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A&A
Volume 643, November 2020
Article Number L14
Number of page(s) 6
Section Letters to the Editor
DOI https://doi.org/10.1051/0004-6361/202039131
Published online 20 November 2020

© ESO 2020

1. Introduction

Geminga (PSR J0633+1746) is an archetype of the radio-quiet gamma-ray pulsar population (Bignami & Caraveo 1996; Caraveo 2014). First detected by SAS-2 and COS-B (Fichtel et al. 1975; Hermsen et al. 1977; Bignami & Caraveo 1992) as a bright gamma-ray source with no counterpart at any other wavelength and subsequently associated with an X-ray source (Bignami et al. 1983), it was ultimately identified as a pulsar by ROSAT and EGRET (Halpern & Holt 1992; Bertsch et al. 1992). It has a period of P ≃ 237 ms and a characteristic age of ∼300 ky. Two independent measurements of the distance reported (Caraveo et al. 1996) and (Faherty et al. 2007), respectively. This makes Geminga one of the closest known pulsars.

The Fermi-LAT detector measured the pulsed gamma-ray spectrum of Geminga using one year of data and found that it can be described by a power law with an exponential cut-off at 2.46 ±  0.04 GeV (Abdo et al. 2010). The increase of Fermi-LAT statistics in the following years favoured a softer sub-exponential cut-off (Abdo et al. 2013; Ahnen et al. 2016). Subsequent ground-based observations by the Imaging Atmospheric Cherenkov Telescopes (IACT) VERITAS (Aliu et al. 2015) and MAGIC (Ahnen et al. 2016) could not detect any significant emission above 100 GeV and 50 GeV, respectively. A ∼2 deg steady halo around Geminga was first detected by the MILAGRO experiment (Abdo et al. 2009), and later reported by the HAWC (Abeysekara et al. 2017) and Fermi-LAT (Manconi et al. 2019) collaborations at energies above 5 TeV and 8 GeV, respectively.

In this paper, we report the detection of pulsed gamma-ray emission from the Geminga pulsar by the MAGIC telescopes. This makes Geminga the first middle-aged pulsar detected by IACTs and the third pulsar detected by these type of telescopes after the Crab (Aliu et al. 2008) and Vela (Abdalla et al. 2018). This detection had become possible thanks to the use of the new low-energy trigger system, dubbed Sum-Trigger-II (Dazzi et al., in prep.; García et al. 2014), designed to improve the performance of the telescopes in the sub-100 GeV energy range.

In Sect. 2 we present the MAGIC observations and the technical innovations that were imperative for this detection. The analysis of Fermi-LAT data is described in Sect. 3. The resulting MAGIC and Fermi-LAT light curves and spectra are presented in Sect. 4 and discussed in Sect. 5. Finally, we compare our observations with the predictions of the pulsar outer gap model (Cheng et al. 1986; Romani & Yadigaroglu 1995) applied to Geminga in Sect. 6.

2. MAGIC observations and data analysis

The MAGIC telescopes are two imaging atmospheric Cherenkov telescopes (IACTs) located on the Canary Island of La Palma (Spain) (Aleksić et al. 2016a). Observations of Geminga with the MAGIC Sum-Trigger-II system began in January 2017 and lasted until March 2019. Aiming for the lowest possible energy threshold, the observation zenith angle of the source was limited to below 25 deg. Data taken in the period between December 2017 and March 2018 were affected by non-optimal weather conditions and were discarded. After this selection, a total of 80 h of good quality data were available. The observations were made in the so-called ‘wobble mode’ (Fomin et al. 1994), in which the telescopes were pointed at sky positions around Geminga with an offset of 0.4 deg. Together with each event image, we recorded the event arrival time with a GPS disciplined Rubidium oscillator, which provides an absolute time stamp precision of 200 ns.

