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