1. Periodicity Search for Possible X-ray Counterparts to
Gamma-ray Pulsar Candidates
Introduction and Background
Archive data of different instruments and their features
Our way to find possible X-ray pulsation
Compare our results with known Gamma-ray pulsars
Conclusion and try to find some way to improve my work

2. Background of my research
Solving the mystery of the unidentified EGRET sources.
Are they pulsars like Vela or Geminga?
According to Lamb and Macomb, 1997; there are around 30 sources in the sky with
GeV fluxes above 4x10-8 photons cm-2 s of these are blazars, 5-6 are identified
pulsars, the rest, which lie almost exclusively along the Galactic plane, are currently
unidentified.
From Roberts and Romani, they present a catalog of 2-10 keV ASCA GIS images of
fields containing bright sources of GeV emission. The images cover ~85% of the 95%
confidence position contour for 28 of the 30 sources.
Among the unidentified sources of Robert’s catalog, we work on the periodicity search
for 13 possible X-ray counterparts to gamma-ray pulsar candidates.

8. --The archive data that we used--
X-ray Satellites:
ROSAT( )
ASCA( )
RXTE(1995-)
BeppoSAX( )
Chandra(1999-)
XMM(1999-)
XMM-Newton
MOS keV ; 1.5 ms-2.6s
PN keV ; 7 μs-73.4 ms
ROSAT
PSPC keV ; 130 μs
HRI keV ; 61 μs
BeepoSAX
LECS keV ; 16 μs
MECS keV ; 15 μs
ASCA
GIS keV ; 62.5ms/2N; 500ms/2N
SIS keV ;
Chandra
ACIS keV ; 2.8 ms
HRC keV ; 16 μs
--The archive data that we used--

9. Our approach Choose the data whose source photons > 100
But in the case of small samples (10 ≤ n ≤ 100):
Prob(H>h)~w(h) e-bn∙h
De Jager et al., 1989

10. Upper limit of pulsed fraction
for H > 0.3
for H > 0.3
De Jager et al., 1994
If we assume all the photons are contributed from the source:
δ=0.3, H=50, N=100; P2σ=0.7599
δ=0.3, H=50, N=400; P2σ=0.3799
δ=0.1, H=50, N=100; P2σ=0.3896
δ=0.3, H=30, N=100; P2σ= (H=30, prob.=9.95x10-6 ; H=50, prob.=4x10-8)
More exposure time may help us get more source photons…..

11. Our approach
Try to find any stronger signal from any way of timing analysis by blind search.
(including epoch folding , Zm2-test, H-test)
Example: The ROSAT data of RXJ (If there isn’t any significant signal…)
1993/10/23+10/26
1996/11/02
MJD= e+04
MJD= e+04
T=316.6 (ks)
　(>46.0)
T=62.3 (ks)
　(>41.0)
Frequency (s-1)
H value
r.p.
4.95E+01
4.49E-08
4.41E+01
1.68E-07
4.13E+01
4.52E-07
4.62E+01
9.91E-08
4.21E+01
2.84E-07
4.82E+01
6.10E-08
4.14E+01
3.42E-07
4.71E+01
7.94E-08
5.11E+01
4.00E-08
5.07E+01
4.27E+01
2.42E-07
242(35'': keV)
6.2x106 trials
159(60'':0.1-2keV)
3.2x107 trials

12. Analysis
1. If there is no evident known pulsar to be the counterpart…..
Based on 4-7 independent significant trial periods of each data, we search related periods
in other data of the same source by the condition that the characteristic age of the pulsar
is larger than 1000 years.
Furthermore, in order to let our choice to be more convincible, we only select that the random
probability to corresponding H-value of the trial period times searching trials is less than 0.02.
Example: The cross-checking results of RXJ
Frequency: Hz ; Period: s
s x Hz yr x10-13
total searching trials ~360
Frequency: Hz ; Period: s
s x Hz yr 6.5x10-13
total searching trials ~6100

13. Analysis 2. If there is evident known pulsar to be the counterpart…..
Example: Chandra data of AX J
Epoch(MJD)=
From the right panel, we can estimate
the pulse frequency of Chandra data =
(13) s-1
(Roberts et al., 2004)
~250 trials
(Telapse=20.8ks)`

14. Roberts et al., 2004

15. Unidentified GeV sources near pulsars
P(ms)
B12(G)
d(kpc)
Age(105 yr)
GeV J
CTA 1
140.0
3.9
1.4
0.2000
GeV J J
68.2
2.4
7.7
0.13
GeV J B
415.8
6.9
3.0
0.5843
GeV J B
101.0
2.8
4.1
0.2143
GeV J B
267.0
7.5
3.3
0.2032
GeV J B
746.6
3.1
9.162
GeV J J
103.7
3.2
12.4
0.17
(L. Zhang & K.S. Cheng, 1998; Roberts et. al, 2001 & 2002; Cordes & Lazio, 2002)

16. Our results of Periodicity Search
We have 13 GeV pulsar candidates to search for X-ray counterparts.
But we can’t resolve the point source in any X-ray archive data corresponding to
the position error box of GeV J and GeV J
(Although there is a radio pulsar in the error box of each γ-ray source……..)
Because we can’t find any significant pulse period in X-ray archival data of these
samples, we must have at least two useable data sets to work on cross-checking.
On the purpose of periodicity search, AX J & AX J which
are the X-ray counterparts of GeV J & GeV J only have one
ASCA data to be analyzed.
Let’s see the recommended pulse periods of the left 9 GeV sources by periodicity
search for possible X-ray counterparts .

