Evidence for γ -ray emission from the remnant of Kepler’s supernova based on deep H.E.S.S. observations

Observations with imaging atmospheric Cherenkov telescopes (IACTs) have enhanced our knowledge of nearby supernova (SN) remnants with ages younger than 500 years by establishing Cassiopeia A and the remnant of Tycho’s SN as very-high-energy (VHE) γ -ray sources. The remnant of Kepler’s SN, which is the product of the most recent naked-eye SN in our Galaxy, is comparable in age to the other two, but is signiﬁcantly more distant. If the γ -ray luminosities of the remnants of Tycho’s and Kepler’s SNe are similar, then the latter is expected to be one of the faintest γ -ray sources within reach of the current generation IACT arrays. Here we report evidence at a statistical level of 4.6 σ for a VHE signal from the remnant of Kepler’s SN based on deep observations by the High Energy Stereoscopic System (H.E.S.S.) with an exposure of 152 hours. The measured integral ﬂux above an energy of 226 GeV is ∼ 0.3% of the ﬂux of the Crab Nebula. The spectral energy distribution (SED) reveals a γ -ray emitting component connecting the VHE emission observed with H.E.S.S. to the emission observed at GeV energies with Fermi -LAT. The overall SED is similar to that of the remnant of Tycho’s SN, possibly indicating the same nonthermal emission processes acting in both these young remnants of thermonuclear SNe.


Introduction
For several decades, supernova remnants (SNRs) have been considered the most likely sources of Galactic cosmic rays (CRs; e.g., Ginzburg & Syrovatskii 1964), that is, CRs with energies at least up to 3 × 10 15 eV. While the detection of radio and Over the last two decades, SNRs have been established as an important population of Galactic γ-ray sources, both in the highenergy (HE) domain (100 MeV to 100 GeV) by the Fermi Large Area Telescope (LAT) observations (Acero et al. 2016) and in the very-high-energy (VHE) domain (> 100 GeV) by observations with imaging atmospheric Cherenkov telescopes (IACTs); an SNR population study is provided in H.E.S.S. Collaboration et al. (2018c) and an overview of VHE γ-ray astrophysics in Hinton & Hofmann (2009).
Very-high-energy spectra by themselves are often insufficient to firmly establish whether the γ-ray emission is produced by accelerated protons and other atomic nuclei (so-called CR hadrons) or by accelerated electrons (CR leptons), or both. However, in some cases the presence of a characteristic pion-decay feature in the sub-GeV part of the γ-ray spectrum (the "piondecay bump") can clearly establish a hadronic origin for the γray emission. This is for example the case for SNRs IC 433 and W44 (Ackermann et al. 2013). In other cases, due to the fact that CR hadrons lead to a softer γ-ray spectrum (with a photon index of Γ = 2.0 for a hadron power-law index of 2) in the HE regime than CR leptons (Γ = 1.5 in the Thomson regime for a lepton power-law index of 2), the spectral shape can indicate the production mechanism of the emission. However, a correspondence between spectral slopes and origin of γ-ray emission can be more complex if gas clumps are present (Gabici & Aharonian 2014) or in the case of nonlinear diffuse shock acceleration (Malkov 1999), as well as for leptonic emission in the Klein-Nishina regime (Porter et al. 2006).
Supernova remnants with ages younger than 2000-3000 years have been established as TeV γ-ray sources. This fact suggests that CRs are accelerated to >10 TeV when the shock velocities are still in excess of a few thousand km s −1 (Helder et al. 2012). Many of these young TeV γ-ray emitting SNRs belong to the class of historical SNRs, that is, SNRs produced by nakedeye supernovae (SNe) recorded in history, such as SN 185/RCW 86 (H.E.S.S. Collaboration et al. 2018d), SN 1006 (Acero et al. 2010), and SN 1572 (also known as Tycho's SNR; Archambault et al. 2017). The young SNRs, RX J1713.7-3946 (H.E.S.S. Collaboration et al. 2018a) and particularly Cassiopeia A (Cas A; Ahnen et al. 2017, Abeysekara et al. 2020, which are the possible remnant of SN 393 (Wang et al. 1997) and the remnant of a nearby 340-year-old SN missing in records, respectively, are also sometimes added to this SNR class. With these additions, both remnants of core-collapse SNe (RX J1713.7-3946 and Cas A) and thermonuclear (Type Ia) SNe (SN 185, SN 1006, and SN 1572/Tycho's SNR) are included. Based on the γ-ray spectral characteristics, the γ-ray emission from Tycho's SNR and Cas A are likely of hadronic origin (Morlino & Caprioli 2012, Ahnen et al. 2017, Abeysekara et al. 2020, whereas for the other, more extended, 1000-to 3000-year-old SNRs a leptonic origin (for RX J0852.0-4622; see Aharonian et al. 2005, Lee et al. 2013, H.E.S.S. Collaboration et al. 2018b) has been suggested. However, a hadronic scenario for these older TeV γ-ray emitters has also been discussed, for example in Berezhko et al. (2012), Inoue et al. (2012), and Gabici & Aharonian (2014).
