PRECISE γ-RAY TIMING AND RADIO OBSERVATIONS OF 17 FERMI γ-RAY PULSARS

For the current analysis, we use LAT data from 2008 August 4 through at least 2010 February 4, the first 18 months of LAT survey operations. We select LAT events from the most restrictive "diffuse" class of the "Pass 6" event reconstructions (Atwood et al. 2009) with a zenith angle of <105° to reduce contamination from atmospheric secondary γ-rays from near Earth's limb. For each pulsar, we find an optimal radius and low-energy cut to maximize the pulse detection significance. The radius cuts ranged from 05 to 16, while the low-energy cuts ranged from 50 to 900 MeV. Only photons that pass these cuts are included in the timing analysis.

The number of photons surviving these cuts ranged from 1174 (PSR J0633+0632) to 14,875 (PSR J1836+5925) in our 18 months of observing, a span in which the pulsars completed several hundred million rotations. This emphasizes the unique nature of timing pulsars using extremely sparse γ-ray data. Typically only of the order of 100 photons go into each TOA determination. In addition, unlike with radio pulsar timing, the integration time per TOA is equal to the spacing between TOAs, requiring the model to maintain phase accuracy over a much longer time than is required for radio pulsar timing where the integration time for a TOA is only minutes or hours. We constructed initial models using the prepfold tool from the PRESTO pulsar analysis software package.¹⁷ This tool performs epoch folding searches over narrow ranges of frequency and frequency first and second derivatives around the ν and $\dot{\nu }$ values found from the blind search to maximize the signal-to-noise ratio. Combined with searching over a grid of possible pulsar positions, we are able to arrive at an initial model that maintains coherence well enough for TOAs to be determined and the pulsar timing to proceed as described below.

Pulsar timing software generally expects pulse TOAs to be measured at an observatory that is at a fixed geographic location on the Earth. Observations from a spacecraft in orbit about the Earth obviously do not satisfy this condition and this must be accounted for before computing a pulse arrival time. One could go directly to a timescale (such as Barycentric Dynamical Time (TDB)) at the solar system barycenter, but this requires a precise knowledge of the pulsar location before the correction can be done and removes the possibility of fitting for the pulsar position as part of the timing model. Instead, in order to remove the effects of the spacecraft motion on the photon arrival times while maintaining the ability to fit for astrometric parameters in the timing model, we correct the measured times to a fictitious observatory located at Earth's geocenter.

LAT photon times are recorded in Mission Elapsed Time, which is referenced to Terrestrial Time (TT) via the MJDREF key word in the FITS file header.¹⁸ Time is maintained onboard the spacecraft to an accuracy of better than 1 μs using a GPS receiver (Smith et al. 2008).

The geocentric time is the satellite time corrected for geometric light travel time to the geocenter. It does not include relativistic terms in the correction. The geocentric photon time t_geo is defined as

$$\begin{equation} t_{\rm geo} = t_{\rm obs} + \frac{\mathbf {r}_{\rm sat}}{c} \cdot \mathbf {\hat{n}}_{\rm psr}, \end{equation} \tag{ 1 }$$

where r_sat is the vector pointing from the geocenter to the spacecraft, $\mathbf {\hat{n}}_{\rm psr}$ is a unit vector pointing in the direction of the pulsar (here assumed to be at an infinite distance), and c is the speed of light.

This correction is applied using the Fermi science tool¹⁹ gtbary with the tcorrect=geo option. After this correction, the time system for the events is still TT, but all times are referenced to the geocenter. This correction has a maximum amplitude of 23.2 ms. Therefore, an error in the assumed pulsar direction as large as 1° causes a maximum error in the corrected time of only 0.4 ms.

A TOA is determined from the photon times in a segment of data by first assigning pulse phases to each photon based on an initial model, then measuring the phase offset (Δ) required to align a standard template profile with the measured pulse profile (see Figure 1). This offset is then converted to a time using the pulse period (P) and added to the observation start time, T₀, to become the measured TOA:

$$\begin{equation} {\rm TOA} = T_0 + \Delta \times P. \end{equation} \tag{ 2 }$$

This TOA is the time when the fiducial point on the pulse profile arrived at the observatory, for a representative pulse during the observation interval. In the case of the geocentered LAT events, the TOA is for a fictitious observatory at the geocenter (observatory code coe in Tempo2; Hobbs et al. (2006)). The measurement can be made using binned pulse profiles (as in Figure 1) or directly from the unbinned photon phases, as described below.

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For this work, we divide the full 18 month observation interval into segments of equal duration and determine a pulse TOA from each segment. The length of each segment is a balance between the signal-to-noise ratio and time resolution. Longer integrations result in a better signal-to-noise ratio and smaller statistical measurement errors on each TOA. On the other hand, shorter integrations provide finer time resolution that better samples the annual sinusoidal signal caused by Earth's motion around the Sun and the timing noise in some very noisy young pulsars. Therefore, we try to achieve at least one TOA per month. Fainter pulsars that require a substantial fraction of a year, or longer, per TOA measurement will be difficult to time with the LAT.

For most radio pulsar timing, the TOAs are determined from binned data. The start time of the observation is precisely known from the observatory clock. During the observation, data are folded using predicted phases for the pulsar based on a provisional ephemeris (e.g., using the -polyco option to Tempo2), and a binned profile for that observation is computed. The arrival time is computed by cross-correlating the observed profile with a high signal-to-noise template profile with the same binning. The accuracy of this measurement is improved if the cross-correlation is implemented as a fit to a linear phase gradient in the Fourier domain (an application of the Fourier shift theorem) rather than as a simple time-domain cross-correlation (Taylor 1992). Finally the TOA is determined as the observation start time plus the measured phase offset (converted back into time units).

The binned TOA determination method can also be applied to photon data, such as that from the LAT, by computing the predicted phase for each photon and building a binned pulse profile from the events. However, since we must make TOA measurements based on a small number of detected photons (often <100 photons go into each TOA), we can improve the TOA determinations by using an unbinned likelihood analysis to compute the TOA directly from the set of photon phases. This has been discussed before (Livingstone et al. 2009), but we have developed and generalized the technique and describe it in detail here.

We use an unbinned maximum likelihood method to estimate both the light-curve template and the TOAs with associated errors. In the likelihood formulation, the template is interpreted as a periodic probability density function to observe a photon at a given phase, f(ϕ; λ, Δ), with λ being some set of parameters describing the light-curve morphology and Δ accounting for the phase shift between the template and the given data set. The TOA is determined by Δ. The template is normalized such that ∫dϕ f(ϕ; λ, Δ) = 1.

