THE SECOND FERMI LARGE AREA TELESCOPE CATALOG OF GAMMA-RAY PULSARS

The first gamma-ray pulsar discovery method, described above, found 61 of the gamma-ray pulsars in this catalog. It uses known rotational ephemerides from radio or X-ray observatories. The 2286 known RPPs (mostly from the ATNF Pulsar Catalog⁹⁴ Manchester et al. 2005; see Table 1) are all candidate gamma-ray pulsars. Nearly all of these were discovered in radio searches, with a handful coming from X-ray observations. Phase-folding with a radio or X-ray ephemeris is the most sensitive way to find gamma-ray pulsations, since no penalties are incurred for trials in position, $P, \dot{P}$, or other search parameters. Having a current ephemeris for as many known pulsars as possible is of critical importance to LAT science and is the key goal of the Pulsar Timing Consortium (Smith et al. 2008). EGRET results (Thompson 2008) as well as theoretical expectations indicated that young pulsars with large spindown power,⁹⁵$\dot{E} > 1\times 10^{34}$ erg s⁻¹, are the most likely gamma-ray pulsar candidates. Because of their intrinsic instabilities, such as timing noise and glitches, these pulsars are also the most resource intensive to maintain ephemerides of sufficient accuracy. To allow for unexpected discoveries, the Timing Consortium also provides ephemerides for essentially all known pulsars that are regularly timed, spanning the $P\dot{P}$ space of known pulsars (Figure 1). In addition to $\dot{E}$, the $P\dot{P}$ diagram shows two other physical parameters derived from the timing information: the magnetic field at the neutron star surface, $B_{\rm S} = (1.5 I_{0} c^{3} P \dot{P})^{1/2}/2\pi R_{\rm NS}^{3}$, assuming an orthogonal rotator with neutron star radius R_NS = 10 km and the speed of light in a vacuum, c; and the characteristic age $\tau _c = P/2\dot{P}$, assuming magnetic dipole braking as the only energy-loss mechanism and an initial spin period much less than the current period. The black dots in Figure 1 show 710 pulsars that we have phase-folded without detecting gamma pulsations, in addition to the 117 gamma-ray pulsars. The locations of all 117 gamma-ray pulsars on the sky are shown in Figure 2.

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Table 1. Pulsar Varieties

Category	Count	Sub-count	Fraction
Known rotation-powered pulsars (RPPs)a	2286
RPPs with measured $\dot{P} > 0$		1944
RPPs with measured $\dot{E} > 3\times 10^{33}$ erg s−1		552
Millisecond pulsars (MSPs; P < 16 ms)	292
Field MSPs		169
MSPs in globular clusters		123
Field MSPs with measured $\dot{E} > 3\times 10^{33}$ erg s−1		96
Globular cluster MSPs with measured $\dot{E} > 3\times 10^{33}$ erg s−1		25
Gamma-ray pulsars in this catalog	117
Young or middle-aged		77
Radio-loud gamma-rayb		42	36%
Radio-quiet gamma-ray		35	30%
Gamma-ray MSPs (isolated + binary)		(10+30) = 40	34%
Radio MSPs discovered in LAT sources	46
with gamma-ray pulsationsc		34

Notes. ^aIncludes the 2193 pulsars, which are all RPPs, in the ATNF Pulsar Catalog (v1.46, Manchester et al. 2005); see http://www.atnf.csiro.au/research/pulsar/psrcat, as well as more recent discoveries. D. Lorimer maintains a list of known field MSPs at http://astro.phys.wvu.edu/GalacticMSPs/. ^bS₁₄₀₀ > 30 μJy, where S₁₄₀₀ is the radio flux density at 1400 MHz. ^cOnly 20 of the new radio MSPs showed gamma-ray pulsations when the dataset for this catalog was frozen.

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For known pulsars we use years of radio and/or X-ray time-of-arrival measurements ("TOAs") to fit the timing model parameters using the standard pulsar timing codes Tempo (Taylor & Weisberg 1989) or Tempo2 (Hobbs et al. 2006). In addition to providing a model for folding the gamma-ray data, the radio observations also provide the information needed to measure the absolute phase alignment (after correcting for interstellar dispersion) between the radio or X-ray and gamma-ray pulses, providing key information about the relative geometry of the different emission regions.

The second method of discovering gamma-ray pulsars, which produced 36 (approximately one-third) of the gamma-ray pulsars in this catalog, involves detecting the rotational period in the LAT data. Both these searches and the radio searches described in the next subsection begin with a target list of candidate pulsars. Some targets are sources known at other wavelengths that are suspected of harboring pulsars. These include supernova remnants (SNRs), pulsar wind nebulae (PWNe), compact central objects (CCOs), unidentified TeV sources, and other high-energy sources, mostly along the Galactic plane. Generally, these sources had already been subjected to deep radio searches independent of Fermi.

In addition, as the LAT surveys the sky, an increasing number of gamma-ray sources are discovered and characterized that are not associated with previously known objects. Several methods have been used to rank these according to their probabilities of being yet-undiscovered pulsars. Most of these rely on the tendency of gamma-ray pulsars to be non-variable and have spectra that can be fit with exponential cutoffs in the few GeV band (Ackermann et al. 2012b; Lee et al. 2012).

Blind searches for pulsars in gamma rays are challenging, due to the wide pulsar parameter ranges that must be searched and due to the sparseness of the data (a few photons per hour for the brightest sources). This results in very long integration times (months to years) making standard Fast Fourier Transform search techniques computationally prohibitive. New semi-coherent search techniques (Atwood et al. 2006; Pletsch et al. 2012a) have been extremely successful at discovering gamma-ray pulsars with modest computational requirements.

LAT blind search sensitivity depends on a number of parameters: the rotation frequency, energy spectrum, pulsed fraction, level of diffuse gamma-ray background, event extraction choices (e.g., ROI and E_min), and the accuracy of the position used to barycenter the data. The 1 yr sensitivity was evaluated using a Monte Carlo study by Dormody et al. (2011). Newer searches (Pletsch et al. 2012a, 2012b) have mitigated dependence on event selection criteria and source localization by weighting events and searching over a grid of positions.

In all, well over one hundred LAT sources have been subjected to blind period searches. Pulsars might have been missed due to (1) low pulsed fraction or very high backgrounds, (2) broad pulse profiles (our algorithms detect sharp pulses more easily), (3) high levels of timing noise or glitches, or (4) being in an unknown binary system. Most MSPs are in binary systems, where the Doppler shifts from the orbital motion smear the signal. In some cases, multiwavelength observations constrain the orbit and position to make the search more like that of an isolated MSP. Optical studies (Romani & Shaw 2011; Kong et al. 2012; Romani 2012) led to the first discovery of a millisecond pulsar, PSR J1311−3430, in a blind search of LAT data (Pletsch et al. 2012c). Detection of radio pulsations followed shortly (Ray et al. 2013). Even isolated MSP searches require massive computation with fine frequency and position gridding. The Einstein@home⁹⁶ project applies the power of global volunteer computing to this problem.

For the LAT pulsars undetected in the radio (see Section 4.1), or too faint for regular radio timing, we must determine the pulsar timing ephemeris directly from the LAT data. Techniques for TOA determination optimized for sparse photon data have been developed and applied to generate the timing models required for the profile analysis (Ray et al. 2011). This timing provides much more precise pulsar positions than can be determined from the LAT event directions, which is important for multiwavelength counterpart searches. It also allows study of timing noise and glitch behavior.

In the third discovery method that we applied, which yielded 20 of this catalog's MSPs, unassociated LAT source positions are searched for radio pulsations. When found, the resulting ephemeris enables gamma-ray phase-folding, as in Section 3.1. A key feature of radio pulsar searches is that they are sensitive to binary systems with the application of techniques to correct for the orbital acceleration in short data sets (with durations much less than the binary period, Ransom et al. 2002). This allows for the discovery of binary MSPs, which are largely inaccessible to gamma-ray blind searches, as described above.

Radio searches of several hundred LAT sources by the Fermi Pulsar Search Consortium (PSC), an international collaboration of radio observers with access to large radio telescopes, have resulted in the discovery of 47 pulsars, including 43 MSPs and four young or middle-aged pulsars (Ray et al. 2012). As the LAT Collaboration generates internal source lists and preliminary catalogs of gamma-ray sources from the accumulating sky-survey data, these target localizations are provided to the PSC for searching, with rankings of how strongly their characteristics resemble those of gamma-ray pulsars, as described in Section 3.2. This technique was employed during the EGRET era as well, but with modest success, in part due to the relatively poor source localizations. With the LAT, there are many more gamma-ray sources detected and each one is localized to an accuracy that is comparable to, or smaller than, the beam width of the radio telescopes being used. This enables deep searches by removing the need to mosaic a large region. It also facilitates repeated searches of the same source, which is important because discoveries can be missed as a result of scintillation or eclipses in binary systems (e.g., PSR J0101−6422, see Kerr et al. 2012).

Guided by these ranked lists of pulsar-like gamma-ray sources, the 43 radio MSPs were discovered in a tiny fraction of the radio telescope time that would have been required to find them in undirected radio pulsar surveys. In particular, because the MSP population out to the LAT's detection limit (∼2 kpc) is distributed nearly uniformly across the sky, full sky surveys are required, whereas most young pulsar searches have concentrated on the Galactic plane. For comparison, after analyzing thousands of pointings carried out since 2007, the High Time Resolution Universe surveys (Keith 2012; Ng & HTRU Collaboration 2013, and references therein) found 29 new radio MSPs.

Interestingly, the success rate for radio searches of LAT sources in the plane has been much poorer. Only four young pulsars have been discovered, and only one of those turned out to be a gamma-ray pulsar (PSR J2030+3641, Camilo et al. 2012), the others being chance associations. This is probably due to a combination of young pulsars having smaller radio beaming fractions than MSPs (as evidenced by the large number of young, radio-quiet pulsars discovered) and the fact that the Galactic plane has been well surveyed for radio pulsars. The great success of the blind gamma searches in the plane is because young pulsars mainly reside there. Their smaller radio beaming fractions leave a large number of radio-quiet pulsars that can only be discovered in high-energy data.

Once a radio pulsar has been discovered positionally coincident with a LAT source, it must be observed for a substantial period (typically six months to a year or more) to determine a timing model that allows a periodicity search in the LAT data, as described in Section 3.1. In several cases, an initial radio model has allowed discovery of the gamma-ray pulsations, then the LAT data themselves have been used to extend the validity of the timing model back through the launch of Fermi, a few years before the radio discovery. This radio follow up has resulted in the confirmed detection of LAT pulsations from 20 of these MSPs. Five more were detected using data beyond the set described in Section 2. Of the remainder, most will have LAT pulsations detected once their radio timing models are well determined, but a few (e.g., PSR J1103−5403; see Keith et al. 2011) are likely to be just chance coincidences with the target LAT source.

The 1400 MHz flux densities, S₁₄₀₀, of the young LAT-detected pulsars are listed in Table 2, and in Table 3 for the MSPs. Figure 3 shows how they compare with the overall pulsar population. Whenever possible, we report S₁₄₀₀ as given in the ATNF Pulsar Catalog. For radio-loud pulsars with no published value at 1400 MHz, we extrapolate to S₁₄₀₀ from measurements at other frequencies, assuming S_ν∝ν^α, where α is the spectral index. For most pulsars α has not been measured, and we use an average value 〈α〉 = −1.7, a middle ground between −1.6 from Lorimer et al. (1995) and −1.8 from Maron et al. (2000). For those pulsars with measured spectral indices, we use the published value of α for the extrapolation. In the table notes, we list those pulsars for which we have extrapolated S₁₄₀₀ from another frequency and/or used a value of α other than −1.7 for the extrapolation.