The detection of the Geminga pulsar with MAGIC was possible thanks to the implementation of the Sum-Trigger-II system. The standard MAGIC trigger requires that the signals of three neighbouring camera pixels exceed a preset threshold of ∼4.0 photo electrons (phe.). In the Sum-Trigger-II, the pixels are grouped into hexagonal-shape cells of 19 pixels each. The analogue sum of all pixel signals within any given cell is compared against a discriminator threshold of ∼18 phe. Integrating the signal from a large area leads to a better signal-to-noise ratio (S/N) for very low energy showers. To counteract the effect of noise after-pulses, which are typical for photo-multiplier tubes, the individual pixel amplitudes are clipped when exceeding 8.5 phe. The trigger geometry, thresholds, and clipping values were optimised by Monte Carlo (MC) simulations with the aim of minimizing the trigger threshold (Dazzi et al., in prep.). Compared to the standard trigger, the trigger energy threshold of the Sum-Trigger-II is about 50% lower. For a spectral index of −5, which is similar to that of Geminga as reported here, the peak of the gamma energy distribution (threshold) is approximately 15 GeV.

The MAGIC data were processed with the Magic Standard Analysis Software (MARS, Zanin et al. 2013). To improve the analysis performance close to the Sum-Trigger-II energy threshold, we developed a new algorithm in which the calibration and the image cleaning are performed in an iterative procedure. The rest of the higher level analysis followed the standard pipeline described in Aleksić et al. (2016b). This comprises the reconstruction of the energy and direction of the incoming gamma rays and the suppression of the hadronic background. Boosted decision trees and look-up tables were built for these purposes, using gamma-ray simulated shower events following the trajectory of Geminga in the sky and background events from dedicated observations.

For the timing analysis, the pulsar rotational phases of the events were computed using the Tempo2 package (Hobbs et al. 2006). An ephemeris for Geminga covering the MAGIC observations was obtained from the analysis of Fermi-LAT data (Kerr et al. 2015).

3. Fermi-LAT data and analysis

To characterise the Geminga emission at energies lower than those accessible to MAGIC, we analysed 10.6 years (from MJD 54682 to 58569) of public Fermi-LAT data across the energy range from 100 MeV to 2 TeV. We processed this data set using the P8R2_SOURCE_V6 instrument response functions and the Fermi Science Tools version v11r5p3. Events were selected within a circular region of interest (ROI) of 15° centred at the pulsar position (RA = 06h33m54.29s, Dec = ). We selected ‘Source’ class events that were recorded only when the telescope was in nominal science mode. The pulsar rotational phase and barycentric corrections of the events were computed with Tempo2, using the same ephemeris as for the MAGIC data analysis. The pulsar light curve was produced applying an additional energy dependent angular cut, according to the approximation of the Fermi-LAT Pass8 point spread function for a 68% confinement radius (Acero et al. 2015).

For the spectral reconstruction, a binned likelihood analysis was performed making use of the pyLikelihood python module of the Fermi Science Tools. Each of the two emission peaks of the Geminga light curve, P1 and P2, were analysed separately. We started the likelihood fits by including all sources in the ROI from the third Fermi Source Catalogue (Acero et al. 2015) in the spectral-spatial model. The spectral parameters for sources with a significance higher than 5σ and located within 5 deg of the centre of the ROI were left free. Also, we let the normalisation factor of the isotropic and Galactic background models free. For the rest of the sources, all parameters were fixed to their catalogue values. In a second step, all sources with TS <  4 were removed from the model. For the calculation of the spectral points, we repeated the procedure in each energy bin using a power law with the normalisation factor free and the spectral index fixed to 2.