We first start with a description of the template, f(ϕ; λ, Δ), which must be a continuous function that can be evaluated at any value of ϕ. In many cases, the statistics are sufficiently limited that the pulse profile can be described as a sum of a constant background component and a small number of Gaussian peaks. That is,

$$\begin{equation} f(\phi) = \left(1 - \sum _{i = 1}^{N_p} p_i\right) + \sum _{i = 1}^{N_p} p_i\ g(\phi,x_i,\sigma _i), \end{equation} \tag{ 3 }$$

with N_p being the number of Gaussian peaks, p_i being the fraction of the total emission belonging to each peak, and g(x, σ) being a Gaussian with mean x and standard deviation σ. The domain of the Gaussian functions is assumed to be wrapped to [0, 1). Here, Δ can be associated with x₁, the location of the first peak, while the remaining parameters are subsumed in λ.

With increasing statistics, the complexity of GeV light curves is no longer well represented by a simple sum of components. Bridge emission and peak asymmetry appears, and in general, no simple functional form is sufficient to describe the profile (e.g., the Vela pulsar; Abdo et al. 2010e). In this case, we prefer kernel density estimation (KDE) methods (de Jager et al. 1986). These methods result in a faithful, non-parametric representation of the light curve. However, even for bright pulsars, the available statistics are such that KDE methods produce a template with broadened peaks and "noisy" valleys, neither of which is desirable for the calculation of a TOA. A good estimator for the template should provide a smooth template (ignore fluctuations) while simultaneously preserving the structure and sharpness of the peaks, which is important because the template sharpness is a factor in the accuracy of the TOA measurements. We outline two approaches below that we have found to be effective.

The first forms the basis for the H-test statistic often used to assess pulsation significance in the absence of a template (de Jager et al. 1989). Coefficients of a Fourier expansion are estimated directly from the unbinned phases. For n photons, the coefficients for the kth harmonic are

$$\begin{equation} \alpha _k = \frac{1}{n} \sum _{i=1}^{n} \cos (k\phi _i),\quad \beta _k = \frac{1}{n} \sum _{i=1}^{n} \sin (k\phi _i) \end{equation} \tag{ 4 }$$

and the light curve is given by

$$\begin{equation} f(\phi) = 1 + 2 \sum _{k = 1}^{m} \alpha _k \cos (k\phi) + \beta _k \sin (k\phi). \end{equation} \tag{ 5 }$$

The only free parameter is the overall phase of the light curve; variation can be implemented with the Fourier shift theorem or simply by adding a constant phase to the data. The number of harmonics retained should offer an optimum balance between peak "sharpness" and noise in the remainder of the profile. We call this the "empirical Fourier" (EF) method.

The second method is a Gaussian KDE with a phase-dependent bandwidth, the idea being to use smaller bandwidth for the peaks while smoothing the valleys with a broader kernel. Here, f(ϕ) = ∑ⁿ_i=1g(ϕ, ϕ_i, σ_i), with g being again the standard Gaussian. The bandwidth is determined by $\sigma _i = (f_{\max } - f_{\min })/f(\phi _i)\sqrt{n}$. Lest the reader worry about this circular definition, in practice we begin with a phase-independent bandwidth $\sigma =\sqrt{n}$ and iterate. As with the Fourier expansion, the only free parameter is the overall template offset.

In summary, for our template, we choose one of the three above methods (Gaussian, EF, or KDE) that produces the best results, as evidenced by the smallest rms residuals. A comparison of a pulse profile fitted with the three different templates is shown in Figure 2. The template choice is documented for each pulsar.

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With the template defined, the next step is to fit for the TOA from each segment of data, always using the chosen template to define the pulse profile and fiducial point. For the fitting, we start with an approximate timing solution (say from a ν-$\dot{\nu }$ search) and fold the photon arrival times to obtain a set of phases {ϕ₁, ϕ₂, ..., ϕ_n}. The probability to observe these data, given the light-curve model, is formally inverted to form the log likelihood for the parameters, ∑ⁿ_i=1log f(λ, Δ; ϕ_i). The parameters are varied to maximize the log likelihood. In the case of a multi-Gaussian template, the full data set is used to determine λ, while in determining TOAs, only Δ is fit. The likelihood surface generally has a Gaussian shape near the best-fit value for Δ, and we estimate the error on Δ by measuring and inverting the curvature of the log likelihood function at the best-fit value. Thus, to determine a TOA, the above fit is carried out for each subset to estimate for Δ and its error σ_Δ.

We mention here an additional challenge brought on by morphology of GeV light curves. An appreciable fraction of pulsars observed so far present light curves with two peaks of similar height with a separation close to 0.5 periods. These light curves are approximately invariant under a half-period translation, and statistical fluctuations may then lead to a likelihood maximum associated with the "wrong" peak. When this happens, a blind search for the maximum likelihood will result in a TOA off by 0.5/ν s which must be excluded from the timing solution fit. To avoid loss of data, rather than employing a blind search, we "track" the solution. That is, provided the trial solution is sufficiently good (and this is always the case with iteration), the drift of the actual arrival time from the predicted arrival time is much less than half of a period. We then simply restrict the search for the likelihood maximum to within a range that excludes the "wrong" peak.

The measured sets of TOAs are then fitted to a timing model using the pulsar timing software Tempo2 (Hobbs et al. 2006; Edwards et al. 2006). There are many parameters that can be used in the timing models. For all pulsars we fit for pulse frequency (ν), frequency first derivative ($\dot{\nu }$), and frequency second derivative ($\ddot{\nu }$). We fit for $\ddot{\nu }$ as a measure of the timing noise present in each pulsar. In most cases, a significant $\ddot{\nu }$ is not detected and we report a 2σ upper limit on the magnitude $|\ddot{\nu }|$. In the cases where $\ddot{\nu }$ is measured, we attribute this solely to timing noise as the $\ddot{\nu }$ expected from any reasonable braking index would be immeasurable over our 18 month data span. If this is still insufficient to whiten the residuals, we add a third frequency derivative, or harmonically related sinusoids (WAVE parameters in Tempo2, see Hobbs et al. (2004)) to the fit until a satisfactory model is achieved. Note that because of large covariances between the parameters, one should avoid fitting the position and WAVE parameters at the same time.

Finally, in three cases (PSRs J0007+7303, J1124−5916, J1813−2332), a glitch was observed and several glitch parameters were added to the fit, as described in Section 3.

