The Einstein@Home Gamma-ray Pulsar Survey. II. Source Selection, Spectral Analysis, and Multiwavelength Follow-up

The third catalog of LAT sources (hereafter 3FGL; Acero et al. 2015) lists the properties of 3033 gamma-ray sources detected by the LAT in the first 4 yr of data taking. More than 30% of the 3FGL sources were unassociated at the time of publication. More than 100 of these unassociated sources have been demonstrated to be previously unknown pulsars, discovered either in deep targeted radio observations or in blind searches using the LAT data. Due to the observing time and processing resources required for a timing search, identifying which of these sources are most likely to be pulsars has become a task of paramount importance. In contrast to several other classes of gamma-ray sources, pulsars have significant cutoffs in their emission spectra at energies of a few GeV and gamma-ray fluxes that are generally very stable (however, see Allafort et al. 2013, for a counterexample); hence, the curvature significance²⁰ ("Signif_Curve", S_c) and the variability index²¹ ("Variability_Index", VI), which are respectively measures of the curvature of a source's spectrum and of its gamma-ray flux variability, have been successfully applied in previous similar surveys (e.g., Pletsch et al. 2012a).

We note that only a preliminary version of the 3FGL catalog was available when our survey was initiated. We therefore assessed the pulsar likelihood of the unassociated sources from this preliminary catalog. As a cross-check of our source selection results, we have compared the data from the preliminary catalog with those from 3FGL, finding differences in one specific parameter only. These differences are discussed in the next section.

Although using S_c and the VI seems to be enough to identify pulsar candidates, extra care needs to be taken, as these two parameters are correlated with the detection significance. A number of groups have developed different schemes for classifying sources, involving machine-learning techniques (Lee et al. 2012; Mirabal et al. 2012; Saz Parkinson et al. 2016). In particular, Lee et al. (2012) have shown that including the gamma-ray flux as a third dimension in the pulsar classification scheme can directly correct the above-mentioned correlation. Applying the Gaussian Mixture Model (GMM) classification scheme from Lee et al. (2012), we used the VI, S_c, and F₁₀₀₀ (gamma-ray flux above 1 GeV) parameters from the catalog to calculate the pulsar likelihood R_s for all the sources. A positive log R_s indicates that the source is likely to be a pulsar (see Lee et al. 2012, for a detailed discussion). A list of 341 sources with positive logarithmic pulsar likelihood (log R_s) values and no firm associations with any other astrophysical sources was obtained.

As mentioned in Section 2.1, the list of pulsar candidates was produced by analyzing a preliminary version of the 3FGL catalog. We verified that the characteristics of most of the sources from the preliminary catalog are identical to those from the final catalog. One difference concerns the definition of the spectral curvature Test Statistic (TS), TS_curve, listed instead of the curvature significance in the preliminary version of the catalog, ${S}_{c}=\sqrt{{\mathrm{TS}}_{\mathrm{curve}}\times {R}_{\mathrm{syst}}}$, where R_syst accounts for systematic uncertainties in the effective area. We verified that using TS_curve instead of S_c as one of the inputs of the GMM does not affect our classification results.

One of the main difficulties in blind searches for gamma-ray pulsars is separating background emission from photons originating from the sources of interest. Due to the wide and energy-dependent point-spread function of the LAT at low energies,²² neighboring sources within a few degrees of a given direction can raise the background level in the data set considered for the search. In the past, blind searches often adopted a so-called "cookie cutter" to select photons and increase the signal-to-noise ratio, i.e., they restricted the region of interest (ROI) by selecting events with reconstructed directions found within, say, $\sim 1^\circ$ of the considered sky location. Although this technique can efficiently separate source and background photons for some bright pulsars or pulsars in regions of low background contamination, most of the young gamma-ray pulsars are located near the Galactic plane, where the diffuse background emission is strong and where the effectiveness of the cookie cutter selection method decreases. Kerr (2011) mitigated this problem by proposing a photon-weighting technique, which uses information about the spectrum of the targeted source and the instrumental response of the LAT. Probabilities that photons originate from the source can then be calculated, relaxing the need to select narrow sky regions and greatly improving our sensitivity to weak periodic signals.

Consequently, accurately determining the spectra of the sources we want to search for pulsations is key for calculating photon weights and thereby increasing the signal-to-noise ratio. We assembled a spectral analysis pipeline based on the Pointlike analysis package (Kerr 2010), allowing us to derive the spectral parameters of the search targets and to assign good photon weights for the selected data sets. We initially considered LAT data recorded between 2008 August 4 and 2014 April 6 for our survey and included photons recorded until 2015 July 7 after a few tens of sources had been searched (see Section 3.2). We used the Fermi Science Tools²³ to extract Pass 8 Source class events, processed with the P8_SOURCE_V3 instrument response functions (IRFs). The Science Tools, IRFs, and models for the Galactic and extragalactic diffuse gamma-ray emission used here are internal pre-release versions of the Pass 8 data analysis, which were the latest versions available to us when the survey began. The differences in the best-fit parameters are marginal, compared to the analysis with the most recent IRFs. Therefore, the weights as calculated with the old IRFs are also very similar. Specifications of follow-up data analyses are given in Section 4. We used gtselect to select photons with reconstructed directions within 8° of the 3FGL positions, photon energies $\gt 100\,\mathrm{MeV}$, and zenith angles $\lt 100^\circ$. We only included photons detected when the LAT was operating in normal science mode and when the rocking angle of the spacecraft was less than $52^\circ$. Photons were then binned into 30 logarithmically spaced energy bins, with a spatial bin size of 01.

For each 3FGL target, a spectral model for the sources within the corresponding ROIs was constructed by including all 3FGL sources within 13°. Spectral parameters of point sources within 5° were allowed to vary. A binned maximum likelihood analysis was performed to measure the gamma-ray spectra of the targeted sources, which were modeled with exponentially cutoff power laws ("PLEC" spectral shapes) of the form

$$\begin{eqnarray}&&\displaystyle \frac{{dN}}{{dE}}=K{\left(\displaystyle \frac{E}{1\mathrm{GeV}}\right)}^{-{\rm{\Gamma }}}\exp \left(-\displaystyle \frac{E}{{E}_{\mathrm{cut}}}\right),\end{eqnarray} \tag{ 1 }$$

where K is a normalization factor, E_cut is the cutoff energy, and Γ is the photon index. The above expression accurately reproduces the phase-averaged spectral properties of the majority of known gamma-ray pulsars (see, e.g., 2PC). The normalization parameters of the Galactic diffuse emission and the isotropic diffuse background components were left free in the fits. The best-fit source models from the likelihood analysis with Pointlike were used as inputs for gtsrcprob, to determine the probabilities that the selected photons were indeed emitted by our targets.

In order to verify the goodness of the fits and check for possible issues in the likelihood results, we produced source significance TS maps and plots of the spectral energy distribution (SED) for each analyzed source. For some of the sources, the best-fit cutoff energies were suspiciously high and were in particular much higher than those of known gamma-ray pulsars. These sources have spectra with low curvature and could potentially be associated with supernova remnants (SNRs) or pulsar wind nebulae (PWNe), which are known to have harder spectra than pulsars. For some sources a very high cutoff energy close to the upper bound of 1 TeV used for the fit was found, suggesting low spectral curvature. In some cases the best-fit photon index Γ was close to 0. These low photon indices were found for sources with low TS values. We flagged these problematic sources, but we included them in the survey despite the abnormal spectral results since we may still be able to detect pulsations from these sources. We note that SEDs for the latter sources were generally consistent with 3FGL results. In addition, for a small number of 3FGL sources our analysis failed to converge, possibly because of complicated sky regions. Those sources were removed from the target list and will be revisited in the future. As a result, the original target list was trimmed down to 118 sources, which are listed in Table 1.

We eventually obtained data sets consisting of lists of photon arrival times to be searched for pulsations, photon weights, and spacecraft positions calculated at each photon time, which are necessary to correct the arrival times for Doppler shifts caused by the motion of the telescope with respect to the sources. These data sets were then passed to the blind search algorithm, for searching for new pulsars among our target sources.

