Transcript Diapositiva 1 - ASDC - ASI Science Data Center Home Page

Pulsar analysis
with LAT data:
A quick tutorial
Massimiliano Razzano
(INFN-Pisa)
Fermi Meeting,
(1 Oct. 2009)
Pulsar Analysis
Spatial
(point source)
Timing
Spectrum
(likelihood)
Known pulsar
Identification
(periodicity)
Gamma-ray selected
pulsar
Overview
Overview
• In this tutorial we will see how to perform timing analysis of
pulsars using official Fermi tools.
• In particular:
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–
–
–
–
–
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Extracting pulsar spin parameters;
Data selection according to ephemeris validity;
Barycentric corrections;
Rotational phase assignment;
Periodicity test;
Periodicity (basic) search;
Orbital phase assignment;
• A dataset is provided for the exercise
• We will not see:
– Blind search
– TEMPO2,PRESTO,etc…
Where Things Get Complicated
• The diffuse Galactic emission is bright and highly
structured. The diffuse model supplied by the LAT
team has recently been updated and is likely to
continue to evolve. Separating weaker sources from
the diffuse Galactic emission is non-trivial.
• The LAT Instrument Response Functions (IRFs) have
significant uncertainties at energies near 100 MeV and
a non-negligible charged particle background at
energies above 10 GeV. Improvements in the IRFs are
expected but are not imminent.
Some Occasions to Think about Contacting
the Instrument Team
• If you are searching for a source that is not in the LAT
catalog, then it is probably weak enough that a simple
analysis will not be adequate.
• If you need a detailed energy spectrum or are looking
for particular spectral features, especially at very low or
very high energies, the LAT team has experience with
non-standard analysis.
• If you are trying to analyze the Galactic Center region,
you are strongly advised not to go it alone!
• If you are interested in the most complete
multiwavelength coverage, consider contacting the LAT
team. We have many cooperating groups across the
spectrum who may be interested in working with you
(even if you don’t include the LAT team).
Data for the tutorial
• We have prepared a dataset of LAT data using the LAT data
server of the FSSC
• The chosen pulsar is PSR J2021+3651 in Cygnus, one of the
first new pulsars studied with the LAT, located in the
“Dragonfly” PWN.
• Dataset contains:
– FT1 file ranging from MJD 54690 (Aug 12 2008) to MJD 54790 (Nov
20 2008);
– Corresponding FT2;
• Analysis of pulsars observed in other energies require a
database with the ephemeris: we call it D4 database
• The D4 used contains radio observations of J2021+3651 by
GBT, as used in the Fermi paper (Abdo et al. ApJ 700, 1059
2009)
Extract pulsar ephemeris
•
•
Usually the D4 contains data relative to many pulsars. We can extract only those of
J2021 using gtpulsardb
The output provides a new D4 containing only the J2021+3651 spin parameters.
Extract pulsar ephemeris
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•
•
•
Looking at the D4 using fv we see that the ephemeris validity range is from MJD
54634 to MJD 54785
Contemporaneus ephemerides!
MJD is the modified Julian Date: MJD = JD – 2400000.5
We need to convert from MJD to MET. We can do it using the HEASARC Web tool
Date converter or remembering that MET 0 (The reference time) corresponds to
midnight of Jan 1, 2001, i.e. in MJD
Integer
Fractional
Using the HEASARC Web tool
TSTART
MJD
MET
http://heasarc.gsfc.nasa.gov/cgi-bin/Tools/xTime/xTime.pl
Using the HEASARC Web tool
TSTOP
MJD
MET
Preparing the data
•
•
•
The D4 contains also the coordinates of the pulsar. We use them in gtselect,
selecting photons at E>100 MeV, within 1 degree from the source and in the
DIFFUSE class.
The event class is selected by the hidden parameters evclsmin, that we can find
using the ftool plist
Pay attention to the phasemin(max) parameter
Don’t’ forget
gtmktime !
Step 1-Time Selection
$$$> gtmktime
Spacecraft data file [] L090923112502E0D2F37E71_SC00.fits
Filter expression [IN_SAA!=T] IN_SAA!=T && DATA_QUAL==1
Apply ROI-based zenith angle cut[yes] : yes
Event data file [] : myROI_filtered.fits
Output event file name [] : myROI_filtered_time.fits
Scriptable form of the command:
gtmktime scfile= L090923112502E0D2F37E71_SC00.fits filter= IN_SAA!=T && DATA_QUAL==1 roicut=yes
Evfile= myROI_filtered.fits
outfile= myROI_filtered_time.fits
Build a skymap
•
Using gtbin we can create a skymap of the data, that can be visualized by DS9
Barycentric corretions
The analysis procedure on pulsars
starts by perfoming the barycentering,
i.e. transform the photon arrival times
at the spacecraft to the Solar System
Barycenter, located near the surface
of the Sun
Several effects that contribute to
the barycentering, mainly:
 Geometrical delays (due to light
propagation);
Relativistic effects (i.e “Shapiro
delay” due to gravitational wall of Sun)
Time [days]
The barycentric corrections
The photon arrival times are affected by the motion of GLAST through Solar
System and by relativistic effects. These effects are compensated by the
barycentric corrections
Corrections are:
Conversion TTTDB;
Geometric corrections due to lighttravel time
The barycentric corrections convert
the photons arrival times,
(expressed in Terrestrial Time TT at
the spacecraft), to the arrival times at
the Solar System Barycenter
(expressed in Barycentric Dynamical
Time TDB)
from GLAST location to Solar System
Barycenter;
Relativistic delay due to gravitaional field of
Sun (e.g. Shapiro delay);
Assigning a rotational phase
We know that pulsar period changes with time because of loss of
rotational energy:
We must take this effect into account in assigning a rotational phase.
Phase assignment in analysis:
•# of rotations:
1
 
