Pulse Patterns in the

Fermi LAT data

Roger W. Romani

Stanford/KIPAC

For the Fermi LAT Collaboration

The Sample

• Young Pulsars

– Radio Selected

– Gamma-selected

• Radio Faint

– Binaries?

• Millisecond Pulsars

– Radio-selected

– Gamma-selected

Fermi LAT Pulsars –RWR - 3

The LAT Pulsar Sky

11 g-sel MSP g/R pulse 26 Young g-selected

33 Young Radio-selected 16 MSP Radio-selected 23 g-sel MSP R pulse

10/10 PSR Census

Public July ‘11

Fermi LAT Pulsars –RWR - 4

The LAT Pulsar Sky 10/10 PSR Census

Other PSR Sites

47 Tuc

W Cen

NGC 6388

NGC 6652

NGC 6440 M 62

M 28

Ter 5

Abdo et al 2010 8 GlCl

NGC 6754

Tam et al 2011 6+ GlCl

NGC 6754 NGC 6624

M 80

Lil 1

NGC 3139

NGC 6624

Globular Clusters

Fermi LAT Pulsars –RWR - 5

The LAT Pulsar Sky 10/10 PSR Census

Other PSR Sites Binary Systems

PSR B1259-63

1FGL J1018.6-5856

HESS J0632+057

LS 5039

Cyg X-3

LS I +61 303

Fermi LAT Pulsars –RWR - 6

Pulse Properties • Detailed profiles are complex; To compare with the models

need a few basic measurables:

– Np Number of peaks

– D (spacing between outermost major g-ray peaks)

– d (lag of first g-ray peak from the radio pulse)

– FB ‘Bridge’ flux and FO ‘Off-pulse flux’ – as fractions of total pulse flux

d

D

Np=2

Off

Bg

Bridge

P1 P2

Fermi LAT Pulsars –RWR - 7

The Basic Pulse Pattern

• Young Pulsars: Mostly double:

– Main peaks are sharp `caustics’

– peak spacing D, seems fixed

– P2/P1 grows with Eg

– Bridge Structure not sharp

– Phase is energy (altitude?) dependent

Example:

Vela PSR

D

The Basic Pulse Pattern

• Young Pulsars: Mostly double:

– peak spacing D,

– d (lag from the radio pulse);

• small D large d. Shrink to anti-pole

– Significant ‘Bridge’ flux > ‘Off-pulse flux’

Exceptions to Basic Pattern

• Single Pulses (Young PSR)

– At f~0.5-0.6, lower f tail: P2 w/o P1,

some bridge emission

– At f~0.4: on d-D correlation

– PSR B0656+14

• Small d ~ single peak

• Odd spectrum,Low luminosity

1 2 3

The Basic Pulse Pattern

• Millisecond Pulsars

– So far only radio-detected (albeit many g-targeted)

– Pulse Patterns are much less regular:

• Triples

• radio/g-aligned

– efficiencies high

Unipolar Inductors through Fermi’s Eye

• The ‘Pulsar Problem’ is simply stated:

• A spinning, magnetized sphere, with a the W-B angle

• Aka Unipolar Inductor, Faraday disk, Homopolar generator

– Energy is lost at rate comparable to 𝑬 from magnetic dipole

• We view PSR at angle z

– Which PSR are detected?

– What pulse profile?

– What spectrum is seen?

• Incl phase variations a

z

Classes of Pulsar models

• Problem is simply stated, but NOT simply solved

• Pair cascades in the magnetosphere

– Mediated by g-B in high fields

– Mediated by g-g on soft X-ray photons

• Pair Density -- compare to rGJ = 7x1010 BzP-1 cm-3.

– Pair-starved `gaps’ -- Cheng, Ho and Ruderman

• Poisson Eq (eg. Hirotani)

• GR-induced field (Muslimov & Harding)

– Dense pair plasma, wind zone emission

• Spitkovsky, Petri,...