Table 1.  Ranked Source List

3FGL Name	Searched R.A.	Searched Decl.	Search Radius	VI	${\mathrm{TS}}_{\mathrm{curve}}$	${\mathrm{TS}}_{\mathrm{cut}}$	${E}_{\mathrm{cut}}$	Γ	TS	log RS	Class
	(J2000)	(J2000)	(arcmin)				(GeV)
J1745.3−2903c	17:45:22.32	−29:03:46.80	2.05	48.42	275.2	378.7	2.2	1.4	3407	18.85	⋯
J1746.3−2851c	17:46:22.51	−28:51:45.72	2.12	57.06	113.0	364.7	4.0	1.5	2373	14.31	pwn
J2017.9+3627	20:17:56.33	+36:27:32.76	3.10	39.86	179.3	198.9	1.9	1.4	1876	13.61	⋯
J1839.3−0552†	18:39:23.52	−05:52:53.76	3.07	37.43	83.7	135.1	2.3	1.2	714	13.26	⋯
J1906.6+0720†	19:06:41.14	+07:20:02.04	3.33	41.70	87.9	68.6	7.0	2.0	1580	12.51	⋯
J1910.9+0906†	19:10:58.61	+09:06:01.80	1.55	52.13	53.2	17.4	41.7	2.1	4790	12.31	snr
J1636.2−4734†	16:36:16.49	−47:34:49.08	4.58	54.63	106.0	47.1	7.1	1.9	1180	12.28	snr
J1848.4−0141	18:48:28.39	−01:41:33.72	7.27	52.63	109.0	13.8	9.8	2.5	1457	11.81	⋯
J1405.4−6119†	14:05:25.46	−61:19:00.48	2.83	43.93	61.1	19.7	8.2	2.1	1671	11.39	⋯
J1111.9−6038†	11:11:58.44	−60:38:27.96	1.96	46.69	81.4	58.5	10.4	1.9	3624	11.36	spp
J1748.3−2815c	17:48:22.20	−28:15:32.04	2.73	34.06	77.4	68.6	4.7	1.4	489	11.26	⋯
J1622.9−5004†	16:22:54.31	−50:04:31.08	2.17	54.35	72.4	73.3	8.0	1.6	891	10.21	⋯
J0223.6+6204†	02:23:37.46	+62:04:51.96	3.51	41.77	86.3	182.6	1.8	1.5	1089	9.78	⋯
J1823.2−1339†	18:23:16.90	−13:39:04.68	2.60	47.54	29.7	47.4	9.0	1.9	1004	9.72	⋯
J1745.1−3011	17:45:11.30	−30:11:57.84	6.17	59.68	92.7	88.8	0.6	0.4	459	9.69	spp
J1800.8−2402†	18:00:53.18	−24:02:06.36	3.13	46.65	36.4	21.3	11.3	1.7	575	9.69	⋯
J1749.2−2911	17:49:15.58	−29:11:34.44	7.21	41.77	50.9	43.6	1.6	1.3	265	9.62	⋯
J1306.4−6043†	13:06:27.50	−60:43:54.12	2.48	35.69	65.9	42.6	8.6	1.7	1108	9.59	⋯
J1104.9−6036†	11:04:59.42	−60:36:32.76	4.10	43.09	77.4	64.6	3.6	1.7	769	9.42	⋯
J0634.1+0424	06:34:06.79	+04:24:22.32	9.77	42.87	123.3	60.2	1.8	2.2	1421	9.41	⋯
J1552.8−5330	15:52:50.90	−53:30:47.16	6.98	46.44	56.6	50.3	1.8	1.0	210	9.26	⋯
J1747.0−2828†	17:47:05.98	−28:28:54.84	3.65	90.61	159.7	135.3	2.5	1.8	1676	9.22	⋯
J1650.3−4600	16:50:23.76	−46:00:50.76	3.14	55.06	54.6	55.0	4.8	1.8	897	9.19	⋯
J2323.4+5849	23:23:28.85	+58:49:09.48	1.49	40.07	62.4	39.1	26.4	1.6	2568	9.17	snr
J1625.1−0021†	16:25:07.06	−00:21:30.96	3.38	37.31	104.3	201.4	1.9	0.8	1778	8.98	⋯
J1714.5−3832	17:14:34.27	−38:32:55.68	2.65	68.77	39.3	23.3	14.7	2.2	2649	8.95	snr
J1857.9+0210†	18:57:57.65	+02:10:13.44	5.41	50.62	42.8	50.5	3.2	1.9	601	8.89	⋯
J1056.7−5853	10:56:42.86	−58:53:45.60	7.77	35.71	88.2	126.1	1.1	1.5	596	8.83	⋯
J1026.2−5730	10:26:14.33	−57:30:59.76	4.85	50.42	54.7	58.1	2.3	1.6	493	8.26	⋯
J1742.6−3321	17:42:39.60	−33:21:22.32	6.00	48.24	67.1	24.4	2.5	1.8	411	8.20	⋯
J1844.3−0344†	18:44:23.93	−03:44:48.48	5.09	44.78	37.0	70.9	1.9	0.8	468	8.12	⋯
J1101.9−6053	11:01:55.46	−60:53:45.96	7.49	23.32	40.8	61.3	2.4	1.8	519	7.95	spp
J2038.4+4212	20:38:29.95	+42:12:30.60	5.30	45.67	51.1	95.8	0.5	0.6	340	7.92	⋯
J1849.4−0057	18:49:25.30	−00:57:06.48	3.55	45.11	23.8	16.6	13.5	2.0	674	7.86	snr
J1112.0−6135	11:12:04.03	−61:35:03.12	8.87	55.72	84.6	35.8	1.7	1.7	293	7.84	⋯
J1754.0−2538	17:54:02.02	−25:38:54.96	2.62	66.89	72.4	107.3	4.0	1.0	500	7.73	⋯
J0854.8−4503†	08:54:50.59	−45:03:41.76	4.37	44.94	47.5	54.9	5.0	1.7	737	7.68	⋯
J1857.2+0059	18:57:14.28	+00:59:10.68	3.82	57.14	32.6	113.2	4.5	1.3	383	7.67	⋯
J1740.5−2843	17:40:30.00	−28:43:01.20	5.87	46.42	25.6	24.2	3.6	2.2	700	7.66	⋯
J1744.1−7619†	17:44:10.85	−76:19:42.96	3.12	51.73	112.5	169.2	2.1	1.2	1759	7.61	⋯
J1035.7−6720†	10:35:42.24	−67:20:00.60	3.34	47.01	80.6	120.2	2.3	1.4	1336	7.39	⋯
J1843.7−0322	18:43:42.77	−03:22:37.92	7.67	70.63	65.5	54.5	3.7	2.6	1113	7.37	⋯
J0359.5+5413†	03:59:31.46	+54:13:19.20	3.66	33.63	42.2	84.1	2.6	1.6	800	7.19	⋯
J1624.2−4041†	16:24:14.26	−40:41:11.40	4.02	50.80	58.8	74.2	2.8	1.6	945	7.18	⋯
J1740.5−2726	17:40:32.28	−27:27:00.00	8.30	43.15	39.9	31.1	1.8	2.0	401	7.04	⋯
J1827.3−1446	18:27:20.16	−14:46:01.92	5.54	40.00	18.2	83.5	2.5	1.4	483	6.96	⋯
J2032.5+3921	20:32:29.78	+39:25:20.60	3.69	49.41	46.2	34.1	0.4	0.8	233	6.95	⋯
J1638.6−4654	16:38:40.16	−46:54:06.33	2.24	77.58	48.0	46.8	3.7	1.8	614	6.84	spp
J1925.4+1727	19:24:58.98	+17:24:41.84	7.38	47.33	42.2	22.3	1.2	1.2	157	6.70	⋯
J1857.9+0355	18:58:03.73	+03:55:08.04	3.45	55.58	31.5	29.6	1.6	1.1	146	6.55	⋯
J1208.4−6239†	12:08:26.89	−62:39:26.13	1.56	64.44	39.2	52.0	4.9	1.8	874	6.43	⋯
J1350.4−6224†	13:50:34.69	−62:23:43.53	1.71	58.24	41.3	90.8	2.4	0.7	357	6.41	⋯
J1037.9−5843*	10:38:01.49	−58:44:20.62	4.29	38.88	24.9	163.9	0.4	0.0	391	6.32	⋯
J2112.5−3044†	21:12:32.39	−30:43:58.53	1.39	51.84	69.0	151.0	2.8	1.1	1805	6.25	⋯
J1636.2−4709c	16:36:22.32	−47:09:53.05	4.41	57.44	13.7	4.4	⋯	2.3	541	6.17	spp
J1358.5−6025	13:58:24.20	−60:25:30.56	2.44	53.16	32.8	21.1	5.7	2.2	639	6.15	⋯
J1048.2−5928	10:48:40.66	−59:26:03.43	3.98	65.78	101.1	60.4	1.5	1.4	381	6.11	⋯