In our models, the absolute phase 0.0 is arbitrary. In the case of pulsars with both radio and γ-ray emission, the convention is usually to assign phase 0 as the peak of the radio pulse (as a proxy for the more physically meaningful point of closest approach of the magnetic axis to the line of sight). However, since we do not observe radio pulsations from most of these pulsars we have not attempted to define a particular phase 0. However, we do report the parameter TZRMJD for our models, which is the reference for phase 0.0. Phase 0.0 is the pulse phase at the time TZRMJD at the geocenter at infinite frequency.

As a final note, we want to emphasize that different timing models are appropriate for different purposes. One of the primary goals of this work is to use the capability of pulsar timing with the LAT to make accurate localizations of γ-ray-selected pulsars, thus enabling multiwavelength studies of potential counterparts. A secondary goal is characterizing the timing noise in this set of pulsars. For other purposes, different models are appropriate. In particular, for many studies it would be preferable to freeze the position using an accurately known counterpart position (from Chandra X-ray observations, for example) to reduce the number of free parameters in the model.

The Tempo2 timing models described here will all be made available electronically at the Fermi Science Support Center (FSSC) Web site.²⁰

One important use of the timing models presented here is to be able to assign an accurate pulse phase to each photon in a LAT observation of a particular pulsar. This is needed for studies of the γ-ray light curve, phase-resolved spectroscopy, or "gating" the data on the off-pulse region to blank out a pulsar to enable studies of faint sources nearby (e.g., Cyg X-3; Abdo et al. 2009c). The standard Fermi Science Tool gtpphase was developed for this application. However, it suffers from the limitation that it cannot represent the full complexity of pulsar timing models that include frequency derivatives above $\ddot{\nu }$, glitches, parallax, proper motion, or WAVE parameters. Tempo2, on the other hand, allows all of these as well as several additional orbital models for pulsars in binary systems.

For these reasons, we have implemented a graphical plugin for calculating pulsar phases for Fermi-LAT data with Tempo2, called fermi_plug.C. This plugin takes LAT event ("FT1") files with the photon arrival dates, spacecraft ("FT2") files with the satellite position as a function of time, and Tempo2 timing solutions and writes photon pulse phases in the FT1 event file. It uses the same spacecraft position interpolation algorithm as implemented in the Fermi science tool gtbary²¹ and derives barycentric photon times with analogous methods. The barycentric times are then treated as TOAs to find the pulsar phases relative to the absolute phase reference given by the TZRMJD parameter in the input ephemeris. The plugin thus allows Fermi-LAT data analysis with an ephemeris built from radio, X-ray, or γ-ray TOAs, with virtually unlimited complexity in the timing model. The plugin has been shown to reproduce the results from the Science Tools when working in tempo1 emulation mode, but using this mode is not required. It is available in the Tempo2 sourceforge distribution²² and from the FSSC.²³ This plugin is suitable for use with any of the timing models presented here.

The timing model parameters for this pulsar are displayed in Table 2 and the timing position determination, post-fit residuals, two-dimensional phaseogram, and folded pulse profile for this pulsar are shown in Figures 4, 5, and 6, respectively.

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Table 2. PSR J0007+7303

Parameter	Value
R.A., α (J2000.0)...............................	00:07:00.6 ±02
Decl., δ (J2000.0)..............................	+73:03:07.0 ±06
Monte Carlo position uncertainty......	2''
Pulse frequency, ν (s−1)....................	3.165827380(3)
Frequency first derivative, $\dot{\nu }$ (s−2).....	−3.6136(2) × 10−12
Frequency second derivative, $\ddot{\nu }$ (s−3)	−7(1) × 10−23
Epoch of frequency (MJD)...............	54952
Glitch epoch......................................	54952.652
Glitch Δν (s−1)..................................	1.759(3) × 10−6
Glitch $\Delta \dot{\nu }$ (s−2)..................................	0
TZRMJD..........................................	54952.334185720257651
Number of photons (nγ)....................	12790
Number of TOAs...............................	55
rms timing residual (ms)....................	2.2
Template profile.................................	KDE
Emin....................................................	150 MeV
ROI...................................................	15
Valid range (MJD)............................	54682–55222

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This was the first pulsar discovered in a blind search of γ-ray data (Abdo et al. 2008) and is believed to be the pulsar powering the compact PWN RX J0007.0+7303 near the center of the shell-type supernova remnant CTA1. As seen in Figure 4, our timing position provides independent confirmation of that conclusion. In addition, we have detected a glitch in this pulsar on 2009 May 1 with a magnitude Δν/ν = 5.53(1) × 10⁻⁷, a typical glitch magnitude for a pulsar of this age. When we fit for position in the timing model, the glitch can be fully accounted for by a simple Δν at the time of the glitch. However, when we hold the position fixed at the Chandra position of the point source (00:07:01.56, 73:03:08.3; see Halpern et al. 2004) we find that an additional parameter is required. This can be modeled as a change in the frequency first derivative at the glitch of $\Delta \dot{\nu }/\dot{\nu }$ of 0.0010(2). It is important to note that $\ddot{\nu }$ and glitch $\Delta \dot{\nu }$ are highly covariant and additional data will likely be required to determine whether timing noise or a frequency derivative change at the glitch is the correct model for the observed behavior. The properties of this source and the glitch will be discussed in more detail in a future paper (A. A. Abdo et al. 2011, in preparation).

The timing model parameters for this pulsar are displayed in Table 3 and the timing position determination, post-fit residuals, two-dimensional phaseogram, and folded pulse profile for this pulsar are shown in Figures 7, 8, and 9, respectively.

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Table 3. PSR J0357+3205

Parameter	Value
R.A., α (J2000.0)...............................	03:57:52.5 ±02
Decl., δ (J2000.0)...............................	+32:05:25 ±6''
Monte Carlo position uncertainty......	18''
Pulse frequency, ν (s−1).....................	2.251722292(3)
Frequency first derivative, $\dot{\nu }$ (s−2).....	−6.61(1)× 10−14
Frequency second derivative, $\ddot{\nu }$ (s−3)	$|\ddot{\nu }|<6\times 10^{-23}$
Epoch of frequency (MJD)................	54946
TZRMJD............................................	54946.341346723796502
Number of photons (nγ)....................	1335
Number of TOAs..............................	25
rms timing residual (ms)...................	5.3
Template profile................................	1 Gaussian
Emin....................................................	250 MeV
ROI....................................................	08
Valid range (MJD).............................	54682–55210

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PSR J0357+3205 is the slowest spin period (444 ms) and lowest $\dot{E}$ (5.8 × 10³³ erg s⁻¹) pulsar in our sample. In the discovery paper (Abdo et al. 2009a), it was flagged as having a potentially large systematic error in the $\dot{\nu }$ and the parameters derived from it, because of the uncertain position. The long period, low count rate, and relatively broad pulse profile still limit the timing precision to an rms of 5.3 ms, but nevertheless the frequency derivative is now determined to an accuracy of ∼0.2%.

