CONSTRAINTS ON THE GALACTIC POPULATION OF TeV PULSAR WIND NEBULAE USING FERMI LARGE AREA TELESCOPE OBSERVATIONS

This paper uses 45 months of data collected from 2008 August 4 to 2012 April 18 (mission elapsed time: 239,557,440–356,439,741 s) for regions centered on the positions of each VHE source. We excluded γ-rays coming from a zenith angle larger than 100°. We used the Pass 7 Clean event class that has substantially less instrumental background above 10 GeV with only a marginal loss in effective area, compared to the Pass 7 Source event class (Ackermann et al. 2012).

We analyzed LAT data only between 10 and 316 GeV to avoid systematics associated with the modeling of adjacent sources with soft spectra. It also reduces systematics associated with imperfect modeling of the Galactic diffuse emission. The maximum energy of 316 GeV increases the overlap between the energy range covered by the VHE experiments and the LAT. The 100–316 GeV energy range was also shown to be crucial in previous analyses like Rousseau et al. (2012).

Figure 1 shows a background-subtracted count map of the Galactic plane observed by the LAT above 10 GeV. The bright Vela (l, b = 26355, −279) and Geminga (l, b = 19513, 427) pulsars and the SNR IC 443 (l, b = 18906, 323) clearly stand out. In addition to these well-known objects, a large number of other sources are apparent. Several are coincident with sources detected by VHE experiments, such as HESS J1614−518 and HESS J1616−508 (Lande et al. 2012), and will be discussed in Section 4. The large number of other sources visible in the map highlights the LAT sensitivity at high energies.

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Two different software packages for maximum likelihood fitting were used to analyze LAT data: $\mathtt {gtlike}$ and $\mathtt {pointlike}$. These tools fit LAT data with a parameterized model of the sky, including models for the instrumental, extragalactic, and Galactic components of the background.

The first one, $\mathtt {gtlike}$, is a maximum likelihood method distributed in the Fermi Science Tools by the FSSC.⁶⁴ We used version 09-28-00 of the package in binned mode. The second, $\mathtt {pointlike}$, is an alternate software package that we used to fit the positions of point-like sources and fit the spatial parameters of spatially extended sources. Kerr (2011) describes the implementation of $\mathtt {pointlike}$, and Lande et al. (2012) validate $\mathtt {pointlike}$'s extension-fitting functionality. In $\mathtt {pointlike}$, the data are binned spatially, using a HEALPix pixelization⁶⁵ (Górski et al. 2005), and spectrally, and the likelihood is maximized over all bins in a region.

We used $\mathtt {pointlike}$ to evaluate a position and extension estimate in the LAT data for each source of our sample. Using those morphologies, we used $\mathtt {gtlike}$ to obtain the best-fit spectral parameters and statistical significances. $\mathtt {gtlike}$ makes fewer approximations in calculating the likelihood for spectra than $\mathtt {pointlike}$. Both methods agree with each other within 10% for all derived quantities, but all spectral parameters quoted in the following were obtained using $\mathtt {gtlike}$.

Since $\mathtt {pointlike}$ and $\mathtt {gtlike}$ use two different shapes for the regions of the sky modeled for each source, we included photons within a radius of 5° centered on our source of interest when using $\mathtt {pointlike}$ and within a 7° × 7° square region aligned with Galactic coordinates when using $\mathtt {gtlike}$. We tried to keep the two methods as close as possible by using the same conventions, i.e., same energy binning of eight energy bins per decade between 10 and 316 GeV, and the same optimizer: MINUIT (James & Roos 1975).

The Galactic diffuse emission was modeled by the standard LAT interstellar emission model ring_2yearp7v6_v0.fits. The residual cosmic-ray background and extragalactic radiation are described by a single isotropic component with a spectral shape described by the file isotrop_2year_P76_clean_v0.txt. The models have been released and described by the Fermi-LAT Collaboration through the FSSC.⁶⁶ In the following, we fit the Galactic diffuse normalization. Since the isotropic diffuse component is not well constrained over the small regions of interest used in this work, we fixed its normalization to 1.

We included in our sky model all cataloged LAT sources within a radius of 10° of each source of interest and listed in the hard source list (Paneque et al. 2013), henceforth "1FHL." The 1FHL catalog is a forthcoming catalog of sources using 3 yr of LAT data above 10 GeV. The data selection used clean events as done in this work. The spectral parameters of sources closer than 2° to the source of interest were fit, while the spectra of all other 1FHL sources were fixed.

γ-ray pulsars are found near many of the VHE sources. Table 2 summarizes the sources analyzed in this paper that are near an LAT-detected pulsar. In the LAT energy range, pulsars tend to be brighter than their associated PWNe (Ackermann et al. 2011). During the fit, the observed photon sample is shared by all modeled sources. The high energy range used in this work prevents a reasonable fit of a pulsar component modeled by a power law with an exponential cutoff spectrum. If a pulsar's model overestimates its emission above 10 GeV, a putative PWN emission would be underestimated. This effect could obscure the detection of a faint PWN. On the contrary, not including an existing source, such as a pulsar, would artificially increase the flux attributed to a putative PWN at low energy. Therefore, we decided to keep as separate sources in the model all pulsars located outside the VHE experiment template and more than 027 away from the source of interest. The 027 radius corresponds to the 68% containment radius of the point-spread function (PSF) averaged over energies above 10 GeV (Ackermann et al. 2012). For VHE sources less than 027 from an LAT-detected pulsar, we analyzed the sources twice. Removing the pulsar from the background model amounts to neglecting it, while leaving it in the background model amounts to subtracting the underlying pulsar contribution from each putative PWN. In all cases, the parameters of the pulsar models have been fixed to those obtained in the 2FGL catalog (Nolan et al. 2012). If contamination from the pulsar is a concern, it is possible to phase-fold photons and analyze the data in the off-peak phase intervals of the pulsar. This will be performed in 2PC. Here we analyze data at all phases to have the largest possible statistics and therefore better sensitivity to faint PWNe.

Due to the 45 month integration time of our analysis compared to the 36 months of the forthcoming 1FHL catalog, we expected to find new statistically significant background sources. To prevent bias from these sources, we included in our model any nearby background sources with a significance above 4σ (TS > 25 with 4 degrees of freedom, dof). We fit their spectra with power laws. The locations and spectra of the six such sources found in our analysis are described in Table 3.