J2034.6+4302	20:34:58.42	+43:05:08.99	6.30	41.40	50.7	112.7	0.4	0.3	324	6.11	⋯
J1754.0−2930†	17:54:14.33	−29:32:08.04	3.72	59.67	49.8	38.4	2.2	2.0	498	6.06	⋯
J1214.0−6236†	12:14:10.04	−62:36:16.69	1.98	58.02	20.3	15.7	13.1	2.2	789	6.05	spp
J1652.8−4351	16:52:32.63	−43:56:50.10	6.40	64.55	31.0	62.0	1.3	0.9	184	6.00	⋯
J1317.6−6315	13:17:35.62	−63:17:18.00	2.96	50.53	25.0	37.0	2.7	1.7	347	5.99	⋯
J2039.4+4111	20:39:45.84	+41:09:34.39	3.61	45.39	48.2	98.1	0.3	0.3	249	5.91	⋯
J1852.8+0158*	18:52:27.92	+02:01:37.54	4.17	54.52	12.1	0.2	⋯	2.8	838	5.89	⋯
J0631.6+0644	06:31:49.76	+06:44:46.66	1.93	43.04	26.6	37.2	4.6	1.6	676	5.84	spp
J1840.1−0412*	18:40:06.15	−04:11:35.22	2.95	30.14	15.9	0.0	⋯	2.5	416	5.83	spp
J1928.9+1739	19:29:02.93	+17:34:58.90	9.16	47.86	26.9	12.0	3.6	2.1	235	5.79	⋯
J0225.8+6159	02:26:20.37	+62:00:10.48	3.49	46.69	28.8	29.7	2.2	1.7	473	5.77	⋯
J0002.6+6218†	00:02:48.88	+62:16:54.71	2.25	48.02	58.0	80.3	1.8	1.5	716	5.76	⋯
J1740.5−2642	17:40:41.52	−26:39:52.98	4.29	33.42	23.2	34.1	2.5	1.8	222	5.74	⋯
J1834.5−0841*	18:34:31.66	−08:40:15.75	4.02	57.10	0.5	0.1	⋯	2.2	287	5.72	snr
J2042.4+4209	20:42:39.77	+42:09:19.64	11.48	49.90	27.1	27.4	0.5	1.0	185	5.68	⋯
J1814.0−1757c	18:13:24.52	−17:53:55.97	5.83	56.91	8.8	7.4	⋯	2.3	662	5.59	⋯
J2041.1+4736†	20:41:08.34	+47:35:50.81	2.01	56.28	38.0	15.9	10.3	2.3	967	5.53	⋯
J1047.3−6005	10:47:21.66	−60:05:11.01	6.22	49.04	22.3	16.4	3.0	1.5	115	5.52	⋯
J2039.6−5618	20:39:36.25	−56:17:12.94	1.82	34.60	30.4	60.3	3.9	1.6	1266	5.47	⋯
J1900.8+0337	19:00:37.96	+03:39:10.57	3.94	45.87	44.9	4.7	⋯	2.3	186	5.42	⋯
J0855.4−4818	08:55:18.44	−48:14:13.02	10.69	33.84	53.0	66.4	0.5	0.9	288	5.39	⋯
J1747.7−2904	17:47:51.94	−29:01:49.54	2.95	65.34	10.3	124.7	7.1	2.2	666	5.37	⋯
J0541.1+3553	05:40:47.47	+35:54:40.72	8.53	35.17	37.3	33.0	1.8	1.9	329	5.34	⋯
J1549.1−5347c*	15:48:38.12	−53:44:00.33	5.02	51.64	10.9	0.1	⋯	2.9	1172	5.27	spp
J1039.1−5809	10:38:25.85	−58:08:23.45	13.63	37.46	24.7	23.4	1.7	1.3	107	5.23	⋯
J1831.7−0230	18:31:33.96	−02:31:25.54	5.83	31.11	17.8	2.1	⋯	2.7	421	5.23	⋯
J1702.8−5656†	17:02:45.00	−56:54:39.46	1.88	58.78	46.9	53.1	3.4	2.1	1917	5.19	⋯
J1736.0−2701*	17:36:07.44	−27:03:29.55	6.88	38.45	25.2	23.7	0.3	0.0	80	5.18	⋯
J2023.5+4126*	20:23:24.65	+41:27:31.08	4.35	48.95	78.1	36.7	0.4	0.0	93	5.12	⋯
J1758.8−2346	17:59:09.58	−23:47:19.28	3.69	41.80	11.8	5.4	⋯	1.9	218	5.01	⋯
J2004.4+3338*	20:04:22.03	+33:39:29.46	1.47	50.29	13.5	0.0	⋯	2.4	708	5.01	⋯
J0212.1+5320	02:12:12.29	+53:20:49.61	1.58	51.47	45.9	82.0	3.3	1.5	1442	5.01	⋯
J1901.1+0728	19:01:09.32	+07:30:01.23	3.29	55.34	25.8	10.5	6.6	2.0	134	4.88	⋯
J1503.5−5801	15:03:39.92	−58:00:43.22	3.88	67.48	26.3	18.7	3.7	2.0	359	4.85	⋯
J1850.5−0024	18:50:31.56	−00:24:33.69	4.83	64.27	14.6	2.8	⋯	2.3	216	4.76	⋯
J0933.9−6232†	09:34:00.41	−62:32:57.43	1.77	59.20	88.0	125.9	2.0	0.8	907	4.73	⋯
J1620.0−5101	16:19:48.66	−51:00:57.34	4.03	50.48	9.7	1.0	⋯	2.1	121	4.72	⋯
J1726.6−3530c	17:26:32.27	−35:33:37.61	5.18	60.31	11.9	1.8	⋯	2.6	335	4.67	⋯
J1919.9+1407	19:20:11.19	+14:11:54.53	7.95	67.73	17.6	0.3	⋯	2.7	642	4.66	⋯
J1119.9−2204†	11:19:59.45	−22:04:25.17	1.80	62.62	103.2	156.9	1.7	1.3	1949	4.63	⋯
J0907.0−4802*	09:07:18.05	−47:58:38.32	10.11	40.75	29.3	28.0	0.4	0.2	123	4.58	⋯
J1718.0−3726	17:18:02.10	−37:26:50.06	1.02	41.58	1.5	2.0	⋯	2.1	593	4.55	snr
J1859.6+0102	18:59:39.72	+01:00:15.56	5.43	68.61	18.9	13.1	3.5	1.8	150	4.40	⋯
J2035.0+3634	20:35:02.11	+36:32:12.74	1.88	52.58	39.2	57.5	2.8	0.8	401	4.39	⋯
J1345.1−6224	13:44:43.61	−62:28:30.64	5.12	58.30	12.8	1.3	⋯	2.7	568	4.39	spp
J0744.1−2523	07:44:06.64	−25:25:17.47	1.97	61.34	40.9	55.3	3.2	1.8	666	4.27	⋯
J0426.7+5437	04:26:33.79	+54:35:00.35	3.01	51.83	63.9	59.0	1.7	2.1	1235	4.27	⋯
J1539.2−3324†	15:39:20.23	−33:24:56.62	1.64	57.87	102.9	129.3	2.3	0.4	694	4.22	⋯
J1641.1−4619c*	16:41:00.45	−46:19:46.25	1.87	39.43	0.7	0.2	⋯	2.3	292	4.15	spp
J1528.3−5836	15:28:23.37	−58:38:05.98	1.87	68.72	44.9	41.4	4.0	1.6	452	4.14	⋯
J1857.9+0355	18:58:03.73	+03:55:08.04	3.45	41.47	11.2	32.2	2.2	1.4	131	4.13	⋯
J1855.4+0454	18:55:12.72	+04:55:38.38	4.46	38.60	6.6	4.4	⋯	2.4	193	4.12	⋯
J1650.0−4438c*	16:49:48.42	−44:38:58.44	6.63	58.81	1.0	0.1	⋯	3.1	843	4.02	⋯
J0901.6−4700	09:01:40.90	−46:52:10.77	7.02	55.10	30.0	52.7	1.0	1.2	221	4.02	⋯
J1329.8−6109	13:29:57.92	−61:08:00.95	2.45	55.66	22.5	21.1	4.9	1.6	246	3.91	⋯
J1639.4−5146	16:39:25.17	−51:46:04.03	1.39	58.03	4.2	2.8	⋯	2.3	945	3.85	⋯
J1833.9−0711*	18:34:10.57	−07:11:34.47	3.12	82.07	1.6	0.4	⋯	2.3	482	3.85	spp
J1814.1−1734c	18:14:07.87	−17:36:39.99	2.96	50.07	7.1	5.3	⋯	1.4	83	3.73	⋯
J1139.0−6244	11:39:07.61	−62:46:04.02	2.31	29.45	7.5	16.5	8.6	1.9	278	3.71	⋯
J1626.2−2428c	16:26:25.40	−24:31:36.54	4.74	46.87	15.9	7.8	⋯	2.1	392	3.66	⋯
3FGL J1212.2−6251	12:12:18.06	−62:53:31.51	2.84	53.70	1.4	12.9	45.8	2.4	426	3.45	spp