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Table 2 also reports upper limits on S₁₄₀₀ for blind search pulsars that have been observed, but not detected, at radio frequencies. We define these upper limits as the sensitivity of the observation given by the pulsar radiometer equation (Equation (7.10) on page 174 of Lorimer & Kramer 2004) assuming a minimum signal-to-noise ratio of 5 for a detection and a pulse duty cycle of 10%. We mention here the unconfirmed radio detections of Geminga and PSR J1732−3131 at low radio frequencies, consistent with their non-detection above 300 MHz (Malofeev & Malov 1997; Maan et al. 2012).

All pulsars discovered in blind searches have been searched deeply for radio pulsations (Saz Parkinson et al. 2010; Ray et al. 2011, 2012), and four of the 36 have been detected (Camilo et al. 2009; Abdo et al. 2010l; Pletsch et al. 2012a). In 1PC we labeled the young pulsars by how they were discovered (radio-selected versus gamma-ray selected), whereas we now define a pulsar as "radio-loud" if S₁₄₀₀ > 30 μJy, and "radio-quiet" if the measured flux density is lower, as for the two pulsars with detections of very faint radio pulsations, or if no radio detection has been achieved. The horizontal line in Figure 3 shows the threshold. This definition favors observational characteristics instead of discovery history. Of the four radio-detected blind-search pulsars, two remain radio-quiet whereas the other two could in principle have been discovered in a sensitive radio survey. The diagonal line in Figure 3 shows a possible alternate threshold at pseudo-luminosity 100 μJy-kpc², for reference. Three of the four have pseudo-luminosities lower than for any previously known young pulsar, and comparable to only a small number of MSPs.

Converting measured pulsar fluxes to emitted luminosities L_γ (detailed in Section 6.3) requires the distances to the sources. Knowing the distances also allows mapping neutron star distributions relative to the Galaxy's spiral arms, as in Figure 4, or evaluating their scale height above the plane. Several methods can be used to estimate pulsar distances; however, the methods vastly differ in reliability. Deciding which method to use can be subjective. Tables 5 and 6 list the distance estimates that we adopt, the methods with which these estimates were acquired, and the appropriate references.

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Table 5. Distance Estimates for Young LAT-detected Pulsars

Pulsar Name	Distance	Method	Reference
	(kpc)
J0007+7303	1.4 ± 0.3	K	Pineault et al. (1993)
J0106+4855	$3.0^{+1.1}_{-0.7}$	DM	Pletsch et al. (2012a)
J0205+6449	1.95 ± 0.04	KP	Xu et al. (2006)
J0248+6021	2.0 ± 0.2	K	Theureau et al. (2011)
J0357+3205	<8.2	DMM	...
J0534+2200	2.0 ± 0.5	O	Trimble (1973)
J0622+3749	<8.3	DMM	...
J0631+1036	1.0 ± 0.2	O	Zepka et al. (1996)
J0633+0632	<8.7	DMM	...
J0633+1746	$0.25^{+0.23}_{-0.08}$	P	Verbiest et al. (2012)
J0659+1414	0.28 ± 0.03	P	Verbiest et al. (2012)
J0729−1448	3.5 ± 0.4	DM	Morris et al. (2002)
J0734−1559	<10.3	DMM	...
J0742−2822	2.1 ± 0.5	DM	Janssen & Stappers (2006)
J0835−4510	$0.29^{+0.02}_{-0.02}$	P	Dodson et al. (2003)
J0908−4913	2.6 ± 0.9	DM	Hobbs et al. (2004a)
J0940−5428	3.0 ± 0.5	DM	Manchester et al. (2001)
J1016−5857	$2.9^{+0.6}_{-1.9}$	K	Ruiz & May (1986)
J1019−5749	$6.8^{+13.2}_{-2.5}$	DM	Kramer et al. (2003)
J1023−5746	<16.8	DMM	...
J1028−5819	2.3 ± 0.3	DM	Keith et al. (2008)
J1044−5737	<17.2	DMM	...
J1048−5832	2.7 ± 0.4	DM	Johnston et al. (1995)
J1057−5226	0.3 ± 0.2	O	Mignani et al. (2010b)
J1105−6107	5.0 ± 1.0	DM	Kaspi et al. (1997)
J1112−6103	$12.2^{+7.8}_{-3.8}$	DM	Manchester et al. (2001)
J1119−6127	8.4 ± 0.4	K	Caswell et al. (2004)
J1124−5916	$4.8^{+0.7}_{-1.2}$	X	Gonzalez & Safi-Harb (2003)
J1135−6055	<18.4	DMM	...
J1357−6429	$2.5^{+0.5}_{-0.4}$	DM	Lorimer et al. (2006)
J1410−6132	$15.6^{+7.4}_{-4.2}$	DM	O'Brien et al. (2008)
J1413−6205	<21.4	DMM	...
J1418−6058	1.6 ± 0.7	O	Yadigaroglu & Romani (1997)
J1420−6048	5.6 ± 0.9	DM	Weltevrede et al. (2010)
J1429−5911	<21.8	DMM	...
J1459−6053	<22.2	DMM	...
J1509−5850	2.6 ± 0.5	DM	Weltevrede et al. (2010)
J1513−5908	4.2 ± 0.6	DM	Hobbs et al. (2004a)
J1531−5610	$2.1^{+0.4}_{-0.3}$	DM	Kramer et al. (2003)
J1620−4927	<24.1	DMM	...
J1648−4611	5.0 ± 0.7	DM	Kramer et al. (2003)
J1702−4128	4.8 ± 0.6	DM	Kramer et al. (2003)
J1709−4429	2.3 ± 0.3	DM	Johnston et al. (1995)
J1718−3825	3.6 ± 0.4	DM	Manchester et al. (2001)
J1730−3350	$3.5^{+0.4}_{-0.5}$	DM	Hobbs et al. (2004b)
J1732−3131	0.6 ± 0.1	DM	Maan et al. (2012)
J1741−2054	0.38 ± 0.02	DM	Camilo et al. (2009)
J1746−3239	<25.3	DMM	...
J1747−2958	4.8 ± 0.8	X	Gaensler et al. (2004)
J1801−2451	$5.2^{+0.6}_{-0.5}$	DM	Hobbs et al. (2004b)
J1803−2149	<25.2	DMM	...
J1809−2332	1.7 ± 1.0	K	Oka et al. (1999)
J1813−1246	<24.7	DMM	...
J1826−1256	<24.7	DMM	...
J1833−1034	4.7 ± 0.4	K	Gupta et al. (2005); Camilo et al. (2006)
J1835−1106	2.8 ± 0.4	DM	D'Amico et al. (1998)
J1836+5925	0.5 ± 0.3	X	Halpern et al. (2002)
J1838−0537	<24.1	DMM	...
J1846+0919	<22.0	DMM	...
J1907+0602	3.2 ± 0.3	DM	Abdo et al. (2010l)
J1952+3252	2.0 ± 0.5	K	Greidanus & Strom (1990)
J1954+2836	<18.6	DMM	...
J1957+5033	<14.5	DMM	...
J1958+2846	<18.5	DMM	...
J2021+3651	$10.0^{+2.0}_{-4.0}$	O	Hessels et al. (2004)
J2021+4026	1.5 ± 0.4	K	Landecker et al. (1980)
J2028+3332	<17.2	DMM	...
J2030+3641	3.0 ± 1.0	O	Camilo et al. (2012)
J2030+4415	<15.7	DMM	...
J2032+4127	3.7 ± 0.6	DM	Camilo et al. (2009)
J2043+2740	1.8 ± 0.3	DM	Ray et al. (1996)
J2055+2539	<15.3	DMM	...
J2111+4606	<14.8	DMM	...
J2139+4716	<14.1	DMM	...
J2229+6114	$0.80^{+0.15}_{-0.20}$	K	Kothes et al. (2001)
J2238+5903	<12.4	DMM	...
J2240+5832	7.7 ± 0.7	O	Theureau et al. (2011)

Notes. The best known distances of the 77 young pulsars detected by Fermi. The methods are: K—kinematic method; P—parallax; DM—from dispersion measure using the Cordes & Lazio (2002) NE2001 model; X—from X-ray measurements; O—other methods. For DM, the reference gives the DM measurement. For the 26 pulsars with no distance estimate, DMM is the distance to the Galaxy's edge, taken as an upper limit, determined from the maximum NE2001 DM value for that line of sight.

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Table 6. Millisecond Pulsar Distances and Spindown Doppler Corrections

PSR	d	Method	Refb	μ	Refc	$\dot{P}^{\rm \, int}$	$\dot{P}^{\rm \, shk}$	$\dot{P}^{\rm \, gal}$	$\dot{E}^{\rm \, int}$	ξ
	(pc)			(mas yr−1)		(10−21)	(10−21)	(10−21)	(1033 erg s−1)	(%)
J0023+0923	$690^{+210}_{-110}$	DM	(1)
J0030+0451	$280^{+100}_{-60}$	P	(2)	5.7 ± 1.1	(1)	10.7 ± 0.1	0.11	−0.60	3.64 ± 0.02	−5
J0034−0534	540 ± 100	DM	(3)	31.0 ± 9.0	(2)	2.9 ± 1.4	2.37	−0.31	17.3 ± 8.6	41
J0101−6422	$550^{+90}_{-80}$	DM	(4)	15.6 ± 1.7	(3)	4.4 ± 0.2	0.84	−0.39	10.1 ± 0.5	9
J0102+4839	$2320^{+500}_{-430}$	DM	(1)
J0218+4232	$2640^{+1080}_{-640}$	DM	(5)	5.0 ± 6.0	(2)	76.9 ± 0.9	0.37	0.09	243.2 ± 2.8	0.6
J0340+4130	1730 ± 300	DM	(1)
J0437−4715	156 ± 1	P	(2)	141.3 ± 0.1	(4)	14.1 ± 0.3	43.59	−0.40	2.9 ± 0.1	75
J0610−2100	$3540^{+5460}_{-1000}$	DM	(6)	18.2 ± 0.2	(5)	$1.2^{+17.0}_{-1.1}$	11.00	0.10	$0.8^{+11.7}_{-0.8}$	90
J0613−0200	$900^{+400}_{-200}$	P	(2)	10.8 ± 0.2	(6)	$8.7^{+0.3}_{-0.2}$	0.77	0.08	$12.0^{+0.5}_{-0.2}$	9
J0614−3329	$1900^{+440}_{-350}$	DM	(7)
J0751+1807	$400^{+200}_{-100}$	P	(2)	6.0 ± 2.0	(7)	7.7 ± 0.1	0.12	−0.02	7.2 ± 0.1	1
J1024−0719	390 ± 40	DMa	(8)	59.9 ± 0.2	(5)	$1.6^{+1.8}_{-1.4}$	17.37	−0.44	$0.4^{+0.5}_{-0.4}$	92
J1124−3653	$1720^{+430}_{-360}$	DM	(1)
J1125−5825	2620 ± 370	DM	(9)
J1231−1411	440 ± 50	DM	(7)	62.2 ± 4.7	(8)a	6.5 ± 2.9	15.15	−0.41	5.1 ± 2.3	70
J1446−4701	1460 ± 220	DM	(10)
J1514−4946	940 ± 120	DM	(4)
J1600−3053	$1630^{+310}_{-270}$	DM	(11)	7.2 ± 0.3	(6)	$8.6^{+0.2}_{-0.1}$	0.74	0.15	7.3 ± 0.1	9
J1614−2230	650 ± 50	P	(12)	36.5 ± 0.2	(9)	3.0 ± 0.5	6.65	−0.003	3.8 ± 0.6	69
J1658−5324	$930^{+110}_{-130}$	DM	(4)
J1713+0747	$1050^{+60}_{-50}$	P	(2)	6.30 ± 0.01	(10)	$8.28^{+0.03}_{-0.02}$	0.46	−0.21	3.42 ± 0.01	3
J1741+1351	$1080^{+40}_{-50}$	P	(13)	11.71 ± 0.01	(11)	29.1 ± 0.1	1.35	−0.20	$21.76^{+0.04}_{-0.05}$	4
J1744−1134	417 ± 17	P	(11)	21.02 ± 0.03	(6)	7.0 ± 0.1	1.82	0.08	4.11 ± 0.04	21
J1747−4036	3390 ± 760	DM	(4)
J1810+1744	$2000^{+310}_{-280}$	DM	(1)
J1823−3021A	7600 ± 400	O	(14)
J1858−2216	$940^{+200}_{-130}$	DM	(15)
J1902−5105	1180 ± 210	DM	(4)
J1939+2134	3560 ± 350	DM	(16)	0.80 ± 0.02	(12)	105.5 ± 0.1	0.01	−0.36	1096.6 ± 0.5	−0.3
J1959+2048	$2490^{+160}_{-490}$	DM	(17)	30.4 ± 0.6	(13)	$8.1^{+0.7}_{-1.8}$	9.00	−0.25	$76.3^{+6.4}_{-17.1}$	52
J2017+0603	1570 ± 150	DM	(18)
J2043+1711	$1760^{+150}_{-320}$	DM	(1)	13.0 ± 2.0	(14)	4.3 ± 0.6	1.72	−0.35	$12.7^{+1.6}_{-1.8}$	24
J2047+1053	$2050^{+320}_{-290}$	DM	(15)
J2051−0827	1040 ± 150	DM	(19)	7.3 ± 0.4	(15)	12.6 ± 0.1	0.61	−0.47	5.43 ± 0.05	1
J2124−3358	$300^{+70}_{-50}$	P	(2)	52.3 ± 0.3	(6)	$11.2^{+2.3}_{-1.6}$	9.83	−0.46	$3.7^{+0.8}_{-0.5}$	46
J2214+3000	1540 ± 180	DM	(7)
J2215+5135	$3010^{+330}_{-370}$	DM	(1)
J2241−5236	510 ± 80	DM	(20)
J2302+4442	$1190^{+90}_{-230}$	DM	(18)