We developed a uniform procedure for analyzing any potential emission in the 58 regions listed in Table 1. The small statistics above 10 GeV and the narrow energy range (1.5 decade) prevent any spectral curvature from being significant as will be discussed in the 1FHL catalog. Therefore, in the following we derived the spectra assuming a power-law spectral model:

$$\begin{equation} \frac{{\it dF}}{{\it dE}}=N_0 \left(\frac{E}{E_0} \right)^{-\Gamma }, \end{equation} \tag{ 1 }$$

where N₀ is the normalization, Γ is the spectral index, and E₀ is the scale parameter. To minimize the covariance between N₀ and Γ, we ran the analysis twice. In the first iteration, we fitted the source assuming a power-law model depending on the integral flux F and Γ,

$$\begin{equation} \frac{{\it dF}}{{\it dE}}=\frac{F (-\Gamma +1) E^{-\Gamma }}{E_{{\rm max}}^{-\Gamma +1}-E_{{\rm min}}^{-\Gamma +1}}. \end{equation} \tag{ 2 }$$

Using the covariance matrix of the fit parameters, we derived the pivot energy E_p, computed as the energy at which the relative uncertainty on the normalization N₀ was minimal (Nolan et al. 2012). In a second iteration, we refitted the spectrum of the source assuming a power-law spectral model (Equation (1)) with the scale parameter E₀ fixed to E_p. For sources not significantly detected, we computed a 99% confidence level (c.l.) Bayesian upper limit on the flux of the source assuming the published VHE morphology and a power-law photon spectral index of 2.

We performed the spatial analysis in two steps. As a first step, we assumed that the LAT emission originates from the same population of emitting particles cooling by the same radiation process as the VHE emission. These assumptions mean that there should be a correlation between the spatial morphology of a source at LAT and VHE energies. While it is possible for the γ-ray emission from PWNe to have both the synchrotron and IC components visible in the LAT energy range (as in the case of the Crab Nebula; Abdo et al. 2010b), this scenario is unlikely for observations above 10 GeV since electrons of energy around 1 PeV should radiate in a magnetic field ∼0.3 G to emit photons above 10 GeV. This value is unrealistic for a PWN. A second exception would appear if the LAT and VHE emissions originate from two different populations of electrons (as in the case of Vela X; Abdo et al. 2010c). However, most PWNe observed by the LAT show only IC emission from the same population responsible for the VHE emission (e.g., Abdo et al. 2010a; Grondin et al. 2011; Rousseau et al. 2012), supporting our assumption in this first step.

We assumed that any LAT emission would have the same morphology as the best-fit VHE morphology. Therefore, we modeled the spatial distribution of the emission as Gaussian with a position and extension fixed at the value of the spatial best fit performed in the VHE energy range. To homogenize the analysis, if the source was modeled with an elliptical Gaussian at VHE, the Gaussian was fixed to the averaged extension. We tested for the significance of the source at LAT energies using a likelihood-ratio test: ${\rm TS}=2\times \log (\mathcal {L}_1/\mathcal {L}_0)$, where $\mathcal {L}$ is the Poisson likelihood of obtaining the observed data given the assumed model, $\mathcal {L}_1$ corresponds to the likelihood obtained by fitting a model of the source of interest and the background model, and $\mathcal {L}_0$ corresponds to the likelihood obtained by fitting the background model only. In the following, we refer to the TS assuming the VHE shape as TS_TeV. By assuming a fixed spatial model, our test has fewer dof, which makes our test more sensitive to the LAT emission, assuming that the VHE spatial model reproduces the LAT observation.

The formal statistical significance of this test can be obtained from the Wilks theorem (Wilks 1938). In the null hypothesis, TS follows a χ² distribution with n dof where n is the number of additional parameters in the model. We consider a source to be significantly detected when TS_TeV ⩾ 16. Our test has only 2 dof (the flux and the spectral index), so our threshold corresponds to a formal significance of 3.6σ. For significantly detected sources, TS_TeV is presented in Table 4.

As a second step, for significantly detected sources, we then independently characterized the best-fit morphology obtained from the LAT emission. Following the method of Nolan et al. (2012), we assumed the source to be point-like and fitted its position. Following the method adopted in Lande et al. (2012), we then assumed the source to be spatially extended with a Gaussian spatial model and fitted its position and extension. From this, we obtained TS_point and TS_Gaussian. We then defined the extension significance TS_ext = TS_Gaussian − TS_point following the method of Lande et al. (2012) and set the threshold for claiming the source to be spatially extended as TS_ext > 16, corresponding to a significance of 4σ. TS_GeV = TS_Gaussian when TS_ext > 16 and TS_GeV = TS_point otherwise. Table 4 lists 8 significantly extended sources and 22 point sources. If the source was not significantly extended, we derived a 99% c.l. Bayesian upper limit on the extension.

The LAT spectra of the sources have been derived assuming the published VHE morphology. In addition to performing a spectral fit over the entire energy range, we computed a spectral energy distribution (SED) by fitting the flux of the source independently in three energy bins spaced uniformly in log from 10 GeV to 316 GeV. During this fit, we fixed the spectral index of the source at 2 as well as the model of background sources to the best fit obtained in the whole energy range. We define a detection in the energy bin when TS ⩾ 10 and otherwise compute a flux upper limit using the same method as for the fit in the full energy range. All spectral results are presented in Tables 5 and 6.