Note. List of the 118 3FGL sources with log R_S > 0 searched for gamma-ray pulsars using Einstein@Home, ranked by their probability to be pulsars according to the GMM analysis presented in Section 2.2. Sources marked with a † symbol were searched in a previous Einstein@Home & Atlas survey for gamma-ray pulsars. Sources for which suspiciously low or high cutoff energies were measured are marked with asterisks. We highlight in boldface the 3FGL sources in which pulsars were discovered in this survey. The discovery and analysis of PSR J1906+0722 and PSR J1208−6238 are presented in Clark et al. (2015, 2016), while PSR J1035−6720 and PSR J1744−7619 discovered in 3FGL J1035.7−6720 and 3FGL J1744.1−7619 will be presented in a future publication. The second, third, and fourth columns list the searched position and radius. The fifth and sixth columns give the variability index, VI, and curvature TS, ${\mathrm{TS}}_{\mathrm{curve}}$, from a preliminary version of the 3FGL catalog, respectively. The seventh through 10th columns give the TS of the spectral cutoff (${\mathrm{TS}}_{\mathrm{cut}}$), the cutoff energy (${E}_{\mathrm{cut}}$), the photon index (Γ), and the source TS value from our binned maximum likelihood analysis with Pointlike, respectively; cutoff energies are listed for sources with ${\mathrm{TS}}_{\mathrm{cut}}\gt 9$. The 11th column lists the pulsar likelihood value from our GMM analysis. The 12th column lists association flags from the 3FGL catalog: "pwn" and "snr" labels indicate possible associations with PWNe and SNRs respectively; sources with class "spp" are special cases with potential PWN or SNR associations. Sources below the horizontal line were searched with relocalized positions, as mentioned in Section 3.2.

A machine-readable version of the table is available.

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Following the first few discoveries (summarized in Section 3.3), we noticed that the timing positions of a few pulsars (see Paper I for the timing positions of the discovered pulsars) were well outside the 95% confidence regions from the 3FGL catalog. The observed discrepancies could be caused by the fact that 3FGL catalog positions were determined using 4 yr of Pass 7 reprocessed data, while we used 5.5 yr of Pass 8 data, which have higher angular resolution. To mitigate this discrepancy, we relocalized the sources using Pointlike, by varying the sky coordinates of the sources until the maximum likelihood was found. The results of the relocalization analysis for the new pulsars are given in Table 2.

Table 2.  Relocalization Results

PSR	3FGL Source	r95	r95	${{\rm{\Delta }}}_{3\mathrm{FGL}}$	${{\rm{\Delta }}}_{\mathrm{new}}$
		(3FGL)	(new)
J0002+6216	J0002.6+6218	36	20	27	13
J0359+5414	J0359.5+5413	24	18	18	06
J0631+0646	J0631.6+0644	28	18	41	16
J1057−5851	J1056.7−5853	52	25	44	29
J1105−6037	J1104.9−6036	27	15	07	08
J1350−6225	J1350.4−6224	24	16	20	23
J1528−5838	J1528.3−5836	33	17	17	01
J1623−5005	J1622.9−5004	15	10	17	15
J1624−4041	J1624.2−4041	27	16	09	14
J1650−4601	J1650.3−4600	21	13	10	09
J1827−1446	J1827.3−1446	37	16	12	07
J1844−0346	J1844.3−0344	34	16	28	23
J2017+3625	J2017.9+3627	21	12	24	09

Note. Results of the relocalization analysis discussed in Section 3.2. For each of the 13 new pulsars reported in Paper I, the second column lists the name of the 3FGL source in which the pulsar was discovered. The third and fourth columns list the semimajor axis of the 3FGL source error ellipse at 95% confidence (r₉₅) and the semimajor axis value from our analysis, respectively. The r₉₅ (new) values are based on statistical uncertainties only. The fifth and sixth columns list the offset between pulsar timing positions and 3FGL positions (${{\rm{\Delta }}}_{3\mathrm{FGL}}$) and the offset between pulsar timing positions and new positions (${{\rm{\Delta }}}_{\mathrm{new}}$), respectively.

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In most cases, the relocalized positions are closer to the pulsar timing positions than the catalog ones. In addition, the 95% semimajor axes of the relocalized positions are smaller than in 3FGL. Although this implies a smaller number of trials in sky position for the blind search, leading to a greatly reduced overall computational cost, the true pulsar positions may still fall outside of the error ellipses. In some cases, the timing position is found to be out of both the 3FGL error ellipse and the ellipse from our analysis. From the 47th source onward, we therefore adopted the relocalized positions with three times the 1σ Gaussian uncertainty reported by Pointlike to obtain a more conservative sky coverage, and we also extended our data set by including photons recorded until 2015 July 7 when the relocalization was done. The inaccurate source locations might have resulted from the imperfect Galactic background model.

The blind search survey of the sources listed in the Appendix, described in detail in Paper I, enabled the discovery of 17 gamma-ray pulsars. Clark et al. (2015) reported on the discovery of PSR J1906+0722, an energetic pulsar with a spin frequency of 8.9 Hz that suffered one of the largest glitches ever observed for a gamma-ray pulsar. Clark et al. (2016) later presented the discovery of PSR J1208−6238, a 2.3 Hz pulsar with a very high surface magnetic field and a measurable braking index of about 2.6. Paper I and the present paper report on 13 young, isolated gamma-ray pulsars also found in this survey. The new pulsars have rotational periods ranging from ∼79 ms to 620 ms. They are all energetic, with spin-down powers between about 10³⁴ and $4\times {10}^{36}\,\mathrm{erg}$ s⁻¹. Among these, PSR J1057−5851 and PSR J1827−1446 are the slowest rotators among currently known gamma-ray pulsars. PSR J1844−0346 experienced a very large glitch in mid-2012 (see Paper I for details). In the next sections we describe dedicated follow-up studies of these 13 pulsars. Finally, we note that two more pulsars were found in this survey: PSR J1035−6720 and PSR J1744−7619. These two pulsars will be presented in a separate publication (Clark et al. 2017).