Notes. Columns 2 and 3 give the distances for the 40 MSPs detected by Fermi, and the method used to find them: P—parallax; DM—from dispersion measure using the Cordes & Lazio (2002) NE2001 model; O—other methods. For DM, the references in Column 4 give the DM measurement. For the 20 MSPs with a proper motion measurement, it is listed in Column 5, obtained from the reference in Column 6. Columns 7 to 10 list the intrinsic $\dot{P}^{\rm \, int}$, the contributions of the Shklovskii effect $\dot{P}^{\rm \, shk}$ and of acceleration due to the Galactic rotation, $\dot{P}^{\rm \, gal}$, and the intrinsic spindown power $\dot{E}^{\rm \, int}$. The relative correction ξ is defined from $\dot{E}^{\rm \, int} = \dot{E} \,(1-\xi)$. ^aProper motion for J1231−1411 from this work: μ_αcos δ = −60.5(44) mas yr⁻¹, μ_δ = −14.3(82) mas yr⁻¹. For J1024−0719, the timing parallax distance measurement gives negative spindown and we use instead the DM distance following Espinoza et al. (2013). ^bDistance and DM references: (1) Hessels et al. 2011; (2) Verbiest et al. 2012; (3) Bailes et al. 1994; (4) Kerr et al. 2012; (5) Hobbs et al. 2004b; (6) Burgay et al. 2006; (7) Ransom et al. 2011; (8) Hotan et al. 2006; (9) Bates et al. 2011; (10) Keith et al. 2012; (11) Verbiest et al. 2009; (12) Lassus 2013; (13) P. C. C. Freire et al. (in preparation); (14) Kuulkers et al. 2003; (15) Ray et al. 2012; (16) Cognard et al. 1995; (17) Arzoumanian et al. 1994; (18) Cognard et al. 2011; (19) Doroshenko et al. 2001; (20) Keith et al. 2011. ^cProper motion references: (1) Abdo et al. 2009e; (2) Hobbs et al. 2005; (3) Kerr et al. 2012; (4) Deller et al. 2009; (5) Espinoza et al. 2013; (6) Verbiest et al. 2009; (7) Nice et al. 2005; (8) This work; (9) Lassus 2013; (10) Splaver et al. 2005; (11) P. C. C. Freire et al. (in preparation); (12) Cognard et al. 1995; (13) Arzoumanian et al. 1994; (14) Guillemot et al. 2012; (15) Lazaridis et al. 2011.

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The most accurate distance estimator is the annual trigonometric parallax. Unfortunately, parallax can only be measured for relatively nearby pulsars, using X-ray or optical images, radio interferometric imaging, or accurate timing. For 14 Fermi pulsars a parallax has been measured. We rejected two with low-significance (<2σ). For the remaining 12 pulsars we consider this the best distance estimate. One caveat when converting parallax measurements to distances is the Lutz–Kelker effect, an overestimate of parallax values (and hence underestimate of distances) that must be corrected for the larger volume of space traced by smaller parallax values (Lutz & Kelker 1973). We use the Lutz–Kelker corrected distance estimates determined by Verbiest et al. (2012).

The dispersion measure (DM) is by far the most commonly used pulsar distance estimator. DM is the column density of free electrons along the path from Earth to the pulsar, in units of pc cm⁻³. The electrons delay the radio pulse arrival by Δt = DM(pν²)⁻¹ where ν is the observation frequency in MHz and p = 2.410 × 10⁻⁴ MHz⁻² pc cm⁻³ s⁻¹. Given a model for the electron density n_e in the various structures of our Galaxy, integrating DM = $\int _0^d n_e dl$ along the line of sight dl yields the distance d for which DM matches the radio measurement. In this work we use the NE2001 model (Cordes & Lazio 2002), available as off-line code. To estimate the distance errors we re-run NE2001 twice, using DM ± 20%, as the authors recommend. The measured DM uncertainty is much lower than this, but this accommodates unmodeled electron-rich or poor regions. This yields distance uncertainties less than 30% for many pulsars. Nevertheless, significant discrepancies with the true pulsar distances along some lines of sight still occur. As examples, the DM distances for PSR J2021+3651 (Abdo et al. 2009d) and PSR J0248+6021 (Theureau et al. 2011) may be more than three times greater than the true distances.

For some pulsars, an absorbing hydrogen column density N_H below 1 keV has been obtained (see Section 9.1). Comparing N_H with the total hydrogen column density for that line of sight obtained from 21 cm radio surveys yields a rough distance estimate. The Doppler shift of neutral hydrogen (H i) absorption or emission lines measured from clouds on the line of sight, together with a Galactic rotation model as described in Section 4.3, can give "kinematic" distances to the clouds. The pulsar distance is then constrained if there is evidence that the pulsar is in one of the clouds, or between some of them. Associations can be uncertain and these distance estimates can be controversial.

With the growing number of gamma-ray pulsars not detected at radio wavelengths, and thus without a DM, and the difficulties of the other methods, we face an ever-growing pulsar distance problem. We have 26 objects with no distance estimates, compared to nine in 1PC. To mitigate this, we determine a maximum distance by assuming that the pulsar is within the Galaxy. We define the Galaxy edge as the distance for a given line of sight where the NE2001 DM reaches its maximum value ("DMM" in Table 5; illustrated in Figure 4).

Many pulsar characteristics, including some listed in Tables 2 and 3, depend on the intrinsic spin period P^int and spindown rate $\dot{P}^{\rm \,int}$. The Doppler shift of the observed period is P = (1 + v_R/c)P^int, where v_R is the pulsar's radial velocity along the unit vector $\textbf {n}_{10}$ from the solar system. The Doppler correction to $\dot{P}$ is obtained by differentiating the equation and separating the effects of the system's proper motion (Shklovskii 1970) from the acceleration due to Galactic rotation:

$$\begin{equation} \dot{P}^{\rm \,int} = \dot{P} -\dot{P}^{\rm \, shk}-\dot{P}^{\rm \, gal} \end{equation} \tag{ 3 }$$

with

$$\begin{equation} \dot{P}^{\rm \,shk} = \frac{1}{c}\,\mu ^2 \,{dP} = k \left({\mu \over {\rm mas\, yr^{-1}}}\right)^2 \left({d \over {\rm kpc}}\right)\left({P \over {\rm s}}\right) \end{equation} \tag{ 4 }$$

and

$$\begin{equation} \dot{P}^{\rm \,gal} = \frac{1}{c}\, \textbf {n}_{10} \cdot (\textbf {a}_{1}-\textbf {a}_{0})P \end{equation} \tag{ 5 }$$

where k = 2.43 × 10⁻²¹ for pulsar distance d and proper motion transverse to the line of sight μ. The Galactic potential model of Carlberg & Innanen (1987) and Kuijken & Gilmore (1989) provides the accelerations $\textbf {a}_{1}$ of the pulsar and $\textbf {a}_{0}$ of the Sun. Since the constant k is small, the corrections are negligible for the young gamma-ray pulsars, which all have $\dot{P} > 10^{-16}$. However, for MSPs μ² d can be large enough that $\dot{P}^{\rm \,int}$ differs noticeably from the observed $\dot{P}$ values and quantities derived from $\dot{P}$ will also be affected.

From the literature we compiled proper motion measurements for 243 pulsars, all but one of which also have distance estimates and $\dot{P}$ measurements, and we calculated $\dot{P}^{\rm \,int}$ and its uncertainties for those 242 pulsars. Of these, 69 have P < 30 ms, and 20 are gamma-ray MSPs, listed in Table 6. The magnitude of the correction is $\xi = (\dot{P} - \dot{P}^{\rm \, int}) /\dot{P}$, or, equivalently, $\dot{E}^{\rm \, int} = \dot{E} \,(1-\xi)$ since $\dot{E} \propto \dot{P}$. For |ξ| greater than a few percent, $\dot{P}^{\rm \,shk} > | \dot{P}^{\rm \,gal}|$ and corrected $\dot{E}^{\rm \,int}$ is less than the observed value. Hence flagging gamma-ray pulsar candidates that have large $\dot{E}$ selects some with lower $\dot{E}^{\rm \,int}$, but we would not miss candidates by neglecting proper motion. For large Doppler corrections, the Galactic term is negligible, $\dot{P}^{\rm \,shk} \gg \dot{P}^{\rm \,gal}$, and we calculate only the uncertainty due to $\dot{P}^{\rm \,shk}$. Unless otherwise noted, throughout this paper we use $\dot{P}^{\rm \, int}$ from Table 6 to replace $\dot{P}$ and the derived quantities ($\dot{E}$, τ, et cetera) in the figures and tables. In Section 6.3 we discuss the Doppler correction's effect on the gamma-ray luminosity for a few cases.

Appendix A contains a small sample of gamma-ray pulse profiles (Figures 22(a)–(h)), overlaid with the radio profiles when available, and showing the fits described in Section 5.2, below. All pulse profiles are provided in the online material. We display gamma-ray light curves by computing a weighted histogram of gamma-ray rotational phases ϕ. The error on the ith histogram bin containing N_i photons is estimated as $\sigma _i^2 = 1 + \sum _{j=0}^{N_i} w_j^2$, using the weights w_j defined in Equation (1). The "1" term mitigates a bias toward low histogram levels and σ_i values caused by background-dominated bins. For these bins, the typical photon weight is very low, but the large weights of rare background photons near the pulsar position (within the PSF) can substantially increase the bin level. The additional term compensates for the spread due to the presence or absence of a single such photon. We choose the number of bins in the histogram according to the weighted H-test: 25 bins (H < 100); 50 bins (100 < H < 1000); and 100 bins (H > 1000).