The remnant of the youngest naked-eye SN, SN 1604 (also known as Kepler's SNR; Green & Stephenson 2017, Vink 2017, is conspicuously absent from the above list of young SNRs detected in VHE γ rays. Kepler's SNR is, however, a known X-ray synchrotron emitter (Allen et al. 1999, Nagayoshi et al. 2021, indicating that particles, at least electrons, are accelerated up to ∼ 10 TeV. Moreover, the relatively high density of its ambient medium (e.g., Williams et al. 2012) makes Kepler's SNR a probable candidate for being a γ-ray source dominated by hadronic emission. The High Energy Stereoscopic System (H.E.S.S.) experiment observed Kepler's SNR in the past, but the previous observations did not result in a detection of the remnant (Aharonian et al. 2008). This is partially due to the relatively short exposure time (13 hours) compared to other SNRs, as well as the fact that Kepler's SNR, located at about 5 kpc (Ruiz-Lapuente 2017), is more distant than the historical SNRs listed above.
At GeV energies, an excess at about a 4σ statistical level from Kepler's SNR was reported by Xiang & Jiang (2021) and in the proceedings by Prokhorov et al. (2021). In Xiang & Jiang (2021), the authors claimed a detection of γ-ray emission from Kepler's SNR despite the presence of residual radiation around Kepler's SNR and concluded that more observation data with IACTs and Fermi-LAT are necessary to firmly confirm the association between the γ-ray source candidate and Kepler's SNR. Using a summed likelihood analysis and a larger allowed range of zenith angles, Acero et al. (2022) confirmed a detection of Kepler's SNR above a 6σ level based on 12 years of Fermi-LAT data.
In this paper, we present the results of deep observations of Kepler's SNR performed with H.E.S.S. for a total of 152 hours. This data set is significantly larger than the data comprising 13 hours of observations used in the previous publication (Aharonian et al. 2008). We report first evidence for VHE γ-ray emission from Kepler's SNR -the last remaining historical SNR that had until now escaped detection at these energies. Combining the H.E.S.S. VHE data with HE data from 10.7 years of Fermi-LAT observations, we explore models to interpret the broad γray spectral energy distribution (SED), in terms of hadronic and leptonic emission processes.

Observations and analysis
In this section, we present data reduction and analyses of H.E.S.S. and Fermi-LAT data (sections 2.1.1 and 2.2.1), and results obtained from these analyses (sections 2.1.2 and 2.2.2).

H.E.S.S. telescopes
The H.E.S.S. experiment is a hybrid array of five IACTs located in the southern hemisphere in Namibia (23 • 16 18 S, 16 • 30 00 E) at an altitude of ∼1800 m above sea level (Aharonian et al. 2006). The H.E.S.S. array consists of four 12 m diameter telescopes (Ashton et al. 2020) placed in a square with 120 m sides and one 28 m diameter telescope in the center of the array. A 28 m diameter telescope installed in 2012 complements the array, but is not used in this analysis. Detection of VHE γ rays with the four 12 m telescopes is based on the stereoscopic reconstruction technique. We performed the dedicated observations of Kepler's SNR with H.E.S.S. reported in this paper using wobble mode with pointing offsets of 0 • .7 in right ascension or declination from Kepler's SNR, allowing a simultaneous measurement of the background in the same field of view (Berge et al. 2007).