17. Results of Cross-checking
GeV J (3EG J ) ↔ RX J (CTA 1) RX
J 　
period (s)
Τc (year)　
dp/dt
(10-13 s/s) 　
Epoch(MJD)
R.P. P1
6350
2.794
7.5x10-3 P2
1750
11.436
2.5x10-3 P3
12430
1.625
4.0x10-3 P4
1710
12.379
2.7x10-3 P5
2590
17.52
1.4x10-2 P6
4110
16.83
5.5x10-4
The R. P. (random prob.) in the Table of each feature has taken into account total number
of trials, but excluding the number of periods which are picked out on discussion in our
method. (Lupin & Chang, 2004)

18. Results of Cross-checking
GeV J (3EG J ) ↔ AX J ↔ 1E AX
J 　
period (s)
Τc (year)　
dp/dt
(10-13 s/s) 　
Epoch(MJD)
R.P. P1
5010
3.713
1.9x10-2
GeV J (3EG J ) ↔ AX J AX
J 　
period (s)
Τc (year)　
dp/dt
(10-13 s/s) 　
Epoch(MJD)
R.P. P1
1830
9.128
1.7x10-2 P2
16100
1.997
6.1x10-3 P3
1040
47.25
2.8x10-3 P4
2020
33.60
5.7x10-3
GeV J (3EG J ) ↔ AX J AX
J 　
period (s)
Τc (year)　
dp/dt
(10-13 s/s) 　
Epoch(MJD)
R.P. P1
2900
6.647
1.2x10-2 P2
12540
2.013
6.1x10-3 P3
2470
17.318
1.7x10-2

19. Results of Cross-checkingAX
J 　
period (s)
Τc (year)　
dp/dt
(10-13 s/s) 　
Epoch(MJD)
R.P. P4
1330
39.39
3.1x10-3 P5
1690
31.04
4.2x10-4 P6
7600
19.14
1.3x10-2
GeV J (3EG J ) ↔ AX J ↔ PSR J AX
J 　
period (s)
Τc (year)　
dp/dt
(10-13 s/s) 　
Epoch(MJD)
R.P. P1
4750
6.0x10-3 P2
3630
4.750
6.7x10-3 P3
1880
10.257
4.3x10-3 P4
8700
2.220
8.4x10-3 P5
4.84
4.7x10-5 P6
3060
13.17
5.8x10-3

20. Results of Cross-checking
GeV J (3EG J ) ↔ AX J AX
J 　
period (s)
Τc (year)　
dp/dt
(10-13 s/s) 　
Epoch(MJD)
R.P. P1
1230
3.6754
1.6x10-2 P2
1910
9.276
1.4x10-3 P3
3370
11.956
1.9x10-2
GeV J (3EG J ) ↔ PSR B AX
J 　
period (s)
Τc (year)　
dp/dt
(10-13 s/s) 　
Epoch(MJD)
R.P. P1
1220
3.0218
4.1x10-3 P2
2310
1.8051
1.9x10-2 P3
3300
7.52
1.8x10-2

21. Results of Cross-checking
GeV J (3EG J ) ↔ AX J , RX J AX J
period (s)
Τc (year)　
dp/dt
(10-13 s/s) 　
Epoch(MJD)
R.P. P1
4590
0.7734
7.2x10-3 P2
1960
2.7014
1.6x10-2 P3
2300
2.3119
4.1x10-3 P4
273800
0.0201
6.0x10-3 P5
169770
0.157
1.0x10-2 P6
1740
340.7
1.8x10-2
GeV J (3EG J ) ↔ AX J
This work is done by Wohemos, and the results will be reported in PSROC 2007.
GeV J (3EG J ) ↔ AX J ↔PSR J AX
J 　
period (s)
Τc (year)　
dp/dt
(10-13 s/s) 　
Epoch(MJD)
R.P. P1
1390
11.452
1.4x10-2 P2
3480
5.960
1.2x10-2

22. Results of Cross-checking
GeV J (3EG J ) ↔ RX J (γCygni, 2CG078+2) RX
J 　
period (s)
Τc (year)　
dp/dt
(10-13 s/s) 　
Epoch(MJD)
R.P. P1
2000
6.5245
9.8x10-3 P2
2090
105.32
8.2x10-3
After the work of cross-checking related data sets, did we find any tentative pulse
period consistent with the pulsation of radio pulsar near these X-ray sources?
NO!!
What does it mean?
1. Our way is not good enough to reduce the effect of background photons.
2. These X-ray sources has no relation with those pulsars.
Is there any significant feature in each data from the periods of those known pulsars?
I have not finished the check of all the data.
But for those obvious features that can be detected had already been reported in some articles.

23. Compare with known γ-ray pulsars
(Thompson et al., 1999)

24. The way to improve our work
Obviously, the easiest way is to apply for a better data.
Based on the pulsed fraction of one selected pulse period, to estimate the related
one can be detected or not in another instrument by it’s upper limit of the pulsed
fraction.
Compare with the similarity of the pulsed profile in the selected cross-checking
results. -- Fisher exact test? Kolmogorov-Smirnov test?
Numerical Recipes -- William H. Press er al
Practical Statistics for Astronomers – J. V. Wall & C. R. Jenkins
Astrostatistics – G. J. Babu and E. D. Feigelson
Is our way really useful to detect the pulse period of the weak pulsar candidates?
We can examine some dim neutron stars with weak pulse.

25. XDINS
(Pavlov, Sanwal & Garmire; 2001)
CCO
(Haberl ; 2004)

26. Future Work
There still remain some candidates of radio-quiet neutron stars.
(Brazier & Johnson; 1999)