the finite opening angle of the disc, we deduce orbital inclinations of approximately 77◦ for 4U1916-053 and approximately 69◦ for 4U1626- 67. We also simulate CygX-2, SMCX-1, CygX-1, and LMCX-3. For high mass X-ray binary (HMXB) parameters, the discs’ maximum angular elevation is invariably at the outer edge. For LMXBs with extreme mass ratios a strong inner disc warp devel-ops, completely shadowing parts of the outer disc. This inner warped disc executes retrograde precession while the outer disc executes prograde apsidal precession. The remaining LMXBs develop a less extreme warp in the inner disc, with the entire disc tilting and precessing in a retrograde direction. For our CV, KRAur, we matched the inferred disc precession period by adopting LX = 1037 erg sec−1, which would require steady nuclear burning on the white dwarf surface