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

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-1. 3-5 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 searchfor 13 possible X-ray counterparts to gamma-ray pulsar candidates.

Background of my research

X-ray Satellites:

ROSAT(1990-1999) ASCA(1993-2001) RXTE(1995-)BeppoSAX(1996-2002) Chandra(1999-)XMM(1999-)

ROSATPSPC 0.1-2 keV ; 130 μsHRI 0.1-2.5 keV ; 61 μs

ASCAGIS 0.8-12 keV ; 62.5ms/2N; 500ms/2N

SIS 0.4-12 keV ;

BeepoSAXLECS 0.1-10 keV ; 16 μsMECS 1.3-10 keV ; 15 μs

ChandraACIS 0.2-10 keV ; 2.8 msHRC 0.1-10 keV ; 16 μs

XMM-NewtonMOS 0.1-15 keV ; 1.5 ms-2.6sPN 0.1-15 keV ; 7 μs-73.4 ms

--The archive data that we used--

Our approach Choose the data whose source photons > 100

8

)h00229005.0h459014.0(

h398025.0

104

e210597.1

e9999755.0

)hH(obPr2

50h,

50h23,

23h0,

But in the case of small samples (10 ≤ n ≤ 100):

Prob(H>h)~w(h) e-bn∙h

De Jager et al., 1989

20.24 0.13

2 101.3 8.7 0.174 exp 0.03 0.13 log 0.174x H H

20.17 0.14

3 101.5 10.7 0.174 exp 0.08 0.15 log 0.174x H H

for H > 0.3

for H > 0.3

t t t bx p N p x N p p N N N

Upper limit of pulsed fraction

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=0.6425 (H=30, prob.=9.95x10-6 ; H=50, prob.=4x10-8)

More exposure time may help us get more source photons…..

Try to find any stronger signal from any way of timing analysis by blind search.(including epoch folding , Zm

2-test, H-test)

Our approach

1993/10/23+10/26

　 1996/11/02 　 　

MJD=4.928568530e+04 　 MJD=5.038968797e+04 　T=316.6 (ks) 　 (>46.0) 　 T=62.3 (ks) 　 (>41.0) 　 Frequency (s-

1)H value r.p. Frequency (s-1) H value r.p.

2.53691060 4.95E+0

14.49E-

080.72059200

4.41E+01

1.68E-07

9.41901060 4.95E+0

14.49E-

0812.15149200

4.13E+01

4.52E-07

14.66677340 4.62E+0

19.91E-

0836.27199600

4.21E+01

2.84E-07

22.655636804.82E+0

16.10E-

0842.88081000

4.14E+01

3.42E-07

29.98823120 4.71E+0

17.94E-

0865.86789900

5.11E+01

4.00E-08

50.31337820 5.07E+0

14.00E-

0899.99785500

4.27E+01

2.42E-07

Example: The ROSAT data of RXJ2020.2+4026 (If there isn’t any significant signal…)

159(60'':0.1-2keV) 3.2x107 trials

242(35'':0.1-2.5keV) 6.2x106 trials

Analysis1. 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 periodsin other data of the same source by the condition that the characteristic age of the pulsaris 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 RXJ2020.2+4026

1996-11-02Frequency: 0.72059200Hz ; Period: 1.3877478518s1993-10-23+1993-10-261.3867432888559s 26.2 3.49x10-5 0.72111400Hz 2087.018yr 105.3x10-13

total searching trials ~360---------------------------------------------------------------------------1996-11-02Frequency: 12.15149200Hz ; Period: 0.0822944211s1993-10-23+1993-10-260.0822321867897s 35.9 1.62x10-6 12.16068840Hz 1997.680yr 6.5x10-13

total searching trials ~6100

2. If there is evident known pulsar to be the counterpart…..

Analysis

Example: Chandra data of AX J2021.1+3651

(Roberts et al., 2004)

Epoch(MJD)=52682.60172

From the right panel, we can estimate the pulse frequency of Chandra data =9.640923869(13) s-1