4. Results

4.1. Light curves

The light curves shown in Fig. 1 are produced by phase folding Fermi-LAT photons and MAGIC events using the same pulsar ephemeris. The two well-known Geminga emission peaks, P1 and P2, are clearly visible above 5 GeV in Fermi-LAT data. At higher energies, only P2 is detected by Fermi-LAT , which is in agreement with the high-energy light curves shown in Ackermann et al. (2013). To characterise each peak at energies as close as possible to the MAGIC energy range, we fit them to symmetric Gaussian functions, using Fermi-LAT events above 5 GeV for P1 and above 15 GeV for P2. The corresponding light curves are shown in Fig. 1, panels a and b. The phase signal regions for the analysis of MAGIC data are then defined as the ±2σ intervals around the fitted peak positions. For estimating the background, we considered the off-pulse region between P2 and P1, where no emission is expected from the pulsar, starting 6σ away from each peak’s centre. Table 1 summarises the signal and background regions used for the MAGIC analysis.

thumbnail Fig. 1.

Geminga light curves measured by Fermi-LAT (panels a and b), and by MAGIC (panel c). For clarity, two rotation cycles are shown. The green-shaded regions highlight the phase intervals corresponding to the P1 and P2 emission, obtained from the fits to Fermi-LAT data above 5 GeV and 15 GeV, respectively. The phase region from which the background is estimated is shown by the grey band. These signal regions were later applied to the analysis of MAGIC data. P2 is detected with MAGIC at a significance level of 6.25σ. No significant signal is detected from P1 in the MAGIC energy range.

Table 1.

Definition of the signal (P1, P2) and background (OFF) regions derived from the analysis of the Fermi-LAT light curves shown in Fig. 1.

The MAGIC light curve for events with reconstructed energies above 15 GeV is shown in Fig. 1, panel c. It was obtained after applying energy-dependent gamma and hadron separation cuts, trained on MC simulated gamma-ray showers. The number of excess events for each emission peak and the corresponding significances were computed using Eq. (17) in Li & Ma (1983) and they are tabulated in Table 1. Emission from P2 is detected with MAGIC at a significance level of 6.25σ, corresponding to 2457 excess events over a scaled background of 112 018 events. A region-independent signal test with the H-test and -test (de Jager & Büsching 2010) results in 4.8σ and 5.2σ significances, respectively. The analysis of MAGIC events in the phase region of P1 does not reveal any significant signal in this energy range.

4.2. Energy spectrum

Figure 2 shows the Spectral Energy Distribution (SED) of Geminga for P2, obtained after the analysis of Fermi-LAT (open circles) and MAGIC data (filled circles). The spill-over effect due to the soft spectral index has been carefully taken into account by unfolding the MAGIC energy spectrum using the Tikhonov regularisation method (Albert et al. 2007), and cross-checked with a forward-folding procedure. The resulting MAGIC unfolded spectral points (filled circles in Figs. 2) are reported in Table 2. The dashed blue line shows the forward-folding power-law fit, F0(E/E0)−Γ, performed on the distribution of MAGIC excess events. The blue butterfly represent the 1σ statistical uncertainty confidence interval of the fit. The spectrum measured by MAGIC in the energy range 15−75 GeV is well-represented by the power law, with an associated χ2 = 15.27 with 15 degrees of freedom. The obtained spectrum is in agreement with the upper limits previously reported by MAGIC (Ahnen et al. 2016). The resulting fit parameters are reported in Table 3. The spectral index Γ = 5.62 ± 0.54 (statistical errors only) is the softest ever measured by MAGIC from any source.

thumbnail Fig. 2.

SED of the second emission peak, P2, of the Geminga pulsar measured by the MAGIC telescopes (filled circles) and the Fermi-LAT (open circles). The MAGIC spectral points were calculated by unfolding the reconstructed energy spectrum by means of the Tikhonov regularisation method. Dashed blue line shows the forward folding fit to the MAGIC data assuming a power law and the blue-shaded area represents the 1σ confidence interval around the power-law fit. Dotted and continuous black lines represent the combined fit to MAGIC and Fermi-LAT data to a power law with an exponential or sub-exponential cutoff, respectively. Dotted-dashed orange line shows the P2 spectrum predicted in the stationary outer gap model applied to Geminga for a magnetic dipole moment μ = 1.4 μd, an angle between the magnetic and the rotational axis of the star, α = 30°, and an observer’s viewing angle, ζ = 95°.