We estimate the background contribution from diffuse sources and neighboring point sources by computing the expectation value of w under the hypothesis that the photon does not originate from the pulsar: $b\equiv \int _0^1\,dw\,w\times [1-f(w)]\approx \sum _{j=0}^{N_{\gamma }}w_j-\sum _{j=0}^{N_{\gamma }}w_j^2$, where f(w) is the probability distribution of the photon weights and we have used a Monte Carlo approximation to evaluate the integral. The corresponding background level for a weighted histogram, shown as a horizontal dashed line in the gamma-ray light curves, is b/N_bins. The dominant error in this quantity arises from systematic errors in the normalization of the diffuse background. We estimate this contribution by increasing/reducing the overall normalization of the background by 6% (see Section 6.1 for discussion.)

For pulsars with known radio profiles, we also display by preference the flux density at 1400 MHz. When 1400 MHz data are unavailable or highly scattered by the ISM, we include lower- or higher-frequency profiles, noting the frequency and provenance of the profile on the figures (Appendix A, and the online material).

The propagation of radio pulses through the dispersive ISM is delayed by Δt∝DM ν⁻². This delay, as well as Roemer-type delays associated with the configuration of the telescope relative to the solar system barycenter, are accounted for by Tempo2, allowing precise alignment of radio and gamma-ray light curves. The absolute time at which ϕ ≡ 0 is indicated in the pulsar par files, provided with the online material, by the parameters TZRMJD (giving the time of arrival of the zero phase), TZRFRQ (giving the frequency for which this time is correct), and TZRSITE (encoding the radio telescope/site of arrival).

The zero of phase—the fiducial phase—is ideally the rotational phase when the magnetic axis, the spin axis, and the line of sight lie in the same plane. For some pulsars, this phase can be identified by fitting the rotating vector model (Radhakrishnan & Cooke 1969) to radio polarization position angle versus phase. However, radio pulses often cover too narrow a phase interval to constrain fits using the rotating vector model.

If radio emission from the polar cap is symmetric, the peak intensity can also be used as a proxy for the fiducial phase, and we adopt this approach here for radio-loud pulsars. In detail, this approach can fail if there is appreciable asymmetry in the radio beam or profile evolution with frequency. Additionally, for pulsars with radio interpulses and for some MSPs, we observe emission from the field lines from both poles and must choose with which to associate the fiducial phase. In these cases, we generally choose the hemisphere furthest separated in phase from the gamma rays, consistent with an interpretation of gamma-ray emission arising from the outer magnetosphere. Finally, some pulsars (e.g., J0034−0534 shown in Figure 22(a)) exhibit a clear double symmetry in the radio light curve. In these cases, we choose a fiducial point near the point of symmetry. We note which prescription we have followed in Tables 7 and 8 with a "p" (fiducial point at peak intensity), "h" (fiducial point from hemisphere opposite to peak intensity), "s" (fiducial point placed at point of symmetry rather than peak). For radio-quiet pulsars, we put the first gamma-ray peak (identified by looking for sharp rises and bridge emission) at ϕ = 0.1 for display purposes.

Generally, the gamma-ray light curve of a pulsar can be represented by a wrapped probability density function (pdf) of ϕ ∈ [0, 1). A compact approximation of the true pdf for photon phases can be constructed as a linear combination of N unimodal, possibly skew distributions:

$$\begin{equation} f(\phi) = \sum _{i=1}^{N} n_i\,g_i(\phi) + \left(1-\sum _{i=1}^{N} n_i\right), \end{equation} \tag{ 6 }$$

where each of the g_i is an individually normalized distribution and $1-\sum _{i=1}^{N} n_i \le 1$ is a uniform distribution representing an unpulsed component. To explicitly enforce normalization, we use spherical polar coordinates lying within the unit sphere as internal parameters. With three components, e.g., the normalizations n_i are given in terms of the internal parameters χ_i as n₁ = sin χ₁cos χ₂; n₂ = sin χ₁sin χ₂cos χ₃; n₃ = sin χ₁sin χ₂sin χ₃.

Although generalized wrapped distributions exist, analytic forms for such distributions are typically unavailable. Instead we adopt well-known pdfs, viz. the Gaussian (normal) and Lorentzian (Cauchy) distributions, by wrapping them onto a circle:

$$\begin{equation} g(\phi) = \sum _{i=-\infty }^{+\infty }g^{\prime }(\phi +i), \end{equation} \tag{ 7 }$$

where g' is defined on the real line and g on the circle. For practical reasons this sum must be truncated, and we define a truncated, wrapped distribution as

$$\begin{equation} g_T(\phi ,N) = \sum _{i=-N}^{+N}g^{\prime }(\phi +i) + \left(1-\int _{-N}^{+N}g^{\prime }(x)dx\right), \end{equation} \tag{ 8 }$$

i.e., we approximate the tails as a uniform distribution. In the fits discussed below, N ≡ 10.

Because the peaks of gamma-ray light curves may have a caustic origin, asymmetric distributions are needed to model their fast rise and slow fall. We generalize the symmetric Gaussian and Lorentzian distributions by matching two distributions with differing width parameters, σ₁ and σ₂, at the maximum, x₀. Defining z ≡ (x − x₀)/σ with σ = σ₁ if z ⩽ 0 and σ = σ₂ otherwise, the functional forms of the resulting distributions on the real line are

$$\begin{equation} g^{\prime }(x) = \frac{2}{\pi (\sigma _1+\sigma _2)(1+z^2)}\ \mathrm{ (Lorentzian),} \end{equation} \tag{ 9 }$$

$$\begin{equation} g^{\prime }(x) = \sqrt{\frac{2}{\pi }}\frac{\exp \left(\frac{-z^2}{2}\right)}{\sigma _1+\sigma _2}\ \mathrm{ (Gaussian).} \end{equation} \tag{ 10 }$$

We employ maximum likelihood to determine the best-fit parameters of the mixture distribution. If w_i is a probability that a photon originates from the pulsar, then the logarithm of the likelihood is

$$\begin{equation} \log \mathcal {L} = \sum _{j=1}^{N_{\gamma }} \log \left[ w_i\, f(\phi _i) + (1-w_i)\right]. \end{equation} \tag{ 11 }$$

For large data sets (N_γ > 10⁴) we speed up the computation by binning f(ϕ) to 512 values.

Most LAT light curves can be modeled with good fidelity by one or two two-sided narrow peak distributions and a single broad bridge component. From these fits, we determine the following quantities: N_peaks, the number of non-bridge components; δ, the offset of the mode of the leading peak from the fiducial phase (see above); and Δ, the difference between the modes of the leading and trailing peak (for N_peaks > 1). These parameters appear in Tables 7 and 8. The strong correlation between Δ and δ in Figure 5, as well as the dependence on spindown power (Figure 6) are discussed in Section 10. The peak widths are included in the online material.

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The uncertainty on δ is estimated by combining in quadrature the statistical uncertainty on the position of the relevant gamma-ray peak with that incurred from uncertainty in the DM. The statistical uncertainty naturally includes a contribution from uncertainty in the timing solution (the Tempo TRES quantity) which serves to smear out light curve features by a characteristic width δϕ ≈ TRES/P. The statistical uncertainty on Δ is determined by the sum in quadrature of the position uncertainty of the relevant gamma-ray peaks.

The representation of the light curve (Gaussian versus Lorentzian, presence or absence of additional components) affects the results for both δ and Δ. In addition to the uncertainties above, we estimate a "model" uncertainty of ∼0.01 in phase.

For spectral analysis we used the data set described in Section 2 for phase-averaged fits. We evaluated the point-source detection significance and the spectral parameters for each LAT pulsar in this catalog with an analysis similar to that performed for 2FGL using the standard LAT Science Tools package.⁹⁷ The spectrum of each LAT pulsar was modeled as a power law with an exponential cutoff,

$$\begin{equation} \frac{d N}{d E} = K \left (\frac{E}{E_{0}}\right)^{-\Gamma } \exp \left(- \frac{E}{E_{\rm cut}} \right)^{b}. \end{equation} \tag{ 12 }$$

The four parameters are the normalization factor (K), the photon index at low energy (Γ), the cutoff energy (E_cut), and a parameter representing the sharpness of the cutoff (b) which is fixed to 1 in the default fit. The energy E₀ at which K is defined is arbitrary; thus, we used the 2FGL pivot energy when it exists and 1 GeV otherwise. In the likelihood analysis we constrained Γ to be between 0 and 5 and E_cut to be between 0.1 and 100 GeV.

We constructed models including all 2FGL sources within 20° of each pulsar but only the spectral parameters of point sources within 8° were left free. For sources known to be significantly extended we used the same spatial templates as 2FGL and fixed the spectral parameters to the 2FGL values. For pulsars with no 2FGL counterpart and an unassociated source within 01 of the pulsar, we moved the source to the timing position; otherwise, we added a new point source to the model at the timing position. The study of the off-peak phase interval in Section 7 yielded four pulsars with wind-like emission ("W"-type), and four pulsars where the origin of the off-peak emission is unidentified ("U"-type) but the emission appears spatially extended without evidence of a spectral cutoff, likely due to poorly modeled diffuse emission. We added a new point source to the model for each of these eight pulsars. We used the same models for diffuse gamma-ray emission as 2FGL to account for the Galactic, isotropic, and Earth limb emission: gal_2yearp7v6_v0.fits, iso_p7v6source.txt, limb_2year_P76_source_v0_smooth.txt, and limb_smooth.fits. These are available from the Fermi Science Support Center.⁹⁸

For each pulsar, we selected a 20° × 20° square region, centered on the timing position, for a binned maximum likelihood $\mathtt {gtlike}$ analysis using the pyLikelihood python module included with the Fermi Science Tools. The best-fit parameters are obtained by maximizing the log-likelihood surface that represents the input model using the MINUIT2 fitting engine.⁹⁹ The statistical uncertainties on the parameters were estimated from the quadratic development of the log-likelihood around the best fit. We first performed a fit with a weak convergence criterion and evaluated the point-source detection significance (the "Test Statistic" TS; Mattox et al. 1996) for each point source that had free parameters, except the pulsar of interest. We removed all point sources with TS < 2 and re-optimized the fit with a stricter convergence criterion.

We report the maximum likelihood values of Γ and E_cut from the phase-averaged analysis and TS values in Tables 9 and 10 for young and millisecond pulsars, respectively. In addition, we report the integrated photon and energy fluxes in the 0.1 to 100 GeV energy band (F₁₀₀ and G₁₀₀, respectively), obtained from the fits as

$$\begin{eqnarray} &&F_{100} = \int _{\rm 100 \, MeV}^{\rm 100 \, GeV} \frac{d N}{d E} d E, \; \; \; \; \; \; G_{100} = \int _{\rm 100 \, MeV}^{\rm 100 \, GeV} E \frac{d N}{d E} d E. \nonumber \\ \end{eqnarray} \tag{ 13 }$$

Statistical uncertainties on F₁₀₀ and G₁₀₀ are obtained using derivatives with respect to the primary parameters and the covariance matrix obtained from the fitting process.

