Pulsars: open questions
and looking forward
Anatoly Spitkovsky (Princeton)

Collaborators:
Xuening Bai (Princeton)
Jon Arons (Berkeley)
Yury Lyubarsky (Ben Gurion)
0910.5740, 0910.5741

Outline•Pulsar basics: spin down andplasma creation•Magnetic geometry: vacuum v.
force-free•Emission modeling: gaps/sheets•Spectral inferences•Future directions

Pulsars in Fermi era
Why pulsars are interesting?

•Unique laboratory for strong B
fields and relativistic plasmas•Prototypes of other astrophysicalobjects: accretion disks, jets, blackhole magnetospheres•Fascinating electromagnetic
machines•Not understood for > 40 yrs
Fermi is probing where most of the energy is.

Properties in gamma-rays
Double peaks with phaseseparation 0.2-0.5
Offset from the radio
γ-ray beams larger thanradio
Spectra are power-laws
with exponential cutoffs
Large B at LC
Large fraction of spindown in γ-rays
Fermi is probing where most of the energy isPulsar physics @ home
WireBattery
MagnetUnipolar induction

HandPulsar physics @ home

Simple?

Pulsar physics in space
Wind1016V
1012G
Faraday disk
Rule of thumb: V ~ΩΦ; P ~ V2 / Z0 = I V
Crab Pulsar
B ~ 1012 G, Ω ~ 200 rad s-1, R ~ 10 km

BVoltage ~ 3 x 1016 V; I ~ 3 x 1014 A; P ~ 1038erg/s

MagnetarB ~ 1014 G; P ~ 1044erg/sfrom R. Blandford

Massive Black Hole in AGN
B ~ 104 G; P ~ 1046 erg/s

Pulsars in Fermi era
Why pulsars are interesting?

•Unique laboratory for strong B
fields and relativistic plasmas•Prototypes of other astrophysicalobjects: accretion disks, jets, blackhole magnetospheres•Fascinating electromagneticmachines•Not understood for > 40 yrs
Fermi is probing where most of the energy is.

Pulsars: energy loss
E•Corotation electric field•Sweepback of B field due topoloidal current•ExB -> Poynting flux

•Electromagnetic energy loss

tner
urc

B

Poynting

Goldreich & Julian 1969

Radiator in Fermi band is tapping into this energy flux

What emits?
Emission process less complicatedthan in the radio: curvature, IC, orsynchrotron.

A. Harding•Need acceleration of particles•Depending on how much plasma

is in the magnetosphere, postulate
emission regions, where E field is
not shorted out: gap models•Trace emission in field geometry,
usually assumed to be rotating
vacuum dipole

A. Harding•Remarkably successful in fitting
the light curves and spectra

Geometry is crucial to the formation of light curves

R. RomaniIs vacuum geometry ok?
•We can find the field structure in two limits: all vacuum (gap), or all plasma(force-free). Reality is in-between.

•Force-free evolution. Inertia is small:•NS is immersed in massless conducting fluid. Includes plasma currents.
Hyperbolic equations, can be evolved in time

Aligned rotator: plasma magnetosphere

Toroidalfield0r/RLC

Properties: current sheet, split-monpolar asymptotics; closed-open lines; Y-point;null charge surface is not very interesting.

Oblique rotator: force-freeOblique rotator: force-freeDistribution of current in the magnetosphere
Force-free field provides amore realistic magnetic
geometry

X. Bai & A. S. arXiv:0910.5041

Tempting toassociate gaps
with currents.
Can we?
A. HardingLight curve calculation
1. Pick field (static dipole, retarded dipole [Deutch], force-free)
2. Find the polar cap (field lines touching LC, or all closed?)
3. Decide which field lines emit
4. Assume uniform emissivity (with cuts in radius)
5. Trace field lines emitting photons along field line
6. Add aberration and time of flight effect
7. Bin photons on the sky -- > sky map + light curves
8. Repeat

Geometry is crucial to the formation of light curves: affects
aberration and definition of polar cap.

Force-free vs Vacuum: Last Closed Lines

Force-free vs Vacuum: Last Open LinesVacuum sky map

Vacuum field, 60 degree inclination, flux tube
starting at 0.9 of the polar cap radius.

cf. work by Harding et al,
Romani et al, Cheng et al.

Vacuum sky map

SG/TPCOG

Vacuum field, 60 degree inclination, flux tube
starting at 0.9 of the polar cap radius.

Force-free sky map

Force-free field, 60 degree inclination, flux tube
starting at 0.9 of the polar cap radius.

“Sky map stagnation”

“Sky map stagnation”
Split-monopolar field is a perfect caustic. Particle
trajectory is near straight-line, compensatingrotation and sweepback. Sky map of monopole.

“Sky map stagnation”
Open field lines in force-free reach split-monopole like solution at LC.

Vacuum vs Force-free

All caustics in force-free form near LC. No close caustic like in TPC
Bai & A. S. arXiv:0910.5741

Force-free from different flux tubes

Emissions from two poles merge at some flux tubes: what’s special about them?
Bai & A. S. arXiv:0910.5041

Association with the current sheet
Color -> current

Field lines that
produce bestforce-free caustics
seem to “hug” thecurrent sheet atand beyond theLC.

Force-free gallery
Viewing angle

Inclination
angle

Double peak profiles very common.

Bai & A. S. arXiv:0910.5041

Force-free gallery: TPC and OG
Viewing angle

Inclination
angle

SG/TPC with FF

OG with FF

SG/TPC and OG with FF field do not produce double peaks!
Bai & A. S. arXiv:0910.5041

Light curve fitting
Impressive fits can beachieved with both
TPC and OG models
based on the vacuum
field.

Vela

Vela

However, similar
emission zones forforce-free field do notwork. We have to use
other field lines.
How to discriminate?

from: A. Harding.
BSpectra. Both phaseresolved andaveraged.

closed fieldregionDyks, Harding, Rudak 04

Dyks, Harding, Rudak 04

Spectral fitting
Spectra are power laws with exponential cutoff.
The shape of the cutoff indicates high altitude emission.
Near surface pair production would attenuate γ-rays with superexponential cutoff, which is not observed.

Highest energy photons
constrain emission to beat > 5Rstar

This is consistent withOG, SG/TPC or FF models.
Contradicts polar cap models

Abdo et al. 2009

Daugherty & Harding 1982
Zhang & Harding 2000
Hibschmann & Arons 2001

Spectral fittingPhase integrated spectra can be fitted rather well now. Phase-resolved
spectra could be more challenging.
Variations in cut-off energy indicate changing height of emission. Different
models predict particular variation of height with phase.
Radiation reaction-limited curvature radiation
cutoff -- depends on height.
Another puzzle: variation of location of peaks withenergy.
Other discriminants: statistics of peak separations,
offsets from radio, etc. (Watters et al 2009).

Abdo et al. 2009

Conclusions
Pulsar emission is coming from the outermagnetosphere.
Two well-established models for the location ofemission in magnetosphere exist: SG & OG. Bothrely on the vacuum field. The physical basis forexistence of these accelerating regions and theirextents is very uncertain, but they fit the data!
More realistic field, force-free magnetosphere, canproduce double peaks. However, neither SG nor OG
locations work for FF. The best fit is from emission
near the current sheet at and beyond the LC.
Caustics in FF due to split-monopolar asymptotics.
Theory of emission from current sheet is not welldeveloped at all, and much more theoretical workhas to be put in. Large Lγ makes sense w/cur sheet.
Large B@LC--> reconnection.
Phase-resolved spectra from Fermi will be crucial!

Kirk et al 02,
Lyubarsky 96
Petri 09