For this low $\dot{E}$, the distance is constrained to be <870 pc, assuming the flux correction factor f_Ω = 1 (Watters et al. 2009) and using the LAT γ-ray flux (G₁₀₀) from Abdo et al. (2010d) to keep the γ-ray efficiency <1. As seen in Figure 7, no X-ray counterpart is apparent in a Swift image of the region, which is not surprising in such a shallow exposure. However, as the pulsar is at such a small distance, this is a promising target for deeper XMM-Newton or Chandra follow-up. Using the Tempo2 simulation capability, we predict a 1σ uncertainty on the timing position of 2'' after 5 years of observation.

The timing model parameters for this pulsar are displayed in Table 4 and the timing position determination, post-fit residuals, two-dimensional phaseogram, and folded pulse profile for this pulsar are shown in Figures 10, 11, and 12, respectively.

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Table 4. PSR J0633+0632

Parameter	Value
R.A., α (J2000.0)...............................	06:33:44.21 ±002
Decl., δ (J2000.0)...............................	+06:32:34.9 ±16
Monte Carlo position uncertainty......	35
Pulse frequency, ν (s−1).....................	3.3625291588(7)
Frequency first derivative, $\dot{\nu }$ (s−2).....	−8.9991(3) × 10−13
Frequency second derivative, $\ddot{\nu }$ (s−3)	−2(1) × 10−23
Epoch of frequency (MJD)................	54945
TZRMJD............................................	54945.385967311181439
Number of photons (nγ)....................	1174
Number of TOAs..............................	23
rms timing residual (ms)...................	1.4
Template profile................................	2 Gaussian
Emin...................................................	550 MeV
ROI....................................................	06
Valid range (MJD)..............................	54682–55208

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This pulsar is also rather slow (297 ms) and faint (only 815 photons detected per year), but the timing is still quite good (rms = 1.4 ms), as a result of the very narrow pulses. The timing localization is close to the X-ray point source Swift J063343.8+063223 which was proposed as the counterpart by Abdo et al. (2009a).

To further study the X-ray counterpart, we obtained a 20 ks Chandra ACIS-S image of the region on 2009 December 11 (ObsID 11123). The X-ray point source counterpart to the pulsar is clearly visible in Figure 10. We measure a position of 06:33:44.142, +06:32:30.40, which is 46 from the best-fit timing position. To fit the spectrum of this source, we analyzed the data using CIAO version 4.3 with the latest calibrations (CALDB 4.1.1) applying the standard particle background subtraction and exposure correction. We extracted 326 photons from a 3.5 pixel extraction region around the source location (for a count rate of 1.63 × 10⁻² counts s⁻¹). We see no evidence for a compact (arcsecond-scale) PWN in the immediate vicinity of the point source. To fit the spectrum, we found that an absorbed blackbody + power-law model is required. We obtain the following parameters from our fits, with 90% confidence error estimates: n_H = 0.15^+0.16_−0.10 × 10²² cm⁻², kT = 0.11^+0.03_−0.02 keV, Γ = 1.5 ± 0.6. This model yields a 0.5–8 keV flux estimate of 9.2^+1.8_−1.2 × 10⁻¹⁴ erg cm⁻² s⁻¹. If we instead fit an absorbed neutron star atmosphere (nsa; Zavlin et al. 1996) plus power-law model, we find a somewhat higher n_H of 0.24^+0.12_−0.21 × 10²² cm⁻², a lower temperature of kT = 0.048^+0.019_−0.016 keV, and a similar photon index Γ = 1.39^+0.6_−0.3.

To look for larger scale extended emission, we smoothed the Chandra image with a Gaussian kernel of 15 width (see Figure 13) and find a faint X-ray nebula extending about an arcminute south of the pulsar. In the region of the PWN (as shown in Figure 13), we find an excess of 738 counts on a background of about 1600 counts and have fit the integrated spectrum with an absorbed power-law model. With all parameters free, we find n_H = 0.1^+0.3_−0.1 × 10²² cm⁻², Γ = 0.9^+0.5_−0.4 for a flux in the 0.5–8 keV band of 2.2 ± 0.5 × 10⁻¹³ erg cm⁻² s⁻¹, where the error regions are at the 90% confidence level. If instead, we freeze n_H at 0.154 × 10²² cm⁻², as found in the blackbody + power-law spectral fits of the point source, we find a 90% confidence range for the photon spectral index Γ of 0.74–1.29.

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The timing model parameters for this pulsar are displayed in Table 5 and the timing position determination, post-fit residuals, two-dimensional phaseogram, and folded pulse profile for this pulsar are shown in Figures 14, 15, and 16, respectively.

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Table 5. PSR J1124−5916

Parameter	Value
R.A., α (J2000.0)...............................	11:24:39.0(1)
Decl., δ (J2000.0)...............................	−59:16:19(1)
Pulse frequency, ν (s−1).....................	7.381334652(9)
Frequency first derivative, $\dot{\nu }$ (s−2).....	−4.10029(9) × 10−11
Frequency second derivative, $\ddot{\nu }$ (s−3)	−8.6(4) × 10−22
Epoch of frequency (MJD)................	54683.281414
Glitch epoch (MJD)...........................	55191
Glitch Δν (s−1)...................................	1.18(9) ×10−7
Glitch $\Delta \dot{\nu }$ (s−2)...................................	1.94(2) ×10−13
TZRMJD............................................	55053.0521054597626
TZRFREQ (MHz)..............................	1371.067
TZRSITE...........................................	7 (Parkes)
Number of photons (nγ)....................	5030
Number of TOAs..............................	40
rms timing residual (ms)...................	2.8
Template profile................................	2 Gaussian
Emin...................................................	200 MeV
ROI....................................................	09
Valid range........................................	54682–55415

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This pulsar with a very small characteristic age ($\tau _c = P/2\dot{P} = 2900$ yr) is associated with the supernova remnant G292.0+1.8 and is the only one in this sample that was previously known as a radio pulsar (Camilo et al. 2002). It has a very high $\dot{E}$ of 1.2 ×10³⁷ erg s⁻¹ and exhibits a great deal of timing noise. It is also is very faint, with a 1.4 GHz flux density of only 0.08 mJy (Camilo et al. 2002) and far enough south that it can only be timed with the Parkes Telescope, where it requires several hours of integration to even get a detection. Therefore, it has not been regularly timed with radio observations since its discovery. Because there was no contemporaneous radio ephemeris available, the LAT pulsations from this source were discovered using a limited blind search around the known spin parameters. With our LAT timing, we are able to obtain TOA uncertainties of 1.5–3.2 ms every two weeks and obtain a phase-connected timing model. The timing position is 18 from the Chandra source CXOU J112439.1−591620 (Camilo et al. 2002). The pulsar exhibited a glitch of magnitude Δν/ν = 1.6 × 10⁻⁸ around MJD 55191. A small $\Delta \dot{\nu }/\dot{\nu }$ of −0.00472(3) was also observed at the glitch.

