Magnetized Stars in the Heterogeneous ISM Olga Toropina Space Research Institute, Moscow M.M. Romanova and R. V. E. Lovelace Cornel University, Ithaca, NY

I. The Guitar Nebula Image from 5-m Hale telescope at Palomar Observatory Bow shocks are observed on a wide variety of astrophysical scales, from planetary magnetospheres to galaxy clusters. Some of the most spectacular bow shock nebulae are associated with neutron stars. A visually example is the Guitar Nebula:

I. The Guitar Nebula Image from 5-m Hale telescope at Palomar Observatory The Guitar Nebula was discovered in It’s produced by an ordinary NS, PSR B , which is travelling at an extraordinarily high speed: about 1600 km/sec. The NS leaves behind a “tail” in the ISM, which just happens to look like a guitar (only at this time, and from our point of view in space).

I. The Guitar Nebula The head of the Guitar Nebula, imaged with the HST Planetary Camera The Guitar Nebula is about 6.5 thousand light years away, in the constellation of Cepheus, and occupies about an arc-minute (0.015 degree) in the sky. This corresponds to about 300 years of travel for the NS.

I. The Guitar Nebula The head of the Guitar Nebula, imaged with the Hubble Space Telescope in 1994, 2001, and The change in shape traces out the changing density of the ISM:

I. The Guitar Nebula An analyze of the optical data by A. Gautam An analyze of the optical data shows that a shape of the head in the third observation is beginning to resemble another guitar shape, suggesting that the pulsar may be travelling through periodic fluctuations in the ISM:

I. Pulsar Wind Nebulae Right panels show radio contours and the direction of the magnetic field. The red and blue colors in the left panels correspond to X-ray and radio, respectively PWNe have been observed via X-ray synchrotron radiation for many sources over many years. Two well-known bow-shock PWNe: "The Mouse’’ powered by PSR J and the PWN powered by PSR J X-ray and radio images of the very long pulsar tails, by Kargaltsev & Pavlov:

I. Pulsar Wind Nebulae PSR J0742−2822 H  Pulsar Bow Shocks, image of PSR J0742−2822 by Brownsberger & Romani. PWNe has a long tail with multiple bumps like of the bubbles Guitar nebula

Rotating MNS pass through different stages in their evolution: Ejector – a rapidly rotating (P<1s) magnetized NS is active as a radiopulsar. The NS spins down owing to the wind of magnetic field and relativistic particles from the region of the light cylinder R L R A > R L Propeller – after the NS spins-down sufficiently, relativistic wind is suppressed by the inflowing matter R L > R A Until R C <R A, the centrifugal force prevents accretion, NS rejects an incoming matter R C <R A < R L Accretor – NS rotates slowly, matter can accrete onto star surface R A < R C, R A < R L Georotator – NS moves fast through the ISM R A > R асс II. Evolution of Magnetized NS

What determines the shape of the bow shock around the moving NS? Form of the bow shock depends on the ratio of the major radii Alfven radius (magnetospheric radius):  V 2 /2 = B 2 /8  Accretion radius: R асс = 2GM * / (c s 2 + v 2 ) Corotation radius: R C =(GM/  2 ) 1/3 Light cylinder radius: R L =cP/2  II. Propagation of Magnetized NS

Two simple examples: 1) R A < R асс a gravitational focusing is important, matter accumulates around the star and interacts with magnetic field (accretor regime) 2) R A > R асс matter from the ISM interacts directly with the star’s magnetosphere, a gravitational focusing is not important (georotator regime) A ratio between R A and R асс depends on B * and V * (or M ->  ). So, shape of the bow shock depends on  and t of the ISM.

III. MHD Simulation We consider an equation system for resistive MHD (Landau, Lifshitz 1960): We use non-relativistic, axisymmetric resistive MHD code. The code incorporates the methods of local iterations and flux-corrected transport. This code was developed by Zhukov, Zabrodin, & Feodoritova (Keldysh Applied Mathematic Inst.) - The equation of state is for an ideal gas, where  = 5/3 is the specific heat ratio and ε is the specific internal energy of the gas. - The equations incorporate Ohm’s law, where σ is an electric conductivity.

