Revised Pulsar Spindown Page: 1 of 8
This article is part of the collection entitled: Office of Scientific & Technical Information Technical Reports and was provided to Digital Library by the UNT Libraries Government Documents Department.
The following text was automatically extracted from the image on this page using optical character recognition software:
REVISED PULSAR SPINDOWN
I. CONTOPOULOS1 AND A. SPJTKOVSKY 2,3
Draft version November 14, 2005
We address the issue of electromagnetic pulsar spindown by combining our experience from the
two limiting idealized cases which have been studied in great extent in the past: that of an aligned
rotator where ideal MHD conditions apply, and that of a misaligned rotator in vacuum. We construct
a spindown formula that takes into account the misalignment of the magnetic and rotation axes, and
the magnetospheric particle acceleration gaps. We show that near the death line aligned rotators spin
down much slower than orthogonal ones. In order to test this approach, we use a simple Monte Carlo
method to simulate the evolution of pulsars and find a good fit to the observed pulsar distribution in
the P - P diagram without invoking magnetic field decay. Our model may also account for individual
pulsars spinning down with braking index n < 3, by allowing the corotating part of the magnetosphere
to end inside the light cylinder. We discuss the role of magnetic reconnection in determining the pulsar
braking index. We show, however, that n ~ 3 remains a good approximation for the pulsar population
as a whole. Moreover, we predict that pulsars near the death line have braking index values n > 3, and
that the older pulsar population has preferentially smaller magnetic inclination angles. We discuss
possible signatures of such alignment in the existing pulsar data.
Subject headings: MHD
The current canonical pulsar paradigm is that of a
magnetized rotating neutron star (see Mestel 1999 for
a review). However, we feel that certain fundamental
aspects of the paradigm still remain unclear.
One aspect of the paradigm which we hope to elucidate
in the present work has to do with the way the neutron
star spins down. Observations of pulsar period increase
suggest that a rotating neutron star with mass M*, ra-
dius r*, and angular velocity Q loses rotational kinetic
energy at a rate
L - iM rS2Q . (1)
Here, M ~ 1.4M , r* ~ 10 km, and (...) _ d(...)/dt.
Energy is lost through electromagnetic torques in the
magnetosphere, although other physical processes have
at times also been discussed (gravitational radiation,
wind outflow, star-disk interaction, etc.).
To a first approximation, the stellar magnetic field may
be considered as that of a rotating magnetic dipole. Even
under such a simplification the general description of the
stellar magnetosphere is a formidable three dimensional
problem, since, in general, the magnetic and rotation
axes do not coincide. Awaiting the development of the
general theory, one can still derive important conclusions
based on two idealized limiting cases which have been
studied in great extent: the case of an aligned magnetic
dipole rotating in an atmosphere with freely available
electric charges (i.e. with ideal MHD conditions), and
that of a misaligned magnetic dipole rotating in vacuum.
The neutron star is not surrounded by vacuum, and
one needs to take into consideration the electric fields
1 Research Center for Astronomy, Academy of Athens, Greece
2 Kavli Institute for Particle Astrophysics and Cosmology, Stan-
ford University, P.O. Box 20450, Stanford, Ca 94309
3 Chandra Fellow
that develop and the electric currents that flow in
the rotating charged magnetosphere (Goldreich & Ju-
lian 1969). The most recent calculation of the simplest
possible case, that of the magnetosphere of an aligned
rotator (Contopoulos 2005, hereafter C05), yielded the
following rather general result for the electromagnetic
(the quantities QF and Vopen are defined below). In that
picture, the magnetosphere consists of a corotating re-
gion of closed fieldlines which extends up to a distance
rc from the rotation axis, and an open fieldline region
with enclosed magnetic flux
'cpen - 2irp B - dS
1.23 2r ,
where B* is the polar value of the magnetic field (Con-
topoulos, Kazanas & Fendt 1999, hereafter CKF; Gruzi-
nov 2005; C05; Timokhin 2005; see also Appendix A).
The above expression is valid when rc r*. In the
limit rc =r*, straightforward calculation yields Vopen
The neutron star spins down because of the establish-
ment of a large scale poloidal electric current circuit flow-
ing along open field lines, and returning along the edge
of the open field line region (see CKF for a detailed de-
scription). The electric current that flows between the
magnetic axis (characterized by p 0) and the edge of
the open field line region (characterized by p -open)
generates the spindown torque which leads to eq. 2. The
quantity QF in eq. 2 is the angular frequency of rotation
of the open field lines. It is set by the electric potential
drop that develops accross open field lines, between the
magnetic axis and the edge of the open field line region.
This potential in the magnetosphere is in general smaller
Submitted to Astrophysical Journal
Work supported in part by Department of Energy contract DE-AC02-76SF00515
SLAC, Stanford University, Stanford, CA 94309
Here’s what’s next.
This article can be searched. Note: Results may vary based on the legibility of text within the document.
Tools / Downloads
Get a copy of this page or view the extracted text.
Citing and Sharing
Basic information for referencing this web page. We also provide extended guidance on usage rights, references, copying or embedding.
Reference the current page of this Article.
Contopoulos, Ioannis; Academy, /Athens; Spitkovsky, Anatoly & /KIPAC, Menlo Park. Revised Pulsar Spindown, article, December 14, 2005; [Menlo Park, California]. (digital.library.unt.edu/ark:/67531/metadc873604/m1/1/: accessed June 19, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.