Data reduction and analysis
We took data with at least three participating telescopes and in 28 min exposures called runs. We used the standard data quality selection procedure to identify observations with satisfactory hardware states of the instrument and good atmospheric conditions (Aharonian et al. 2006). We analyzed 152.2 h of good-quality data recorded during 353 runs. Of these, 122 h were accumulated in 2017-2020, whereas the remaining 30 h were spread over the years 2004-2013. The mean zenith angle of these observations is 26 • . Given the age of Kepler's SNR, we assume its VHE γ-ray emission to be steady during the time interval of 16 years (4% of the age of Kepler's SNR) in which the H.E.S.S. observations took place. This permits a simultaneous spectral fit of both the Fermi-LAT and H.E.S.S. data.
We analyzed the H.E.S.S. data using the Model Analysis (de Naurois & Rolland 2009) and used an analysis configuration that requires a minimum of 60 photo-electrons per image and considers events with an estimated direction reconstruction uncertainty of less than 0 • .1. We cross-checked the results with the Image Pixel-wise fit for Atmospheric Cherenkov Telescope (ImPACT) analysis (Parsons & Hinton 2014). We defined a circular region-of-interest with a radius of 6 around the geometrical center of Kepler's SNR (at RA=17h30m40.8s, Dec=-21 • 29 11 ) -hereafter referred to as the source region. This radius corresponds to the selection cut for a VHE point-like source. Kepler's SNR with 3.5 diameter can be considered as a point-like source for H.E.S.S. enclosed within the source region.

VHE γ-ray results
The data analysis yields 1524 γ-ray-like events from the source region and 23667 γ-ray-like events from a large ring-shaped background (off-source) region, from which we excluded the region with a 0 • .3 radius around another potential VHE γ-ray source (SNR G4.8+6.2; see Appendix A). The ratio of the onsource exposure to the off-source exposure, α, is 0.0569. We computed the number of excess counts by subtracting the number of off-source events multiplied by α from the number of events coming from the source region. The γ-ray excess is 178 counts above the background, which corresponds to a significance of 4.6σ according to Eq. 17 from Li & Ma (1983). The H.E.S.S. significance map is shown in the left panel of Fig. 1. The main and cross-check analyses used in this paper provide compatible results.
We derived the energy spectrum using a reflected region background method (Berge et al. 2007) and a forward-folding technique (Piron et al. 2001). The analysis energy threshold for this data set is 226 GeV given by the energy at which the effective area falls to 15% of its maximum value. The likelihood maximization yields a photon index of Γ = 2.3 ± 0.2 stat ± 0.2 syst and a normalization constant of N 0 = (9.5±2.3 stat ±2.9 sys )×10 −14 cm −2 s −1 TeV −1 at E 0 =1 TeV for a power-law spectrum dN/dE = N 0 (E/E 0 ) −Γ . We binned the spectrum in such a way that spectral points require a minimum significance level of 2.0σ each. The derived SED in the energy range from 226 GeV to 19 TeV is shown in Fig. 2. The derived VHE flux is lower by a factor of 2.2 than the 99% flux upper limit reported in the previous publication. The systematic uncertainties are conservatively estimated to be ±0.2 on the photon index and ±30% on the normalization coefficient (Aharonian et al. 2006).
In addition to the VHE excess at the position of Kepler's SNR, Fig. 1 shows the presence of a hotspot at the position of SNR G4.8+6.2 (see Appendix A), which is ≈ 0 • .7 to the east of Kepler's SNR. The analysis of this hotspot yields a γ-ray excess of 185 counts above the background. The numbers of on-and off-source events are N ON = 2007 and N OFF = 35049, respectively, with a background-normalization factor α = 0.0520. This γ-ray excess is significant at a level of 4.2σ.

Fermi-LAT
The principal instrument on board the Fermi Gamma Ray Space Telescope is the Large Area Telescope (LAT; Atwood et al. 2009), a pair-conversion telescope covering the energy range from about 20 MeV to more than 300 GeV. Fermi-LAT has been scanning the entire sky continuously since August 2008.