~250 trials (Telapse=20.8ks)`

Roberts et al., 2004

Unidentified GeV sources near pulsars

GeV source Pulsar P(ms) B12(G) d(kpc) Age(105 yr)

GeV J0008+7304 CTA 1 140.0 3.9 1.4 0.2000

GeV J417-6100 J1420-6048 68.2 2.4 7.7 0.13

GeV J1800-2328 B1758-23 415.8 6.9 3.0 0.5843

GeV J1825-1310 B1823-13 101.0 2.8 4.1 0.2143

GeV J1856+0115 B1853+01 267.0 7.5 3.3 0.2032

GeV J1907+0557 B1900+05 746.6 3.1 3.9 9.162

GeV J2020+3658 J2021+3651 103.7 3.2 12.4 0.17

(L. Zhang & K.S. Cheng, 1998; Roberts et. al, 2001 & 2002; Cordes & Lazio, 2002)

Our results of Periodicity SearchWe 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 J1800-2328 and GeV J1856+0115. (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 thesesamples, we must have at least two useable data sets to work on cross-checking. On the purpose of periodicity search, AX J1907.1+0549 & AX J2035.4+4222 which are the X-ray counterparts of GeV J1907+0557 & GeV J2035+4214 only have oneASCA 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 .

RX J0007.0+7302 　 period (s) Τc (year)　 dp/dt

(10-13 s/s) 　 Epoch(MJD) R.P.

P1 0.11200955 6350 2.794 52327.03399 7.5x10-3

P2 0.12640382 1750 11.436 50107.83546 2.5x10-3

P3 0.12751210 12430 1.625 50107.83546 4.0x10-3

P4 0.1339784 1710 12.379 52327.03399 2.7x10-3

P5 0.2865859 2590 17.52 50107.83546 1.4x10-2

P6 0.4365495 4110 16.83 52327.03399 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)

Results of Cross-checkingGeV J0008+7304(3EG J0010+7309) ↔ RX J0007.0+7302(CTA 1)

Results of Cross-checkingGeV J1025-5809(3EG J1027-5817) ↔ AX J1025.9-5749 ↔ 1E 1024.0-5732

AX J1025.9-5749

　period (s) Τc (year)　 dp/dt

(10-13 s/s) 　 Epoch(MJD) R.P.

P1 0.11736978 5010 3.713 49566.76771 1.9x10-2

GeV J1417-6100(3EG J1420-6048) ↔ AX J1418.2-6047

AXJ1418.2-6047

　period (s) Τc (year)　 dp/dt

(10-13 s/s) 　 Epoch(MJD) R.P.

P1 0.10546507 1830 9.128 51223.68497 1.7x10-2

P2 0.20296902 16100 1.997 50317.00727 6.1x10-3

P3 0.3097181 1040 47.25 51223.68497 2.8x10-3

P4 0.4289840 2020 33.60 51223.68497 5.7x10-3

GeV J1417-6100(3EG J1420-6048) ↔ AX J1418.6-6045

AX J1418.6-6045 　 period (s) Τc (year)　 dp/dt

(10-13 s/s) 　 Epoch(MJD) R.P.

P1 0.12180376 2900 6.647 51223.68497 1.2x10-2

P2 0.1593580 12540 2.013 50317.00727 6.1x10-3

P3 0.2700303 2470 17.318 50317.00727 1.7x10-2

Results of Cross-checking

GeV J1417-6100(3EG J1420-6048) ↔ AX J1420.1-6049 ↔ PSR J1420-6048

AXJ1420.1-6049

　period (s) Τc (year)　 dp/dt

(10-13 s/s) 　 Epoch(MJD) R.P.

P1 0.0108968655 4750 0.36334 52289.79033 6.0x10-3

P2 0.10882128 3630 4.750 51223.68495 6.7x10-3

P3 0.12200264 1880 10.257 52534.12055 4.3x10-3

P4 0.12200264 8700 2.220 52534.12055 8.4x10-3

P5 0.1452297 4750 4.84 51223.68495 4.7x10-5

P6 0.2540350 3060 13.17 50317.00729 5.8x10-3

AXJ1418.6-6045

　period (s) Τc (year)　 dp/dt

(10-13 s/s) 　 Epoch(MJD) R.P.