2


dN

f
(
t
)
d
t

f
(
t
0
)

f
(
t
0
)(
t

t
0
)

f
(
t
0
)(
t

t
0
)

...
d
t


2


•Integrating and taking the fractional part:
1 2
1 3
φ(
t
)

φ(
t
0
)

f
0
(
t

t
0
)

f
1
(
t

t
0
)

f
2
(
t

t
0
)

...
2
6
1
f (t) 
P(t)
f 0  f (t0)
f 1  f(t0) f 2  f(t0)
Barycentering and phase
•
•
•
•
•
We have a tool called gtpphase that perform
barycentering+phase assignment.
We can also just do the barycentering using gtbary
gtpphase add a PULSE_PHASE column, that can be
plotted with fv to see the light curve
In case of pulsars in binary systems, gpphase
considers also the binary demodulation
The gtophase tool assign ORBITAL_PHASE;
Periodicity tests
If we know that D4 contains valid
ephemerides, we can test if our
gamma source has the same
periodicity of the radio counterpart. In
this case we have identified the
source as a gamma-ray pulsar (for
faint objects)
Tests against the null hypotesis:
H0 = no periodicity
Tests implemented:
Chi-squared test (Leahy et al. 1983,ApJ 266;
Z2n test (Buccheri et al. 1983
A&A128),Rayleigh test;
H test (De Jager et al., 1989 A&A 221)
Z2n test and H test
Other 2 tests are implemented in gtptest: Z2n test and H-test. For more
details, see the references.
Z2n test
The other 2 tests give similar results.
H test
The number of bins is Z2n is equivalent to the
number of harmonics we want to consider.
Z2
n has
p.d.f of
χ2
2n
(See for details:
The H test is more efficient for
unknown-a-priori lightcurves
(see for details:
Buccheri et al. 1983, A&A128)
De Jager et al., 1989 A&A 221)
Periodicity test
•
We test periodicity using gtptest
Periodicity search with gtpsearch
Here we use as example the 2 test
•For each photon a phase is assigned for a
trial frequency, then an histogram of phase
bin mj is created;
•In absence of pulsation every phase bin will
have the same mean count mexpected;
•The quantity:
Example of
2 periodicity test
•For large counts is every bin, S is distributed
Frequency space is scanned in fractions of
Fourier resolution fF=1/T, where T is the
duration of the observation. It represents the
spacing between 2 independent frequencies in
FT.
•Then it is possible to test the non-periodicity
hypothesis and give a chance probability
p(2>S)
For example 1-week observation:
is computed;
as a 2n-1
fF 1/(86400*7)≈1.6E-06 Hz
Search for periodicity
•
A limited search for periodicity around a candidate frequency can be done using
gtpsearch
Search for periodicity
•
A limited
search for
periodicity
around a
candidate
frequency can
be done using
gtpsearch
•
Not effective for
blind
search
because
of
high number of
trials
Manipulating ephemerides
•
•
•
Using the spin parameters is is possible to extrapolate for obtaining spin
parameters at any epoch.
We can do it using gtephem
But the extrapolation accuracy is limited by the timing noise, so it can be used
coupled to gtpsearch.
Conclusions
•
•
•
•
•
Basic pulsar analysis can be performed using official Fermi
tools
Spectral analysis can be done with standard likelihood
By combining general tools (i.e. gtselect) and pulsarspecific tools (i.e. gtptest), more complex analyses can be
done (i.e. light curve evolution with energy)
The data provided should allow some practice with this
analysis
We chosen a bright pulsar. With faintest ones the data
selection is much more important
Enjoy your favourite pulsar !