1. Periodicity Search of Possible Counterparts to unidentified EGRET sources Periodicity as a multiwavelength tool Outline : Our method to perform periodicity search Possible candidates of the next Geminga Contribution of the archive data in our work

2. Periodicity as a Multiwavelength Tool Variability studies have shown that pulsars have low variability (except for their pulsations), while blazars typically show more variability. Periodic variability at multiple wavelengths is a definitive identifier. Pulsars (rotating neutron stars) are the prototype of this approach. The approach: search out a periodic signal at one wavelength, then fold data from other wavelength bands at the expected period. In addition to identification, periodic sources allow exploration of physical processes. At some level, gamma-ray sources will have X-ray counterparts. If the X-ray counterpart can be found, the better X-ray position information allows deep searches at longer wavelengths. The classic example is Geminga. Bignami, Caraveo, Lamb, and Halpern started this search in 1983. The final result appeared in 1992 with the detection of pulsations from this isolated neutron star.

3. (Thompson, 2001) J0218+4252 B1055-52 Geminga B0656+14 B1509-58 B1046-58 B1706-44 Vela B1951+32 Crab Characteristic age: Spin-down energy: Magnetic field: Open field line voltage: The current of relativistic particles flow: year erg/s gauss volt s -1 Period v. Period derivative diagram for known Pulsars

4. 0.5-2 KeV 2-100 KeV 0.1-10 MeV >100 MeV Additional candidates: >100 MeV (Thompson, 2001) Gamma-ray pulsars and Possible candidates:

5. Gamma-ray pulsars :

6. Neutron stars Neutron Stars (~1400) Isolated Neutron Stars Radio-quiet INS AXPs (~6) SGRs (~5) RQINs with γ-ray RQINs without γ- ray CCOs (~5) XDINs (~7) Others (>7) With SNR ? With γ-ray ? Isolated Radio Pulsars Radio emission ? In Binary systems Companion?

7. Possible Gamma-ray Pulsar Candidates Surveying the Universe with EGRET 1991-1996 1st EGRET catalogue: 127 (1EG) 2nd EGRET catalogue: 129 (2EG) Supplement to 2nd EGRET catalogue: 157 (2EGS) 3th EGRET catalogue: 271 (3EG) Oct, 2002

8. Unidentified EGRET sources 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. Some of them which lie almost exclusively along the Galactic plane are currently unidentified. From Roberts and Romani (2001), 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.

9. (Roberts,Romani & Kawai ;2001)

10. X-ray archive data we used Recent X-ray Missions: ROSAT(1990-1999)ASCA(1993-2001)RXTE(1995-)BeppoSAX( 1996-2002 ) Chandra(1999-)XMM(1999-) ROSAT PSPC 0.1-2 keV ; 130 μs HRI 0.1-2.5 keV ; 61 μs ASCA GIS 0.8-12 keV ; 62.5ms/2 N ; 500ms/2 N SIS 0.4-12 keV ; BeepoSAX LECS 0.1-10 keV ; 16 μs MECS 1.3-10 keV ; 15 μs Chandra ACIS 0.2-10 keV ; 2.8 ms HRC 0.1-10 keV ; 16 μs XMM-Newton MOS 0.1-15 keV ; 1.5 ms-2.6s PN 0.1-15 keV ; 7 μs-73.4 ms --The archive data that we used--

11. Our method in periodicity search There are different methods to perform periodicity search, e.g., FFT, epoch folding, Z m 2 -test, H-test, etc. H-test: The H-test involves the Z m 2 -static and Z m 2 -Test as basis with chosen smoothing parameter (m=1,…,20) The H-statistic is defined as And the Z m 2 -statistic is given by here N is total number of detected photons, and φis the arrival phase of the ith photon where ν is the trial frequency, t is the barycentic corrected arrival time of the photon, and t 0 is time-zero epoch The H-test offers some advantages over the other tests when searching for an unknown pulse shape in sparse data. It is independent of the binning of the data, and it is sensitive to a wide variety of pulse shapes.