P4 0.3311744 1330 39.39 50317.00727 3.1x10-3

P5 0.3311744 1690 31.04 50317.00727 4.2x10-4

P6 0.917719 7600 19.14 50317.00727 1.3x10-2

Results of Cross-checkingGeV J1809-2327(3EG J1809-2328) ↔ AX J1809.8-2332

AXJ1809.8-2332

　period (s) Τc (year)　 dp/dt

(10-13 s/s) 　 Epoch(MJD) R.P.

P1 0.028499942 1230 3.6754 52539.07915 1.6x10-2

P2 0.11196607 1910 9.276 50526.78845 1.4x10-3

P3 0.2543817 3370 11.956 53280.71956 1.9x10-2

GeV J1825-1310(3EG J1826-1302) ↔ PSR B1823-13

AXJ1418.2-6047

　period (s) Τc (year)　 dp/dt

(10-13 s/s) 　 Epoch(MJD) R.P.

P1 0.023309690 1220 3.0218 50902.40923 4.1x10-3

P2 0.026302114 2310 1.8051 52200.36170 1.9x10-2

P3 0.1565487 3300 7.52 49614.45908 1.8x10-2

Results of Cross-checkingGeV J1835+5921(3EG J1835+5918) ↔ AX J1836.2+5928, RX J1836.2+5925

AXJ1836.2+5928 period (s) Τc (year)　 dp/dt

(10-13 s/s) 　 Epoch(MJD) R.P.

P1 0.022425706 4590 0.7734 53440.60818 7.2x10-3

P2 0.033509095 1960 2.7014 53438.80937 1.6x10-2

P3 0.033509095 2300 2.3119 53438.80937 4.1x10-3

P4 0.034677614 273800 0.0201 50800.00499 6.0x10-3

P5 0.1679234 169770 0.157 53440.60818 1.0x10-2

P6 3.74065 1740 340.7 50800.00499 1.8x10-2

GeV J2020+3658(3EG J2021+3716) ↔ AX J2021.1+3651 ↔PSR J2021+3651

AX J2021.1+3651

　period (s) Τc (year)　 dp/dt

(10-13 s/s) 　 Epoch(MJD) R.P.

P1 0.10081213 1390 11.452 52682.60172 1.4x10-2

P2 0.13080665 3480 5.960 51300.06891 1.2x10-2

GeV J1837-0610(3EG J1837-0606) ↔ AX J1837.5-0610

This work is done by Wohemos, and the results will be reported in PSROC 2007.

Results of Cross-checkingGeV J2020+4023(3EG J2020+4017) ↔ RX J2020.2+4026(γCygni, 2CG078+2)

RXJ2020.2+4026

　period (s) Τc (year)　 dp/dt

(10-13 s/s) 　 Epoch(MJD) R.P.

P1 0.08229442 2000 6.5245 50389.68797 9.8x10-3

P2 1.3877479 2090 105.32 50389.68797 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!!

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.

What does it mean?

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.

Compare with known γ-ray pulsars

(Thompson et al., 1999)

The way to improve our workObviously, the easiest way is to apply for a better data.

Based on the pulsed fraction of one selected pulse period, to estimate the relatedone can be detected or not in another instrument by it’s upper limit of the pulsedfraction.

Compare with the similarity of the pulsed profile in the selected cross-checkingresults. -- Fisher exact test? Kolmogorov-Smirnov test?

Numerical Recipes -- William H. Press er alPractical Statistics for Astronomers – J. V. Wall & C. R. JenkinsAstrostatistics – 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.

XDINS

CCO(Pavlov, Sanwal & Garmire; 2001)

(Haberl ; 2004)

Future WorkThere still remain some candidates of radio-quiet neutron stars.

(Brazier & Johnson; 1999)