Table 5. Spectral Results for Detected Sources

Name	TS	$F_{10\,{\rm GeV}}^{316\,{\rm GeV}}$	Γ	TS$_{10\,{\rm GeV}}^{31\,{\rm GeV}}$	$F_{10\,{\rm GeV}}^{31\,{\rm GeV}}$	TS$_{31\,{\rm GeV}}^{100\,{\rm GeV}}$	$F_{31\,{\rm GeV}}^{100\,{\rm GeV}}$	TS$_{100\,{\rm GeV}}^{316\,{\rm GeV}}$	$F_{100\,{\rm GeV}}^{316\,{\rm GeV}}$
		(10−10 cm−2 s−1)			(10−10 cm−2 s−1)		(10−10 cm−2 s−1)		(10−10 cm−2 s−1)
VER J0006+727	655	11.3 ± 0.9 ± 1.2	3.96 ± 0.25 ± 0.36	647	11.2 ± 0.9 ± 2.0	11	0.4 ± 0.2 ± 0.2	0	<0.3
a	2	<1.2	⋅⋅⋅	3	<1.2	0	<0.4	0	<0.3
MGRO J0632+17	699	34.9 ± 2.1 ± 10.2	4.53 ± 0.25 ± 0.51	695	36.8 ± 2.0 ± 10.1	6	<1.6	1	<0.7
a	5	<5.1	⋅⋅⋅	9	<5.5	1	<1.1	0	<0.6
HESS J1018−589	29	1.7 ± 0.5 ± 0.7	2.41 ± 0.49 ± 0.49	25	1.4 ± 0.5 ± 0.6	0	<0.6	6	<0.6
a	25	1.5 ± 0.5 ± 0.7	2.31 ± 0.50 ± 0.49	20	1.3 ± 0.4 ± 0.6	0	<0.6	6	<0.6
HESS J1023−575	52	4.6 ± 0.9 ± 1.2	1.99 ± 0.24 ± 0.32	40	3.8 ± 0.8 ± 1.8	2	<0.9	9	<1.2
a	52	4.6 ± 0.9 ± 1.2	1.99 ± 0.24 ± 0.32	40	3.8 ± 0.8 ± 1.8	2	<0.9	9	<1.2
HESS J1119−614	27	2.1 ± 0.6 ± 0.8	2.15 ± 0.37 ± 0.36	17	1.5 ± 0.5 ± 0.5	1	<0.7	11	0.2 ± 0.1 ± 0.1
a	16	2.0 ± 0.6 ± 0.8	1.83 ± 0.41 ± 0.36	5	<2.1	1	<0.8	11	0.2 ± 0.1 ± 0.1
HESS J1303−631	37	3.6 ± 0.9 ± 2.1	1.53 ± 0.23 ± 0.37	10	1.6 ± 0.7 ± 1.5	25	1.6 ± 0.5 ± 0.7	3	<0.7
HESS J1356−645	24	1.1 ± 0.4 ± 0.5	0.95 ± 0.40 ± 0.40	0	<0.9	14	0.6 ± 0.3 ± 0.3	10	0.3 ± 0.2 ± 0.2
a	24	1.1 ± 0.4 ± 0.5	0.94 ± 0.40 ± 0.40	0	<0.9	14	0.6 ± 0.3 ± 0.3	10	0.3 ± 0.2 ± 0.2
HESS J1418−609	31	4.0 ± 1.0 ± 1.3	3.52 ± 0.81 ± 0.61	29	3.6 ± 0.9 ± 1.2	2	<1.0	0	<0.6
a	15	<4.3	⋅⋅⋅	13	2.6 ± 0.9 ± 1.2	2	<1.0	0	<0.6
HESS J1420−607	42	3.7 ± 0.9 ± 1.1	1.89 ± 0.28 ± 0.31	19	2.4 ± 0.7 ± 0.7	13	0.8 ± 0.3 ± 0.3	12	0.5 ± 0.2 ± 0.2
a	36	3.4 ± 0.9 ± 1.1	1.81 ± 0.29 ± 0.31	15	2.2 ± 0.7 ± 0.7	13	0.8 ± 0.3 ± 0.3	12	0.5 ± 0.2 ± 0.2
HESS J1507−622	21	1.5 ± 0.5 ± 0.5	2.33 ± 0.48 ± 0.48	18	1.2 ± 0.4 ± 0.4	3	<0.7	0	<0.4
HESS J1514−591	156	6.2 ± 0.9 ± 1.3	1.72 ± 0.16 ± 0.17	69	3.9 ± 0.7 ± 1.1	54	1.7 ± 0.4 ± 0.4	36	0.7 ± 0.3 ± 0.4
HESS J1614−518	110	9.9 ± 1.4 ± 3.1	1.75 ± 0.15 ± 0.18	47	6.1 ± 1.1 ± 2.7	37	2.6 ± 0.6 ± 0.8	31	1.1 ± 0.4 ± 0.3
HESS J1616−508	75	9.3 ± 1.4 ± 2.3	2.18 ± 0.19 ± 0.20	46	6.5 ± 1.2 ± 2.1	29	2.3 ± 0.6 ± 0.6	3	<1.0
HESS J1632−478	137	11.8 ± 1.5 ± 5.3	1.82 ± 0.14 ± 0.19	69	7.8 ± 1.2 ± 4.2	37	2.6 ± 0.6 ± 0.9	39	1.5 ± 0.4 ± 0.5
HESS J1634−472	33	5.6 ± 1.3 ± 2.5	1.96 ± 0.25 ± 0.29	20	3.6 ± 1.0 ± 2.1	12	1.3 ± 0.5 ± 0.5	2	<0.8
HESS J1640−465	47	5.0 ± 1.0 ± 1.7	1.95 ± 0.23 ± 0.20	24	3.4 ± 0.9 ± 1.3	28	1.7 ± 0.5 ± 0.5	0	<0.5
HESS J1708−443	722	24.5 ± 1.7 ± 3.5	3.80 ± 0.24 ± 0.33	714	23.9 ± 1.6 ± 3.0	14	1.1 ± 0.4 ± 0.5	6	<1.0
a	33	5.5 ± 1.3 ± 3.5	2.13 ± 0.31 ± 0.33	17	4.0 ± 1.2 ± 3.0	11	1.0 ± 0.4 ± 0.5	6	<1.0
HESS J1804−216	138	14.2 ± 1.6 ± 3.1	2.10 ± 0.16 ± 0.24	91	10.1 ± 1.4 ± 2.3	38	2.9 ± 0.7 ± 0.6	21	1.2 ± 0.4 ± 0.4
a	124	13.4 ± 1.6 ± 3.1	2.04 ± 0.16 ± 0.24	77	9.3 ± 1.4 ± 2.3	36	2.8 ± 0.7 ± 0.6	21	1.2 ± 0.4 ± 0.4
HESS J1825−137	56	5.6 ± 1.2 ± 9.0	1.32 ± 0.20 ± 0.39	10	1.7 ± 0.9 ± 1.5	30	2.9 ± 0.7 ± 1.6	17	0.8 ± 0.3 ± 0.8
HESS J1834−087	27	5.5 ± 1.2 ± 2.5	2.24 ± 0.34 ± 0.42	19	4.2 ± 1.1 ± 1.9	7	<1.9	3	<1.0
HESS J1837−069	73	7.5 ± 1.3 ± 4.2	1.47 ± 0.18 ± 0.30	28	4.3 ± 1.1 ± 3.5	21	1.9 ± 0.6 ± 0.9	27	1.4 ± 0.5 ± 0.5
HESS J1841−055	64	10.9 ± 0.8 ± 4.1	1.60 ± 0.27 ± 0.33	20	7.4 ± 1.6 ± 2.9	13	2.1 ± 0.7 ± 1.0	31	1.8 ± 0.5 ± 0.7
HESS J1848−018	19	7.4 ± 1.9 ± 2.7	2.46 ± 0.50 ± 0.51	16	5.8 ± 1.6 ± 2.9	4	<2.6	0	<1.0
HESS J1857+026	53	4.2 ± 0.3 ± 1.3	1.01 ± 0.24 ± 0.25	6	<2.9	19	1.2 ± 0.4 ± 0.4	31	1.5 ± 0.4 ± 0.4
MGRO J1908+06	16	4.6 ± 1.3 ± 1.5	3.50 ± 1.11 ± 1.60	11	3.4 ± 1.2 ± 1.2	2	<1.6	7	<1.5
a	9	<5.6	⋅⋅⋅	3	<3.9	2	<1.6	7	<1.5
MGRO J1958+2848	21	1.3 ± 0.4 ± 0.7	4.36 ± 1.09 ± 1.21	19	1.3 ± 0.5 ± 0.5	0	<0.3	0	<0.3
a	8	<1.8	⋅⋅⋅	15	1.2 ± 0.5 ± 0.5	0	<0.3	0	<0.3
VER J2016+372	31	1.8 ± 0.5 ± 0.8	2.45 ± 0.44 ± 0.49	26	1.6 ± 0.5 ± 0.5	3	<0.6	3	<0.5
MGRO J2019+37	31	4.4 ± 1.7 ± 1.1	6.37 ± 3.04 ± 1.21	26	5.4 ± 1.2 ± 1.8	0	<0.7	1	<0.8
a	5	<4.7	⋅⋅⋅	9	<5.3	0	<0.8	1	<0.8
MGRO J2031+41B	58	6.4 ± 1.0 ± 1.1	3.07 ± 0.33 ± 0.37	58	6.2 ± 1.0 ± 1.3	3	<1.0	0	<0.4
a	12	<4.4	⋅⋅⋅	11	3.0 ± 0.9 ± 1.0	1	<0.9	0	<0.4
MGRO J2228+61	94	2.8 ± 0.5 ± 0.5	3.06 ± 0.41 ± 0.42	87	2.5 ± 0.5 ± 0.5	7	<0.8	0	<0.2
a	15	<2.0	⋅⋅⋅	9	<1.8	7	<0.8	0	<0.2