Table 9. Spectral Fitting Results for Young LAT-detected Pulsars

PSRa	Photon Flux	Energy Flux	Γ	Ecut	TS	TScut	TSb free	Luminosity	Efficiencyb
	(ph cm−2 s−1)	(erg cm−2 s−1)		(GeV)				(1033 erg s−1)	(%)
	(× 10−8)	(× 10−11)
J0007+7303	323 ± 0.4	40.1 ± 0.4	1.4 ± 0.1	4.7 ± 0.2	43388	1884	4	94 ± 1 ± 40	21.0 ± 0.2 ± 8
J0106+4855	1.7 ± 0.4	1.9 ± 0.2	1.2 ± 0.2	2.7 ± 0.6	544	58	2	$21 \pm 2^{{+20}}_{{-8}}$	$71 \pm 7^{{+60}}_{{-30}}$
J0205+6449	10.5 ± 0.7	5.4 ± 0.2	1.8 ± 0.1	1.6 ± 0.3	1019	86	7	24 ± 1 ± 1.0	0.09 ± 0.01 ± 0.01
J0248+6021	9.9 ± 1.3	5.2 ± 0.4	1.8 ± 0.1	1.6 ± 0.3	578	61	0	25 ± 2 ± 5	12 ± 1 ± 2
J0357+3205	9.0 ± 0.4	6.4 ± 0.2	1.0 ± 0.1	0.8 ± 0.1	3468	461	2	...	...
J0534+2200	208 ± 1	129.3 ± 0.8	1.9 ± 0.1	4.2 ± 0.2	102653	1461	13	619 ± 4 ± 300	0.14 ± 0.01 ± 0.1
J0622+3749	2.0 ± 0.3	1.4 ± 0.1	0.6 ± 0.4	0.6 ± 0.1	302	91	0	...	...
J0631+1036	6.4 ± 0.6	4.7 ± 0.3	1.8 ± 0.1	6 ± 1	621	39	1	$5.6 \pm 0.3^{{+3}}_{{-2}}$	$3.2 \pm 0.2^{{+2}}_{{-1}}$
J0633+0632	9.7 ± 1.1	9.4 ± 0.5	1.4 ± 0.1	2.7 ± 0.3	2448	203	9	...	...
J0633+1746	416 ± 1	423.3 ± 1.2	1.2 ± 0.1	2.2 ± 0.1	906994	33861	277	$31.7 \pm 0.1^{{+90}}_{{-20}}$	$97.4 \pm 0.3^{{+300}}_{{-50}}$
J0659+1414	7.1 ± 0.6	2.5 ± 0.2	1.7 ± 0.5	0.4 ± 0.2	419	33	0	0.24 ± 0.02 ± 0.05	0.62 ± 0.04 ± 0.1
J0729−1448†	...	...	...	...	54	26	0	...	...
J0734−1559	10.8 ± 0.7	5.6 ± 0.2	2.0 ± 0.1	3.2 ± 0.9	916	39	9	...	...
J0742−2822	3.2 ± 0.6	1.7 ± 0.2	1.7 ± 0.3	1.6 ± 0.8	112	11	2	9 ± 1 ± 4	6.2 ± 0.7 ± 3
J0835−4510	1088 ± 2	906 ± 2	1.5 ± 0.1	3.0 ± 0.1	1659005	43084	916	89.3 ± 0.2 ± 10	1.3 ± 0.1 ± 0.1
J0908−4913	7.9 ± 1.3	4.4 ± 0.4	1.0 ± 0.4	0.5 ± 0.2	315	82	0	$35 \pm 3^{{+30}}_{{-20}}$	$7.1 \pm 0.7^{{+6}}_{{-4}}$
J0940−5428†	...	...	...	...	14	13	8	...	...
J1016−5857	6.9 ± 2.4	5.4 ± 0.9	1.8 ± 0.2	6 ± 3	290	13	0	$55 \pm 9^{{+30}}_{{-50}}$	$2.1 \pm 0.4^{{+1}}_{{-2}}$
J1019−5749†	...	...	...	...	21	0	0	...	...
J1023−5746	30 ± 3	19.5 ± 1.2	1.7 ± 0.1	2.5 ± 0.4	2926	162	20	...	...
J1028−5819	31 ± 2	24.3 ± 0.8	1.7 ± 0.1	4.6 ± 0.5	5096	235	28	158 ± 5 ± 40	18.9 ± 0.6 ± 5
J1044−5737	26 ± 1	15.6 ± 0.5	1.8 ± 0.1	2.8 ± 0.3	3380	202	19	...	...
J1048−5832	25 ± 2	19.6 ± 0.6	1.6 ± 0.1	3.0 ± 0.3	5389	325	30	176 ± 5 ± 40	8.8 ± 0.3 ± 2
J1057−5226	32 ± 1	29.5 ± 0.3	1.0 ± 0.1	1.4 ± 0.1	27848	2377	5	$4.3 \pm 0.1^{{+5}}_{{-3}}$	14.4 ± 0.2±10
J1105−6107	7.8 ± 1.6	4.9 ± 0.6	1.5 ± 0.3	1.3 ± 0.6	309	42	8	150 ± 20 ± 50	5.9 ± 0.7 ± 2
J1112−6103	1.9 ± 0.9	2.0 ± 0.5	1.6 ± 0.3	6 ± 3	58	6	0	$360 \pm 90^{{+600}}_{{-200}}$	$8 \pm 2^{{+10}}_{{-4}}$
J1119−6127	11 ± 2	7.1 ± 0.5	1.8 ± 0.1	3.2 ± 0.8	661	37	13	600 ± 40 ± 60	26 ± 2 ± 2
J1124−5916	10 ± 1	6.2 ± 0.4	1.8 ± 0.1	2.1 ± 0.4	1058	79	6	$170 \pm 10^{{+50}}_{{-70}}$	$1.4 \pm 0.1^{{+0.4}}_{{-0.6}}$
J1135−6055	7.4 ± 0.9	4.8 ± 0.3	1.7 ± 0.1	2.4 ± 0.5	498	61	3	...	...
J1357−6429	7.8 ± 1.1	3.4 ± 0.3	1.8 ± 0.4	0.9 ± 0.5	187	20	0	$25 \pm 2^{{+10}}_{{-8}}$	$0.82 \pm 0.08^{{+0.4}}_{{-0.3}}$
J1410−6132†	3 ± 3	3 ± 1	...	...	40	9	0	$800 \pm 300^{{+900}}_{{-400}}$	$8 \pm 3^{{+9}}_{{-4}}$
J1413−6205	16 ± 2	15.7 ± 0.6	1.5 ± 0.1	4.1 ± 0.5	1795	180	1	...	...
J1418−6058	38 ± 3	30.2 ± 1.4	1.8 ± 0.1	5.5 ± 0.5	3487	172	1	$92 \pm 4^{{+100}}_{{-60}}$	$1.9 \pm 0.1^{{+2}}_{{-1}}$
J1420−6048	26 ± 3	17.0 ± 1.4	1.5 ± 0.1	1.6 ± 0.2	1220	51	2	640 ± 50 ± 200	6.2 ± 0.5 ± 2
J1429−5911	12 ± 1	8.0 ± 0.4	1.6 ± 0.1	2.2 ± 0.3	822	124	0	...	...
J1459−6053	24 ± 2	12.9 ± 0.4	2.0 ± 0.1	2.9 ± 0.5	2046	103	15	...	...
J1509−5850	20 ± 2	12.7 ± 0.7	1.9 ± 0.1	4.6 ± 0.9	1152	67	0	105 ± 6 ± 40	20 ± 1 ± 7
J1513−5908†	10 ± 2	3.2 ± 0.7	...	...	98	5	1	70 ± 10 ± 20	0.4 ± 0.1 ± 0.1
J1531−5610†⋆	0.1 ± 0.05	0.2 ± 0.1	...	...	2	2	1	1.0 ± 0.6 ± 0.4	0.11 ± 0.07 ± 0.04
J1620−4927	15 ± 2	15.7 ± 0.8	1.3 ± 0.1	2.5 ± 0.3	1407	199	4	...	...
J1648−4611	5.3 ± 1.6	5.4 ± 0.8	1.6 ± 0.3	6 ± 4	176	17	0	160 ± 20 ± 40	80 ± 10 ± 20
J1702−4128⋆	4.4 ± 5.2	2.8 ± 2.7	1.1 ± 0.9	0.8 ± 0.5	62	7	0	80 ± 70 ± 20	20 ± 20 ± 5
J1709−4429	160 ± 2	135 ± 1	1.6 ± 0.1	4.2 ± 0.1	96893	3433	132	853 ± 6 ± 200	25.1 ± 0.2 ± 5
J1718−3825	14 ± 1	8.9 ± 0.5	1.5 ± 0.1	1.4 ± 0.1	462	81	1	138 ± 8 ± 30	11.0 ± 0.6 ± 3
J1730−3350⋆	3.4 ± 0.1	2.4 ± 0.4	1.5 ± 0.3	1.2 ± 0.3	100	21	1	36 ± 6 ± 9	2.9 ± 0.5 ± 0.7
J1732−3131	17 ± 1	19.4 ± 0.6	1.0 ± 0.1	1.9 ± 0.1	2821	550	0	8.6 ± 0.3 ± 2	5.9 ± 0.2 ± 1
J1741−2054	17 ± 1	11.7 ± 0.4	1.1 ± 0.1	0.9 ± 0.1	3014	464	0	2.1 ± 0.1 ± 0.2	22 ± 1 ± 3
J1746−3239	10 ± 1	7.2 ± 0.5	1.4 ± 0.1	1.5 ± 0.2	654	109	0	...	...
J1747−2958	33 ± 3	21.1 ± 1.0	1.6 ± 0.1	1.9 ± 0.1	1689	211	2	570 ± 30 ± 200	23 ± 1 ± 7
J1801−2451⋆	1.4 ± 1.0	1.2 ± 0.5	1.5 ± 0.5	3 ± 2	58	10	6	$40 \pm 10^{{+9}}_{{-7}}$	$1.5 \pm 0.6^{{+0.4}}_{{-0.3}}$
J1803−2149	11 ± 2	9.2 ± 0.8	1.6 ± 0.1	3.6 ± 0.8	410	40	1	...	...
J1809−2332	60 ± 2	47.4 ± 0.8	1.6 ± 0.1	3.4 ± 0.2	15781	901	41	$164 \pm 3^{{+200}}_{{-100}}$	$38 \pm 1^{{+60}}_{{-30}}$
J1813−1246	45 ± 2	25.3 ± 0.6	1.9 ± 0.1	2.6 ± 0.3	4664	272	1	...	...
J1826−1256	54 ± 3	38.3 ± 0.9	1.6 ± 0.1	2.2 ± 0.2	5160	533	23	...	...
J1833−1034	7.0 ± 1.1	5.9 ± 0.5	0.9 ± 0.2	0.9 ± 0.2	258	78	0	160 ± 10 ± 30	0.46 ± 0.04 ± 0.08
J1835−1106†⋆	0.4 ± 0.1	0.6 ± 0.2	...	...	30	18	0	6 ± 2 ± 2	3 ± 1 ± 0.9
J1836+5925	63 ± 1	60.6 ± 0.4	1.2 ± 0.1	2.0 ± 0.1	142427	5747	28	$20.4 \pm 0.1^{{+30}}_{{-20}}$	$180 \pm 1^{{+200}}_{{-100}}$
J1838−0537	22 ± 2	18.8 ± 0.9	1.6 ± 0.1	4.1 ± 0.4	1325	114	1	...	...
J1846+0919	1.4 ± 0.3	2.4 ± 0.2	0.7 ± 0.3	2.2 ± 0.5	428	79	0	...	...
J1907+0602	34 ± 2	25.4 ± 0.6	1.6 ± 0.1	2.9 ± 0.3	3773	390	35	314 ± 8 ± 60	11.1 ± 0.3 ± 2
J1952+3252	17 ± 1	13.8 ± 0.3	1.5 ± 0.1	2.5 ± 0.2	4469	365	11	$66 \pm 2^{{+40}}_{{-30}}$	$1.8 \pm 0.1^{{+1.0}}_{{-0.8}}$
J1954+2836	13 ± 1	10.3 ± 0.4	1.6 ± 0.1	3.3 ± 0.4	1592	168	11	...	...
J1957+5033	4.0 ± 0.4	2.6 ± 0.1	1.3 ± 0.2	1.0 ± 0.2	846	105	0	...	...
J1958+2846	11 ± 1	9.1 ± 0.4	1.4 ± 0.1	2.0 ± 0.3	1519	206	25	...	...
J2021+3651	68 ± 2	49.4 ± 0.8	1.7 ± 0.1	3.0 ± 0.2	17821	998	23	$5910 \pm 90^{{+3000}}_{{-4000}}$	$175 \pm 3^{{+80}}_{{-100}}$
J2021+4026	138 ± 2	95.5 ± 0.9	1.6 ± 0.1	2.6 ± 0.1	53955	2343	72	$257 \pm 2^{{+200}}_{{-100}}$	$225 \pm 2^{{+200}}_{{-100}}$
J2028+3332	5.8 ± 0.9	5.8 ± 0.4	1.2 ± 0.2	1.9 ± 0.3	1058	161	0	...	...
J2030+3641	2.3 ± 0.6	3.1 ± 0.3	0.7 ± 0.4	1.5 ± 0.4	313	91	0	$34 \pm 4^{{+30}}_{{-20}}$	$110 \pm 10^{{+80}}_{{-60}}$
J2030+4415	9.3 ± 1.0	5.8 ± 0.4	1.6 ± 0.1	1.7 ± 0.3	504	74	0	...	...
J2032+4127	7.4 ± 1.1	10.6 ± 0.6	1.1 ± 0.1	3.2 ± 0.5	1383	162	0	169 ± 10 ± 50	62 ± 4 ± 20
J2043+2740	1.5 ± 0.4	1.0 ± 0.1	1.4 ± 0.4	1.2 ± 0.6	97	18	2	3.8 ± 0.6 ± 1	7 ± 1 ± 2
J2055+2539	6.2 ± 0.4	5.4 ± 0.2	1.0 ± 0.1	1.1 ± 0.1	2751	361	1	...	...
J2111+4606	5.3 ± 0.7	4.4 ± 0.3	1.7 ± 0.1	5 ± 1	731	45	0	...	...
J2139+4716	3.1 ± 0.5	2.3 ± 0.2	1.3 ± 0.2	1.3 ± 0.3	369	71	2	...	...
J2229+6114	38 ± 1	25.3 ± 0.4	1.8 ± 0.1	4.3 ± 0.3	12101	424	54	19.4 ± 0.3 ± 8	0.09 ± 0.01 ± 0.04
J2238+5903	9.3 ± 0.9	6.4 ± 0.3	1.6 ± 0.1	2.1 ± 0.3	1165	123	10	...	...
J2240+5832	1.1 ± 0.7	1.1 ± 0.3	1.5 ± 0.5	3 ± 2	54	11	0	80 ± 20 ± 10	40 ± 10 ± 6