• Pairs radiation reaction-limited – Lg large fraction of 𝑬 – Curvature radiation

– ICS

– Synchrotron

Three Levels of Interpretation

• Topology – what’s the basic shape of the emission region?

• Geometry – How does the distribution of radiating field lines

depend on pulsar parameters and the observer orientation?

What does this mean for the pulsar sample?

• Physics – How do we connect the observed pulses and

spectrum to the physics of the acceleration zone?

Topology -- Done

• Well-established radio pulsar phenomenology – radio emission is

from modest altitudes (few to tens of R*) above the polar cap

– flux may span open zone (core) or concentrate to edges (cone)

– detailed tests from polarization studies

• Double g-pulses with a ‘bridge’ prevail

– 80% Young (radio- and g-selected)

– ~40% MSP

single hollow cone dominates

• Young PSR: g pulse brackets radio f+p

opposite pole open zone dominates

most g-rays are from r > rNC (typically 100-1000 R*)

• MSP have more complex radio and g-ray profiles

– A number have aligned radio and g-ray pulses

– for MSP ~10R* is > rNC

MSP: we expect emission zones to overlap.

RLC

B

Geometry – In Progress

• Exactly where does the radiation arise?

• How does this change with a and z?

• What does spin-down do to the magnetosphere structure?

• Caveat Emptor: The ‘Open Zone’ projects to the full sky --

by ‘illuminating’ appropriate subsets of the open zone, one can

produce any desired light curve!

– Model tests are most meaningful when a and z are well

constrained by external observations.

– A sucessful model should have a simple pattern of

illuminated field lines that works across the population –

ultimately traceable to physics.

Geom. for Individual PSR: match at actual a, z!

• In a number of cases we know the actual geometry. We should fit

using these constraints.

• Radio gives best constraint on b=a-z.

– for interpulsars radio can

provide both a and z ,

accurate to ~0.10!

• Robust measurements of z from CXO imaging: X-ray torus/jets

Pulsar Population in the Galaxy

• Preliminary

Geom. for Populations: Match Distributions!

• Start simple: The LAT BSL (Abdo et al 2009)

– 205 Sources (`0FGL’) 10s in 3months

• 9 SRC not found in later deeper catalogs (split or BG errs?)

• 7 at present not ‘IDed’ EF: (really ‘associated’)

– Thus 96% complete associations!! We really know the population

of the (bright) g-ray sky.

– 25% of the BSL associated sources are puslars

– Of the 7 unassociated sources ~4 are PSR-like

– 49 young PSR: 25g-sel/14 r-sel

Young PSR are >64% radio-quiet

– 10 MSP (all r-detected)

– Let’s assume 4 PSR-like unk are radio quiet MSP

MSP are <28% radio-quiet

– (probably less, since 2 at |b|<0.1deg)

Geom. for Populations: Match Distributions!

• Detailed studies of the LAT young pulsar sample

– Watters & RWR 2010, RWR et al 2011 (OG r>rNC radiation does well:

incl R-only and INS. Suggests alignment, wider radio beams)

– Takata et al 2010 (g/R ratios OK; tot # large)

– Pierbattista, Grenier, et al. modeling

• MSP

– Less mature

• New pulsar sample:Takata at Fermi Symp (r-quiet MSP?)

• more complex phenomenology

– But probably more important for backgrounds, populations...