Notes. Results of the maximum likelihood spectral fits for LAT-detected VHE sources. These results are obtained assuming that the sources have the same morphology as was measured by VHE experiments. "a" in the first column corresponds to the results with the contribution of pulsars associated in Table 2 subtracted from the SED for the source just above. Columns 2, 3, and 4, respectively, give the TS, the integrated flux, and the spectral index of the source fit in the energy range from 10 GeV to 316 GeV. Columns 5–10 give the TS and the integrated flux fit in three logarithmically spaced energy ranges: 10–31 GeV, 31–100 GeV, and 100–316 GeV. When the TS in the energy bin is <10, a 99% c.l. upper limit on the flux is given instead. The two uncertainties respectively correspond to the statistical and systematic uncertainties.

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Table 6. Spectral Results for Undetected Sources

Name	TS	$F_{10\,{\rm GeV}}^{316\,{\rm GeV}}$	TS$_{10\,{\rm GeV}}^{31\,{\rm GeV}}$	$F_{10\,{\rm GeV}}^{31\,{\rm GeV}}$	TS$_{31\,{\rm GeV}}^{100\,{\rm GeV}}$	$F_{31\,{\rm GeV}}^{100\,{\rm GeV}}$	TS$_{100\,{\rm GeV}}^{316\,{\rm GeV}}$	$F_{100\,{\rm GeV}}^{316\,{\rm GeV}}$
		(10−10 cm−2 s−1)		(10−10 cm−2 s−1)		(10−10 cm−2 s−1)		(10−10 cm−2 s−1)
MGRO J0631+105	6	<1.4	4	<1.2	3	<0.6	0	<0.4
a	2	<1.0	0	<0.8	3	<0.6	0	<0.4
HESS J1026−582	1	<1.6	0	<1.6	0	<0.4	6	<0.7
a	1	<1.6	0	<1.6	0	<0.4	6	<0.7
HESS J1427−608	5	<1.9	0	<1.2	2	<0.8	4	<0.6
HESS J1458−608	13	<2.6	13	1.7 ± 0.5 ± 0.7	0	<0.5	0	<0.3
a	13	<2.6	13	1.7 ± 0.5 ± 0.7	0	<0.5	0	<0.3
HESS J1503−582	10	<3.9	1	<2.2	4	<1.5	9	<1.0
HESS J1554−550	0	<0.5	0	<0.6	0	<0.3	0	<0.3
HESS J1626−490	1	<2.3	1	<2.0	1	<1.0	0	<0.6
HESS J1646−458A	0	<2.8	0	<1.7	1	<1.9	1	<1.0
a	0	<2.7	0	<1.7	1	<1.9	1	<1.0
HESS J1646−458B	6	<4.7	0	<2.6	4	<1.9	5	<1.2
a	4	<4.3	0	<2.2	4	<1.9	5	<1.3
HESS J1702−420	6	<4.7	0	<2.6	8	<2.4	1	<0.8
a	6	<4.5	0	<2.5	8	<2.4	1	<0.8
HESS J1718−385	3	<2.1	0	<1.5	0	<0.8	6	<0.9
a	3	<2.1	0	<1.5	0	<0.8	6	<0.9
HESS J1729−345	0	<1.4	0	<1.4	0	<0.8	0	<0.5
HESS J1809−193	15	<8.5	11	4.7 ± 1.5 ± 2.1	3	<2.3	1	<1.0
HESS J1813−178	3	<2.5	0	<1.4	5	<1.6	1	<0.7
HESS J1818−154	0	<1.6	0	<1.6	0	<0.8	0	<0.4
HESS J1831−098	0	<1.9	0	<1.5	0	<1.0	0	<0.6
HESS J1833−105	4	<2.1	3	<1.9	1	<0.7	0	<0.7
a	4	<2.1	3	<1.9	1	<0.7	0	<0.7
HESS J1843−033	0	<0.9	0	<1.0	0	<0.5	0	<0.5
MGRO J1844−035	0	<1.4	0	<1.2	0	<0.9	0	<0.5
HESS J1846−029	2	<2.0	5	<2.4	0	<0.5	0	<0.4
HESS J1849−000	0	<1.3	1	<1.5	0	<0.5	0	<0.5
HESS J1858+020	0	<1.1	0	<1.2	0	<0.5	0	<0.4
MGRO J1900+039	0	<1.2	0	<1.3	0	<0.6	0	<0.4
HESS J1912+101	10	<4.6	2	<2.7	8	<2.0	4	<1.1
VER J1930+188	0	<1.0	1	<1.1	0	<0.4	0	<0.3
VER J1959+208	0	<0.3	0	<0.3	0	<0.3	0	<0.4
MGRO J2031+41A	14	<29.6	9	<22.6	3	<8.4	4	<2.3
W49A	3	<2.4	0	<1.6	3	<1.0	3	<0.8