Notes. Unbinned maximum likelihood spectral fit results for the young LAT gamma-ray pulsars, using the PLEC1 model (Equation (12) in Section 6). Columns 2 and 3 list the phase-averaged integral photon and energy fluxes in the 0.1 to 100 GeV energy band, F₁₀₀ and G₁₀₀. Columns 4 and 5 list the photon index Γ and cutoff energy E_cut. Columns 6, 7, and 8 list the source significance TS, significance TS_cut of the exponential cutoff compared to a simple power law, and significance TS_b free of the PLEC compared to a PLEC1 shape. A value TS_cut < 9 indicates that a spectral cutoff is not significantly detected. Columns 9 and 10 give the total gamma-ray luminosity L_γ in the 0.1 to 100 GeV energy band, and the gamma-ray conversion efficiency $\eta \equiv L_\gamma /\dot{E}$, assuming $f_\Omega =1$ as described in Section 6.3. The first uncertainty in L_γ and η comes from the statistical uncertainties in the spectral fit, whereas the second is due to the distance uncertainty. The strong dependence of these quantities on distance (see Table 5) and beaming factor means that these values should be considered with care. ^aA dagger (†) means the spectral fit is unreliable (see text). A star (⋆) means that the spectrum was calculated using the on-peak data only. ^bOverestimated distances or the assumed beaming factor, f_Ω = 1, can result in an efficiency >100%.

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Table 10. Spectral Fitting Results for LAT-detected Millisecond Pulsars

PSRa	Photon Flux	Energy Flux	Γ	Ecut	TS	TScut	TSb free	Luminosity	Efficiencyb
	(ph cm−2 s−1)	(erg cm−2 s−1)		(GeV)				(1032 erg s−1)	(%)
	(× 10−8)	(× 10−11)
J0023+0923	1.2 ± 0.4	0.80 ± 0.12	1.4 ± 0.4	1.4 ± 0.6	131	16	7	$4.6 \pm 0.7^{{+3}}_{{-1}}$	$3.0 \pm 0.5^{{+2}}_{{-1}}$
J0030+0451	6.6 ± 0.3	6.14 ± 0.18	1.2 ± 0.1	1.8 ± 0.2	4788	316	10	$5.8 \pm 0.2^{{+5}}_{{-2}}$	$16 \pm 1^{{+13}}_{{-6}}$
J0034−0534	2.2 ± 0.3	1.62 ± 0.12	1.4 ± 0.2	1.8 ± 0.4	563	45	0	$5.7 \pm 0.4^{{+3}}_{{-2}}$	$3.3 \pm 0.2^{{+1.5}}_{{-1.1}}$
J0101−6422	0.75 ± 0.14	1.05 ± 0.09	0.7 ± 0.3	1.5 ± 0.4	491	59	1	3.8 ± 0.3 ± 1	$3.8 \pm 0.3^{{+1.3}}_{{-1.0}}$
J0102+4839	1.3 ± 0.3	1.32 ± 0.16	1.4 ± 0.3	3.2 ± 1.1	251	29	1	$90 \pm 10^{{+40}}_{{-30}}$	$49 \pm 6^{{+23}}_{{-16}}$
J0218+4232	7.7 ± 0.7	4.56 ± 0.24	2.0 ± 0.1	4.6 ± 1.2	1313	38	1	$380 \pm 20^{{+400}}_{{-200}}$	$16 \pm 1^{{+15}}_{{-7}}$
J0340+4130	1.5 ± 0.2	2.04 ± 0.15	1.1 ± 0.2	2.6 ± 0.6	553	73	4	73 ± 6 ± 20	92.6 ± 7.0 ± 29
J0437−4715	2.7 ± 0.3	1.67 ± 0.11	1.4 ± 0.2	1.1 ± 0.3	687	67	1	0.49 ± 0.03 ± 0.01	1.7 ± 0.1 ± 0.1
J0610−2100	0.78 ± 0.25	0.66 ± 0.11	1.2 ± 0.4	1.6 ± 0.8	98	14	1	$100 \pm 20^{{+500}}_{{-50}}$	$1180 \pm 190^{{+6400}}_{{-570}}$
J0613−0200	2.7 ± 0.4	2.99 ± 0.19	1.2 ± 0.2	2.5 ± 0.5	760	88	0	$29 \pm 2^{{+30}}_{{-10}}$	$24.1 \pm 1.5^{{+26}}_{{-9.5}}$
J0614−3329	8.5 ± 0.3	10.94 ± 0.27	1.3 ± 0.1	3.9 ± 0.3	9408	416	11	470 ± 10 ± 200	$215 \pm 5^{{+110}}_{{-72}}$
J0751+1807	1.1 ± 0.2	1.33 ± 0.12	1.1 ± 0.2	2.6 ± 0.7	427	46	1	$2.5 \pm 0.2^{{+3}}_{{-1}}$	$3.5 \pm 0.3^{{+4.4}}_{{-1.5}}$
J1024−0719†	0.2 ± 0.2	0.3 ± 0.1	...	...	46	11	0	0.6 ± 0.2 ± 0.1	12 ± 4 ± 2.3
J1124−3653	0.94 ± 0.23	1.21 ± 0.13	1.1 ± 0.3	2.5 ± 0.7	293	39	0	43 ± 5 ± 20	$25.0 \pm 2.7^{{+14}}_{{-9.4}}$
J1125−5825	1.1 ± 0.5	0.89 ± 0.20	1.7 ± 0.2	4.8 ± 2.4	41	4	1	70 ± 20±20	$9.1 \pm 2.0^{{+3.0}}_{{-2.4}}$
J1231−1411	9.2 ± 0.4	10.28 ± 0.26	1.2 ± 0.1	2.7 ± 0.2	7931	446	3	24 ± 0.6 ± 5	45.9 ± 1.2 ± 9.9
J1446−4701	0.73 ± 0.31	0.74 ± 0.14	1.4 ± 0.4	3.0 ± 1.7	71	9	0	19 ± 4 ± 5	5.2 ± 1.0 ± 1.4
J1514−4946	4.1 ± 0.6	4.50 ± 0.28	1.5 ± 0.1	5.3 ± 1.1	999	66	0	48 ± 3 ± 10	29.7 ± 1.8 ± 7.1
J1600−3053⋆	0.22 ± 0.16	0.53 ± 0.28	0.40 ± 0.47	2.0 ± 0.7	147	26	0	$17 \pm 9^{{+7}}_{{-5}}$	$23 \pm 12^{{+9.6}}_{{-7.0}}$
J1614−2230	2.0 ± 0.4	2.44 ± 0.20	0.96 ± 0.22	1.9 ± 0.4	599	81	1	12 ± 1 ± 2	32.6 ± 2.6 ± 4.8
J1658−5324	5.7 ± 0.7	2.89 ± 0.23	1.8 ± 0.2	1.4 ± 0.4	327	34	0	30 ± 2 ± 8	9.9 ± 0.8 ± 2.6
J1713+0747	1.3 ± 0.4	1.02 ± 0.14	1.6 ± 0.3	2.7 ± 1.2	126	17	2	$13 \pm 2^{{+2}}_{{-1}}$	$39.0 \pm 5.6^{{+4.6}}_{{-3.6}}$
J1741+1351†	0.12 ± 0.04	0.24 ± 0.08	...	...	23	7	0	3 ± 1 ± 0.3	1.5 ± 0.5 ± 0.1
J1744−1134	4.6 ± 0.7	3.25 ± 0.25	1.3 ± 0.2	1.2 ± 0.3	394	65	0	6.8 ± 0.5 ± 0.5	16.5 ± 1.3 ± 1.3
J1747−4036	1.5 ± 0.7	0.99 ± 0.23	1.9 ± 0.3	5.4 ± 3.3	43	4	0	$140 \pm 30^{{+70}}_{{-50}}$	$11.7 \pm 2.7^{{+6.3}}_{{-4.7}}$
J1810+1744	4.2 ± 0.5	2.34 ± 0.17	1.9 ± 0.2	3.2 ± 1.1	442	23	3	$112 \pm 8^{{+40}}_{{-30}}$	$28.2 \pm 2.1^{{+9.4}}_{{-7.3}}$
J1823−3021A	1.5 ± 0.4	1.07 ± 0.15	1.6 ± 0.2	2.5 ± 0.6	64	0	5	700 ± 100 ± 80	8.9 ± 1.3 ± 0.9
J1858−2216	0.55 ± 0.28	0.72 ± 0.15	0.84 ± 0.74	1.7 ± 1.1	75	17	0	$8 \pm 2^{{+4}}_{{-2}}$	$6.8 \pm 1.4^{{+3.2}}_{{-1.7}}$
J1902−5105	3.1 ± 0.4	2.16 ± 0.15	1.7 ± 0.2	3.4 ± 1.1	536	31	2	36 ± 2 ± 10	$5.2 \pm 0.4^{{+2.1}}_{{-1.7}}$
J1939+2134†	1.5 ± 0.8	0.9 ± 0.3	...	...	10	4	1	140 ± 50 ± 30	1.3 ± 0.5 ± 0.2
J1959+2048	2.4 ± 0.5	1.70 ± 0.19	1.4 ± 0.3	1.4 ± 0.4	185	43	0	$130 \pm 10^{{+20}}_{{-40}}$	$16.5 \pm 1.8^{{+2.2}}_{{-5.8}}$
J2017+0603	2.0 ± 0.3	3.33 ± 0.21	1.0 ± 0.2	3.4 ± 0.6	1196	100	1	98 ± 6 ± 20	75.5 ± 4.8 ± 14
J2043+1711	2.7 ± 0.3	2.70 ± 0.16	1.4 ± 0.1	3.3 ± 0.7	918	65	0	$100 \pm 6^{{+20}}_{{-30}}$	$79 \pm 5^{{+14}}_{{-26}}$
J2047+1053	0.83 ± 0.36	0.62 ± 0.14	1.5 ± 0.5	2.0 ± 1.1	69	11	2	$31 \pm 7^{{+10}}_{{-8}}$	$29.4 \pm 6.6^{{+9.9}}_{{-7.7}}$
J2051−0827⋆	0.24 ± 0.13	0.34 ± 0.10	0.50 ± 0.76	1.3 ± 0.7	68	15	0	4 ± 1 ± 1	8.1 ± 2.5 ± 2.2
J2124−3358	2.7 ± 0.3	3.68 ± 0.16	0.78 ± 0.13	1.63 ± 0.19	1993	237	3	$4.0 \pm 0.2^{{+2}}_{{-1}}$	$10.8 \pm 0.5^{{+5.6}}_{{-3.3}}$
J2214+3000	3.0 ± 0.3	3.28 ± 0.15	1.2 ± 0.1	2.2 ± 0.3	1689	146	2	93 ± 4 ± 20	48.4 ± 2.2 ± 11
J2215+5135	1.0 ± 0.3	1.18 ± 0.14	1.3 ± 0.3	3.4 ± 1.0	183	25	1	130 ± 20 ± 30	24.6 ± 3.0 ± 5.7
J2241−5236	3.0 ± 0.3	3.33 ± 0.16	1.3 ± 0.1	3.0 ± 0.5	2150	115	1	10.5 ± 0.5 ± 3	4.0 ± 0.2 ± 1.1
J2302+4442	2.6 ± 0.3	3.67 ± 0.17	0.94 ± 0.12	2.1 ± 0.3	1716	189	2	$62 \pm 3^{{+10}}_{{-20}}$	$162.6 \pm 7.5^{{+26}}_{{-57}}$