Table 2.

MAGIC SED points.

5. Discussion

We performed a joint fit of MAGIC and Fermi-LAT spectral points in the combined energy range, from 100 MeV to 75 GeV, by using a power law with an exponential cut-off function:

(1)

where E0 is the energy scale, Γ the spectral index, Ec the cut-off energy, and β the cut-off strength. We considered two different cases: a pure exponential cut-off, β = 1, and the general case in which the β parameter is set free. The parameters resulting from the fits are given in Table 3. The best fit is found for β = 0.738 ± 0.013. In a likelihood-ratio test versus the free exponential cut-off model, the pure exponential case can be rejected with TS = −2Δ log ℒ = 336.6, which, according to a chi-square distribution with one degree of freedom, corresponds to a significance of 18.3σ. Also, the sub-exponential cut-off is disfavoured by the data at the level of 3.6σ, according to a goodness-of-fit chi-square test.

Table 3.

Results from the spectral fits performed to the MAGIC data alone (first row) to a power law function (PL), and from the joint fits to Fermi-LAT and MAGIC data (abbreviated as F & M) to power laws with exponential (PL Exp) or sub-exponential (PL Subexp) cut-offs, and to a log-parabola model (LP).

In order to assess whether there is any preference for curvature in the high energy tail of the spectrum, we fitted MAGIC and Fermi-LAT spectral points above 10 GeV to a log-parabola model, F0(E/E0)−Γ − βlog(E/E0), obtaining a best-fit value for the curvature index of . We performed a likelihood-ratio test between this model and a power law. This results in TS = 1.7 with 1 degree of freedom, corresponding to 1.3σ against the power-law model. This shows that the log-parabola model is not significantly preferred over the power-law one. The power-law index derived from the joint fit, Γ  =  5.18 ± 0.15, is compatible with the one obtained with MAGIC data alone.

The effect of systematic uncertainties on the MAGIC spectral reconstruction has been studied. A 5% change in the estimated energy of the events has little effect in the reconstructed spectral index (below 1%), but makes the MAGIC fluxes fluctuate by up to 20%. This results from the combined effect of the softness of the Geminga spectrum and the steeply falling effective collection area close to the MAGIC energy threshold. The joint fit with Fermi-LAT data in the overlapping energy range helps to constrain these uncertainties. To test this we introduced a MAGIC flux scale factor, s, as a nuisance parameter in the fits. Maximum-likelihood values of the scale parameter are always found to be compatible with unity within the uncertainties, with s = 0.88 ± 0.11 and s = 0.98 ± 0.14 for the sub-exponential and the log-parabolic fits, respectively. Likelihood-ratio tests versus a model with no scaling provide, in both cases, TS <  1.0. We conclude that the energy calibration of MAGIC with respect to Fermi-LAT is accurate.

6. Modelling the high-energy emission

Two main radiation processes are considered to be responsible for the gamma-ray emission detected in pulsars: synchro-curvature radiation or Inverse Compton Scattering (ICS), or a combination of both. The first can explain the exponential cut-offs at a few GeV seen in the vast majority of Fermi-LAT pulsars, while the second process may account for the power-law spectral tail detected in the Crab pulsar up to TeV energies (Ansoldi et al. 2016).

