On the Spectral Shape of Nonrecycled γ ray Pulsars
 Author: Hui ChungYue, Lee Jongsu
 Publish: Journal of Astronomy and Space Sciences Volume 33, Issue2, p101~104, 15 June 2016

ABSTRACT
More than 100
γ −ray pulsars have been discovered by theFermi Gammaray Space Telescope. With a significantly enlarged sample size, it is possible to compare the properties of different classes. Radioquiet (RQ)γ −ray pulsars form a distinct population, and various studies have shown that the properties of the RQ population can be intrinsically different from those of radioloud (RL) pulsars. Utilizing these differences, it is possible to further classify the pulsarlike unidentifiedγ −ray sources into subgroups. In this study, we suggest the possibility of distinguishing RQ/RL pulsars by their spectral shape. We compute the probabilities of a pulsar to be RQ or RL for a given spectral curvature. This can provide a key to the estimation of the intrinsic fraction of radioquietness in theγ −ray pulsar population, which can place a tight constraint on the emission geometry.

KEYWORD
gamma rays: stars , pulsars: genera

1. INTRODUCTION
Together with an improved pulsation search algorithm (e.g., Kerr 2011), the large area telescope (LAT) onboard
Fermi γ ray Space Telescope has significantly enlarged the population ofγ ray pulsars with its unprecedented sensitivity. In the secondFermi LAT pulsar catalog (2PC Abdo et al. 2013), 117 pulsar detections at energies > 100 MeV are reported using three years of data. It comprises 42 radioloud (RL) pulsars, 35 radioquiet (RQ) pulsars and 40 millisecond pulsars (Abdo et al. 2013)1 . It should be noted that the fractions of RL and RQ are comparable in the knownγ −ray pulsar population. However, the true RL/RQ fractions can be different from the observed values in the presence of various selection effects. For example, blind searches for RQ pulsars can only be performed in high energy regimes, which are photonlimited. On the other hand, in the case of searching RLγ ray pulsars, one can utilize the ephemeris obtained in radio. This implies that the intrinsic RQ fraction can be larger than the observed one by ~30%. In a recent study,Sokolova & Rubtsov (2016) estimated that the intrinsic fraction of radioquietγ −ray pulsars can be as large as ~70%.Knowing the true fraction of RQ is important for constraining the pulsar emission models. The outergap model suggests that
γ −rays originate from the outer magnetosphere and form a fan beam (see Cheng & Zhang 1998; Takata et al. 2006, 2008). On the other hand, the radio emission forms a narrow cone when it originates from the polar cap region (Kijak & Gil 1998, 2003). The ratio of RL and RQ populations can help us to constrain the emission and viewing geometry. As RL and RQ pulsars form two distinct populations, a number of investigations have compared the properties of these two classes. Marelli et al. (2011, 2015) and Marelli (2012) found the difference between these two populations in terms of theγ −raytoXray flux ratioF_{γ} /F_{X} .F_{γ} /F_{X} of the RQ population was found to be significantly higher than that of the RL population. Sokolova & Rubtsov (2016) also reported a possible difference in the distributions of their rotation periods. Very recently, Hui et al. (2016) examined the various physical properties of RQ and RLγ −ray pulsars. Among all the possible differences found in these two populations, the most significant is the curvatures of theirγ −ray spectra.Using various different properties identified for RQ and RL pulsars, we suggest a method to estimate the intrinsic fraction of radioquietness in the population of
γ −ray pulsars. In the thirdFermi γ −ray point sources catalog (3FGL; Acero et al. 2015), among 3,033 sources detected at a significance > 4σ , more than 1,000 sources do not have any known counterparts at other energy bands. Using theγ −ray properties of pulsars (e.g., variability, curvature significance, locations in our galaxy) together with the machine learning techniques, Saz Parkinson et al. (2016) selected a group of pulsarlike unidentifiedγ −ray sources and further classified them into the categories of young pulsars and millisecond pulsars. Applying the same techniques together with the aforementioned features that can distinguish the RQ and RL pulsars, it is feasible to select the nonrecycled pulsar candidates from the unidentified source population and classify them into RQ or RL classes. This can provide a less biased estimate for the radioquietness fraction. In this paper, we discuss the possibility of using theγ −ray spectral shape to distinguish RQ and RL pulsars.2. DATA ANALYSIS
The
γ −ray spectra of pulsars are characterized by the form of a powerlaw with an exponential cutoff (PLE),where