Notes. Unbinned maximum likelihood spectral fit results for the LAT MSPs, using the PLEC1 model (Equation (12), Section 6). Columns 2 and 3 list the phase-averaged integral photon and energy fluxes in the 0.1 to 100 GeV energy band, F₁₀₀ and G₁₀₀. Columns 4 and 5 list the photon index Γ and cutoff energy E_cut. Columns 6, 7, and 8 list the source significance TS, significance TS_cut of the exponential cutoff compared to a simple power law, and significance TS_b free of the PLEC compared to a PLEC1 shape. A value TS_cut < 9 indicates that a spectral cutoff is not significantly detected. Column 9 gives the total gamma-ray luminosity L_γ in the 0.1 to 100 GeV energy band. The gamma-ray conversion efficiency $\eta \equiv L_\gamma /\dot{E}^{\rm int}$ in Column 10 assumes a beam correction factor $f_\Omega =1$ as described in Section 6.3, and the Shklovskii-corrected $\dot{E}^{\rm int}$ values from Table 6 in Section 4.3. The first uncertainty in L_γ and η comes from the statistical uncertainties in the spectral fit, whereas the second is due to the distance uncertainty. The strong dependence of these quantities on distance (see Table 6) and beaming factor means that these values should be considered with care. ^aA dagger (†) means the spectral fit is unreliable (see text). A star (⋆) means that the spectrum was calculated using the on-peak data only. ^bOverestimated distances or the assumed beaming factor, f_Ω = 1, can result in an efficiency >100%.

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We tested the validity of modeling the pulsar spectrum as a power law with a simple exponential cutoff shape (PLEC1; Equation (12) with b  ≡  1) by repeating the analysis using a pure power-law shape (PL), and a power law with a more general exponential cutoff shape leaving the b parameter free (PLEC). For a number of pulsars, a PLEC1 spectral model is not significantly better than a PL. We identified these by computing TS_cut ≡ 2Δlog (likelihood) (comparable to a χ² distribution with one degree of freedom) between the models with and without the cutoff. We say that the PLEC1 model is not significantly preferred over the PL model for pulsars with TS_cut < 9, listed in Tables 9 and 10. Similarly, we calculated TS_b free ≡ 2Δlog (likelihood) between the PLEC1 and PLEC models, also listed in the tables.

In all cases where PLEC is significantly preferred over the PLEC1 model (TS_b free ⩾ 9), the maximum likelihood value of b is significantly less than 1, indicating a sub-exponential cutoff. As noted by Abdo et al. (2010n) and Celik & Johnson (2011), a sub-exponential cutoff is a functional form which approximates the superposition of several PLEC1 models with varying values of Γ and E_cut as different regions of the pulsar magnetosphere cut across our line of sight. This is further supported by analysis of PSR J1057−5226 for which the b parameter in a PLEC fit is consistent with 1 and the spectral parameters show very little variation with phase (Abdo et al. 2010o). Thus, no physical quantities can be derived from the PLEC best-fit parameters, whereas the PLEC1 best-fit parameters can be used if taken as flux-weighted, average measures of E_cut and Γ. Further, in our PLEC fits, the E_cut value was often at the minimum boundary (0.1 GeV) with unrealistically small uncertainties. Therefore, we do not report the PLEC fit values in the tables and instead indicate pulsars with high TS_b free as interesting candidates for phase-resolved spectral analysis, a task beyond the scope of this catalog. For pulsars with TS_b free ⩾ 9, the PLEC fit results are included in the spectral plots (see the examples amongst Figures 23(a)–(i) in Appendix A) and in the auxiliary files (Appendix B). We encourage comparing predicted spectra from different emission models to the energy sub-band fluxes, which are also included in the auxiliary files. In some pulsars, particularly the Crab, a preference for b < 1 may indicate either the presence of a secondary spectral component that dominates above ≳10 GeV or that the curvature radiation assumption is incorrect (as argued by Lyutikov et al. 2012, for example). Such a determination is difficult using the LAT data alone (see Section 8.4).

For some pulsars with low duty cycles, the phase-averaged analysis returned a low TS value and/or could not constrain the spectral parameters well. We selected the off-peak intervals for these sources and followed the same prescription as for the phase-averaged analyses but without the pulsar in the model. We then fixed the parameters of all sources >4° from the pulsar, left the normalization parameters of the remaining point sources and diffuse models free, added the pulsar back to the model, and performed an on-peak spectral analysis. These pulsars are indicated by a star (⋆) in Tables 9 and 10. The values of F₁₀₀ and G₁₀₀ reported for these pulsars have been corrected to phase-averaged values. Additionally, the spatial residuals for PSR J1702−4128 revealed a large deficit near the pulsar attributed to the Galactic diffuse model. In lieu of a new Galactic diffuse template, we increased the minimum event energy to 300 MeV and performed an on-peak spectral analysis as described previously. Thus, for PSR J1702−4128 the reported values of F₁₀₀ and G₁₀₀ are extrapolations below the energy range of the data, which increases the quoted uncertainties beyond the statistical values.

To estimate systematic uncertainties on the maximum likelihood spectral parameters we selected eight pulsars with representative characteristics (J0218+4232, J0248+6021, J0357+3205, J0614−3329, J0631+1036, J1658−5324, J1833−1034, and J1846+0919) and studied how their spectra changed when perturbing the Galactic diffuse emission and LAT effective area (A_eff).

The distribution of Galactic diffuse normalization parameters, from all the fits, has a mean of 1.01 with 1σ deviation of 4%. To estimate possible systematic effects due to an imperfect knowledge of this diffuse component, we repeated the spectral analysis with the normalization of the Galactic diffuse emission fixed to (1 ± 0.06) times the best-fit value, corresponding to ±1.5σ deviations. The average and largest deviations for Γ, E_cut, F₁₀₀, and G₁₀₀ from this test are listed in the first row of Table 11.

Systematic uncertainties on A_eff are estimated to be 10% for log₁₀E/1 MeV ⩽ 2, 5% for log₁₀E/1 MeV = 2.75, and 10% for log₁₀E/1 MeV ⩾ 4 with linear extrapolation in between, in log space (Ackermann et al. 2012a). To estimate the effects of these uncertainties we generated bracketing IRFs in which the usual A_eff was replaced by,

$$\begin{equation} A_{\rm B}(E)\ =\ A_{\rm eff}(E) (1 + {\rm err}(E) B(E)), \end{equation} \tag{ 14 }$$

where err(E) represents the A_eff uncertainties with B(E) = ±1 for the normalization factor K and B(E) = ± tanh (log₁₀(E/E₀)/κ) for Γ and E_cut. Choosing κ = 0.13 smoothes over twice the energy resolution. When using bracketing IRFs, it is important to isolate changes in the source of interest caused by the modified A_eff from changes in the diffuse background spectrum introduced by this perturbation. Since the diffuse background spectra were derived from flight data, we multiply the spectrum of the Galactic diffuse model by (1 + err(E)B(E))⁻¹, ensuring that the predicted counts spectra from the diffuse background remains unchanged during the bracketing studies.

We integrate the fit results for the different bracketing IRFs to obtain F₁₀₀ and G₁₀₀. The second row of Table 11 lists the average and largest deviations for Γ, E_cut, F₁₀₀, and G₁₀₀ due to bracketing. G₁₀₀ is more robust than F₁₀₀. The considerably lower average deviations (columns 2 through 5) than maximum values (columns 6 through 9) shows that most deviations are much smaller than the outlying values.

Finally, to plot the spectra, we divided the 0.1 to 100 GeV energy band into 4 (2) bins per decade for pulsars with TS above (below) 250 and fit a power law in each bin, curvature within the bins being negligible. We fixed the spectral parameters of all sources more than 4° from the pulsar of interest and of the diffuse components at their full band fit results. The spectra of the pulsar of interest and the other point sources within the 4° region were modeled as power laws with index fixed at 2. Their flux levels in each energy band were obtained from a two-step fit. In the first step, sources with TS ⩽ 0 were removed, from that energy band only, as leaving them can adversely affect the fit uncertainties. The second step is to re-fit with the modified model. Sample spectra are shown in Figures 23(a)–(i) in Appendix A. For pulsars with TS_b free ⩾ 9, the figures show both the PLEC1 and PLEC fits. The spectra obtained for all pulsars with TS  ⩾  25 and reliable spectral fits are included in the online material.

Table 9 lists the phase-averaged spectral results for the non-recycled pulsars, and Table 10 for the MSPs. For ten pulsars, flagged with a† symbol, the spectral fits were unreliable, for different reasons. Five are undetected as point sources, having TS < 25. For two of these the likelihood analysis fails and we report no spectral parameters, as is the case for PSR J0729−1448 in spite of its larger TS value. For the other three the integrated flux is robust and we report F₁₀₀ and G₁₀₀. Similarly, we report only the integrated fluxes for four more pulsars, either because the maximum likelihood fit solution favored Γ ≈ 0, or because the parameter uncertainties were of order 100%. For PSRs J1112−6103 and J1410−6132, analysis of the off-peak phase intervals (Section 7) showed significant extended emission, which we added to the phase-averaged source model, improving the spectral results.