We compare our observational results with the predictions of the stationary three-dimensional pulsar outer gap (OG) model (Hirotani 2006, 2013). We assume that the magnetic field lines are given by the rotating vacuum dipole solution (Cheng et al. 2000; Aliu et al. 2015), and we solve Gauss’s law, the stationary Boltzmann equations for electrons and positrons, and the radiative transfer equation of the emitted photons from IR to very-high-energy (VHE) gamma rays. Accordingly, we can obtain the pulse profile and the phase-resolved spectrum of the emitted photons, by setting the following five parameters of the neutron star (NS): the rotational angular frequency, ΩF; the surface temperature, T; the area of the star, A; the magnetic dipole moment, μ; and the angle α between the NS magnetic and rotational axes. The NS rotational period, P, is an observable and readily gives ΩF = 2π/P. Using the soft X-ray data (Halpern & Wang 1997), we constrain the NS surface emission with temperature kT = 49.74 eV and area , where denotes the whole NS surface area measured by a distant observer. The distance to source is assumed to be 250 pc (Faherty et al. 2007). We also include in the seed X-ray spectrum a harder component (kT ∼ 185 eV) associated with the heated polar cap region discussed in Caraveo et al. (2004). The value of μ will not be very different from its dipole value μd, which is constrained by P and its temporal derivative, Ṗ, under the assumption of magnetic dipole radiation. Therefore, μ/μd, α, and the observer’s viewing angle with respect to the rotation axis, ζ, remain as free parameters. We constrain these parameters by comparing the predicted pulse profile and phase-resolved spectrum with the MAGIC and Fermi-LAT observations.

For the Geminga pulsar, unlike in young pulsars like the Crab, ICS is negligible in the outer magnetosphere because the IR photon fields are too weak. As a result, the positrons accelerated outward in the gap, produces negligible VHE fluxes. Nevertheless, gap-accelerated electrons continue propagating towards the star to efficiently up-scatter soft X-ray photons from the NS surface by head-on collisions. Accordingly, if we are observing Geminga nearly perpendicularly to its rotation axis, the inward VHE photons emitted by the electrons would appear in the same rotational phase as the outward HE photons emitted by the positrons.

To explain the MAGIC flux and the double-peaked pulse profile observed at lower energies by Fermi-LAT with a peak separation of 183° (Abdo et al. 2013), we find that μ = 1.4 μd, α ∼ 30° and 95° < ζ <  100° are necessary. A similar viewing angle of ζ = 90° was also obtained in Pierbattista et al. (2015), by fitting the Fermi-LAT light curve on the basis of the OG model. The dotted-dashed orange line in Fig. 2 shows the predicted Geminga flux from the P2 phase region defined in Table 1 for a viewing angle ζ = 95°. The OG solutions predicting emission in the MAGIC energy range tend to under predict the Fermi-LAT flux at few GeV. This may indicate the limitation of stationary OG models, suggesting the need for non-stationary particle-in-cell simulations of pulsar magnetospheres1. At the viewing angle of ζ = 95°, below 40 GeV, the flux of P2 is dominated by the outward photons emitted in the northern OG via mainly the curvature process. Above 40 GeV, the P2 flux is instead dominated by the inward photons emitted via ICS in the same northern OG. The emission from the southern OG is relatively small for P2, whereas for P1, the role of northern and southern OGs are exchanged. At ζ = 100° the inward ICS emission dominates the outward one above 100 GeV. At ζ ≥ 105°, the ICS component becomes negligible. It also follows that the present stationary OG model predicts an extension of the ICS pulsed component above the energies reported by MAGIC.

7. Summary

In this paper, we present the detection of pulsed gamma-ray emission from the Geminga pulsar with the MAGIC telescopes. The emission coincides in pulse phase with the position of P2 and is detected up to 75 GeV. This makes Geminga the first middle-aged pulsar detected up to such energies. The spectrum measured by MAGIC is well-described by a power law of spectral index Γ = 5.62 ± 0.54. A joint fit to MAGIC and Fermi-LAT data rules out the existence of an exponential cut-off in the combined energy range. A sub-exponential cut-off is also disfavoured at the 3.6σ level. According to the outer gap model, the emission detected by MAGIC implies that we are observing Geminga nearly perpendicularly to its rotation axis and that the emission originates in the northern outer gap. The energy range covered by MAGIC would correspond to the transition from curvature radiation by outward accelerated positrons to ICS by electrons accelerated towards the star. The ICS component is predicted to extend above the energies detected by MAGIC. This should be confirmed by future Geminga observations by IACTs, as well as by non-stationary pulsar gap models.

