### Abstract

We formulate a variation principle for the force-free magnetosphere of an inclined pulsar: ε+ Ω · M (where ε and M are electromagnetic energy and angular momentum and Ω is the angular velocity of the star) is stationary under isotopological variations of the magnetic field and arbitrary variations of the electric field. The variation principle gives the reason for the existence and proves the local stability of singular current layers along magnetic separatrices. Magnetic field lines of inclined pulsar magnetospheres lie on magnetic surfaces and do have magnetic separatrices. In the framework of the isotopological variation principle, inclined magnetospheres are expected to be simple deformations of the axisymmetric pulsar magnetosphere. A singular line should exist on the light cylinder, where the inner separatrix terminates and the outer separatrix emanates. The electromagnetic field should have an inverse square root singularity near the singular line inside the inner magnetic separatrix. The large-distance asymptotic solution is calculated and used to estimate the pulsar power, L ≈ c^{-3}μ^{2}Ω^{4} for spin-dipole inclinations ≲30°.

Original language | English (US) |
---|---|

Journal | Astrophysical Journal |

Volume | 647 |

Issue number | 2 II |

DOIs | |

State | Published - Aug 20 2006 |

### Fingerprint

### Keywords

- Pulsars: general

### ASJC Scopus subject areas

- Space and Planetary Science

### Cite this

*Astrophysical Journal*,

*647*(2 II). https://doi.org/10.1086/506590

**Pulsar magnetospheres : Variation principle, singularities, and estimate of power.** / Gruzinov, Andrei.

Research output: Contribution to journal › Article

*Astrophysical Journal*, vol. 647, no. 2 II. https://doi.org/10.1086/506590

}

TY - JOUR

T1 - Pulsar magnetospheres

T2 - Variation principle, singularities, and estimate of power

AU - Gruzinov, Andrei

PY - 2006/8/20

Y1 - 2006/8/20

N2 - We formulate a variation principle for the force-free magnetosphere of an inclined pulsar: ε+ Ω · M (where ε and M are electromagnetic energy and angular momentum and Ω is the angular velocity of the star) is stationary under isotopological variations of the magnetic field and arbitrary variations of the electric field. The variation principle gives the reason for the existence and proves the local stability of singular current layers along magnetic separatrices. Magnetic field lines of inclined pulsar magnetospheres lie on magnetic surfaces and do have magnetic separatrices. In the framework of the isotopological variation principle, inclined magnetospheres are expected to be simple deformations of the axisymmetric pulsar magnetosphere. A singular line should exist on the light cylinder, where the inner separatrix terminates and the outer separatrix emanates. The electromagnetic field should have an inverse square root singularity near the singular line inside the inner magnetic separatrix. The large-distance asymptotic solution is calculated and used to estimate the pulsar power, L ≈ c-3μ2Ω4 for spin-dipole inclinations ≲30°.

AB - We formulate a variation principle for the force-free magnetosphere of an inclined pulsar: ε+ Ω · M (where ε and M are electromagnetic energy and angular momentum and Ω is the angular velocity of the star) is stationary under isotopological variations of the magnetic field and arbitrary variations of the electric field. The variation principle gives the reason for the existence and proves the local stability of singular current layers along magnetic separatrices. Magnetic field lines of inclined pulsar magnetospheres lie on magnetic surfaces and do have magnetic separatrices. In the framework of the isotopological variation principle, inclined magnetospheres are expected to be simple deformations of the axisymmetric pulsar magnetosphere. A singular line should exist on the light cylinder, where the inner separatrix terminates and the outer separatrix emanates. The electromagnetic field should have an inverse square root singularity near the singular line inside the inner magnetic separatrix. The large-distance asymptotic solution is calculated and used to estimate the pulsar power, L ≈ c-3μ2Ω4 for spin-dipole inclinations ≲30°.

KW - Pulsars: general

UR - http://www.scopus.com/inward/record.url?scp=33748531281&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33748531281&partnerID=8YFLogxK

U2 - 10.1086/506590

DO - 10.1086/506590

M3 - Article

VL - 647

JO - Astrophysical Journal

JF - Astrophysical Journal

SN - 0004-637X

IS - 2 II

ER -