Notes. Results of the maximum likelihood spectral fits for sources not detected in our LAT analysis. These results are obtained assuming that the sources have the same morphology as was measured by VHE. "a" in the first column corresponds to the results with the contribution of pulsars associated in Table 2 subtracted from the SED for the source just above. Columns 2 and 3, respectively, give the TS and a 99% c.l. upper limit on the integrated flux in the 10–316 GeV energy range. Columns 4–9 give the TS and the integrated flux in three logarithmically spaced energy ranges: 10–31 GeV, 31–100 GeV, and 100–316 GeV. When the TS in the energy bin is <10, a 99% c.l. upper limit on the flux is given. The two uncertainties respectively correspond to the statistical and systematic uncertainties.

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Two main systematic uncertainties can affect the extension fit: uncertainties in our model of the Galactic diffuse emission and uncertainties in our knowledge of the LAT PSF. We used the procedure described in Lande et al. (2012) and obtained the total systematic error on the source extension by adding the two errors in quadrature.

Three main systematic uncertainties can affect the LAT flux estimate for an extended source: uncertainties on the Galactic diffuse background, on the effective area, and on the shape of the source. We combined these errors in quadrature to obtain an estimate of the total systematic uncertainty on spectral parameters.

The dominant uncertainty comes from the Galactic diffuse emission and was estimated by using the alternative model for Galactic diffuse emission described in Lande et al. (2012). The systematic due to the effective area was determined by using modified instrument response functions as explained in Ackermann et al. (2012).

The imperfect knowledge of the true γ-ray morphology introduces a last source of error. We derived an estimate of the uncertainty on the spectral parameters due to the uncertainty on the γ-ray morphology by computing the difference between the values obtained assuming the published VHE spatial model and those obtained assuming the best-fit GeV extension obtained in this analysis.

As discussed in Section 3.2, for the sources near LAT-detected pulsars, a fourth source of systematic uncertainties can affect the LAT flux estimate: the pulsar model. For these sources, we studied any potential contamination of the putative LAT γ-ray sources by pulsars by performing a second fit of the regions including the pulsars in our background models. The results are also included in Tables 4–6 and are flagged with an "a." The effects of pulsar contamination are discussed for individual sources in Section 4.

We caution that some LAT-detected pulsars may have spectra at LAT energies that deviate from the simple exponential cutoff power-law model assumed in the 2FGL catalog, for energies above 10 GeV. Aliu et al. (2011) show this to be the case for the Crab pulsar. In such cases, our fit could still be contaminated by the pulsar, especially in the lowest energy bin between 10 and 31.6 GeV. For instance, in the case of Geminga for which this analysis detected no significant PWN-like emission, the comparison of the energy flux above 10GeV between the 2FGL and the 1FHL catalogs shows a factor ∼2 smaller flux for 2FGL.

Table 5 shows that HESS J1825−137 and MGRO J0632+17 have large systematic uncertainties. The uncertainty on HESS J1825−137 mainly comes from the term corresponding to the source morphology. As can be seen in Tables 1 and 4, the LAT best-fit Gaussian has σ = 044 while the VHE symmetric Gaussian has σ = 0125. This difference of morphology yields a difference in maximum likelihood flux of +155%.

The large systematic uncertainty on MGRO J0632+17 is not surprising since the VHE source has an extension of more than 1°, while the LAT morphology is best fit as a point source located at the pulsar's position.

Assigning an association between an LAT source and a VHE source depends on two considerations: the spatial and spectral consistency with the counterpart. Spatial consistency has two aspects: centroid coincidence and extension compatibility. For assessing the degree of spatial coincidence, we considered an LAT emission to be spatially coincident with the VHE source if the distance between the LAT and VHE experiments' best-fit positions was inside a circle whose radius is the quadratic sum of (1) the 68% c.l. uncertainty on the LAT best-fit position, (2) the 68% c.l. position uncertainty of the VHE source, and (3) the 99% containment radius of the source based on the VHE-fitted angular extent. These data are summarized in Table 8. Only one source is not spatially coincident using this criterion: HESS J1018−589. We removed from this table the sources likely to be associated with pulsar emission. These sources will be discussed in Section 4.2.