The very large measured $\ddot{\nu }$ results in a Monte Carlo position error estimate of about 1', but given the good agreement between the timing position and the Chandra position, this must be a large overestimate, perhaps because the assumptions inherent in the Monte Carlo estimate are violated. The measured $\ddot{\nu }$ results in a braking index $n = \frac{\nu \ddot{\nu }}{\dot{\nu }^2} = -3.78$, which is of comparable magnitude, but opposite in sign to the n = 3 expected for vacuum dipole braking (Lorimer & Kramer 2005). This measurement along with the substantial red noise still present in the timing residuals (see Figure 15) all suggest that the spin down of this pulsar is rather noisy.

To measure the radio to γ-ray phase alignment of this pulsar, we made a 5 hr observation with the Parkes Radio Telescope at a frequency of 1.4 GHz. Since this pulsar is not timed routinely in the radio, we required a new, contemporaneous, observation because the extreme timing noise in this system prevents the timing model from being extrapolated forward or backward in time. This radio light curve was presented previously in the First Fermi LAT Catalog of Gamma-ray Pulsars (Abdo et al. 2010d), but the absolute phase alignment presented there was incorrect. The version presented here correctly accounts for the delay from interstellar dispersion using DM = 330 pc cm⁻³. The new value for the lag from the radio peak to the first γ-ray peak (δ) is 0.128(3). This correction was also made to the catalog in an erratum (Abdo et al. 2010d).

The timing model parameters for this pulsar are displayed in Table 6 and the timing position determination, post-fit residuals, two-dimensional phaseogram, and folded pulse profile for this pulsar are shown in Figures 17, 18, and 19, respectively.

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Table 6. PSR J1418−6058

Parameter	Value
R.A., α (J2000.0)...............................	14:18:42.7 ±01
Decl., δ (J2000.0)...............................	−60:57:49 ±2''
Monte Carlo position uncertainty......	7''
Pulse frequency, ν (s−1).....................	9.043798163(1)
Frequency first derivative, $\dot{\nu }$ (s−2).....	−1.38548(8) × 10−11
Frequency second derivative, $\ddot{\nu }$ (s−3)	6.4(3) × 10−22
Frequency third derivative, $\tdot{\nu }$ (s−4)....	−8(2) × 10−29
Epoch of frequency (MJD)................	54944
TZRMJD............................................	54944.2886329214
Number of photons (nγ).....................	7283
Number of TOAs..............................	33
rms timing residual (ms)...................	1.9
Template profile................................	KDE
Emin...................................................	250 MeV
ROI....................................................	05
Valid range (MJD).............................	54682–55205

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In the discovery paper, this pulsar was proposed to be associated with the PWN G313.3+0.1 ("The Rabbit"). Ng et al. (2005) find two point sources (R1 and R2) in Chandra and XMM observations of the region. Recently, Roberts (2009) reported a weak detection of X-ray pulsations at the period of PSR J1418−6058 in XMM data, so it is believed that R1 is the correct counterpart. However, the timing position is 14'' from the position of R1 (R.A. = 14:18:42.7, decl. = −60:58:03), which is significantly larger than the 2'' statistical error on the position. It is important to note that this pulsar is very noisy and the timing model, which includes terms up to the frequency third derivative, clearly does not fully describe the data (see Figures 18 and 19). This causes the statistical error to be underestimated and there is a significant systematic error on the position as well. For example, adding a fourth frequency derivative to the model causes the position to shift by 10''. As seen in Figure 17, there are three X-ray point sources near the nominal timing position, but none are coincident with the timing position. The X-ray point source R2 is not apparent in this image, so it is likely variable, and probably not the counterpart to the pulsar. A Monte Carlo estimation of the systematic error (see Section 3) on the position induced by the timing noise seen in this pulsar is 7'' for the polynomial model for timing noise and 40'' using the red noise model with an rms of 62 ms (as computed from the measured $\ddot{\nu }$ and $\tdot{\nu }$ for the pulsar). Therefore, we cannot exclude R1 as being the counterpart based on the positional disagreement. In addition, the faint X-ray source just north of the pulsar, which we call CXOU J141843.3−605734, is equally consistent with the timing and so further data, or a confirmation of the X-ray pulsations from R1, will be required to confirm the association with either source.

The timing model parameters for this pulsar are displayed in Table 7 and the timing position determination, post-fit residuals, two-dimensional phaseogram, and folded pulse profile for this pulsar are shown in Figures 20, 21, and 22, respectively.

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Table 7. PSR J1459−6053

Parameter	Value
R.A., α (J2000.0)...............................	14:59:29.99 ±006
Decl., δ (J2000.0)...............................	−60:53:20.7 ±04
Monte Carlo position uncertainty......	13
Pulse frequency, ν (s−1).....................	9.694559498(1)
Frequency first derivative, $\dot{\nu }$ (s−2).....	−2.37503(5) × 10−12
Frequency second derivative, $\ddot{\nu }$ (s−3)	−4(2) × 10−23
Epoch of frequency (MJD)................	54935
TZRMJD............................................	54936.19962194
Number of photons (nγ)....................	3305
Number of TOAs..............................	26
rms timing residual (ms)...................	1.1
Template profile................................	KDE
Emin...................................................	350 MeV
ROI....................................................	07
Valid range (MJD).............................	54682–55210

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In the discovery paper, no counterpart was known for this pulsar. With the high precision timing now available, we see that the Swift image shows an apparent faint point source near (98 offset from) the timing position (see Figure 20). We call this source Swift J145931.3−605319, but its properties are not well constrained because of the faintness in the 6 ks Swift image. A deeper X-ray image is required to confirm this source.

The timing model parameters for this pulsar are displayed in Table 8 and the timing position determination, post-fit residuals, two-dimensional phaseogram, and folded pulse profile for this pulsar are shown in Figures 23, 24, and 25, respectively.