12. The power of the H -test (De Jager,Swanepoel & Raubenheimer ;1989)

13. The power of the H -test (De Jager,Swanepoel & Raubenheimer ;1989) According to the sensitivity of the sample size shown on the power of the H-test, I restricted the arbitrary condition that source photons > 100.

14. Unidentified Sources near radio pulsars I. Figure 1a. Results of periodicity search with the method of H-test in the frequency range [14.66725,14.668] Hz which covers the estimated period of PSR J1420-6048. Fig 1b. Pulse profile of ASCA data folded at 14.6676470 Hz. Total source counts are 252 and Fourier width is 5.78x10 -6 Hz. Observation Date (Mission) Name of pulsar Epoch of ephemeris (MJD) Estimated pulse frequency (Hz) The maximum H value of the trial Random prob. 1999-02-13 (ASCA) J1420-604851223.6849514.667647032(7)~13.15.44x10 -3 The pulse frequency of AX J1420.1-6049 can be inferred from PSR J1420-6048 (D’ Amico et al., 2001)

15. Unidentified Sources near radio pulsars II. Observation Date (Mission) Name of pulsar Epoch of ephemeris (MJD) Estimated pulse frequency (Hz) The maximum H value of the trial Random prob. 2001-10-18 (XMM)B1823-1352200.361709.85473263939(5)~14.43.24x10 -3 Figure 2a. Results of periodicity search with the method of H-test in the frequency range [9.851,9.86] Hz which covers the estimated period of PSR J1823-13. Fig 2b. Pulse profile of XMM data folded at 8.854744 Hz. Total source counts are 1389 and Fourier width is 4.24x10 -5 Hz. The pulse frequency of *PSR B1823-13 can be infer from PSR B1823-13 (Gaensler et al., 2003) (Note: *PSR B1823-13 here implies the X-ray point source whose space position is consistent with the radio pulsar PSR B1823-13)

16. Observation Date (Mission) Name of pulsar Epoch of ephemeris (MJD) Estimated pulse frequency (Hz) The maximum H value of the trial Random prob. 2003-02-12 (Chandra)J2021+365152682.601729.6409485566(1)~21.02.34x10 -4 Unidentified Sources near radio pulsars III. The pulse frequency of AX J2021.1+3651 can be inferred from PSR J2021+3651 (Roberts et al., 2002) Figure 3a. Results of periodicity search with the method of H-test in the frequency range [9.62,9.665] Hz which covers the estimated period of PSR J2021+3651. Fig 3b. Pulse profile of Chandra data folded at 9.64094856 Hz. Total source counts are 575 and Fourier width is 4.81x10 -5 Hz..

17. Unidentified GeV sources which might be next Grminga blind searchcross-checking The only way is blind search and cross-checking Based on 4-7 independent significant trial periods which are selected by H-test from each X-ray data, we search related periods in other data of the same point 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 consider that (The Random Probability to Corresponding H-value of Related Period) X (Number of Searching Trials under the Constraint of Characteristic Age) < 0.02. To proof our method can be used to detect the weak pulsar candidates, we can examine our method in some CCOs and XDINs with their marginal evidence of the periodicity detection.

18. XDINS CCO (Pavlov, Sanwal & Garmire; 2001)

19. XMM-Newton Discovery of 7 s Pulsations in the INS RX J1856.5-3754 RX J1856.5-3754 Tiengo & Mereghetti (2007) reported the marginal period 7.055s of RX J1856.5-3754 by the periodicity search in XMM-Newton observation on 2006 Oct 24. Can we get any possible detection from the other archive data by using our searching method? DateInstrumentModeExposure(ks)Epoch(MJD)Counts 2002 Apr 8 pn MOS2 SW 57 58 52373.00618 328663 80202 2004 Apr 17pnTI6553113.30249276881 2004 Sep 24 pn MOS1 MOS2 SW 33 70 53272.47993 185225 64914 42733 2005 Sep 24 pn MOS1 MOS2 SW 35 53637.53865 180770 31662 35323 2006 Mar 26 pn MOS1 MOS2 SW 70 53821.05897 378952 68662 73664 2007 Mar 14 pn MOS1 MOS2 SW 66 69 54174.23687 282559 61108 74751 Table. Log of XMM-Newton Observations of RX J1856.5-3754