Table 8. Comparison between the LAT and VHE Positions

Name	UncGeV	UncTeV	$r_{99\%}$ TeV	Distance
	(deg)	(deg)	(deg)	(deg)
HESS J1018−589	0.04	0.02	0.00	0.12
HESS J1023−575	0.04	0.09	0.55	0.10
HESS J1119−614	0.05	⋅⋅⋅	0.15	0.09
HESS J1303−631	0.05	0.01	0.49	0.41
HESS J1356−645	0.05	0.03	0.61	0.19
HESS J1420−607	0.04	0.02	0.18	0.01
HESS J1507−622	0.06	0.04	0.46	0.21
HESS J1514−591	0.03	0.07	0.23	0.06
HESS J1614−518	0.05	0.03	0.58	0.19
HESS J1616−508	0.04	0.01	0.42	0.16
HESS J1632−478	0.04	0.04	0.41	0.15
HESS J1634−472	0.03	0.05	0.33	0.18
HESS J1640−465	0.05	0.01	0.12	0.07
HESS J1804−216	0.04	0.02	0.65	0.06
HESS J1825−137	0.06	0.03	0.38	0.28
HESS J1834−087	0.05	0.02	0.27	0.06
HESS J1837−069	0.06	0.02	0.26	0.12
HESS J1841−055	0.06	0.05	1.00	0.22
HESS J1848−018	0.04	⋅⋅⋅	0.97	0.11
HESS J1857+026	0.04	0.05	0.29	0.14
VER J2016+372	0.05	⋅⋅⋅	⋅⋅⋅	0.11

Notes. Comparison of the localization and localization uncertainty for the sources observed at LAT and VHE energies and classified as "PWN," "PWNc," or "O." Columns 2, 3, 4, and 5, respectively, give the averaged uncertainty on the position obtained using Fermi-LAT data and assuming a point source if TS_ext < 16 or a Gaussian if TS_ext > 16, the quadratic sum of the statistical (68% confidence radius) and systematic uncertainties on the VHE position given in Table 1, the 99% containment radius of the VHE emission assuming the extension listed in Table 1, and the distance between the positions of the source fit at LAT and VHE energies.

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Although VER J2016+372 is spatially extended as announced in Aliu (2011), neither the extension nor the uncertainties of the spatial parameters are yet available. There is little doubt that these parameters will show that the VERITAS and LAT emissions are spatially coincident. This case will be discussed in Section 4.4.

A finite measured extension of a γ-ray source is a direct way to discriminate between a pulsar and a PWN. Therefore, we searched for significant angular extensions of the LAT sources. Of the 21 sources not labeled as PSR in Section 4.2, 8 are significantly extended: HESS J1303−631, HESS J1614−518, HESS J1616−508, HESS J1632−478, HESS J1804−216, HESS J1825−137, HESS J1837−069, and HESS J1841−055. Six of them were already detected by Lande et al. (2012). Only HESS J1632−478 has an extension inconsistent with that work. For this source, Lande et al. (2012) measured an extension of 035 ± 006 assuming a disk, while we obtained 030 ± 004 for a Gaussian. Comparison between 68% containment radius of a disk and a Gaussian yields σ_Disk ∼ 1.84σ_Gaussian (Lande et al. 2012), where σ_Disk and σ_Gaussian, respectively, represent the disk radius and the Gaussian standard deviation. Therefore, for HESS J1632−478, our analysis led to an extension bigger than that obtained in Lande et al. (2012). This difference certainly comes from the three additional 2FGL sources (2FGL J1631.7−4720c, 2FGL J1630.2−4752, and 2FGL J1632.4−4820c) included in the model used by Lande et al. (2012). These sources are not included in the 1FHL catalog and are below the pre-defined TS > 25 threshold for additional sources. Since they are unidentified, we chose not to add them.

Figure 2 compares the sizes measured by the LAT and VHE. The only source with σ_GeV < σ_TeV is HESS J1708−443, whose LAT emission is likely coming from the pulsar. As we discussed above and in Section 4.5, we suspect that the extensions of HESS J1303−631 and HESS J1632−478 are overestimated. We assumed a linear relation between the VHE experiment and the LAT extension (σ_GeV = α × σ_TeV) and fit the data points, obtaining α = 1.4 ± 0.2 with a χ²/dof = 15/7. In the case in which we fixed α = 1 we obtained a χ²/dof = 24/8. This implies that, with the current statistics, the LAT extension is larger than the one measured by VHE experiments at the 2.8σ level. Additional exposure and a more precise analysis of crowded regions (e.g., the regions of HESS J1303−631, HESS J1632−478, HESS J1837−069, or HESS J1841−055) are needed to draw any conclusion. Indeed, in these regions the γ-ray emission could be due to more than one source, as discussed below in the case of HESS J1841−055 or as discussed in Gotthelf & Halpern (2008) for the case of HESS J1837−069.

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In the LAT energy range, 22 sources are found to be point-like, i.e., not significantly extended. Table 5 demonstrates that among these 22 point-like sources, 9 have a soft spectral index (Γ > 3): HESS J1418−609, HESS J1708−443, MGRO J0632+17, MGRO J1908+06, MGRO J1958+2848, MGRO J2019+37, MGRO J2228+61, MGRO J2031+41B, and VER J0006+727. Tables 2 and 9 demonstrate that all of them are located close to an LAT-detected pulsar. Table 5 shows that their γ-ray emission significantly decreases when the contribution of the associated LAT-detected pulsar is included. Furthermore, the spectra obtained above 10 GeV for these sources agree with the nearby pulsars' spectra given in the 2FGL catalog as shown in Figures 3–6. These figures only show SEDs for sources with no X-ray and radio information available. The spectra for the other sources will be discussed in Section 4.5.

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To study the contamination of the LAT data for the VHE sources by these pulsars, we accounted for the pulsar contribution to photons in the region as explained in Section 3.2. Tables 4 and 5 and Figures 3–6 show the results of this new fit using the 2FGL models of the pulsars. For these nine sources, in Figures 3–6 the low-energy part of the emission (<30 GeV) tends to disappear, suggesting that we primarily detected pulsar emission. For these reasons, we infer that the observed LAT emission coming from these sources is likely due to the pulsars themselves. We labeled these nine sources as "PSR" in Table 4.