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Data reduction and analysis
As part of the motivation and preparation for the H.E.S.S. observations in 2020, we performed and took into account the analysis of Fermi-LAT HE γ-ray data presented in this section. The presence of γ-ray excesses both in H.E.S.S. and Fermi-LAT lends credence to the association between these γ-ray signals and Kepler's SNR.
For the data analysis, we used the Fermitools v1.2.23 package 1 and P8R3_SOURCE_V2 instrument response functions. We selected Fermi-LAT γ-ray events with reconstructed energies between 750 MeV and 300 GeV and performed a binned analysis by choosing a 10 • × 10 • square region centered at RA=17h30m48.7s, Dec=-20 • 1 55 (region of interest, ROI). We shifted the position of the ROI center from that of Kepler SNR by 1 • .4 in declination to reduce systematic effects due to the presence of a molecular cloud, the Pipe Nebula, and the Galactic plane in the ROI and their contributions to the foreground emission. For this analysis, we selected events accumulated from 2008 August 4 to 2019 May 16. To reduce the contamination by the γ-ray emission from the Earth's limb, we selected events with zenith angles < 90 • . We applied standard quality cuts (DATA_QUAL>0 && LAT_CONFIG==1).
To model the sources within the ROI, we included sources from the 4FGL catalog (Abdollahi et al. 2020) within a region of 17 • .5 radius around the center of the ROI. To model the Galactic and isotropic background diffuse emission, we used the standard templates gll_iem_v07.fits and iso_P8R3_SOURCE_V2_v1.txt. The point spread function of Fermi-LAT is sufficiently wide that Kepler's SNR can be treated as a point source. We applied the binned likelihood analysis on the data by using the Fermitools routine, gtlike. We binned the data in 25 logarithmically spaced bands in energy and used the spatial binning with a pixel size of 0 • .1. We allowed the power-law normalization and photon index of Kepler's SNR and the normalizations of the Galactic and isotropic diffuse sources to vary. We also allowed the normalizations of 4FGL γ-ray sources within 3 • of Kepler's SNR to vary, while keeping the normalizations of other 4FGL sources fixed. We evaluated the significance of model components or additional parameters using the test statistic, TS = 2(logL-logL 0 ), where L 0 is the likelihood of the reference model without the additional parameters or components (Mattox et al. 1996).

HE γ-ray results
For the 0.75-300 GeV energy interval, the derived TS value for Kepler's SNR is 16.8 which corresponds to about 4σ significance. The likelihood maximization yields a photon index of Γ = 2.1 ± 0.3 and a normalization constant, N 0 = (9.3 ± 3.1) × 10 −15 cm −2 s −1 MeV −1 at E 0 =4750 MeV for a power-law spectrum. Figure 1 shows the TS map, based on a source model including 4FGL sources plus diffuse backgrounds, generated for the energy range of 4.75-300 GeV for the sake of comparison with the VHE γ-ray results. It reveals similarities between the Fermi-LAT TS map and the H.E.S.S. significance map at VHE energies. The positive TS values and significances for Kepler's SNR and SNR G4.8+6.2 are present on both these maps in Fig. 1. The butterfly shaped area shown in Figs. 2 and 3 corresponds to the 68% statistical uncertainty region of the differential flux. The excesses both in Fermi-LAT and H.E.S.S. data provide strong support for the identification of Kepler's SNR in the HE and VHE γ-ray bands. Between 0.75-300 GeV, the residual emission at the position of SNR G4.8+6.2 is significant at a 3.3σ statistical level (TS=10.9).

Young SNRs as γ-ray sources
The hadronic scenario-in which the γ-ray emission is produced through the two-photon decay of neutral pions created in hadron collisions of CRs with background gas-results in viable models for both the Tycho's and Cas A SNRs (Zhang et al. 2013, Ahnen et al. 2017. The leptonic scenario, in which inverse Compton (IC) mechanism dominates the VHE emission, is still a viable scenario for Tycho's SNR under the assumption that its GeV γray emission is due to hadronic interactions (Yuan et al. 2012) or in the two-zone approach (Atoyan & Dermer 2012). However, more recently developed physical models suggest that the γ-ray emission is primarily due to hadronic processes (Morlino & Caprioli 2012, Slane et al. 2014). Tycho's and Cas A SNRs are comparable in age with Kepler's SNR, which allows the radiative properties of SNRs to be investigated at an early stage in their evolution.