20. Date The independent significant trial frequency picked by blind search (Hz) H value Corresponding R.P. with considering total trials 2002 Apr 8 (52373.00618 MJD) 0.03983200 0.14174550 0.18550600 0.41662300 0.55784200 0.56404300 0.62697400 31.5 28.5 30.4 32.0 28.6 29.3 28.3 0.2987 0.6060 0.3953 0.2617 0.5939 0.5119 0.6301 2004 Apr 17 (53113.30249 MJD) 0.02527900 0.03285700 0.03792100 0.07584100 0.38080000 0.62003800 33.0 34.7 33.2 36.4 39.3 33.3 0.2209 0.1383 0.2092 0.08604 0.03853 0.2035 2004 Sep 24 (53272.47993 MJD) 0.05747750 0.10789750 0.62827500 0.66026750 0.94912250 26.2 26.5 26.3 26.4 32.8 0.9158 0.8917 0.9079 0.8999 0.2512 2005 Sep 24 (53637.53865 MJD) 0.01128000 0.01142500 0.01316000 0.02354500 33.7 29.5 29.9 34.7 0.1035 0.3358 0.3020 0.07759 2006 Mar 26 (53821.05897 MJD) 0.88242400 0.89726600 0.92011600 32.0 33.8 30.3 0.3055 0.1888 0.4643 2007 Mar 14 (54174.23687MJD) 0.01032750 0.07086750 0.14173400 37.3 36.4 36.6 0.07094 0.09112 0.08618 Table. The possible signal picked from each data by blind search

21. Results of Data Cross-Checking Compare to the periodicity data cross-checking in the X-ray counterparts of unidentified GeV sources, we show the possible pulsar candidates with the significance higher than 3.5  (r.p. < 4.65x10 -4 ) to eliminate the fake results induced by random noise at low frequencies. RX J1856.6-3754 period (s) Τ c (year) dp/dt (10 -13 s/s) Epoch(MJD)R.P. P12.400252XXX-0.7452373.00618-54174.236871.84x10 -4 P27.0548982688041.5852373.00618-54174.236872.68x10 -5 P37.0548983039036.7852373.00618-54174.236872.31x10 -5 P47.0548984369025.5952373.00618-54174.236871.23x10 -4 P57.0548987182015.5652373.00618-53113.302493.92x10 -4 P67.0554702167051.58953113.30249-54174.236877.81x10 -5 P77.05547010292010.8653113.30249-54174.236873.89x10 -4 P87.0554702058054.3153272.47993-54174.236872.69x10 -4 P97.0554703181035.1453272.47993-54174.236877.28x10 -5 P107.0554704960225.4153637.53865-54174.236874.58x10 -4 P117.0554709920112.7153637.53865-54174.236871.57x10 -4 P1214.1108420830107.3553637.53865-54174.236877.76x10 -5 P1325.1054XXX-3628.6652373.00618-53637.538656.67x10 -5 P1439.55924480256.0953113.30249-54174.236877.59x10 -5 Table. Possible pulsed candidates of RX J1856.5-3754