After selecting the 13 pulsars, we performed dedicated spectral analyses with extended data sets in order to characterize their spectral properties with extra sensitivity. We used updated Pass 8 (P8R2) event selections and updated IRFs for events recorded from 2008 August 4 until 2015 September 9. The sizes of the ROIs around each pulsar were extended to 15° to collect more gamma-ray photons for the follow-up analysis, and we selected photon energies >100 MeV and zenith angles <90°. The more restrictive zenith angle cut was used to better reject events from the Earth's limb in support of spectral analysis down to 100 MeV. In our dedicated spectral analyses we used the gll_iem_v06.fits²⁴ map cube and iso_P8R2_SOURCE_V6_v06.txt²⁵ template for modeling the Galactic diffuse emission and the isotropic diffuse background, to match with the current recommendations (Acero et al. 2016a). The numbers of point sources in the models were increased to include all 3FGL sources within 20°. The details of the timing analysis using these extended data sets, including the determination of timing and positional parameters, are presented in Paper I. For the spectral analysis of the 13 pulsars we used the positions obtained from pulsar timing. In order to further minimize contamination from the diffuse background or from neighboring sources, we restricted our data sets to the pulsed part of the pulse profiles. To determine the "on"- and "off"-pulse phase regions of the pulse profiles, we selected gamma-ray photons with weights above 0.05 and constructed unweighted pulse profiles, which we then analyzed with the Bayesian block decomposition method described by Scargle et al. (2013). Bayesian blocks represent a model of time series of events generated by an inhomogeneous Poisson process, involving a sequence of constant flux levels. This method is useful for discriminating random flux changes from real ones, but it is not a physical representation of the pulse profiles. The on- and off-pulse regions are shown in Figure 1. We selected photons in the on-pulse regions and performed spectral analyses of these restricted data sets. We determined the significance of the spectral cutoff (TS_cut) by comparing the change in log-likelihood when using a simple power-law model for the spectra of the pulsars instead of assuming the PLEC model, as follows: ${\mathrm{TS}}_{\mathrm{cut}}=-2\mathrm{log}{\rm{\Delta }}{ \mathcal L }$. The results of the spectral analysis of the on-pulse data are given in Table 3; the corresponding SEDs are displayed in Figure 2, and the best-fit cutoff energy and power-law index values are shown in Figure 3, along with those of 2PC pulsars.

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To search for unpulsed magnetospheric pulsar emission or emission from a putative PWN associated with the pulsar, we conducted analyses of the off-pulse phases of the data sets. Point-like test sources were added to the spectral models at the locations of the pulsars, and the spectral properties of these sources were determined by running new likelihood analyses. We alternatively assumed a simple power-law model and a PLEC model for the test sources, in order to test for spectral curvature. Significant off-pulse emission was detected for PSR J1623−5005, PSR J1624−4041, and PSR J2017+3625, with evidence for spectral curvature suggestive of magnetospheric emission from the pulsars, as can be seen from Table 4. Such off-pulse pulsar emission is not atypical for known gamma-ray pulsars (see, e.g., 2PC); nevertheless, small, unmodeled spatial fluctuations in the bright diffuse background emission could also account for this emission. Detailed analyses with extended data sets and comparisons of the best-fit spectral parameters with those of other known gamma-ray pulsars with off-pulse emission are necessary to firmly establish PSR J1623−5005, PSR J1624−4041, and PSR J2017+3625 as pulsars exhibiting gamma-ray emission at all phases. The on-pulse emission was then refitted with the addition of sources detected in the off-pulse region scaled to the on-pulse interval with the normalization and spectral parameters fixed.

Table 3.  On-pulse Spectral Parameters

PSR	TS	TScut	Γ	Ecut	Photon Flux, F100	Energy Flux, G100
				(GeV)	(${10}^{-8}\ \mathrm{ph}\,{\mathrm{cm}}^{-2}\,{{\rm{s}}}^{-1}$)	(${10}^{-11}\,\mathrm{erg}\,{\mathrm{cm}}^{-2}\,{{\rm{s}}}^{-1}$)
J0002+6216	975	145	1.04 ± 0.16 ± 0.14	1.39 ± 0.21 ± 0.07	2.8 ± 0.3 ± 0.8	2.6 ± 0.2 ± 0.4
J0359+5414	1610	93	1.80 ± 0.07 ± 0.10	3.72 ± 0.61 ± 0.26	8.4 ± 0.6 ± 2.0	5.6 ± 0.2 ± 0.8
J0631+0646	881	81	1.30 ± 0.17 ± 0.12	3.93 ± 0.84 ± 0.33	2.9 ± 0.6 ± 0.6	3.7 ± 0.3 ± 0.3
J1057−5851	813	123	1.39 ± 0.16 ± 0.05	1.13 ± 0.19 ± 0.09	7.9 ± 0.9 ± 0.8	5.0 ± 0.3 ± 0.5
J1105−6037	1084	94	1.66 ± 0.11 ± 0.04	3.49 ± 0.60 ± 0.26	8.3 ± 1.2 ± 0.4	6.4 ± 0.5 ± 0.4
J1350−6225	704	85	1.21 ± 0.16 ± 0.44	3.80 ± 0.70 ± 1.13	4.2 ± 0.8 ± 4.1	6.0 ± 0.4 ± 2.1
J1528−5838	593	87	0.97 ± 0.07 ± 0.36	2.27 ± 0.12 ± 0.43	2.2 ± 0.5 ± 1.3	3.0 ± 0.3 ± 0.7
J1623−5005	854	106	1.33 ± 0.01 ± 0.29	7.17 ± 0.17 ± 1.48	4.7 ± 0.1 ± 3.3	8.1 ± 0.2 ± 2.0
J1624−4041	255	31	1.50 ± 0.21 ± 0.38	3.59 ± 1.07 ± 0.85	1.6 ± 0.8 ± 0.9	1.6 ± 0.5 ± 0.5
J1650−4601	1368	83	1.70 ± 0.10 ± 0.07	4.04 ± 0.71 ± 0.59	15.9 ± 1.4 ± 4.6	12.3 ± 0.6 ± 2.3
J1827−1446	818	134	0.47 ± 0.28 ± 0.32	1.36 ± 0.22 ± 0.15	3.7 ± 0.7 ± 1.0	5.8 ± 0.5 ± 0.6
J1844−0346	840	75	1.21 ± 0.22 ± 0.23	2.59 ± 0.53 ± 0.41	8.3 ± 1.9 ± 2.6	9.5 ± 0.9 ± 1.5
J2017+3625	1148	216	0.78 ± 0.15 ± 0.22	1.61 ± 0.18 ± 0.18	4.7 ± 1.3 ± 1.3	6.2 ± 1.1 ± 1.2

Note. Binned maximum likelihood spectral fit results for the 13 Einstein@Home gamma-ray pulsars. For each pulsar, the second and third columns list the TS of the source and the cutoff TS for the exponentially cutoff model over a simple power-law model, respectively. The fourth and fifth columns list the best-fit photon index Γ and cutoff energy ${E}_{\mathrm{cut}}$, respectively. The next two columns give the on-pulse phase-averaged integral photon and energy fluxes in the 0.1–100 GeV band, F₁₀₀ and G₁₀₀, scaled to full interval values. The first reported uncertainties are statistical, while the second uncertainties are systematic, determined by reanalyzing the data with bracketing IRFs and artificially changing the normalization of the Galactic diffuse model by ±6%, as described in Acero et al. (2016b).

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We characterized the pulse profiles displayed in Figure 5 of Paper I by fitting the weighted profiles to Gaussian or Lorentzian profiles, depending on which gave a higher log likelihood. The derived peak multiplicities and gamma-ray peak separations are reported in Table 5. Most of the new pulsars show double-peaked profiles, with well-separated components that are typical of young gamma-ray pulsar light curves (see 2PC). Two of the 13 newly discovered pulsars, PSR J0002+6216 and PSR J0631+1036, are detected in the radio band (see Section 4.2). For these pulsars we measured the phase offset between the radio peak and the first gamma-ray peak.

Table 4.  Off-pulse Spectral Parameters

PSR	TS	${\mathrm{TS}}_{\mathrm{cut}}$	Γ	${E}_{\mathrm{cut}}$
				(GeV)
J1623−5005	57	18	⋯a	0.87 ± 0.07 ± 0.21
J1624−4041	47	10	1.02 ± 0.95 ± 0.96	1.33 ± 1.23 ± 0.41
J2017+3625	215	88	0.69 ± 0.06 ± 0.06	0.59 ± 0.01 ± 0.06

Note. Results of the maximum likelihood analysis of the off-pulse phase ranges of pulsars with significant off-pulse emission, as discussed in Section 4.1. The first column lists the name of the pulsar. The remaining columns list the TS of the source in the off-pulse phase range, the test statistic ${\mathrm{TS}}_{\mathrm{cut}}$ of an exponentially cutoff model over a simple power-law model, the photon index Γ, and the energy cutoff E_cut.

^aAlthough the spectral index is consistent with zero, the well-defined E_cut allows integration to a finite total flux.