Figure 7 shows correlation between Γ and $\dot{E}$. The Pearson correlation factor is 0.68 for the young, radio-quiet pulsars and 0.58 for the MSPs, with probabilities of occurring by chance (two-sided p-values) of 5  ×  10⁻⁶ and 1.5  ×  10⁻⁴, respectively. For the young radio-loud pulsars, the correlation is smaller (0.40) and marginally significant (two-sided p-value of 0.017). For all pulsars together the correlation factor is 0.57, with high significance (2 × 10⁻¹⁰), even allowing for trials. We fit the measurements with $\Gamma = \mathcal {A} \log (\dot{E}) + \mathcal {B}$ (dashed lines in the figure). For young pulsars we find similar trends in the radio-loud and radio-quiet populations with $\mathcal {A} \approx 0.2$ and $\mathcal {B} \approx -5$. The exact fit values are sensitive to the outliers with small statistical uncertainties, such as the Crab. The MSPs have more dispersion in Γ and a narrower $\dot{E}$ range, with a steeper slope than for the young population, $\mathcal {A} \approx 0.4$ and $\mathcal {B} \approx -12$.

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In 1PC we noted a possible correlation between E_cut and the magnetic field strength at the light cylinder ($B_{\rm LC} = 4\pi ^{2} (1.5 I_{0} \dot{P})^{1/2}(c^{3} P^{5})^{-1/2}$, assuming an orthogonal rotator). For the radio-quiet pulsars, Figure 8 confirms the trend, with a Pearson correlation factor of 0.64 (p-value 4 × 10⁻⁵). The factor is 0.52 for the MSPs, with p-value 0.0007. Here too, the correlation for the young, radio-loud pulsars is small (0.24) and insignificant (p-value 0.17).

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Gamma-ray emission models predict different relations between the spindown power $\dot{E}$ and the gamma-ray luminosity,

$$\begin{equation} L_\gamma = 4\pi d^2 f_\Omega G_{100}, \end{equation} \tag{ 15 }$$

making this a discriminating observable when applied to a large sample of gamma-ray pulsars. Following Romani & Watters (2010), we define the beam correction factor $f_\Omega$ as

$$\begin{equation} f_\Omega (\alpha ,\zeta _E) = {\int F_\gamma (\alpha ;\zeta ,\phi)\sin \zeta d \zeta d \phi \over 2\int F_\gamma (\alpha ;\zeta _E,\phi)d \phi }, \end{equation} \tag{ 16 }$$

to extrapolate the observed flux to the full sky for some beam shape model. The angle α between the neutron star's magnetic and rotation axes is one model parameter. The angle ζ_E between the rotation axis and the Earth line of sight describes the inclination of the system relative to Earth. The numerator integrates emission into all space (all inclinations ζ) whereas the denominator is the observed flux integrated over a neutron star rotation, with pulsar phase ϕ. In the past, the gamma-ray beam was conventionally assumed to sweep out a 1 sr solid angle, in which case L_γ = d²G₁₀₀. Such a beam is appropriate to near-surface polar cap emission and corresponds to $f_\Omega = (1/4\pi) = 0.08$. An outer magnetosphere fan-like beam sweeping the entire sky (4π steradians) gives $f_\Omega \approx 1$, which is the value we adopt for calculating L_γ. However, Pierbattista et al. (2012) found a large spread in $f_\Omega$ values for different emission models and for radio-loud versus radio-quiet young pulsars. Values of $f_\Omega$ exceeding 1 correspond to beams that are narrow in ϕ, extended in ζ, and/or have average intensity exceeding the value sampled at ζ_E.

Figure 9 shows L_γ versus $\dot{E}$. Pulsars with poor spectral fits have been excluded. The open field-line voltage is $V \simeq 3.18 \times 10^{-3} \sqrt{\dot{E} }$ volts. Above some threshold voltage, gamma-ray emitting electron-positron cascades occur, and a linear dependence of L_γ on V would give $L_\gamma \propto \sqrt{\dot{E}}$ (Arons 1996), as for the lower diagonal line. With arbitrary normalization, we call this the "heuristic" gamma-ray pulsar luminosity,

$$\begin{equation} L_\gamma ^h = 10^{33} \sqrt{\dot{E} / 10^{33}} = \sqrt{10^{33} \dot{E}} \, {\rm erg \, s}^{-1}. \end{equation} \tag{ 17 }$$

At low $\dot{E}$ values L_γ seems to be falling below $L_\gamma ^h$. The upper diagonal line shows $L_\gamma = \dot{E}$, that is, a 100% efficiency $\eta = L_\gamma /\dot{E}$ for converting spindown power into gamma rays. A few pulsars appear above this line, likely due to over-estimated distances or f_Ω values. Figure 10 plots η versus $\dot{E}$. Overall, the expected $\eta \propto 1 / \sqrt{\dot{E}}$ trend is roughly respected. However, the large dispersion due to the distance uncertainties, as well as beaming effects, limits the extent to which the data constrain the theory.

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The Doppler correction to $\dot{E}$ is small (|ξ| < 10%) for 9 of the 20 pulsars with proper motion corrections (Table 6). For the five with 20% < ξ < 60%, the correction refines their positions in e.g., the L_γ versus $\dot{E}^{\rm \, int}$ plane. The Doppler correction for PSR J0437−4715, with a large ξ = 75%, produces a qualitative change: observed $\dot{E} = 12 \times 10^{33}$ erg s⁻¹ decreases to corrected $\dot{E}^{\rm \, int}= 3 \times 10^{33}$ erg s⁻¹, right at the apparent deathline, and the efficiency changes from the lowest outlier amongst MSPs, to a low, but typical, η = 1.7%.

The remaining four pulsars with ξ > 60% bear special discussion. Figure 11 plots lines of constant $\dot{E}$, L_γ, and transverse velocity v_T in μ versus d space for different assumptions: $\dot{E} = 0$, $\dot{E} = L_\gamma$, and $\eta \dot{E} = L_\gamma$ with η = 30%, at the high end of the observed range. The curve for v_T = μd = 150 km s⁻¹ is the 3σ extremum of the MSP velocity distribution of Lyne et al. (1998). Faster recycled pulsars are possible, but unusual. Allowed (or favored) regions are to the left of the curves. The curve for $\dot{E} = 3\times 10^{33}$ erg s⁻¹ shows how an $\dot{E}$ value lower than those seen to date would compare with the other constraints. The shaded zones correspond to the measurements and their uncertainties adopted in this paper along with previous measurements, for comparison. We recall that here, as throughout the paper, we adopt the moment of inertia I₀ = 10⁴⁵ gm cm², corresponding to a neutron star mass of 1.4 M_☉ and radius of 10 km.

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PSR J0610−2100 was recently discussed by Espinoza et al. (2013): the intrinsic spindown power is well below the empirical deathline, the space velocity is much higher than typical, and the gamma-ray efficiency exceeds 100%. In Figure 11 the nominal (μ, d) point for this pulsar is to the right of most of the curves. These apparent paradoxes are resolved if the pulsar is closer than 2 kpc. Upon inspection of NE2001, minor changes in the "Local Super Bubble" shape and density for this line of sight could yield a distance less than 2 kpc. Espinoza et al. (2013) also describe material along the line of sight that is unmodeled in NE2001.

They also discussed PSR J1024−0719. We show both the corrected parallax distance from Verbiest et al. (2012) as well as the NE2001 distance, for which the 10% uncertainty is probably underestimated given the small DM = 6.5 pc cm⁻³ in that direction. However, any distance compatible with the parallax yields the lowest intrinsic spindown power $\dot{E}^{\rm \, int}$ of any gamma-ray pulsar, and well below the 3 × 10³³ erg s⁻¹ current minimum.

For PSR J1231−1411, discovered in an unassociated LAT source, Ransom et al. (2011) measured a large proper motion, μ > 100 mas yr⁻¹, indicated in Figure 11. The Doppler correction using that large μ gave negative $\dot{E}^{\rm \, int}$ values, which is unphysical. Radio observations since the initial measurement allowed us to update the timing model, resulting in the smaller proper motion value listed in Table 6 and plotted in Figure 11. The Doppler corrections now lead to rather typical parameters for this pulsar.

PSR J1614−2230 is one of the rare pulsars with a neutron star mass measurement. Demorest et al. (2010) measured the Shapiro delay precisely in this binary system to obtain M = 1.97 ± 0.04 M_☉, well above the Chandrasekhar mass of 1.4 M_☉. The DM distance, 1.27 kpc, along with the proper motion measured in the same paper yields implausible $\dot{E}^{\rm \, int}$ and η values. A moment of inertia greater than I₀ would improve the situation, favoring "rigid" neutron star equations-of-state. However, the parallax distance and proper motion recently measured by Lassus (2013) brings this pulsar back in line with the rest of the population.¹⁰⁰

Demorest et al. (2010) conclude that M > 1.4 M_☉ is probably true for many or most MSPs. For I > I₀, $\dot{E}^{\rm \, int}$ is larger than the "standard" values in Table 6. This would shrink the spread between the $\dot{E}^{\rm \, int}$ distributions for the young and MSP gamma-ray pulsars.

We first developed a systematic, model-independent, and computationally-efficient method to define the off-peak interval of a pulsar light curve.

We begin by deconstructing the light curve into simple Bayesian Blocks using the algorithm described in Jackson et al. (2005) and Scargle et al. (2013). We could not apply the Bayesian Block algorithm to the weighted-counts light curves because they do not follow Poisson statistics, required by the algorithm. We therefore use an unweighted-counts light curve in which the angular radius and minimum energy selection have been varied to maximize the H-test statistic. To produce Bayesian Blocks on a periodic light curve, we extend the data over three rotations, by copying and shifting the observed phases to cover the phase range from −1 to 2. We do, however, define the final blocks to be between phases 0 and 1. To avoid potential contamination from the trailing or leading edges of the peaks, we reduce the extent of the block by 10% on either side, referenced to the center of the block.

There is one free parameter in the Bayesian Block algorithm called ncp_prior which modifies the probability that the algorithm will divide a block into smaller intervals. We found that, in most cases, setting ncp_prior = 8 protects against the Bayesian Block decomposition containing unphysically small blocks. For a few marginally-detected pulsars, the algorithm failed to find more than one block and we had to decrease ncp_prior until the algorithm found a variable light curve. Finally, for a few pulsars the Bayesian-block decomposition of the light curves failed to model weak peaks found by the light-curve fitting method presented in Section 5.2 or extended too far into the other peaks. For these pulsars, we conservatively shrink the off-peak region.

For some pulsars, the observed light curve has two well-separated peaks with no significant bridge emission, which leads to two well-defined off-peak intervals. We account for this possibility by finding the second-lowest Bayesian block and accepting it as a second off-peak interval if the emission is consistent with that in the lowest block (at the 99% confidence level) and if the extent of the second block is at least half that of the first block.

Figure 12 shows the energy-and-radius optimized light curves, the Bayesian block decompositions, and the off-peak intervals for six pulsars. Figures 22(a)–(h) overlay off-peak intervals over the weighted light curves of several pulsars. The off-peak intervals for all pulsars in this catalog are given in Tables 7 and 8.

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Characterizing both the spatial and spectral characteristics of any off-peak emission helps discern its origin. We employ a somewhat different analysis procedure here than for the phase-averaged analysis described in Section 6.1. To evaluate the spatial characteristics of any off-peak emission we use the likelihood fitting package $\mathtt {pointlike}$ (detailed in Lande et al. 2012), and to fit the spectrum we use $\mathtt {gtlike}$ in binned mode via pyLikelihood as was done for the phase-averaged analysis.