• E.g. OG model predictions of populations of

g-Selected, Radio-Selected, Radio only and INS

Young Pulsar Detectability

High Edot Low Edot

Flux at Earth See Waters & Romani 2011

Magnetosphere Physics – the Future

• Radiation physics

– good progress at the single zone level

– A number of attempts to simulate 3D under (idealized)

assumptions

• Acceleration Physics

– Basic energetics plausible

– Attempts to follow vaccum accelerators in detail

– Speculations about processes in dense plasmas

Acceleration Physics: Luminosity

• Some dimensional analysis

– Observed trend 𝑳𝜸~𝑬 𝟏/𝟐 (Thompson `04)

• Emission at 𝒙𝑹𝑳𝑪 with radius of curvature 𝝆𝒄~𝒙𝒄𝒙𝑹𝑳𝑪 and

acceleration field 𝑬||~𝒙𝒆𝑩𝒗/𝒄~𝒙𝒆𝒙𝟐𝑩𝒔𝑷

−𝟑

• Total power:

𝒏𝑮𝑱𝐜 𝐭𝐡𝐫𝐨𝐮𝐠𝐡 𝚽~𝑬||𝑹𝑳𝑪 𝐢𝐧 𝐚 𝐜𝐚𝐩 𝐨𝐟 𝐚𝐫𝐞𝐚 ~𝐰 𝐒𝐢𝐧𝟐𝜽𝒄𝟐~𝐰/𝑷

– IF 𝚽~𝐜𝐨𝐧𝐬𝐭 ⇒ 𝑳𝜸~𝒏𝑮𝑱𝑨𝒄𝒂𝒑~𝑩𝒔

𝑷 𝒘

𝑷 ~𝒘𝑬 𝟏/𝟐

– Poisson suggests 𝒙𝒆~𝒘𝟐 so that 𝑳𝜸~𝑬

𝟏/𝟐 trend implies

𝐰~𝑬 −𝟏/𝟔, i.e w varies weakly w/ spindown.

• w should be computable from gap closure

– E.g. Wang, Takata, Cheng ‘10 (ApJ 720, 178)

• 𝑳𝜸 ∝ 𝑬 𝟏/𝟏𝟒, 𝑬 > 𝟏𝟎𝟑𝟔

𝒆𝒓𝒈

𝒔 (𝑻𝒉𝒆𝒓𝒎 𝜸

𝜸−𝜸 𝒑𝒂𝒊𝒓𝒔 )

𝑬 𝟓/𝟖, 𝑬 < 𝟏𝟎𝟑𝟔 𝒆𝒓𝒈

𝒔 (𝑴𝒂𝒈𝒏 𝜸

𝜸−𝑩 𝒑𝒂𝒊𝒓𝒔 )

RLC

xRLC

Hints from Energetics

• It seems that the gamma-ray efficiency 𝛈 ≡ 𝑳𝜸/𝑬 increases with

decreasing spindown power. Saturation at ~1033-34 erg/s.

After Harding

Simple 𝐸 1/2

WTC prescription

So...

Why can’t we do better?

𝑳𝜸 = 𝟒𝝅𝒅𝟐𝑭𝜸𝒇𝜴

ds are poor

Beaming affects fW

Acceleration Physics: Spectrum

• Dimensional analysis for cutoff energy (eg. RWR ‘96, Baring ‘10)

• Emission at 𝒙𝑹𝑳𝑪 with radius of curvature 𝝆𝒄~𝒙𝒄𝒙𝑹𝑳𝑪 and

acceleration field 𝑬||~𝒙𝒆𝑩~𝒙𝒆𝒙𝟐𝑩𝒔𝑷

−𝟑

• We expect 𝒙(𝜶, 𝝇) and 𝒙𝒄(𝜶, 𝝇) while 𝒙𝒆(𝑬 ).

• Spectrum: Curvature RRL -- 𝜺𝒎𝒂𝒙~𝑬||𝟑/𝟒

𝝆𝒄𝟏/𝟒

~ 𝒙𝒆𝟑/𝟒

𝒙𝒄𝟏/𝟐

/𝒙 𝑩𝒔𝟑/𝟒

𝑷−𝟕/𝟒

• Assume 𝒙𝒆~𝒘𝟐 ~𝑬 −𝟏/𝟑 (from Poisson, 𝑳𝜸~𝑬

𝟏/𝟐)