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The new pulsars were searched for radio pulsations by reanalyzing archival observations from previous targeted radio surveys of Fermi LAT unassociated sources, or by conducting new dedicated observations. Because we have timing parameters for the new pulsars, the only parameter to search for when analyzing the radio observations is the dispersion measure (DM), a quantity representing the integrated column density of free electrons along the line of sight to the pulsars, causing radio waves to arrive at different times depending on the frequency. Radio observations were therefore folded at the periods determined from the gamma-ray timing (see Paper I) and searched in DM values only, resulting in a reduced number of trials compared to a typical radio pulsar search.

The list of telescopes and backends used is given in Table 6. For each observing configuration we give the gain G, the central frequency, the frequency bandwidth ${\rm{\Delta }}F$, the sensitivity degradation factor β, the number of polarizations n_p, the half-width at half-maximum of the radio beam (HWHM), and the receiver temperature T_rec. Table 7 lists the radio observations processed in our follow-up study. Sensitivities were calculated using the modified radiometer equation given in Lorimer & Kramer (2005):

$$\begin{eqnarray}&&{S}_{\min }=\beta \displaystyle \frac{5{T}_{\mathrm{sys}}}{G\sqrt{{n}_{p}{t}_{\mathrm{int}}{\rm{\Delta }}F}}\sqrt{\displaystyle \frac{W}{P-W}},\end{eqnarray} \tag{ 2 }$$

where a value of 5 is assumed for the threshold signal-to-noise ratio for a detection, ${T}_{\mathrm{sys}}={T}_{\mathrm{rec}}+{T}_{\mathrm{sky}}$, t_int is the integration time, P is the rotational period, and W is the pulse width, assumed to be $0.1\times P$. The quantity T_sky is the temperature from the Galactic synchrotron component, estimated by scaling the 408 MHz map of Haslam et al. (1982) to the observing frequency, assuming a spectral index of −2.6. For some observations the pointing direction was offset from the actual sky location of the pulsar. In those cases the flux density limit S_min as calculated using Equation (2) was divided by ${e}^{-{(\theta /\mathrm{HWHM})}^{2}/1.5}$, where θ is the offset. For the majority of pulsars we failed to detect pulsations in the radio data and placed limits on their radio flux densities.

Table 5.  Pulse Shape Parameters and Derived Pulsar Parameters

PSR	Peaks	δ	Δ	Off-pulse Phase Range	$\dot{E}$	DM Distance	Heuristic Distance, dh
					$({10}^{33}\,\mathrm{erg}\,{{\rm{s}}}^{-1})$	(kpc)	(kpc)
J0002+6216	2	0.171 ± 0.011	0.361 ± 0.012	0.59–1.00	153	7.7, 6.3	2.0
J0359+5414	1	⋯	⋯	0.00–0.58	1318	⋯	2.3
J0631+0646	2	0.469 ± 0.013	0.278 ± 0.013	0.83–0.31	104	>42.2, 4.6	1.5
J1057−5851	1	⋯	⋯	0.75–0.24	17	⋯	0.8
J1105−6037	2	⋯	0.317 ± 0.006	0.90–0.38	116	⋯	1.2
J1350−6225	2	⋯	0.485 ± 0.002	0.92–0.24, 0.52–0.77	133	⋯	1.3
J1528−5838	2	⋯	0.243 ± 0.022	0.48–1.00	22	⋯	1.1
J1623−5005	2	⋯	0.352 ± 0.005	0.99–0.45	267	⋯	1.3
J1624−4041	2	⋯	0.429 ± 0.003	0.44–0.70	39	⋯	1.8
J1650−4601	2	⋯	0.331 ± 0.005	0.48–1.00	291	⋯	1.1
J1827−1446	2	⋯	0.256 ± 0.008	0.82–0.32	14	⋯	0.7
J1844−0346	1	⋯	⋯	0.31–0.92	4249	⋯	2.4
J2017+3625	2	⋯	0.374 ± 0.004	0.02–0.42, 0.58–0.68	12	⋯	0.7

Note. The second, third, fourth, and fifth columns list the gamma-ray peak multiplicity, radio to gamma-ray phase lag (δ), gamma-ray peak separation (Δ) for pulse profiles with two components, and definition of the off-pulse phase interval, respectively, for each pulsar considered in our study. Uncertainties on δ and Δ are statistical only. The sixth column gives the spin-down power for each pulsar. The seventh column lists the DM distances for the radio-detected pulsars PSR J0002+6216 and PSR J0631+1036 as inferred with the NE2001 model of Cordes & Lazio (2002) and the model of Yao et al. (2017). The last column lists the heuristic distance, described in Section 4.4.

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Table 6.  Definition of Radio Observation Codes

Obs. Code	Telescope	Gain	Frequency	Bandwidth ${\rm{\Delta }}F$	β	np	HWHM	Trec
		(K Jy−1)	(MHz)	(MHz)			(arcmin)	(K)
AO-327	Arecibo	11	327	68	1.12	2	6.3	116
AO-ALFA	Arecibo	10	1400	100	1.12	2	1.5	30
AO-Lwide	Arecibo	10	1510	300	1.12	2	1.5	27
Eff-7B	Effelsberg	1.5	1400	240	1.05	2	9.1	22
Eff-L1	Effelsberg	1.5	1400	240	1.05	2	9.1	22
GBT-820	GBT	2.0	820	200	1.05	2	7.9	29
GBT-S	GBT	1.9	2000	700	1.05	2	3.1	22
GMRT-322	GMRT	1.6	322	32	1	2	40	106
GMRT-610	GMRT	1.6	607	32	1	2	20	102
Nancay-L	Nancay	1.4	1398	128	1.05	2	2 × 11	35
Parkes-AFB	Parkes	0.735	1374	288	1.25	2	7	25
Parkes-BPSR	Parkes	0.735	1352	340	1.05	2	7	25
Parkes-DFB4	Parkes	0.735	1369	256	1.1	2	7	25

Note. Radio telescopes and backend parameters used for follow-up observations of the new pulsars, described in Section 4.2.

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For two pulsars, PSR J0002+6216 and PSR J0631+0646, the analysis resulted in the detection of significant radio pulsations. PSR J0002+6216 was detected in a 2 hr observation conducted at 1.4 GHz with the Effelsberg radio telescope, with a DM of 218.6(6) pc cm⁻³. PSR J0631+0636 was detected with Arecibo at 327 MHz and at 1.4 GHz in ∼70-minute observations and was also seen with Effelsberg at 1.4 GHz during a 2 hr follow-up observation. The best determined DM value from the Arecibo 327 MHz observation was 195.2(2) pc cm⁻³. Phase-aligned radio and gamma-ray pulse profiles for PSR J0002+6216 and PSR J0631+0646 are displayed in Figure 4. In both cases the gamma-ray emission is seen to lag the weak radio emission, as commonly observed in other radio and gamma-ray pulsars, and suggesting that radio and gamma-ray emissions have different magnetospheric origins (see, e.g., 2PC).

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Using photons selected within 5° radius around the pulsars, we constructed weighted counts pulse profiles with 90, 60, or 30 bins if the weighted H-test TS, the statistical test for pulsation significance (de Jager et al. 1989), for a given pulsar was ≥1000, between 100 and 1000, or <100, respectively. For PSR J0002+6216 and PSR J0631+0646 with radio detections, we rebinned the radio pulse profiles to have the same number of bins as the corresponding gamma-ray profile. We performed likelihood fits, minimizing $-\mathrm{ln}{ \mathcal L }$, where ${ \mathcal L }$ is the likelihood value, of the gamma-ray pulse profile or the combination of the radio and gamma-ray pulse profiles, of all 13 pulsars using the geometric simulations and fitting technique of Johnson et al. (2014).

Following Clark et al. (2016), we used simulations with P = 100 ms and $\dot{P}={10}^{-15}\,{\rm{s}}$ s⁻¹ and constructed likelihood values using a ${\chi }^{2}$ statistic. Each pulsar was fit using the outer gap (OG, e.g., Cheng et al. 1986) and the slot gap (e.g., Muslimov & Harding 2003, 2004) models, where we used the two-pole caustic model (TPC; Dyks & Rudak 2003) as a geometric representation of the slot gap. For both models we use the vacuum retarded dipole solution for the magnetic field geometry (Deutsch 1955). The simulations were produced with 1° resolution in both the magnetic inclination angle (α) and observer angle (ζ) and a resolution of 1% of the polar cap opening angle in emitting and accelerating gap widths. For radio simulations, we assumed a frequency of 1400 MHz with the conal geometry and emission altitude of Story et al. (2007).