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Table 8. PSR J1732−3131

Parameter	Value
R.A., α (J2000.0)...............................	17:32:33.54 ±003
Decl., δ (J2000.0)...............................	−31:31:23 ±2''
Monte Carlo position uncertainty......	3''
Pulse frequency, ν (s−1).....................	5.0879411200(5)
Frequency first derivative, $\dot{\nu }$ (s−2).....	−7.2609(3) × 10−13
Frequency second derivative, $\ddot{\nu }$ (s−3)	$|\ddot{\nu }|<2\times 10^{-23}$
Epoch of frequency (MJD)................	54933
TZRMJD............................................	54957.3282196892
Number of photons (nγ)....................	4236
Number of TOAs..............................	22
rms timing residual (ms)...................	1.0
Template profile................................	KDE
Emin...................................................	400 MeV
ROI....................................................	05
Valid range (MJD)............................	54682–55207

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This source shows minimal timing noise, with only an upper limit of 2 × 10⁻²³ s⁻³ on $|\ddot{\nu }|$. The timing error ellipse is significantly elongated because of the low ecliptic latitude of the source (β = −82), causing the declination to be more poorly constrained than the R.A. Earlier Swift imaging showed no significantly detected X-ray source at the pulsar location, so we pursued a deeper observation with Chandra. Our 20 ks Chandra ACIS-S image (ObsID 11125) reveals an X-ray point source consistent with the timing position (see Figure 23). We measure the position as 17:32:33.551, −31:31:23.92, which is 09 from the timing position, well within the 95% confidence region.

We performed a spectral analysis of the source based on 79 photons from the point source (with ≲1 count from the background). Since the source is still detected even with a low-energy cut of 3.5 keV, it is clear that a non-thermal component is required. However, with the small number of counts, the power-law photon index cannot be constrained, so we freeze it at Γ = 1.5 in the fits. The spectral parameters from our fits to an absorbed blackbody + power-law are (with 90% confidence error regions) n_H = 0.22^+0.50_−0.22 × 10²² cm⁻², kT = 0.19^+0.20_−0.07 keV. The implied 0.5–8 keV flux estimate is (2.8 ± 0.7) × 10⁻¹⁴ erg cm⁻² s⁻¹ with the error at the 68% confidence interval. This corresponds to an unabsorbed flux of 4 × 10⁻¹⁴ erg cm⁻² s⁻¹.

The timing model parameters for this pulsar are displayed in Table 9 and the timing position determination, post-fit residuals, two-dimensional phaseogram, and folded pulse profile for this pulsar are shown in Figures 26, 27, and 28, respectively.

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Table 9. PSR J1741−2054

Parameter	Value
R.A., α (J2000.0)...............................	17:41:57.23 ±005
Decl., δ (J2000.0)...............................	−20:53:57 ±19''
Monte Carlo position uncertainty......	20''
Pulse frequency, ν (s−1).....................	2.417209833(1)
Frequency first derivative, $\dot{\nu }$ (s−2).....	−9.923(3) × 10−14
Frequency second derivative, $\ddot{\nu }$ (s−3)	$|\ddot{\nu }|<2\times 10^{-23}$
Epoch of frequency (MJD)................	54933
TZRMJD............................................	54945.3859666189
Number of photons (nγ)....................	3135
Number of TOAs..............................	23
rms timing residual (ms)...................	2.6
Template profile................................	KDE
Emin...................................................	300 MeV
ROI....................................................	08
Valid range (MJD)............................	54682–55208

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The bright X-ray counterpart (Swift J174157.6−205411) seen in Figure 26 was proposed as the likely counterpart to this pulsar in the discovery paper. Subsequently, a LAT timing position presented by Camilo et al. (2009), who also reported the discovery of radio pulsations from this pulsar, added confidence to this proposal, and the model we present here strengthens the case. The position error is still highly elongated in the declination direction because of the very low ecliptic latitude of the source. The X-ray source properties are studied in detail in Camilo et al. (2009). The larger span of data included in this model results in significantly more counts in the light curve, confirming the apparent 3-peak nature as proposed by Camilo et al. (2009), in contrast to the peak multiplicity of 2 assigned by Abdo et al. (2010d).

The timing model parameters for this pulsar are displayed in Table 10 and the timing position determination, post-fit residuals, two-dimensional phaseogram, and folded pulse profile for this pulsar are shown in Figures 29, 30, and 31, respectively.

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Table 10. PSR J1809−2332

Parameter	Value
R.A., α (J2000.0)...............................	18:09:50.31 ±006
Decl., δ (J2000.0)...............................	−23:33:35 ±51''
Monte Carlo position uncertainty......	28''
Pulse frequency, ν (s−1).....................	6.8125205463(3)
Frequency first derivative, $\dot{\nu }$ (s−2).....	−1.59748(1) × 10−12
Frequency second derivative, $\ddot{\nu }$ (s−3)	$|\ddot{\nu }|<1\times 10^{-23}$
Epoch of frequency (MJD)................	54935
TZRMJD............................................	54947.1551911038
Number of photons (nγ)....................	10422
Number of TOAs..............................	27
rms timing residual (ms)...................	0.4
Template profile................................	KDE
Emin...................................................	250 MeV
ROI....................................................	08
Valid range (MJD)............................	54682–55211

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This pulsar was discovered in the direction of the Galactic unidentified γ-ray source GeV J1809−2327. Chandra observations revealed a probable pulsar with PWN that was proposed as the source of the γ-rays (Braje et al. 2002). The point source, CXOU J180950.2−233223, was assumed as the counterpart by Abdo et al. (2009a). As seen in Figure 29, the position error ellipse is very strongly elongated, again because of the very low ecliptic latitude of the source. Nevertheless, the X-ray point source is within the timing error ellipse, strengthening the identification with this point source. If the TOAs are fitted with the position held fixed at the location of the Chandra point source, there are significant correlated residuals, which require a frequency third derivative term in the model to give a reasonable χ² for the fit.

The timing model parameters for this pulsar are displayed in Table 11 and the timing position determination, post-fit residuals, two-dimensional phaseogram, and folded pulse profile for this pulsar are shown in Figures 32, 33, and 34, respectively.