N _{0},Γ , andE_{C} are the normalization, photon index, and cutoff energy, respectively. This is signaificantly curved in comparison with a simple powerlaw(PL):In the 3FGL catalog, the curvature of the pulsars’
γ ray spectra is quantified by the parameter Curve Significance, which is obtained by comparing the difference between the PLE and PL model fittings in unit ofσ . Using the KS test, Hui et al. (2016) found that the distributions of Curve Significance show the most significant difference between RQ and RL pulsars among all the tested parameters. The difference is found at a confidence level of > 99.999%. In Table 1, we have tabulated the Curve Significance for all the nonrecycled RQ nad RL pulsars in 2PC. All the data in this table are collected from 3FGL (Acero et al. 2015). Hui et al. (2016) showed histograms of Curve Significance for both populations. Using these distributions, we can compute the posterior probabilities of being RQ (P(RQCur)) or RL (P(RLCur)) for a given Curve Significance.In examining the distributions reported by Hui et al. (2016), we notice the fluctuations appear at the large values of Curve Significance. This can be ascribed to the small statistics in this range. For a simple parametric estimation of the underlying probability density function, we suppress these noises by fitting the histograms with Gaussian models with the following form:
where
A ,μ , andσ are the parameters that depict the peak, the mean, and the width of the model, respectively. For the RQ population, all three parameters,A ,μ , andσ , are set to be free in the fitting. For the RL population, visual inspection clearly indicates that the peak and the mean are located around zero Curve Significance. Therefore,A andμ are fixed and we only let the width of the functionσ be free. The bestfit functions are shown in the left panel of Fig. 1, which provides a reasonable approximation of the distributions. Using these estimates of probability density functions, we further construct the posterior probabilities P(RQCur) and P(RLCur) and have shown them in the right panel of Fig. 1.3. DISCUSSIONS
As
γ −ray spectral curvatures of nonrecycled RQ and RL pulsars in 2PC are found to be significantly different (Hui et al. 2016), one can use this aspect as an additional feature in classifying those sources that have no known multiwavelength counterparts. To facilitate the classification, we have computed P(RQCur) and P(RLCur), which can help to estimate the probability of any nonrecycled pulsarlike candidate being RQ or RL by giving its Curve Significance.We strongly believe such investigation as this can provide a less biased estimate of the intrinsic fraction of radioquietness. By performing a blind pulsation search for all point sources in 3FGL with
Fermi LAT data alone, Sokolva & Rubtsov (2016) estimated the radioquietness fraction to beє_{RQ} = 63 ± 8%. The catalog they compiled is free from the bias as RL pulsar search can utilize the information through radio observations. However, one should note that blind search of such a large sample is computationally demanding. On the other hand, our proposed method can provide an independent estimate by using the spectral curvature. Combining the spectral feature with the method of selecting pulsar candidates (e.g. see Fig. 1 in Hui et al. 2015), one may estimateє_{RQ} simply using Curve Significance, P(RQCur) and P(RLCur) as inputs.The aforementioned comparison of the
γ −ray spectral curvature is only for the nonrecycled pulsars. There is no existing literature on a similar analysis of millisecond pulsars (MSPs). It will be interesting to compare the spectral features and otherγ −ray properties of MSPs with those of nonrecycled RQ and RL pulsars. This kind of study can help to search for the possible features that can make the MSP candidate selection more accurate (see Hui et al. 2015). Also, to date, no MSP has been found to be RQ. Through such comparison, one may draw insights on the expected properties of RQ MSPs, if they exist.Finally, we would like to stress that the density estimation in this work is obtained through a simple parametric estimation and limited by the relatively small sample size. With an enlarged
γ −ray pulsar population in the future, our estimation can be improved by employing a more sophisticated method of density estimation (e.g., using kernels).

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[Table 1.] Curvature Significances of RL γray pulsar (Acero et al. 2015)

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[Fig. 1.] (Left panel) Distributions of Curve Significance for RL (dashed lines) and RQ (solid lines) γ？ray pulsars in 2PC. The bestfit Gaussian functions of both populations are overlaid (right panel). The probabilities of a nonrecycled γ？ray pulsar to be RL P(RLCur) or RQ P(RQCur) for a given Curve Significance are computed from the bestfit Gaussians.