Study of Pulsars  with

Fermi­LAT

InstructorsBiswajit Paul, Dave Thompson, Wim Hermsen

Group MembersAhmed, Bhaswati, Chetana, Du Yuan,  Jincy,  Wang

Pulsars studied Vela• Brightest persistent source in GeV sky• Spin period – 89 ms

Geminga• Second brightest in GeV sky• Spin period – 237 ms

Crab• Well studied in the entire electromagnetic spectrum• Spin period – 33 ms

PSR J2021+3651• Spin period – 103.7 ms

Timing analysis

Pulse Phase

Full Energy Range

300 MeV – 1 GeV

1 GeV – 5 GeV

5 GeV – 50 GeV

In the Full Energy Range (up to 300 GeV) The Pulse Profile reveals 2 distinct peaks

VELA

In the 300 MeV – 1 GeV range, the pulse profile does not vary with energy. However; the number of counts is reduced by a factor of ~2

In the 1 GeV – 5 GeV range, the first peak is suppressed as the energy evolves and a third broad peak is observed and shifts with energy

P3

Above 5 GeV, Very few counts available and the first peak is almost smeared out

P1 P2

GemingaFull energy

Energy<800 MeV

Energy > 1 GeV

Dual peaked profile

Intensity of the second peak decreases with increasing energy

Pulse phase

Energy<300MeV

Counts Pulsar is seen upto 9 GeV

less than 300 MeV the second peakis more intense

Two asymmetric peaks

Few photons >10 GeV

Phases of the two peaks do not show significant shift with energy

Both peaks become narrower with increasing energy

Ratio of P1/P2 decreases with increasing energy

Crab

J0007+73

Full energy

Energy >1 Gev

Energy<1Gev

Energy>7GEV

Profile has two components

Both the components evolve similarly with energy/frequency

Pulsar seen upto 7 Gev

Pulse phase

100-300 MeV

300-1000 MeV

1-3 GeV

3-10 GeV

PSR J2021+3651

1) Pulse profile consists of two peaks separated by a phase of ~0.5

2) At lower energies P1 dominates but its intensity fades away with increasing energies

3) Peak positions are stable with energy

P1 P2

Investigation of the off-pulse emission

Vela

Off Pulse emission

Crab

Off pulse emission

Gamma-ray PSF is energy dependent

Maximize the pulsed signal over the background --> Optimize the annular region around the source ROI

68% of photons have reconstructed directions within θ ~ c-d of a point source

Fselect

Input file: out_gtpphase.fits

Output file: out_fselect.fits

• Condition: angsep(305.273, 36.851, RA, DEC)<=min(a, max(b,(c*(ENERGY*1.0e-3)^(-d))))"

Crab – 3.1, 0.47, 0.84, 1.19

PSR J2021+3651 – 2.5, 0.35, 1.3, 0.1

Energy dependent Event selection

Chi-Square Test Statistic : 1738.290933172

Chi-SquareTest Statistic: 2102.3273880981

Before Optimal

PSR J2021+3651

Spectral analysis

PL SuperExpCutOffFitting ModelPL SuperExpCutOffFitting ModelPower Law2

Fitting Model

ExpCutOffFitting Model

Maximum likelihood analysisto fit the phase averaged spectraof Vela with different fitting models

Power law with super exponential cut off gives the best fit

Broadly emission models can be divided into four different families that place the emitting regions at different locations of pulsar magnetosphere

• Polar cap model : gamma ray photons are produced closed to neutron star surface(Daugherty & Harding 1996)

• Outer gap model : emitting region near light cylinder(Romani & Yadigaroglu et al. 1995)

• Slot-gap model : particle acceleration occurs in a region bordering the open field lines : two-pole caustic model - geometrical realization(Muslimov & Harding 2004; Dyks & Rudak 2003)

Annular gap is located in the magnetospheric region between critical field lines and last open field lines. IAG includes the advantages of both Outer Gap and Slot gap. It is a promising model for pulsars’ gamma-ray emission.

• Light curve changes with observer angle

• Different sections of light curve corresponds to LOS cuts to different parts of emission region.

• Spectra of different parts of light curve (say P1 and P2)can probe different parts of emission region

• We perform phase-resolved spectroscopy for the peaks of emission for 4 pulsars

Repeat the maximum likelihood analysis forP1 & P2 : Phase resolved spectra

P1

P2

Profile of Geminga

Results

• Different emission peaks evolve differently with energy

• Energy of the components is related with separation between peaks?

[trend seen for Geminga and J0007+73 : for higher separation between peaks difference between spectral index of two peaks is more]

What about other pulsars? (Not true for vela and crab?)

Future Plans

• Simulations on light curves for young and millisecond pulsars have been done (using the Annular gap model). Next will fit the pulsar multi-wavelength spectrum.

• Finally Justify the different high energy emission models for PSRs.

Improved statistics, energy resolution and high sensitivity ofLAT enable tests of the theoretical models for individual pulsars

Extending timing solution of the pulsars (using gtpphase, gtpsearch, and TEMPO2)

Follow up of the newly discovered gamma-ray pulsars in Radio

Search for pulsation from the unidentified gamma-ray sourcesin other wavelengths

Thank you

Geminga : two peaks have very different spectra [P- 1.02 & P2- 1.5] peak separation is 0.5

J0007+73 : two peaks have similar spectra [P1 – 1.5 & P2 – 1.4] peak separation is 0.28

Crab : two peaks with similar spectra [P1 -1.91 & P2 – 1.92] peak separation is 0.39

Vela : two peaks with similar spectra [P1 -1.6 & P2 – 1.5] peak separation is 0.43

Likelihood Analysis Procedure

Input Event Data File

Selection Cuts“gtselect”

(Time, Phase and Energy Selection)

Hypercube and Exposure map“gtltcube”

“gtexpmap”

Source ModelXML File

“modeleditor”

Likelihood Analysis“gtlike”

Likelihood Analysis Results and Spectral Fitting

Slide from Dave Thomson's presentation