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Table 11. PSR J1813−1246

Parameter	Value
R.A., α (J2000.0)...............................	18:13:23.77 ±001
Decl., δ (J2000.0)...............................	−12:45:59.2 ±15
Monte Carlo position uncertainty......	15
Pulse frequency, ν (s−1).....................	20.802023359(3)
Frequency first derivative, $\dot{\nu }$ (s−2).....	−7.60023(9) × 10−12
Frequency second derivative, $\ddot{\nu }$ (s−3)	$|\ddot{\nu }|<6\times 10^{-23}$
Glitch epoch.......................................	55094.1227
Glitch Δν (s−1)...................................	2.4256(9) × 10−5
Glitch $\Delta \dot{\nu }$ (s−2)...................................	−4.9(2) × 10−14
TZRMJD............................................	54954.309848738
Number of photons (nγ)....................	11611
Number of TOAs..............................	91
rms timing residual (ms)...................	0.7
Template profile................................	KDE
Emin...................................................	200 MeV
ROI....................................................	10
Valid range........................................	54682–55226

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This pulsar, which has the highest spin-down luminosity of the first 16 blind search pulsars discovered with the LAT, exhibited a glitch on about 2009 September 20 with magnitude Δν/ν = 1.17 × 10⁻⁶. The timing model for the glitch presented here represents the data fairly well, but is not unique. Our model includes an instantaneous and permanent jump in the pulsar frequency and frequency derivative at the glitch. Other solutions are possible with slightly different glitch epochs (within a day or so) and different parameters, or with decaying transient changes in the spin parameters at the glitch. With 6 days between TOA measurements and significant timing noise seen in this pulsar, we are not able to distinguish between these possibilities. It is clear in Figure 33 that there are significant non-white residuals remaining in the data, indicating that the model is not fully accounting for the spin-down behavior of the pulsar. With a longer span of post-glitch data a more definitive model may be possible.

The bright X-ray source, Swift J181323.4−124600, was noted as the counterpart to this pulsar in the discovery paper and our timing confirms the association.

The timing model parameters for this pulsar are displayed in Table 12 and the timing position determination, post-fit residuals, two-dimensional phaseogram, and folded pulse profile for this pulsar are shown in Figures 35, 36, and 37, respectively.

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Table 12. PSR J1826−1256

Parameter	Value
R.A., α (J2000.0)...............................	18:26:08.53 ±001
Decl., δ (J2000.0)...............................	−12:56:33.0 ±05
Monte Carlo position uncertainty......	17''
Pulse frequency, ν (s−1).....................	9.0724588059(3)
Frequency first derivative, $\dot{\nu }$ (s−2).....	−9.99654(1) × 10−12
Frequency second derivative, $\ddot{\nu }$ (s−3)	1.85(5) × 10−22
Epoch of frequency (MJD)................	54934
TZRMJD............................................	54946.3413482956
Number of photons (nγ)....................	10860
Number of TOAs..............................	25
rms timing residual (ms)...................	0.28
Template profile................................	KDE
Emin...................................................	200 MeV
ROI....................................................	06
Valid range........................................	54682–55210

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The fast spin and narrow pulse profile allow this pulsar to be localized to about 1''. The timing position is consistent with the X-ray point source AX J1826.1−1257 (R.A. = 18:26:08.2, decl. = −12:56:46), which was discovered in ASCA observations of the EGRET γ-ray source GeV J1825−1310 (Roberts et al. 2001). An improved position of the X-ray point source (R.A. = 18:26:08.54, decl. = −12:56:34.6) was derived from a Chandra image (M. Roberts 2010, private communication), which is 16 from the timing position. The measured $\ddot{\nu }$ for this pulsar is quite large, and the Monte Carlo error estimate yields 17'', which is much larger than the offset seen between the timing position and the X-ray counterpart.

The timing model parameters for this pulsar are displayed in Table 13 and the timing position determination, post-fit residuals, two-dimensional phaseogram, and folded pulse profile for this pulsar are shown in Figures 38, 39, and 40, respectively.

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Table 13. PSR J1836+5925

Parameter	Value
R.A., α (J2000.0)...............................	18:36:13.69 ±002
Decl., δ (J2000.0)...............................	+59:25:30.0 ±03
Monte Carlo position uncertainty......	<3''
Pulse frequency, ν (s−1).....................	5.7715509149(4)
Frequency first derivative, $\dot{\nu }$ (s−2).....	−5.007(2) × 10−14
Frequency second derivative, $\ddot{\nu }$ (s−3)	−1.3(8) × 10−23
Epoch of frequency (MJD)................	54935
TZRMJD............................................	54936.1996219705
Number of photons (nγ)....................	14875
Number of TOAs..............................	26
rms timing residual (ms)...................	0.85
Template profile................................	KDE
Emin...................................................	200 MeV
ROI....................................................	16
Valid range........................................	54682–55210

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A detailed analysis and earlier timing model for this source were published by Abdo et al. (2010a). Our model, which includes an additional 6 months of data is consistent with the earlier results with the addition of a weak detection of a frequency second derivative term. As seen in Figure 38, the timing position is fully consistent with the X-ray source RX J1836.2+5925, with the offset being only 02.

The timing model parameters for this pulsar are displayed in Table 14 and the timing position determination, post-fit residuals, two-dimensional phaseogram, and folded pulse profile for this pulsar are shown in Figures 41, 42, and 43, respectively.

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Table 14. PSR J1907+0602

Parameter	Value
R.A., α (J2000.0)...............................	19:07:54.74 ±001
Decl., δ (J2000.0)...............................	+06:02:16.9 ±03
Monte Carlo position uncertainty......	25
Pulse frequency, ν (s−1).....................	9.3779822336(4)
Frequency first derivative, $\dot{\nu }$ (s−2).....	−7.63559(2) × 10−12
Frequency second derivative, $\ddot{\nu }$ (s−3)	1.88(7) × 10−22
Epoch of frequency (MJD)................	54935
TZRMJD............................................	54947.1551911789
Number of photons (nγ)....................	10629
Number of TOAs..............................	27
rms timing residual (ms)...................	0.47
Template profile................................	KDE
Emin...................................................	50 MeV
ROI....................................................	07
Valid range........................................	54682–55211

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A detailed analysis of this pulsar, including an earlier timing solution and the discovery of radio pulsations, was presented by Abdo et al. (2010c). Our timing model is fully consistent within the errors to the one they presented, though we now have almost 5 months of additional data, which significantly reduces the uncertainties in the parameters. The position reported for the Chandra point source is 23 from our best timing position, which is significantly larger than the 06 statistical error in the timing position or the 06 error in the Chandra position. However, the offset is comparable to the expected systematic error from timing noise, based on the Monte Carlo simulations, so this is not strong evidence against the association.

The timing model parameters for this pulsar are displayed in Table 15 and the timing position determination, post-fit residuals, two-dimensional phaseogram, and folded pulse profile for this pulsar are shown in Figures 44, 45, and 46, respectively.