Both Type Ia and core-collapse SNe deliver similar kinetic energies of ∼ 10 51 erg. However, the type of SN does matter for both the ejected mass and the density and structure of the ambient medium. It is conceivable that the TeV emission detected from the Cas A SNR, which resulted from a core-collapse explosion, originates dominantly from the reverse shock instead of from the region heated by the forward shock (e.g., Helder & Vink 2008, Telezhinsky et al. 2013, Zirakashvili et al. 2014). The reverse shock accelerates particles of the ejecta, which, in turn, collide with the metal-rich plasma of the SN ejecta, leading to strong hadronic emission due to the high ejecta density in corecollapse SNRs. This circumstance might hinder a direct comparison of the radiation model for the Cas A SNR with the radiation models for Tycho's and Kepler's SNRs, for which the γ-ray emission is thought to be dominated by forward-shock accelerated particles. The Galactic CR chemical composition, meanwhile, conforms better to acceleration of a well-mixed interstellar medium than metal-rich ejecta (Ellison et al. 1997). For thermonuclear SNe, more time is necessary for the progenitor system to evolve (e.g., Totani et al. 2008); this extra time allows it to wander a long distance away from the parent molecular cloud. Thus, the environment in which the remnants of thermonuclear SNe evolve can be significantly different from the environment of core-collapse SNe of massive stars.
Multiwavelength studies of Kepler's SNR (Vink 2017, for a review) have established that SN 1604 was a Type Ia SN. At a likely distance of 5 kpc (Sankrit et al. 2016, Vink 2017, Ruiz-Lapuente 2017, given the Galactic latitude of 6 • .8, Kepler's SNR is located 590 pc above the Galactic plane. The relatively high density around Kepler's SNR, in particular in the northwestern part of the SNR, is attributed to mass lost by the progenitor system (Bandiera 1987, Chiotellis et al. 2012, Williams et al. 2012, Burkey et al. 2013, Toledo-Roy et al. 2014. Apart from its relatively large distance and high Galactic latitude, Kepler's SNR is best compared to Tycho's SNR located at a distance of about 2.5 kpc: both are Type Ia SNRs of similar age and develop in a relatively dense ambient medium with n ≈ 1-10 cm −3 .
Article number, page 4 of 9 H.E.S.S. Collaboration: Evidence for γ rays from Kepler's SNR

SED models
A variety of multiwavelength data is available for Kepler's SNR. It allows us to construct a characteristic SED for the nonthermal radiation caused by accelerated particles. In addition to the γ-ray data points described above, we use radio and X-ray spectral data points of Kepler's SNR from Reynolds & Ellison (1992), Allen et al. (1999) along with the WMAP data points at 33 and 41 GHz from Massardi et al. (2009) and the Swift-BAT data points at (4.2, 4.5, 5.3, 7.0, and 10.0)×10 18 Hz from Oh et al. (2018). For comparison with the SED of Tycho's SNR, the data points in the radio and X-ray bands are from Zhang et al. (2013, and references therein), and the Fermi-LAT and VERITAS γ-ray data points are from Archambault et al. (2017). The properties of Kepler's and Tycho's SNRs are described in the Appendix B.