– Then 𝜺𝒎𝒂𝒙~ 𝑬 −𝟏

𝟒 𝒇 𝜶, 𝝇 𝑩𝒔

𝟑/𝟒𝑷−𝟕/𝟒

• Other formulations give different PL dependencies

– E.g. Takata, Wang & Cheng ‘10 (ApJ 715, 1318)

• 𝜺𝒄 ≈ 𝑲𝟑𝑩𝟑/𝟒𝑷−𝟏, K~2 (Young) ~15 (MSP)

Hints from Spectral Cut-off: Ec

• Measurements from

Abdo et al 2010 (1st

LAT Pulsar catalog)

• Correlation is indeed

best when {}~𝑬 −𝟏/𝟒 (with slope 0.9)

• Not a tight

correlation...

• But of course r and rc

(here x, xc) vary with

a, z, f.

• Variation w/ f phase

dependence

Cut-off Shape: NOT super exponential

(Excludes Polar Cap B)

• near surface gB e+e-

– Super-exponential cut-off

(Baring ‘04, Lee et al ‘10)

– Highest e pulsed photon

1

1

() exp( )

8()exp

3 'sin

af A

CBB

g

g

e t

t

e

e

-= -

-

7/1

7/2

12max* GeV76.1

/ -

PB

Rre

bcE

eF)/(

~ee --

b=2 rejected @ 16s

r > 4.5R* (LAT PSR B1706-44)

r > 6.5R* (MAGIC Crab 60GeV,

VERITAS : even higher!)

Cut-off Shape: Should be Sub-exponential

• Pulsars are `adequately’ fit by PL+ (sub-) exponential cut-off

– PL are ~ 1.1 – 2.2

• Monoenergetic curvature ~1.3

• Steeper spectra require multi-zone or e spectrum

• Well-measured Cut-offs are NOT super-exponential

(Good, simple exponential Ec does not determine physics!)

– Expect sub-exponential for

phase average spectrum

– Detailed Understanding

requires phase-resolved

spectra/modeling

Vela: exemplar of the

phase-resolved spectral study

Abdo et al 2010, ApJ 713, 154

Ec Variation through Gap

• Radiation-reaction limited CR cut-off depends on gap fields

4/32/1~2/11/4

||

3

c ~E~ , || p

cc

rE

cc

rp

rergr

ge

Ec

Vela Geminga

How are Modelers Responding to the Wealth

of Detailed LAT Measurements?

• Numbers of detections – match the populations (see above)

• Enrich the details of the emission zone shape and brightness

• Try to add physically motivated currents

• Extend the emitting zone beyond the light cylinder

• Work toward self-consistent electrodynamic models

OG Model: Including variation in E||, current

• Wang, Takata, Cheng 2011 (ArXiv 1102.4474)

2-layer gap,

Vary widths

Vary brightness Possible to

get a phase-

varying ‘P3’

Tuning the illuminated field lines

• Du et al 2011, ApJ 731, 2

– by careful choice of

illuminated field lines very

nice light curves can be

made for individual

pulsars.

– Example here is Vela

– Predictive power?

Generalization?

What About Slot-Gaps?

• Geometry

– classic ‘TPC’ topology – comparable high and low emissivity,

two poles one detected high, one low – does poorly

– when r > rNC (i.e. OG zone) dominates, does well

• assymmetry may help – different pattern from two poles

• Physics

– use of the GR accelerating potential attractive

• but needs strong screening assumption to get above few R*

• Luminosity is typically ~0.01x that observed (Hirotani ‘08)

• However extra freedom of lower altitude emission provides

improved light curves for some pulsars with DC components

– weaker low altitude emisison may very well be a SG/polar gap

– MSP: everything is low – GR contribution strong!

– Fit examples by Harding and colleagues

Onward and Outward: SW Model

• Much of the spin-down power is carried off in the B/e+/e-

striped wind – why not associate this with the g-rays, as well?