22. Results of Data Cross-Checking If RX J1856.5-3754 is a normal pulsar without glitch, we can drop P1 & P13. From P2-P11, these pulsed candidates may attribute to the same period ~7.055s. And P12 might be induced by the half harmonic of the main pulsation. The most significant case is P3 and reaches to 4  level. In our search, the spin period of RX J1856.5-3754 may range from 7.05490s to 7.05547s among 2002-2007, and This result is consistent with the pulsed period 7.05515  0.00007s reported by Tiengo & Mereghetti using the XMM observation on Oct. 24, 2006. P3 is picked from 2 data cross-checking between [Apr. 8,2002] & [Mar. 14, 2007]. To raise the significant level, we can check the pulsed strength in the other data. DateTrial frequencyH valueR.P. 2002 Apr 8 0.14174550 28.5---- 2004 Apr 170.1417400721.42.01x10 -4 2004 Sep 240.1417397624.85.62x10 -5 2005 Sep 240.1417374316.01.73x10 -3 2006 Mar 260.1417362514.43.29x10 -3 2006 Oct 240.1417349128.31.73x10 -5 2007 Mar 140.1417340036.6----

23. Compare with the pulsed profile Simple Linear Regression The minimization procedure for estimating parameters is called method of least squares: Differentiating SSE with respect to a and b, we have Solving 2 equations, we get: & If we set 3 notations, ;

24. Compare with the pulsed profile ; thus & So, To estimate the linear relationship between two variables x and y, we can define Pearson r : If we consider r 2, then 100 r 2 % of the variation in the values of y may be accounted for by the linear relationship with the variable x. This relationship can be proved by the normal conditional distribution, and we can treat r 2 as the proportion of the total variance that is explained from the prediction. If we want to compare with 2 light curves, we can set the photon counts (after subtracting the average background photons) of each bin from the same pulsed profile in one parameter (x or y). Then the correlation coefficient r will give us a basic information of the similarity.

26. Discovery of 424 ms Pulsations from the CCO 1E 1207.4-5209 1E 1207.4-5209 Zavlin & Pavlov et. al. (2000, 2002) reported the marginal pulsation 424ms of 1E 1207.4-5209 by the periodicity search in the Chandra observation on 2000 Jan 6 & 2002 Jan 5. (424ms~2.35777Hz) Date The independent significant trial frequency picked by blind search (Hz) H value Corresponding R.P. with considering total trials 1992 Aug 2 (48836.74673 MJD) 7.31748400 9.13183300 53.3894650 59.6318350 66.3571000 95.2259800 40.8 42.6 41.7 41.9 42.2 43.5 0.8837 0.7344 0.8144 0.7974 0.7709 0.6491 1994 Jul 10 (49543.21054 MJD) 26.2448000 58.4588000 61.6169000 64.5493000 34.9 33.2 33.6 37.3 0.3238 0.4805 0.4398 0.1758 1994 Jul 15 (49548.60205 MJD) 1.31196600 4.40755600 4.45637400 5.96028200 39.2 53.7 38.8 40.6 0.4436 0.0004391 0.4810 0.3285 1994 Jul 18 (49556.25311 MJD) 20.7648880 22.5953298 50.0459344 72.5599852 89.0471336 48.3 49.6 57.3 50.1 0.4071 0.3197 0.0009756 0.01724 2000 Jan 17 (51561.69778 MJD) 0.2645860 52.544853 55.717511 81.255803 95.996820 46.5 44.8 43.6 48.1 46.4 0.8276 0.9363 <1 0.6965 0.8350 Table. The possible signal picked from each data by blind search

28. Bright g-ray pulsar future

29. Conclusion Obviously, applying for the better data is necessary to verify our results. To avoid a blind search with a huge number of trials, these candidate periods can serve as the target periods for future search when new data become available. Period in the emission of other energy bands from the counterpart of the gamma-ray source may help to establish the periodicity in the gamma-ray emission and therefore strengthen the identification of the source in different energy bands. We develop a procedure, by cross-checking at least two X-ray data sets, to find candidate periods for some specified sources. Our method can be examined in some CCO/XDIN data with marginal evidence for periodicity. We present our results of this method, which are part of our efforts to find the next radio-quiet gamma-ray pulsars.