In the framework of a hadronic model, we chose typical numerical values for physical parameters and described both SEDs of Kepler's and Tycho's SNRs by using the modeling package, Naima (Zabalza 2015). The radio band to X-ray band SEDs are attributed to the synchrotron radiation of a CR electron population, while the broad γ-ray SED is attributed to radiation driven by the collisions of relativistic CR protons with gas. Our model setup includes: (i) E sn = 10 51 erg for the SN Ia explosion energy; (ii) the distances to Kepler's and Tycho's SNRs of 5.0 kpc (Ruiz-Lapuente 2017) and 2.5 kpc (Zhang et al. 2013, Kozlova & Blinnikov 2018, respectively; (iii) n = 1 cm −3 for the gas target particle density; (iv) the kinetic energy of CR hadrons above 1 GeV of E CR /E SN =7% of the SN Ia explosion energy; (v) B = 200 µG for the magnetic field strength 2 (Völk et al. 2005, Helder et al. 2012); (vi) the ratio of energy in CR electrons to that in CR hadrons is 0.5%, constrained by fitting the synchrotron SED component; (vii) q = 2.3 for the CR electron and proton spectral indices, dN p,e /dE ∝ E −q , assumed to be the same and chosen to provide us with a fit in the radio-frequency band (DeLaney et al. 2002, Kothes et al. 2006; and (viii) exponential cut-off energies in the CR proton spectrum at 100 TeV and in the CR electron spectrum at 7.5 TeV, respectively. We assumed a fraction of the SN explosion energy converted into the energy of CRs similar to that given by Berezhko et al. (2006) (that is 10%). The parameter values (iii), (vi), and (viii) are chosen such that the hadronic model matches the SEDs of Kepler's and Tycho's SNRs. The constraint on the proton exponential cut-off energy is however premature, since the power-law hypothesis is currently sufficient to describe the observed SED in the VHE band. We note that the model is sensitive to the combination E CR × n rather than these two parameters individually. A model-dependent constraint on the density can be set by the size of the SNR at its given age during the adiabatic (Sedov) stage (e.g., Berezhko et al. 2006).
The left and right panels in Fig. 2 show the broadband SEDs of Kepler's and Tycho's SNRs, respectively, along with the hadronic model described above. The observations support the similarity between the shapes of their broadband SEDs. In the framework of this model, the hadronic γ-ray component dominates over the γ-ray component produced by CR electrons.
A comparison of the results presented in Fig. 2 shows that the same hadronic model scaled according to the different distances to the two SNRs describes both the SEDs of Kepler's and Tycho's SNRs. This conclusion supports that these remnants, similar in at least SN type and age, have also similar broadband nonthermal emission properties. The luminosities of Tycho's and Kepler's SNRs at 1 TeV are similar for the assumed distances, whereas the TeV luminosity of Cas A is five times higher. However, the TeV luminosity depends on several parameters, such as the CR energy in the source and the average density. So there is a possibility that the similarity of Tycho's and Kepler's SNR may hide some underlying differences in these parameters. This SED model can also describe the SEDs of Kepler's and Tycho's SNRs even if they are located at 7 kpc and 3.5 kpc, respectively, keeping the same distance ratio as above (that is 5/2.5=2), but increasing the gas density from 1 cm −3 to (7/5) 2 ×1 cm −3 = 2 cm −3 . The gas density around Kepler's SNR has a strong gradient, with the southeastern part being more tenuous than the northwestern part. Moreover, the gas appears to be clumpy. Hence, gas densities vary from n ∼ 1-250 cm −3 (Williams et al. 2012), and the average gas density is not well constrained. The distribution of γ-ray emission from different gas accumulations in these remnants remains hidden in the model. In future works on modeling, Article number, page 5 of 9 A&A proofs: manuscript no. output inverse Compton broadband SED 10 -6 10 -4 10 -2 10 0 10 2 10 4 10 6 10 8 10 10 10 12 10 14 Energy (eV) questions to be addressed are the implementation of a gas density distribution, the efficiency of conversion of kinetic energy to HE particles, the cutoff shape in the electron spectrum, and the connection to the dynamical evolution of the SNRs. Future γ-ray studies of Kepler's SNR are required for precise determination of its spectral and morphological characteristics in the VHE γ-ray band and further examination of this joint interpretation. In a leptonic scenario, the γ-ray emission is produced via IC scattering of photons from the cosmic microwave background (CMB), the infrared photon field emitted by dust in SNRs, and the Galactic interstellar radiation field by energetic electrons. To compute the IC γ-ray component, we included these three photon fields making similar contributions and took energy densities and spectra of the latter two photon fields from Gomez et al. (2012) and Porter et al. (2006). Since