– Split monopole solution (Bogovalov 1999) applied by Kirk et

al ’02, Petri ‘011

– posit a dense ~10 wind of g~105 e+/- in the current sheet

– ICS of CMB (outside RLC) to get g-ray pulses.

Bogovalov ‘99

Petri ‘11

Radio

(PC)

g-ray (wind) Plus: g-ray lags radio

Minus: always centered on

Df=0.5

no bridge emission

Magnetosphere Electrodynamics

• The grand goal: Self-consistent particles and fields

• Two approaches

– Assume a background field geometry estimate E, acceleration,

radiation in this geometry

• true vacuum has no radiation above n ~1/P!

• acceleration relies on `gapology’

• Not really self-consistent

– Completely Force free

• small E, no accel/radiation beyond ~mec2. (i.e. no g-rays)

• Numerically expensive

• Can’t contain physical variation w/ Edot etc.

• The truth must lie between...

Toward Self-consistent Particles and Fields

• K. Hirotani (‘06,’08,’11) -- solve Poisson and Boltzmann

equations on (fixed) background geometry. Pairs, CR and ICS

– apply to both OG and SG accel. fields, pair formation fronts

– H ’08; SG accel: Lg ~0.01-0.03 Lobs, (wide) OG fine.

– More recent works attempts to follow

gg e+e- pair formation in 3D

– e.g. H’11 finds

• OG geometry is stable & self-consistent

• straighter photon paths in trailing pulse P2

make larger rc, higher Ec, as seen.

SG for Crab

Log Fg Encouraging

initial matches

to phase-

resolved

spectra...

Adding Currents

• All ‘gapologists’ concede that currents can perturb the

assumed background vacuum geometry

– Muslimov & Harding ‘09 – current, field structure in a pair-

starved open zone (PC/SG)

– RWR & Watters ‘10 – shifts to beaming and light curves for

this model and idealized OG open zone currents

– These are idealized: Real progress likely will come from

numerical models

Numerical Force-Free Modeling

• Spitkovsky ‘06, Bai & Spitkovsky ’10

– fully force free, currents adjust B field structure

– choose a set of field lines that overlaps to make current

sheet in wind-zone (bulk of radiation from separation layer

in striped wind)

• posit that moderately hot pairs with bulk give beamed

synchrotron emission from this layer `SL’ Model

• Lock solution to radio/X-ray constraints: known a, z, f :

How Do These Models Fare? Vela Test

BG: Match to Fermi LC;

dark colors=good

OG TPC SL

Radio and X-ray data

say we must be here.

• Allow some perturbation: e.g. currents, radio pulse phase f :

How Do These Models Fare? Vela Test

Match to Fermi LC;

dark colors=good

OG+current TPC

SL f+27o

To Move Ahead

• Marry the virtues of the charge separated (gap-

like) magnetosphere to realistic current

distributions

• Numerical models with finite resistivity

– Spitkovsky ‘11 just starting w/ global finite r

– Similar sums by (Kalapothorakos et al. 2011)

For realistic results need local prescription

for gg r(e+e-) [maybe also dynamic]

Spitkovsky ‘11 – SLAC Reconnection Wkshp

Summary – LAT Data Killing Off Models

• Polar Cap – Dead --Killed by Topology

• Classic TPC – Dead -- Killed By Topology

• Basic OG – Ailing – Challenged by Geometry, Physics

• SG – On Life Support – Geometry OG zone,

Physics challenges, low natural luminosity

• SL, SW models – On Life support – major Geometry

change for viability, physics is appealing

• All in the running for MSP where r range is modest

• Today: A useful phenomenology for interpreting data

• The Path Forward – Physics

– Curvature Radiation Predictions:

Check the viable (High altitude) models for consistency

– Don’t expect much from current numerical generation –

comparably wrong (albeit in new ways)

– Need 3D, ge+e- models for significantly improved data matches

Fermi provides the data needed for serious tests!