Relativistic magnetohydrodynamics winds from rotating neutron stars

We solve for the time-dependent dynamics of axisymmetric, general relativistic magnetohydrodynamic winds from rotating neutron stars. The mass-loss rate as a function of latitude is obtained self-consistently as a solution to the magnetohydrodynamics equations, subject to a finite thermal pressure at the stellar surface. We consider both monopole and dipole magnetic field geometries and we explore the parameter regime extending from low magnetization (low sigma(0)), almost thermally driven winds to high magnetization (high sigma(0)), relativistic Poynting-flux-dominated outflows (sigma=B-2/4 pi rho gamma c(2)beta(2)approximate to sigma(0)/gamma(infinity),beta=v/c with sigma(0) = omega(2)Phi/M, where omega is the rotation rate, Phi is the open magnetic flux, and M is the mass flux). We compute the angular momentum and rotational energy-loss rates as a function of sigma(0) and compare with analytic expectations from the classical theory of pulsars and magnetized stellar winds. In the case of the monopole, our high-sigma(0) calculations asymptotically approach the analytic force-free limit. If we define the spindown rate in terms of the open magnetic flux, we similarly reproduce the spindown rate from recent force-free calculations of the aligned dipole. However, even for sigma(0) as high as similar to 20, we find that the location of the Y-type point (r(Y)), which specifies the radius of the last closed field line in the equatorial plane, is not the radius of the Light Cylinder R-L=c/omega (R= cylindrical radius), as has previously been assumed in most estimates and force-free calculations. Instead, although the Alfven radius at intermediate latitudes quickly approaches R-L as sigma(0) exceeds unity, r(Y) remains significantly less than R-L. In addition, r(Y) is a weak function of sigma(0), suggesting that high magnetizations may be required to quantitatively approach the force-free magnetospheric structure, with r(Y)=R-L. Because r(Y) < R-L, our calculated spindown rates thus exceed the classic 'vacuum dipole' rate: equivalently, for a given spindown rate, the corresponding dipole field is smaller than traditionally inferred. In addition, our results suggest a braking index generically less than 3. We discuss the implications of our results for models of rotation-powered pulsars and magnetars, both in their observed states and in their hypothesized rapidly rotating initial states.