the same electron population is emitting both X-rays via the synchrotron mechanism and the HE and VHE γ rays via the IC mechanism, we constrain the magnetic-field strength by requiring that the model reproduces the observed flux of X-ray emission and does not overshoot the H.E.S.S. SED data points. In case the γ-ray emission is dominated by hadronic processes, this constraint should be regarded as a lower limit to the magnetic-field strength (Aharonian et al. 2008). From the γ-ray observations reported above, it follows that for magnetic field values greater than 80 µG the resulting IC flux would be less than the measured γ-ray flux. Figure 3 illustrates the leptonic model with a magnetic field strength of 80 µG. This magnetic-field strength is marginally below than the measured downstream magnetic field strength value for Kepler's SNR, which is in the range of 100-200µG (Völk et al. 2005, Helder et al. 2012. The photon index measured from the Fermi-LAT data, Γ = 2.1±0.3, is softer than that expected for the leptonic scenario, Γ = 1.7. In order to better determine which emission scenario is preferred, we compared the two models using the likelihood ratio test based on the Fermi-LAT data with energies between 750 MeV and 300 GeV. The null model assumes emission via IC scattering with a γ-ray spectrum fit to the H.E.S.S. data. Between 750 MeV and 300 GeV, the γ-ray spectrum in the null model is well approximated by a power law with fixed parameters. The alternative model assumes a power-law model with a free flux normalization and a free photon index, and the best-fit spectral parameters in this model better correspond to the hadronic scenario. The likelihood analysis described in Sec-tion 2.2 gives the TS value 5.1 with 2 degrees of freedom for a comparison of the null and alternative models. Therefore, the spectral shape favors a hadronic model over a leptonic model with a 1.8σ significance. Acero et al. (2022) have recently performed an analysis of 12 years of the Fermi-LAT data, selecting γ rays above 100 MeV. The derived photon index value is in agreement with that reported above and their lowest energy flux point provides further support for a hadronic model. The SED at γ-ray energies can also be explained by a mixed scenario involving both leptonic and hadronic contributions.

Summary and conclusions
Gamma-ray observations of young SNRs provide insights into the particle acceleration mechanisms and HE emission processes. HE and VHE γ-ray observations of the Tycho and Cas A SNRs show that remnants younger than 500 years old emit γ rays likely via the decay of neutral pions created in protonproton collisions. Sharing a number of the physical properties with Tycho's SNR, Kepler's SNR is an important testbed for a connection between CRs and SNRs.
This paper reports the results of 152 hours of VHE observations of Kepler's SNR with H.E.S.S. and provides a characterization of the whole data set using advanced analysis methods. This data set is significantly larger than that used in the previous publication. VHE γ-ray emission from Kepler's SNR is significant at a 4.6σ statistical level. A spectral analysis of this data set yields a photon index of Γ = 2.3 ± 0.2 stat ± 0.2 sys and a normalization constant of N 0 = (9.5 ± 2.3 stat ± 2.9 sys ) × 10 −13 cm −2 s −1 TeV −1 at E 0 = 1 TeV. This paper also includes an analysis of 10.7 years of Fermi-LAT data performed before making the decision on H.E.S.S. observations of Kepler's SNR in 2020. This analysis provides an indication of a GeV counterpart of Kepler's SNR and confirms the results reported by Xiang & Jiang (2021) and Acero et al. (2022). The compatibility of the signals in the HE and VHE γ-ray bands supports their common origin and association with Kepler's SNR.
Although the detection at the 4.6σ level falls short of the gold-standard in the field of VHE γ-ray astronomy of > 5σ, our results are based on observations targeting Kepler's SNR directly, and not a blind search. Moreover, Kepler's SNR, being a young SNR and an X-ray synchrotron source, is a priori expected to be a VHE γ-ray source. These arguments altogether provide a strong reason to endorse Kepler's SNR as a faint HE and VHE γ-ray source.
The results show that the observed SED of Kepler's SNR is similar to that of Tycho's SNR, possibly indicating the same nonthermal emission processes acting in both these SNRs. This fact allows us for the first time to tentatively propose a model of γ-ray emission that describes both the SEDs of Kepler's and Tycho's SNRs. It assumes a hadronic origin of the observed γray emission and requires (1) ≈ 10% of the SN Ia explosion energy to be converted to CR hadron energy and (2) the gas target particle density of ≈ 1 cm −3 . A lower limit on the magnetic field strength of B > 80 µG derived from the requirement that the IC γ-ray component does not overshoot the H.E.S.S. SED data points is tighter than the previous lower limit (Aharonian et al. 2008) by a factor of ≈1.5.