The best-fit results for all but PSR J0631+0646 are given in Table 8; estimated uncertainties are quoted at the 95% confidence level, but note that systematic error estimates from the fitting method (see Johnson et al. 2014) and/or from fitting only the gamma-ray profiles (Pierbattista et al. 2015) could be as large as 10°. Johnson et al. (2014) noted that it was necessary to renormalize the ${\rm{\Delta }}\mathrm{ln}{ \mathcal L }$ surface, making the best fit approximately correspond to a reduced ${\chi }^{2}$ value of 1, in order to have more realistic confidence contours. In some cases, however, we found that this renormalization was unnecessary, either having no effect on the estimated uncertainties or shrinking them. We denote the pulsars for which we did not renormalize the likelihood surface with a † in the first column of Table 8. For each model, we also estimated the beaming fraction ${f}_{{\rm{\Omega }}}$ (as defined, e.g., in Watters et al. 2009; Venter et al. 2009) for the best-fit geometry, used when calculating the gamma-ray luminosity.

For each pulsar with no radio detection, we examined the simulated radio sky map at 1400 MHz, and evaluated the model predictions for the best-fit geometry, in regard to expected radio-loudness; the predictions are indicated in the sixth and 11th columns of Table 8. The model predictions are "L" for radio-loud, meaning that the predicted geometry has the radio cone clearly and strongly intersecting our line of sight; "F" for radio-faint, meaning the predicted geometry has our line of sight either narrowly missing the cone or clipping the very edge, suggesting that only weak emission would be detected; and "Q" for radio-quiet, meaning that the predicted geometry has our line of sight clearly missing the radio cone. The radio-faint sources are of particular interest, as searches at frequencies lower than 1400 MHz, where the cone is predicted to be larger (e.g., Story et al. 2007), may yield detections. Following Johnson et al. (2014), we conservatively consider one model to be significantly favored over another, for a given pulsar, if the $\mathrm{ln}{ \mathcal L }$ value is greater by at least 15; however, in some cases the best-fit geometry for the TPC model clearly predicts a radio-loud pulsar where none has been detected, and we therefore claim that the OG model is favored, regardless of the ${\rm{\Delta }}\mathrm{ln}{ \mathcal L }$ value. In particular, this is the case for PSR J0359+5414, PSR J1528−5838, and PSR J1827−1446. For PSR J1350−6225, both the TPC and OG models predict a radio-loud pulsar, with a near-orthogonal rotator viewed near the spin equator, either casting doubts on the models or raising questions concerning the nondetection. In modeling the "radio-quiet" pulsars in 2PC, Pierbattista et al. (2015) similarly found some solutions where the line of sight was near enough to the magnetic axis that we might expect to intersect the radio emission cone. These authors used a different fitting technique but similar simulations. This may further suggest that our results regarding the aforementioned pulsars point to issues with the models and not with the nondections in radio.

Our joint gamma-ray and radio fits of PSR J0631+0646 did not produce acceptable results: the standard approach tended to ignore the radio data. Following Johnson et al. (2014), we decreased the radio uncertainty value in order to increase its importance in the likelihood, but this proved ineffective, leading to fits that ignored the gamma-ray data. Under the assumption that the difficulty was in matching the observed phase lag between the radio peak and the gamma-ray peaks, we followed Guillemot et al. (2013) in allowing the phase of the magnetic pole in the radio and gamma-ray simulations to be different by as much as 0.1 (following realistic simulations of the pulsar magnetosphere by Kalapotharakos et al. (2012), which suggested an offset of the low-altitude polar gap from the outer magnetosphere by up to this amount). These new fits were, similarly, unsatisfactory. We investigated relaxing the maximum phase offset condition and found more acceptable fits with offsets of ∼0.3 in phase for both the TPC and OG models. The maximum phase offset of 0.1 is inferred from Kalapotharakos et al. (2012) by comparing predicted light curves from the vacuum retarded dipole geometry to models with increasing conductivity and finally full force-free models. It seems implausible that this offset could be a factor of 3 larger than predicted in the force-free simulations. With our different attempts to model the radio and gamma-ray profiles jointly being unsuccessful, we do not report modeling results for PSR J0631+0646 in Table 8. New approaches for modeling this pulsar's emission geometry are needed. For instance, based on the work of Kalapotharakos et al. (2014), it is possible that gamma-ray emission from the current sheet outside the light cylinder could explain the extra phase lag for PSR J0631+0646, as their simulations did tend to show larger radio to gamma-ray phase lags.

The fraction of their energy budgets that pulsars convert into gamma-ray radiation is a key question for understanding pulsar emission mechanisms. This requires converting the measured energy flux in gamma rays G₁₀₀ (see Table 3 for the values) into the gamma-ray luminosity, with the relation ${L}_{\gamma }\,=4\pi {f}_{{\rm{\Omega }}}{G}_{100}{d}^{2}$, where d is the distance. As discussed in Section 4.2, most of the 13 Einstein@Home pulsars considered in this study are undetected in radio. For these pulsars we therefore cannot use the DM to infer distances, e.g., using the NE2001 model of free electrons in the Galaxy (Cordes & Lazio 2002). We can, however, calculate "heuristic" distances, d_h, and luminosities, ${L}_{\gamma }^{h}$, as follows:

$$\begin{eqnarray}&&{d}_{h}=\sqrt{{L}_{\gamma }^{h}/4\pi {G}_{100}},\end{eqnarray} \tag{ 3 }$$

where

$$\begin{eqnarray}&&{L}_{\gamma }^{h}=\sqrt{\dot{E}/{10}^{33}\mathrm{erg}\,{{\rm{s}}}^{-1}}\times {10}^{33}\,\mathrm{erg}\,{{\rm{s}}}^{-1},\end{eqnarray} \tag{ 4 }$$

i.e., assuming that the gamma-ray luminosity scales as $\sqrt{\dot{E}}$ for these young pulsars (see 2PC) and assuming a typical geometrical factor f_Ω of 1. Heuristic distances for the 13 pulsars are given in Table 5. In most cases the values suggest that the pulsars lie at small or intermediate distances, as is also the case for the majority of known gamma-ray pulsars.

From the radio detections of PSR J0002+6216 and PSR J0631+0646 we could determine DM values and use the NE2001 model to extract the DM distances given in Table 5. For both pulsars the NE2001 distance is very large. The distance for PSR J0002+6216 of 7.7 kpc leads to a gamma-ray efficiency $\eta ={L}_{\gamma }/\dot{E}$ of about 120%. For PSR J0631+0646 a conversion efficiency of 100% is found for a distance of about 6.7 kpc. The NE2001 model therefore probably underestimates the density of free electrons along the lines of sight to these pulsars. Interestingly, the recently published model for the distribution of free electrons in the Galaxy of Yao et al. (2017) finds DM distances of 6.3 and 4.6 kpc for PSR J0002+6216 and PSR J0631+0646, respectively. The latter distance values lead to realistic efficiency estimates below 100% (81% and 90%, respectively).

We reanalyzed archival X-ray observations to search for counterparts to the new gamma-ray pulsars and to characterize their X-ray spectra. All our targets except PSR J1827−1446 have adequate coverage by at least one of the major contemporary observatories operating in the soft X-ray band: Swift (Burrows et al. 2005), XMM-Newton (Strüder et al. 2001; Turner et al. 2001), and Chandra (Garmire et al. 2003). The X-ray coverage ranges from few-kilosecond shallow snapshots with Swift to orbit-long, deep observations by Chandra and XMM-Newton. Almost all the detected pulsars have been observed by Swift as part of a systematic survey of the gamma-ray error boxes of the unidentified Fermi LAT sources (Stroh & Falcone 2013).

We reduced and analyzed the XMM-Newton data through the most recent release of the XMM-Newton Science Analysis Software (SAS) v15.0. We performed a standard data processing, using the epproc and emproc tools, and screening for high particle background time intervals following Salvetti et al. (2015). For the Chandra data analysis we used the Chandra Interactive Analysis of Observations (CIAO) software version 4.8. We recalibrated event data by using the chandra_repro tool. Swift data were processed and filtered with standard procedures and quality cuts²⁶ using FTOOLS tasks in the HEASOFT software package v6.19 and the calibration files in the latest Calibration Database release.

