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

We present three-dimensional smoothed particle hydrodynamics 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 potential. We simulate 10 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 a single parameter: our model X-ray luminosity (L(*)), to reproduce the observed or inferred superorbital periods. Without exception, across a wide range of parameter space, we find an astonishingly good match between the observed L(X) and the model L*. We conclude irradiation-driven warping is the mechanism underlying the long periods in X-ray binaries. Our Her X-1 simulation simultaneously reproduces the observed L(X), the 'main-' and 'short-high' X-ray states and the orbital inclination. Our simulations of SS 433 give a maximum warp angle of 18 degrees.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 degrees and the maximum disc warp is less than and or equal to 21 degrees. In particular, the disc warp in 4U 1626-67 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 degrees for 4U 1916-053 and approximately 69 degrees for 4U1626-67. We also simulate CygX-2, SMCX-1, CygX-1 and LMCX-3. For high-mass X-ray binary parameters, the discs' maximum angular elevation is invariably at the outer edge. For LMXBs with extreme mass ratios a strong inner disc warp develops, 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, KR Aur, we matched the inferred disc precession period by adopting L(X) = 10(37) erg s(-1), which would require steady nuclear burning on the white dwarf surface.