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Table 15. PSR J1958+2846

Parameter	Value
R.A., α (J2000.0)...............................	19:58:40.07 ±003
Decl., δ (J2000.0)...............................	+28:45:54 ±1''
Monte Carlo position uncertainty......	35
Pulse frequency, ν (s−1).....................	3.4436537099(5)
Frequency first derivative, $\dot{\nu }$ (s−2).....	−2.5145(2) × 10−12
Frequency second derivative, $\ddot{\nu }$ (s−3)	3(2) × 10−23
Epoch of frequency (MJD)................	54800
TZRMJD............................................	54957.3282188686
Number of photons (nγ)....................	1910
Number of TOAs..............................	26
rms timing residual (ms)...................	2.1
Template profile................................	2 Gaussian
Emin...................................................	550 MeV
ROI....................................................	06
Valid range........................................	54682–55210

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In the discovery paper (Abdo et al. 2009a), the X-ray source Swift J195846.1+284602 was proposed as the likely counterpart and used for the name of the pulsar. As shown in Figure 44, the timing position no longer supports this identification, being offset from the X-ray source by 80''. There is no significant X-ray counterpart detected at the timing position. There is also no indication for strong timing noise in this pulsar, which might cause a large systematic error in the timing position. Deeper X-ray observations will be required to detect the true X-ray counterpart for this source.

The timing model parameters for this pulsar are displayed in Table 16 and the timing position determination, post-fit residuals, two-dimensional phaseogram, and folded pulse profile for this pulsar are shown in Figures 47, 48, and 49, respectively.

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Table 16. PSR J2021+4026

Parameter	Value
R.A., α (J2000.0)...............................	20:21:29.99 ±003
Decl., δ (J2000.0)...............................	+40:26:45.1 ±07
Monte Carlo position uncertainty......	25
Pulse frequency, ν (s−1).....................	3.7690668480(6)
Frequency first derivative, $\dot{\nu }$ (s−2).....	−7.7681(3) × 10−13
Frequency second derivative, $\ddot{\nu }$ (s−3)	3.9(2) × 10−22
Epoch of frequency (MJD)................	54936
TZRMJD............................................	54957.3282196715
Number of photons (nγ)....................	11853
Number of TOAs..............................	30
rms timing residual (ms)...................	2.0
Template profile................................	KDE
Emin...................................................	400 MeV
ROI....................................................	07
Valid range........................................	54682–55213

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PSR J2021+4026 is the long-sought pulsar in the γ Cygni supernova remnant (SNR G78.2+2.1). In the discovery paper (Abdo et al. 2009a), it was pointed out that the X-ray source S21, as identified earlier in Chandra observations (Weisskopf et al. 2006), was the most likely counterpart based on the initial pulsar timing. Our best-fit position is 77 to the west of S21 (see Figure 47), an offset that is somewhat larger than the predicted systematic error of 25 based on our Monte Carlo. However, when $\tdot{\nu }$ is added to the model, the position shifts by 46, so this is a lower bound on the systematic error from the timing noise. As S21 is still the closest X-ray source to the timing position, we conclude that it is indeed the likely counterpart. Longer term timing will improve our localization and reduce the systematic error contribution from timing noise. A similar conclusion was reached by Trepl et al. (2010).

Both the timing position and the X-ray source S21 are well outside the 95% confidence localization ellipse of the LAT sources, as seen in Figure 47. However, this region includes statistical errors only and this source is in the very complicated Cygnus region of the Galaxy. The localization of 0FGL J2021.5+4026 in the LAT Bright Source List (Abdo et al. 2009b) did include S21, but with the improved statistics using 18 months of data, systematic errors due to improperly modeled diffuse emission or unknown point sources can start to dominate the error budget. The association of the LAT source with the pulsar is beyond doubt because of the detection of pulsations.

The timing model parameters for this pulsar are displayed in Table 17 and the timing position determination, post-fit residuals, two-dimensional phaseogram, and folded pulse profile for this pulsar are shown in Figures 50, 51, and 52, respectively.

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Table 17. PSR J2032+4127

Parameter	Value
R.A., α (J2000.0)...............................	20:32:13.25 ±001
Decl., δ (J2000.0)...............................	+41:27:24.8 ±03
Monte Carlo position uncertainty......	3''
Pulse frequency, ν (s−1).....................	6.9809196293(4)
Frequency first derivative, $\dot{\nu }$ (s−2).....	−9.9293(2) × 10−13
Frequency second derivative, $\ddot{\nu }$ (s−3)	−1.88(1) × 10−21
Epoch of frequency (MJD)................	54938
TZRMJD............................................	54951.224402859
Number of photons (nγ)....................	1633
Number of TOAs..............................	45
rms timing residual (ms)...................	0.9
Template profile................................	2 Gaussian
Emin...................................................	900 MeV
ROI....................................................	05
Valid range........................................	54682–55220

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This pulsar is studied in detail by Camilo et al. (2009) who reported the discovery of radio pulsations from this source. The model presented here is consistent with theirs, and the positional association with the Chandra point source MT91 213 is confirmed (see Figure 50).

The timing model parameters for this pulsar are displayed in Table 18 and the timing position determination, post-fit residuals, two-dimensional phaseogram, and folded pulse profile for this pulsar are shown in Figures 53, 54, and 55, respectively.

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Table 18. PSR J2238+5903

Parameter	Value
R.A., α (J2000.0)...............................	22:38:28.27 ±004
Decl., δ (J2000.0)...............................	+59:03:40.8 ±04
Monte Carlo position uncertainty......	3''
Pulse frequency, ν (s−1).....................	6.1450029089(4)
Frequency first derivative, $\dot{\nu }$ (s−2).....	−3.6641(2) × 10−12
Frequency second derivative, $\ddot{\nu }$ (s−3)	1.1(2) × 10−22
Epoch of frequency (MJD)................	54800
TZRMJD............................................	54947.1551907197
Number of photons (nγ)....................	1697
Number of TOAs..............................	27
rms timing residual (μs)......	1171
Template profile................................	2 Gaussian
Emin...................................................	250 MeV
ROI....................................................	05
Valid range........................................	54682–55211

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Even though this pulsar is quite faint, it can be timed with an rms residual of 1 ms because of its very sharp pulse profile. Consequently, we now have a very precise timing position, but there is no significant X-ray counterpart detected in the Swift image (see Figure 53). The pulsar is located 0°.6 from the radio pulsar J2240+5832 detected recently in γ-rays (Theureau et al. 2011). The narrow pulse profile means that this pulsar can be blanked from the LAT data with a loss of only ∼20% of the exposure time.