We performed a standard data analysis and source detection in the 0.3−10 keV energy range of the XMM-Newton-EPIC, Chandra-ACIS, and Swift-XRT observations (e.g., Marelli et al. 2015; Salvetti et al. 2015). We preferred the XMM and Chandra observatories if the same field has been observed because of the better performance in terms of effective area and spatial resolution. For each of the X-ray counterparts we performed a spectral analysis using XSPEC v12.9. After extracting response matrices and effective area files, we extracted X-ray fluxes by fitting the spectra with a power-law (PL) model using either a ${\chi }^{2}$ or the C-statistic (Cash 1979) in the case of low counts (<100 photons) and negligible background. For sources characterized by low statistics (typically $\leqslant 30\,\mathrm{photons}$), we fixed the column density to the value of the Galactic ${N}_{{\rm{H}}}$ integrated along the line of sight (Dickey & Lockman 1990) and scaled for the heuristic distance, and, if necessary, we set the X-ray PL photon index (${{\rm{\Gamma }}}_{{\rm{X}}}$) to 2. All quoted uncertainties on the spectral parameters are reported at the 1σ confidence level. For each pulsar we computed the corresponding gamma-ray-to-X-ray flux ratio. As reported in Marelli et al. (2015), this could give important information on the nature of the detected pulsar. Finally, for all undetected ones, we computed the 3σ X-ray detection limit based on the measured signal-to-noise ratio, assuming a PL spectrum with ${{\rm{\Gamma }}}_{{\rm{X}}}=2$ and the integrated Galactic ${N}_{{\rm{H}}}$, scaled for the heuristic distance. The detailed results of these analyses are reported in Table 9.

Table 8.  Light-curve Modeling Results

PSR	TPC $-\mathrm{ln}{ \mathcal L }$	TPC α	TPC ζ	TPC ${f}_{{\rm{\Omega }}}$	TPC Radio Flag	OG $-\mathrm{ln}{ \mathcal L }$	OG α	OG ζ	OG ${f}_{{\rm{\Omega }}}$	OG Radio Flag
		(deg)	(deg)				(deg)	(deg)
J0002+6216	110.26	${64}_{-2}^{+3}$	54 ± 2	1.05 ± 0.04	⋯	105.70	${69}_{-1}^{+8}$	${58}_{-1}^{+25}$	${1.08}_{-0.27}^{+0.05}$	⋯
J0359+5414†	39.88	1 ± 1	2 ± 1	${19.62}_{-8.52}^{+0.01}$	L	38.04	${80}_{-6}^{+8}$	24 ± 4	$1,{01}_{-0.41}^{+0.09}$	Q
J1057−5851†	32.62	${57}_{-3}^{+2}$	${40}_{-2}^{+7}$	${0.95}_{-0.18}^{+0.05}$	F	42.94	${65}^{+2}+-1$	${28}_{-2}^{+1}$	${0.76}_{-0.03}^{+0.10}$	Q
J1105−6037	46.11	${61}_{-27}^{+4}$	${49}_{-7}^{+21}$	${0.98}_{-0.31}^{+0.05}$	F	67.40	${8}_{-2}^{+5}$	${71}_{-1}^{+4}$	${0.99}_{-0.09}^{+0.01}$	Q
J1350−6225	79.42	${82}_{-4}^{+2}$	${85}_{-2}^{+1}$	0.82 ± 0.10	L	48.16	90 ± 9	${88}_{4}^{+1}$	0.70 ± 0.03	L
J1528−5838†	29.71	2 ± 1	2 ± 1	${3.77}_{-0.28}^{+0.01}$	L	27.21	${9}_{-6}^{+9}$	${74}_{-3}^{+6}$	${0.95}_{-0.09}^{+0.04}$	Q
J1623−5005	31.28	${32}_{-1}^{+2}$	68 ± 1	${0.62}_{-0.01}^{+0.02}$	Q	58.83	${9}_{-1}^{+12}$	${72}_{-1}^{+3}$	${0.21}_{-0.01}^{+0.19}$	Q
J1624−4041	86.57	${71}_{-5}^{+2}$	${58}_{-5}^{+1}$	1.13 ± 0.03	F	72.90	86 ± 1	68 ± 1	${1.02}_{-0.01}^{+0.02}$	F
J1650−4601	46.30	${13}_{-7}^{+2}$	69 ± 1	${0.47}_{-0.09}^{+0.01}$	Q	54.13	${11}_{-4}^{+2}$	${74}_{-3}^{+6}$	${0.21}_{-0.16}^{+0.19}$	Q
J1827−1446†	52.65	1 ± 1	2 ± 1	${69.16}_{-5.67}^{+0.01}$	L	45.04	${75}_{-11}^{+1}$	${26}_{-1}^{+5}$	${1.34}_{-0.71}^{+0.01}$	Q
J1844−0346†	23.06	10 ± 1	68 ± 1	0.49 ± 0.07	Q	22.08	${79}_{-4}^{+6}$	${22}_{-3}^{+1}$	${0.99}_{-0.39}^{+0.31}$	Q
J2017+3625	168.10	23 ± 5	69 ± 1	${0.52}_{-0.01}^{+0.16}$	Q	127.47	${16}_{-5}^{+12}$	${80}_{-5}^{+1}$	${0.23}_{-0.04}^{+0.10}$	Q

Note. Light-curve fitting results for all pulsars except PSR J0631+0646. The first column gives the pulsar name; a † indicates that the ${\rm{\Delta }}\mathrm{ln}{ \mathcal L }$ surface was not renormalized. The second (seventh) column gives the best-fit $-\mathrm{ln}{ \mathcal L }$ value for the TPC (OG) model. The third, fourth, and fifth (eight, ninth, and 10th) columns give the best-fit α and ζ with corresponding ${f}_{{\rm{\Omega }}}$ for the TPC (OG) model. For pulsars without a radio detection, the sixth (11th) column gives a radio-loudness prediction from the best-fit geometry for the TPC (OG) model: L = radio-loud, F = radio-faint, and Q = radio-quiet; see the text for details.

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Out of the 13 gamma-ray pulsars, we detected a significant X-ray counterpart for six. PSR J0002+6216, PSR J1105−6037, and PSR J1844−0344 were detected with Swift-XRT. These sources are listed in the First Swift-XRT Point Source (1SXPS) Catalog (Evans et al. 2014) as 1SXPS J000257.6+621609, 1SXPS J110500.3−603713, and 1SXPS J184432.9−034626, respectively. These sources are located at (α, δ) (J2000) = (07404, +622692), (1662515, −606203), and (2811371, −37740) with 90% confidence error circles of $4\buildrel{\prime\prime}\over{.} 9$, $6\buildrel{\prime\prime}\over{.} 4$, and $2\buildrel{\prime\prime}\over{.} 7$. Owing to the long Chandra exposure time, we clearly detected both the pulsar and the associated nebula of PSR J0359+5414. The pulsar is located at (α, δ) = (598586, +542486) with a 90% confidence error circle of $1^{\prime\prime}$. The nebula is approximately elliptical, with semimajor and semiminor axes of $\sim 15^{\prime\prime}$ and $\sim 7^{\prime\prime}$, respectively, roughly centered on the pulsar position. The nebula is well fitted by an absorbed PL model with photon index equal to 1.4 ± 0.2 and unabsorbed flux in the 0.3−10 keV energy band of (1.3 ± 0.3) × 10⁻¹⁴ erg cm⁻² s⁻¹. We also detected the counterpart for PSR J2017+3625 at (α, δ) = (3044827, 364189), with a $2^{\prime\prime}$ error, from analysis of a Chandra observation. From XMM-Newton data we detected two possible counterparts for PSR J1624−4041 at $\sim 13^{\prime\prime}$ from the gamma-ray pulsar position. The two plausible X-ray counterparts are located at (α, δ) = (2460372, −406931) and (2460459, −406899), both with a $0\buildrel{\prime\prime}\over{.} 8$ statistical plus $1\buildrel{\prime\prime}\over{.} 5$ systematic error. We report both counterparts in Table 9, as src1 and src2, respectively.