1. MAGIC pulsar workshop, Padova, Feb 2010

2. Pulsar Timing Analysis
MAGIC pulsar workshop, Padova, Feb 2010

3. /hadron separation (I)
Different kind primary particles
 different showers
 different images
/hadron separation based on image parameter distributions
-images are smaller and point to camera center
Hadron showers are broader are randomly oriented
MAGIC pulsar workshop, Padova, Feb 2010

4. /hadron separation (II)
After applying /hadron cuts based on image shape, exploit shower direction
MAGIC pulsar workshop, Padova, Feb 2010

5. Timing analysis
Goal: Find the periodic signal of the pulsar, hidden in
the arrival times of the atmospheric showers
The timing analysis involves 4 steps:
Barycenter correction
Obtain the Light curve
Application of Uniformity test
Upper limits calculation
All these steps have been implemented in a dedicated software, for the pulsar Analysis in MAGIC
MAGIC pulsar workshop, Padova, Feb 2010

6. Timing analysis (I) Barycenter correction
Remove the effect of the earth movement on the arrival times tUTC.
Transform the measured arrival times to the Solar System Barycenter:
Total Barycenter correction
MAGIC pulsar workshop, Padova, Feb 2010

7. Timing analysis (II) Ligth curve
If F is the known rotational frequency of the pulsar at time T0, the number of revolutions in dt=t-T0 is:
Integrating, and taking the fractional part, we get the rotational phase :
where t is the barycenter time
Taylor
MAGIC pulsar workshop, Padova, Feb 2010

8. Timing analysis (III) Crab is “glitching” once every 3-6 years !
Ephemeris are usually taken from radio observations but affected by irregularities in pulsar rotation:
Timing noise Glitches
Crab pulsar
Crab is “glitching” once every 3-6 years !
Need to have contemporaneous ephemeris
We use monthly ephemeris by
Jodrell Bank
MAGIC pulsar workshop, Padova, Feb 2010

9. Timing analysis (III) Uniformity tests
If no periodicity  events will be uniformly distributed
² - test
Applied to k-bins histograms
Powerful test for narrow pulses
Probability follows a 2 of k-1 d.o.f
Zm2-test
Independent of k
Based on trigonometric moments of pulse profile
m=number of harmonics
Sensitive to narrower pulses as m increases
H test
Find optimal m
Powerful against a large variety of light curves
MAGIC pulsar workshop, Padova, Feb 2010

10. MAGIC Timing Analysis Toolkit
Developed a full pulsar analysis toolkit for MAGIC
You can do all you need, both for optical & gamma-ray data
Input files can be ascii, raw or root files:
Extract Central Pixel signal
Do barycenter correction
Search best ephemeris for each arrival time
Calc pulsar phase & create light curves
Apply periodicity tests
And moreover..
Apply cuts
Calc. collection areas
Calc. upper limits
Calc. spectrum
MAGIC pulsar workshop, Padova, Feb 2010

11. MAGIC Timing Analysis Toolkit
Code at
MARS/mtemp/mucm/mpulsar
More that lines of code
Manual at: MARS/mtemp/mucm/mpulsar/docmpulsar.pdf
MAGIC pulsar workshop, Padova, Feb 2010

12. MAGIC Timing Analysis Toolkit
How to compile it
Compile the classes adding the following lines to the Makefile:
SUBDIRS = manalysis \
mastro \ …
mtemp/mucm/classes \

mtemp/mucm/pulsar
Compile the SearchPeriod program
PROGRAMS = callisto celestina … SearchPeriod
MAGIC pulsar workshop, Padova, Feb 2010

13. MAGIC Timing Analysis Toolkit
Main Classes
MAGIC pulsar workshop, Padova, Feb 2010

14. MAGIC Timing Analysis Toolkit
How to use it
You can use the classes writing your our macro. E.g.: mtemp/mucm/mpulsar/macros
Or using the compiled program SearchPeriod (similar to callisto,..)
It has a basic GUI (search.tcl)
MAGIC pulsar workshop, Padova, Feb 2010

15. MAGIC Timing Analysis Toolkit
Tests
Toolkit tested on:
Crab optical signal
EGRET data
XMM data
Results checked against TEMPO
MAGIC pulsar workshop, Padova, Feb 2010