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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
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:
Image from 5-m Hale telescope at Palomar Observatory
I. The Guitar Nebula
The Guitar Nebula was discovered in 1992. It’s produced by an ordinary NS,
PSR B2224+65, 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).
Image from 5-m Hale telescope at Palomar Observatory
I. The Guitar Nebula
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.
The head of the Guitar Nebula, imaged with the HST Planetary Camera
I. The Guitar Nebula
The head of the Guitar Nebula, imaged with the Hubble Space Telescope in
1994, 2001, and 2006. The change in shape traces out the changing density
of the ISM:
I. The Guitar Nebula
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:
An analyze of the optical data by A. Gautam
I. Pulsar Wind Nebulae
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 J1747-2958 and the PWN powered by PSR J1509-5850.
X-ray and radio images of the very long pulsar tails, by Kargaltsev & Pavlov:
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
I. Pulsar Wind Nebulae
Ha 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
PSR J0742−2822
II. Evolution of Magnetized NS
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 RL
RA > RL
Propeller – after the NS spins-down sufficiently, relativistic wind is
suppressed by the inflowing matter RL > RA
Until RC<RA, the centrifugal force prevents accretion, NS rejects an
incoming matter
RC<RA< RL
Accretor – NS rotates slowly, matter can accrete onto star surface
RA < RC , RA < RL
Georotator – NS moves fast through the ISM RA > Rасс
II. Propagation 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):
rV2/2 = B2/8p
Accretion radius:
Rасс = 2GM* / (cs2 + v2)
Corotation radius:
RC =(GM/W2)1/3
Light cylinder radius:
RL=cP/2p
II. Propagation of Magnetized NS
Two simple examples:
1) RA < Rасс a gravitational focusing is important, matter accumulates around
the star and interacts with magnetic field (accretor regime)
2) RA > Rасс matter from the ISM interacts directly with the star’s
magnetosphere, a gravitational focusing is not important (georotator regime)
A ratio between RA and Rасс depends on B* and V* (or M -> r). So, shape of
the bow shock depends on r 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 g = 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, f, z) with the z-axis parallel to
the star's dipole moment m and rotation axis W.
A magnetic field of the star is taken to be an aligned dipole, with vector potential
A = m 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:
III. Geometry of Simulation Region
Cylindrical inertial coordinate system (r, f, z), with origin at the star’s center.
Z-axis is parallel to the velocity v and magnetic moment m. 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 (RB )=1. Uniform
greed (r, z) 1281 x 385
IV. Moving NS in the Uniform ISM
Simulations of propagation of a magnetized NS at Mach number M = 3,
RA ~ Rасс , 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,
RA ~ Rасс , 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,
RA ~ Rасс , 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 = 6,
RA > Rасс , 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,
RA > Rасс , 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=10,
RA >> Rасс , 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 t0 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,
RA >> Rасс , 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
Tail density and field variation at different Mach numbers:
Density in the magnetotail is low. Magnetic field in the magnetotail reduced
gradually.
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 nonuniform 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, r1 / r0 = 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, r1 / r0 = 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, r1 / r0 = 6. Variations of the density of the flow.
V. Observations
VLT observations by Kerkwijk and Kulkarni