The hardness of the γ-ray spectrum and the presence of a pulsar energetic enough to power a potential PWN are important criteria for source classification as a PWN. In addition to these criteria, to label a source as a "PWN" or a "PWNc" for PWN candidate, we required that its LAT spectrum connects with the VHE spectrum, i.e., that the differential fluxes at the highest LAT energies and in the VHE low energy range be approximately equivalent, such that they can be interpreted as a continuous multi-wavelength spectrum. An exception has been made for HESS J1848−018, which is classified as "PWNc" as explained in Section 4.5.6. Based on multi-wavelength analyses, we labeled three sources as "PWN": HESS J1356−645, HESS J1514−591, and HESS J1825−137. HESS J1356−645 is considered as "PWN" based upon the morphology of the source observed in the radio and X-ray domain (H.E.S.S. Collaboration et al. 2011c). HESS J1514−591 is considered as a "PWN" because of the correlation observed between the H.E.S.S. and X-ray emissions and the observation of pulsar jets in the X-ray domain (Aharonian et al. 2005b). And finally, HESS J1825−137 is considered to be a "PWN" since Aharonian et al. (2006b) have shown that it has an energy-dependent morphology in the H.E.S.S. energy range.

Detections of seven of the PWN candidates have been previously published. For HESS J1023−575 (Ackermann et al. 2011), HESS J1640−465 (Slane et al. 2010), HESS J1857+026 (Rousseau et al. 2012), HESS J1616−508, HESS J1632−478, HESS J1837−069 (Lande et al. 2012), and HESS J1848−018 (Tam et al. 2010), the LAT emission has been discussed in previous work and proposed to be of PWN origin.

We detected four new PWN candidates (HESS J1119−614, HESS J1303−631, HESS J1420−607, and HESS J1841−055) and one new PWN (HESS J1356−645). These sources are spatially consistent with pulsars able to power them (respectively, PSR J1119−6127, PSR J1301−6305, PSR J1420−6048, PSR J1838−0537, and PSR J1357−6429). Moreover, their LAT emissions are best modeled by hard spectra and are compatible with the VHE SEDs. The new LAT sources and PWN candidates are described in Section 4.5.

The seven sources that cannot be associated with a PWN or a pulsar are labeled "O" for other. These sources cannot be associated because either no sufficiently energetic pulsar is known at that location or the spectral connection from the LAT to the VHE measurements does not support a PWN interpretation.

Three sources have relatively hard spectra at LAT energies that connect spectrally to the associated VHE source: HESS J1614−518, HESS J1634−472, and HESS J1804−216. These sources are not classified as PWNe due to previous multi-wavelength analyses. The former is spatially coincident with five detected pulsars, but none are luminous enough to power a PWN that would explain the γ-ray emission (Rowell et al. 2008). Sakai et al. (2011) found two X-ray counterparts to the H.E.S.S. source and proposed an SNR identification. As discussed in Lande et al. (2012), the nature of the source remains unclear. HESS J1634−472 does not have any counterpart pulsars energetic enough to power it. Finally, Ajello et al. (2012) studied the link between the H.E.S.S. and the LAT emission coming from the region of HESS J1804−216 and concluded that the emission is more likely due to the energy-dependent scattering of particles accelerated in an SNR than to a PWN.

The remaining four sources are HESS J1018−589, HESS J1507−622, HESS J1834−087, and VER J2016+372. In the LAT energy range, they are point-like with relatively soft spectra (3 > Γ > 2). Therefore, the association of the LAT emission with their VHE counterparts is uncertain. HESS J1018−589 is close to both the γ-ray binary 1FGL J1018.6−5856 (Coe et al. 2012) and the nearby SNR G284.3−1.8. The LAT source appears to be spatially coincident with SNR G284.3−1.8. SNR G284.3−1.8 is not included in our list of candidates and will be analyzed in the SNR catalog. Domainko & Ohm (2012) were not able to conclusively determine the origin of the γ-ray emission of HESS J1507−622 and confirm the result of H.E.S.S. Collaboration et al. (2011e): a leptonic scenario seems favored, while a hadronic one seems unlikely. HESS J1834−087 and VER J2016+372 lack a pulsar energetic enough to power their emission. But Albert et al. (2006b) have suggested that the interaction of SNR W41 with a nearby molecular cloud could explain HESS J1834−087. Another analysis of LAT and H.E.S.S. observations of HESS J1834−087 will be presented elsewhere.

In this section, we compare source spectra with previously published models (the references to those models are provided below for each case). We do not refit those models incorporating the LAT data. Therefore, disagreements between the published models and the LAT data do not necessarily imply that the models are ruled out as it may be possible to accommodate our results under these models with a different set of parameters.

4.5.1. HESS J1119−614

4.5.2. HESS J1303−631

HESS J1303−631 was serendipitously discovered in 2004 (Aharonian et al. 2005c) during an observation campaign of the binary system PSR B1259−63. It is the first H.E.S.S. source classified as a UNID due to the lack of detected counterparts in radio and X-rays with Chandra (Mukherjee & Halpern 2005). H.E.S.S. Collaboration et al. (2012b) found only one plausible counterpart in the vicinity of HESS J1303−631: PSR J1301−6305 with a spin-down power of $\dot{E} = 1.70 \times 10^{36}$ erg s⁻¹. The authors also presented the detection of a very weak X-ray PWN using XMM-Newton observations. This, with the energy-dependent morphology observed by H.E.S.S., led to the conclusion that HESS J1303−631 is an old PWN offset from the pulsar powering it.

Wu et al. (2011) found no significant emission from HESS J1303−631 using 30 months of Fermi-LAT data between 1 and 20 GeV. With 15 months of additional data and a higher energy threshold, our analysis now provides a first detection of LAT emission coincident with the HESS source. Nevertheless, Figure 7 shows that the detected emission might be contaminated by γ-ray emission from the nearby SNR Kes 17. Since we cannot separate these two sources using our strategy with the current statistics, we decided to include the effect of source confusion in our estimate of systematic uncertainties for HESS J1303−631. Therefore, we ran the analysis again, adding a source at the position of Kes 17. We quantify the systematic error as the differences in parameter values resulting from fitting with the two background models. The maximal variation is in the lowest energy bin of the SED.

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For our best LAT morphology of a Gaussian of dispersion 045 (see Table 4), we obtained an index of Γ = 1.71 ± 0.26 ± 0.37 (we obtained Γ = 1.53 ± 0.23 ± 0.37 assuming the H.E.S.S. best fit Gaussian; Table 5). This hard index is in the range of values obtained for LAT-detected PWNe and is inconsistent with the spectral index of ∼2.4 derived by Wu et al. (2011) for Kes 17. This is evidence that the γ-ray emission above 10 GeV is dominated by the PWN candidate. As can be seen in Figure 8, even though the connection between the LAT and the H.E.S.S. energy range is not perfect, LAT and H.E.S.S. spectra are not inconsistent, suggesting a potential physical relationship.

