Investigating $\gamma$-ray halos around three HAWC bright sources in $Fermi$-LAT data

Numerous extended sources around Galactic pulsars have shown significant $\gamma$-ray emission from GeV to TeV energies, revealing hundreds of TeV energy electrons scattering off of the underlying photon fields through inverse Compton scattering (ICS). HAWC TeV gamma-ray observations of few-degree extended emission around the pulsars Geminga and Monogem, and LAT GeV emission around Geminga, suggest that systems older than 100 kyr have multi-TeV $e^{\pm }$ propagating beyond the SNR-PWN system into the interstellar medium. Following the discovery of few $\gamma$-ray sources by HAWC at energies $\mathrm{E}>100\mathrm{TeV}$, we investigate the presence of an extended $\gamma$-ray emission in Fermi-LAT data around the three brightest sources detected by HAWC up to 100 TeV. We find an extended emission of ${\theta }_{68}=1.00_{-0.07}^{+0.05}\mathrm{deg}$ around eHWC J1825-134 and ${\theta }_{68}=0.71\pm 0.10\mathrm{deg}$ eHWC $\mathrm{J}1907+063$. The analysis with ICS templates on Fermi-LAT data point to diffusion coefficient values which are significantly lower than the average Galactic one. When studied along with HAWC data, the $\gamma$-ray Fermi-LAT data provide invaluable insight into the very high-energy electron and positron parent populations.

Figure 1

Ratio $P/P^{\max }$ between the inverse Compton power $P(E_e,E_{\gamma })$ and its maximum value $P^{\max }$, varying $E_{\gamma }\text{−}{E}_e$. The colors (in logarithmic scale) indicate the $P/P^{\max }$ values. The maximum of $P/P^{\max }$ corresponds to white regions in the plot.

Figure 2

Top panel: $\sqrt{TS}$ map of the ROI analyzed in Fermi-LAT data for the source eHWC J1825-134 after subtracting the best-fit model obtained as described in Sec. 4. The cyan star indicates the position of the eHWC source, while the associated pulsars are located at the ROI center Bottom panel: same as the left panel but without accounting for the source of interest in the model. The green star and circle indicate the best fit position and angular extension of the source as found in our analysis between 1–1000 GeV with a Gaussian template. The maps are smoothed with a Gaussian kernel of $1\sigma$.

Figure 3

Upper Panel: Weighted average for the extension of the $\gamma$-ray flux around the source eHWC J1825-134 (black data) as measured in our analysis of Fermi-LAT data using a gaussian template with three IEM models (see values in Table 2), shown along the analysis of HESS data [42]. We also report the ICS predictions (cyan solid line) fixing $D_0=2\times {10}^{27}{\mathrm{cm}}^2/\mathrm{s}$ and $b_0=2\times {10}^{-16}\mathrm{GeV}/\mathrm{s}$ (see Fig. 7) and the case where only diffusion is considered in the calculation (red dashed line). Lower Panel: Best-fit position obtained in different energy bins on Fermi-LAT data. The center (size) of the circles describes the best-fit ($1\sigma$ error) of the position. We also display the best-fit position reported in [42] between 1–10 TeV, and the position of the pulsar as found in the ATNF catalog.

Figure 4

$\sqrt{TS}$ map of the ROI analyzed in Fermi-LAT data for the source eHWC $\mathrm{J}1907+063$, after subtracting the best-fit model obtained as described in Sec. 4. This figure has been obtained using the background model IEM-4FGL.

Figure 5

$\sqrt{TS}$ map found in the energy range between 1–1000 GeV for the ROI considered around the source eHWC $\mathrm{J}2019+368$. In the left panel we show the $\sqrt{TS}$ map that we find when we use the 4FGL sources, IEM and isotropic templates. We also display the position of the peaks that are re-absorbed when we add three additional extended sources. In the right panel we show the $\sqrt{TS}$ when Source 1, 2 and 3 are included in the background model.

Figure 6

Flux as a function of energy for the three extended sources found in the Fermi-LAT ROI considered for the source eHWC $\mathrm{J}2019+368$. Downward arrows stay for upper limits.

Figure 7

Relative change in the $\log \mathcal{L}$ profile for eHWC1825-137 (left panel) and eHWC $\mathrm{J}1907+063$ (right panel) as a function of the diffusion coefficient normalization $D_0$, and for three different IEMs. The dashed vertical lines show the $D_0$ values in correspondence to the maximum likelihood, whose respective TS values are reported in the plot. Two reference values for $D_0$ found on Galactic scales are also reported [33, 34].

Figure 8

Flux as a function of energy found for the source eHWC J1825-134 with the ICS template generated at the best-fit value of $D_0$ found with our analysis. We show the data found when using three different IEMs. Together with the flux data we also show the best-fit and the $3\sigma$ band for the ICS theoretical predictions found by fitting the flux data.

Figure 9

Same as Fig. 8 for the source eHWC $\mathrm{J}1907+063$.

Figure 10

Same as Fig. 8 for the source eHWC $\mathrm{J}2019+368$.

Figure 11

Study of the effect of the proper motion on the J1826-1334 surface brightness at 5 GeV, as a function of the observed angular distance $\theta$ from the centre of the pulsar. We assume $v_T=200\mathrm{km}/\mathrm{s}$, and show surface brightness for different angles $\alpha$, defined with respect to the direction of ${\overrightarrow{v}}_T$ (fixed at $\alpha =\pi /2$). The solid black curve represents the minimal distortion of the surface brightness obtained for $\alpha =\pi /2$ (i.e., $\theta$ changes along the $x$ axis and thus perpendicular to ${\overrightarrow{v}}_T$), while the other lines are for intermediate angles $\alpha =0$ (blue), $\pi /4$ (green), and $3\pi /4$ (red). The dashed black line indicates the value averaged over $\alpha$.