III. MHD Simulation We consider an equation system for resistive MHD (Landau, Lifshitz 1960): We assume axisymmetry (∂/∂ ϕ = 0), but calculate all three components of v and B. We use a vector potential A so that the magnetic field B =  x A automatically satisfies  B = 0. We use a cylindrical, inertial coordinate system (r, , z) with the z-axis parallel to the star's dipole moment  and rotation axis . A magnetic field of the star is taken to be an aligned dipole, with vector potential A =  x R/R3

III. MHD Simulation We consider an equation system for resistive MHD (Landau, Lifshitz 1960): After reduction to dimensionless form, the MHD equations involve the dimensionless parameters:

Cylindrical inertial coordinate system (r, , z), with origin at the star’s center. Z-axis is parallel to the velocity v  and magnetic moment . Supersonic inflow with Mach number M from right boundary. The incoming matter is assumed to be unmagnetized. Manetic field of the star is dipole. Bondi radius (R B )=1. Uniform greed (r, z) 1281 x 385 III. Geometry of Simulation Region

Poloidal magnetic B field lines and velocity vectors are shown. Magnetic field acts as an obstacle for the flow; and clear conical shock wave forms. Magnetic field line are stretched by the flow and forms a magnetotail. IV. Moving NS in the Uniform ISM Simulations of propagation of a magnetized NS at Mach number M = 3, R A ~ R асс, gravitational focusing is not important

Poloidal magnetic B field lines and velocity vectors are shown. Magnetic field acts as an obstacle for the flow; and clear conical shock wave forms. Magnetic field line are stretched by the flow and forms a magnetotail. IV. Moving NS in the Uniform ISM Simulations of propagation of a magnetized NS at Mach number M = 3, R A ~ R асс, gravitational focusing is not important

Energy distribution in magnetotail. M=3, magnetic energy dominates. IV. Moving NS in the Uniform ISM Simulations of propagation of a magnetized NS at Mach number M = 3, R A ~ R асс, gravitational focusing is not important

Poloidal magnetic B field lines and velocity vectors are shown. Bow shock is narrow. Magnetic field line are stretched by the flow and forms long magnetotail. IV. Moving NS in the Uniform ISM Simulations of propagation of a magnetized NS at Mach number M = 6, R A > R асс, gravitational focusing is not important

Poloidal magnetic B field lines and velocity vectors are shown. Magnetic field line are stretched by the flow and forms long magnetotail. IV. Moving NS in the Uniform ISM Simulations of propagation of a magnetized NS at Mach number M = 6, R A > R асс, gravitational focusing is not important

Georotator regime. Results of simulations of accretion to a magnetized star at Mach number M = 10. Poloidal magnetic B field lines and velocity vectors are shown. Bow shock is narrow. Magnetic field line are stretched by the flow and forms long magnetotail. t = 4.5 t 0 Density in the magnetotail is low. IV. Moving NS in the Uniform ISM Simulations of propagation of a magnetized NS at Mach number M=10, R A >> R асс, gravitational focusing is not important

Georotator regime. Results of simulations of accretion to a magnetized star at Mach number M = 10. Poloidal magnetic B field lines and velocity vectors are shown. Magnetic field line are stretched by the flow and forms long magnetotail. IV. Moving NS in the Uniform ISM Simulations of propagation of a magnetized NS at Mach number M=10, R A >> R асс, gravitational focusing is not important

Density in the magnetotail is low. Magnetic field in the magnetotail reduced gradually. IV. Moving NS in the Uniform ISM Tail density and field variation at different Mach numbers:

V. Moving NS in the Non-Uniform ISM We already have the simulation of propagation of a magnetized NS through the uniform ISM with M = 6. Now we can take the results of this simulation as initial conditions for an investigation of the non- uniform ISM. Imagine that our NS went into a dense cloud.

V. Moving NS in the Non-Uniform ISM We changed a density of incoming matter and observes variation of the bow shock and magnetic field lines. Case for M=6,  1 /  0 = 6. Variations of the density of the flow.

V. Moving NS in the Non-Uniform ISM We changed a density of incoming matter and observes variation of the bow shock and magnetic field lines. Case for M=6,  1 /  0 = 6. Variations of the temperature of the flow.

V. Moving NS in the Non-Uniform ISM We changed a density of incoming matter and observes variation of the bow shock and magnetic field lines. Variations of the density and temperature across a tail.

V. Moving NS in the Non-Uniform ISM We changed a density of incoming matter and observes variation of the bow shock and magnetic field lines. Case for M=6,  1 /  0 = 6. Variations of the density of the flow.

V. Observations VLT observations by Kerkwijk and Kulkarni