1

Particle-in-cell simulations (see e.g. Brambilla et al. 2018 and references therein), are currently limited to much weaker magnetic field strengths than the actual values found in pulsar magnetospheres. Consequently, they cannot be used at present to probe pulsar emission above GeV energies.

Acknowledgments

The authors would like to thank Matthew Kerr for helping in the production of the ephemeris used in this analysis. We would also like to thank the Instituto de Astrofísica de Canarias for the excellent working conditions at the Observatorio del Roque de los Muchachos in La Palma. The financial support of the German BMBF and MPG; the Italian INFN and INAF; the Swiss National Fund SNF; the ERDF under the Spanish MINECO (FPA2017-87859-P, FPA2017-85668-P, FPA2017-82729-C6-2-R, FPA2017-82729-C6-6-R, FPA2017-82729-C6-5-R, AYA2015-71042-P, AYA2016-76012-C3-1-P, ESP2017-87055-C2-2-P, FPA2017-90566-REDC); the Indian Department of Atomic Energy; the Japanese ICRR, the University of Tokyo, JSPS, and MEXT; the Bulgarian Ministry of Education and Science, National RI Roadmap Project DO1-268/16.12.2019 and the Academy of Finland grant nr. 320045 is gratefully acknowledged. This work was also supported by the Spanish Centro de Excelencia “Severo Ochoa” SEV-2016-0588 and SEV-2015-0548, the Unidad de Excelencia “María de Maeztu” MDM-2014-0369 and the “la Caixa” Foundation (fellowship LCF/BQ/PI18/11630012), by the Croatian Science Foundation (HrZZ) Project IP-2016-06-9782 and the University of Rijeka Project 13.12.1.3.02, by the DFG Collaborative Research Centers SFB823/C4 and SFB876/C3, the Polish National Research Centre grant UMO-2016/22/M/ST9/00382, by the Brazilian MCTIC, CNPq and FAPERJ, and at HKU by a GRF grant (Project 17307618) from the Hong Kong Government.

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All Tables

Table 1.

Definition of the signal (P1, P2) and background (OFF) regions derived from the analysis of the Fermi-LAT light curves shown in Fig. 1.

In the text
Table 2.

MAGIC SED points.

In the text
Table 3.

Results from the spectral fits performed to the MAGIC data alone (first row) to a power law function (PL), and from the joint fits to Fermi-LAT and MAGIC data (abbreviated as F & M) to power laws with exponential (PL Exp) or sub-exponential (PL Subexp) cut-offs, and to a log-parabola model (LP).

In the text

All Figures

thumbnail Fig. 1.

Geminga light curves measured by Fermi-LAT (panels a and b), and by MAGIC (panel c). For clarity, two rotation cycles are shown. The green-shaded regions highlight the phase intervals corresponding to the P1 and P2 emission, obtained from the fits to Fermi-LAT data above 5 GeV and 15 GeV, respectively. The phase region from which the background is estimated is shown by the grey band. These signal regions were later applied to the analysis of MAGIC data. P2 is detected with MAGIC at a significance level of 6.25σ. No significant signal is detected from P1 in the MAGIC energy range.
In the text
thumbnail Fig. 2.

SED of the second emission peak, P2, of the Geminga pulsar measured by the MAGIC telescopes (filled circles) and the Fermi-LAT (open circles). The MAGIC spectral points were calculated by unfolding the reconstructed energy spectrum by means of the Tikhonov regularisation method. Dashed blue line shows the forward folding fit to the MAGIC data assuming a power law and the blue-shaded area represents the 1σ confidence interval around the power-law fit. Dotted and continuous black lines represent the combined fit to MAGIC and Fermi-LAT data to a power law with an exponential or sub-exponential cutoff, respectively. Dotted-dashed orange line shows the P2 spectrum predicted in the stationary outer gap model applied to Geminga for a magnetic dipole moment μ = 1.4 μd, an angle between the magnetic and the rotational axis of the star, α = 30°, and an observer’s viewing angle, ζ = 95°.
In the text

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