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Figure 8 shows the SED of HESS J1303−631 together with the one-zone leptonic model proposed by H.E.S.S. Collaboration et al. (2012b). In this model, VHE γ-rays are created via IC scattering of electrons on the CMB photons. Infrared and optical target photons are neglected. The model reproduces the radio, X-ray, and H.E.S.S. data with an electron spectral index of 1.8 ± 0.1, a cutoff energy of $31^{+5}_{-4}$ TeV, and an average magnetic field of 1.4 ± 0.2 μG. However, the flux predicted in the LAT energy range is well below the flux detected by the Fermi-LAT. This may be due to the absence of infrared and optical photon fields in the model described above or to the contamination produced by Kes 17. A specific analysis is needed to make conclusions about the constraints that the Fermi-LAT could yield on the γ-ray emission of this source.

4.5.3. HESS J1356−645

4.5.4. HESS J1420−607

The complex of compact and extended radio/X-ray sources, called Kookaburra (Roberts et al. 1999), spans over 1 deg² along the Galactic plane. It has been extensively studied to explain the EGRET source 3EG J1420−6038/GEV J1417−6100 (Hartman et al. 1999; Lamb & Macomb 1997). Within its northeast excess, designated "K3," the young and energetic pulsar PSR J1420−6048 with period 68 ms, characteristic age τ_C = 13 kyr, and spin-down power 10³⁷ erg s⁻¹ was discovered (D'Amico et al. 2001). X-ray observations by ASCA and later by Chandra and XMM-Newton revealed extended X-ray emission surrounding this pulsar and identified as a potential PWN (Roberts et al. 2001; Ng et al. 2005). On the southwest side of the Kookaburra complex lies a bright nebula exhibiting extended hard X-ray emission, G313.1+0.1 (aka the "Rabbit"; Roberts et al. 1999). This X-ray excess was also proposed as a PWN contributing to the γ-ray emission detected by EGRET.

The H.E.S.S. Galactic Plane Survey revealed two VHE sources in this region: HESS J1420−607 and HESS J1418−609 (Aharonian et al. 2006a). HESS J1420−607 is centered north of PSR J1420−6048 (near K3), while HESS J1418−609 is coincident with the Rabbit nebula. More recently, Fermi-LAT detected pulsed γ-ray emission from PSR J1420−6048 and PSR J1418−6058, the latter being a new γ-ray pulsar found through blind frequency searches (Abdo et al. 2010e, 2009a). PSR J1418−6058 is coincident with an X-ray source in the Rabbit PWN and has a spin-down power high enough to power the PWN candidate HESS J1418−609.

Figure 9 shows two smoothed count maps centered on the location of the K3 nebula. The Galactic and the isotropic diffuse emissions were subtracted to show the excesses coming from HESS J1420−607 and HESS J1418−609. Above 10 GeV, HESS J1418−609 and HESS J1420−607 are confused due to the size of the LAT PSF and to the limited statistics. However, on the count map above 31 GeV, the emission from HESS J1418−609 disappears, confirming the soft spectrum and the pulsar-like emission coming from HESS J1418−609 and the harder spectrum from HESS J1420−607.

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Van Etten & Romani (2010) used a two-zone time-dependent numerical model with constant injection luminosity to investigate the physical properties of HESS J1420−607. The authors injected relativistic particles following a power-law spectrum into the inner nebula zone; they evolved this spectrum over time and injected the resultant spectrum into the outer nebula zone. Figure 8 shows the results obtained for a hadronic + leptonic model on the assumption of a low-density environment (n ∼ 1 cm⁻³) and magnetic fields of 12 μG and 9 μG, respectively, in the inner and outer nebula. The same figure presents a leptonic scenario assuming magnetic fields of 12 μG and 8 μG, respectively, in the inner and outer nebula. The strength of this magnetic field implies a lepton spectral break at ∼100 TeV after evolution in the inner nebula. More recently, Kishishita et al. (2012) proposed a one-zone leptonic model assuming a power-law injection spectrum with an index of 2.3 with a cutoff at ∼40 TeV and a magnetic field of ∼3 μG; the model SED is shown in the same figure.

As explained in Section 3, the model used for PSR J1420−6048 was fixed to the 2FGL spectrum. Therefore, if this model does not perfectly reproduce the data with 21 additional months, the LAT spectral points of HESS J1420−608 might still be contaminated by the pulsar's emission. With the current statistics, all models reproduce the LAT and H.E.S.S. data reasonably well. A future off-pulse analysis of LAT data for this pulsar performed with more statistics could help discriminate between the models.

4.5.5. HESS J1841−055

4.5.6. HESS J1848−018

This section presents the sources for which no γ-ray emission is detected but the corresponding upper limits constrain the models.

4.6.1. HESS J1026−582

4.6.2. HESS J1458−608

4.6.3. HESS J1626−490

4.6.4. HESS J1813−178

The Fermi LAT Collaboration acknowledges generous ongoing support from a number of agencies and institutes that have supported both the development and the operation of the LAT as well as scientific data analysis. These include the National Aeronautics and Space Administration and the Department of Energy in the United States; the Commissariat à l'Energie Atomique and the Centre National de la Recherche Scientifique/Institut National de Physique Nucléaire et de Physique des Particules in France; the Agenzia Spaziale Italiana and the Istituto Nazionale di Fisica Nucleare in Italy; the Ministry of Education, Culture, Sports, Science and Technology (MEXT), High Energy Accelerator Research Organization (KEK), and Japan Aerospace Exploration Agency (JAXA) in Japan; and the K. A. Wallenberg Foundation, the Swedish Research Council, and the Swedish National Space Board in Sweden.

Additional support for science analysis during the operations' phase is gratefully acknowledged from the Istituto Nazionale di Astrofisica in Italy and the Centre National d'Études Spatiales in France.

This research made use of pywcsgrid2, an open-source plotting package for Python.⁶⁹ The authors acknowledge the use of the TeV catalog Web site⁷⁰ provided by the University of Chicago. The authors acknowledge the use of the Australia Telescope National Facility pulsar catalog.⁷¹