AGILE Detection of Gamma-Ray Sources Coincident with Cosmic Neutrino Events

The discovery of a diffuse flux of cosmic neutrinos by the IceCube experiment (Aartsen et al. 2013, 2015) opened a new field of investigation in the context of neutrino astronomy (after the detections of the Sun and SN 1987a). Energetic neutrinos of energies above 10 TeV can be produced in astrophysical beam dumps, where cosmic rays are accelerated in regions near compact objects or in shock fronts, and interact via proton–proton (p–p) or proton–photon (p–γ) collisions with matter or radiation fields surrounding the central engine or within an ejected plasma flow (see Halzen 2017 for a review). High-energy gamma-ray emission above GeV is expected to be associated with these hadronic processes, with intensities that vary depending on source characteristics and environment (Mészáros 2017).

No significant clustering of neutrinos above the expected background has been observed so far from any of the current experiments after several years of observations (Aartsen et al. 2017a; Albert et al. 2017). Active galactic nuclei (AGNs) of the blazar category are considered the main cosmic neutrino source candidates (Mannheim 1995), although it has been suggested, based on average properties, that they contribute only to a fraction of the observed diffuse flux (Aartsen et al. 2017b). A contribution from other types of active galaxies (starburst galaxies, radio galaxies; Loeb & Waxman 2006; Becker Tjus et al. 2014; Tavecchio et al. 2018), galaxy clusters/groups (Murase et al. 2008; Kotera et al. 2009), AGN winds (Wang & Loeb 2016; Lamastra et al. 2017), and Galactic sources (supernovae remnants expanding in dense molecular clouds, microquasars, hidden compact objects; Bednarek 2005; Vissani 2006; Anchordoqui et al. 2014; Sahakyan et al. 2014; Ahlers et al. 2016) should also be considered.

Observation of transient gamma-ray emission, spatially and temporally compatible with the IceCube neutrinos, is then crucial to identify their electromagnetic (EM) counterparts. Since 2016 April, the IceCube Collaboration has been alerting the astronomical community almost in real time whenever a single-track high-energy starting event (HESE) or an extremely high-energy (EHE) through-going track event, with an energy higher than several hundred TeV, is detected (Aartsen et al. 2017c). The implementation of the IceCube alert system with the possibility of fast follow-up observations by several space- and ground-based instruments allows a global search for this association. On 2017 September a first significant association (at the level of 3σ) was announced: the gamma-ray flaring blazar of the BL Lac class, TXS 0506+056, was identified as a likely EM counterpart to the IceCube event IC-170922 (Aartsen et al. 2018a). Furthermore, from the analysis of archival data, an excess of very high-energy (VHE) neutrinos from the direction of the same source has been also detected in 2014/2015 (Aartsen et al. 2018b). TXS 0506+056 is thus suggested as the first extragalactic neutrino point-like source ever detected.

We report here on a systematic search for Astro-rivelatore Gamma a Immagini Leggero (AGILE) transient gamma-ray counterparts to the IceCube HESE/EHE events announced through the GCN/AMON system. The paper is organized as follows: in Section 2 we present the results of the systematic search for gamma-ray sources, in coincidence with neutrino events, automatically detected by the AGILE Quick Look (QL) transient detection system. The level of AGILE/IceCube correlation for some significant gamma-ray detections found in the search is evaluated, estimating the probability to be accidental using the AGILE false alarm rate (FAR) computed through the method discussed in Appendix A. In Section 3, we further investigate the common AGILE/IceCube detections, and we explore the possible EM counterpart candidates using the cross-catalog search tools available from the ASI Space Science Data Center.¹⁹ Finally, in Section 4, we discuss the astrophysical implications of the AGILE observations.

The AGILE satellite monitors cosmic gamma-ray sources in the energy range from 30 MeV to 30 GeV (Tavani et al. 2009). Since 2009 November, the satellite has been scanning the whole sky in spinning mode, being an all-sky detector for transient gamma-ray sources capable of exposing about 80% of the whole sky at any given time with good sensitivity and angular resolution to gamma-rays above 100 MeV.

In this observing mode, at the end of 2016 July, the main instrument onboard of the satellite, the gamma-ray imager GRID, detected a gamma-ray transient (AGL J1418+0008) spatially and temporally consistent with the IceCube event IC-160731 (Lucarelli et al. 2017b). This detection was the result of the automatic and QL search for gamma-ray transients above 100 MeV, performed daily over predefined 2 day integration time-bins of AGILE-GRID data (Bulgarelli et al. 2014).

Motivated by this first detection, we have explored the AGILE QL database to search for other transient gamma-ray detections with the following characteristics: (1) a centroid positionally compatible, within the AGILE angular resolution, with the reconstructed arrival directions of the IceCube HESE/EHE neutrino events, and (2) temporally occurring within a fixed search time window around the neutrino event time T₀. Since 2016 April, a total of 13 neutrino events have been made public²⁰ (see Appendix B for the complete list); 10 events survive additional checks by the IceCube team. In this paper, we consider these 10 events as the basis for our study.

Typical IceCube HESE/EHE error circles are of order of 1° in radius, and the mean AGILE angular resolution measured from in-flight and calibration data is ∼15 in the energy range 100 MeV–1 GeV (Sabatini et al. 2015). Based on this, we have tried three values for the database search radius around the 10 IceCube input sky positions (10, 15, and 20), which are within the range of the AGILE point-spread function (PSF). Concerning the time window of interest, the astrophysics and timescales of the phenomena related to the emission of these EHE neutrinos and their likely correlated gamma-ray emission are still uncertain. Thus, based on the typical AGILE sensitivity to a transient gamma-ray source, we consider the AGILE QL detection temporally consistent with the neutrino event if it occurs within a time interval of plus/minus 4 days around T₀.

From the QL database mining, using the optimized 15 search cone radius, we found three significant AGILE detections which satisfy the temporal and spatial association criteria defined above in correspondence with the three IceCube events: IC-160731, IC-170321, and IC-170922. From now on, we will indicate the corresponding three AGILE detections as AGILE Source A, Source B, and Source C. Table 1 shows the details of the three AGILE QL detections, along with the main parameters of the closest IceCube detection (event ID, neutrino event time T₀, and best-fit reconstructed centroid position in equatorial coordinates). In all cases, the gamma-ray position is within the AGILE angular resolution (15) from the best-fit IceCube reconstructed arrival direction. The table also shows the time difference Δt between T₀ and the center of the 2 day integration interval of the closest QL detection, and the corresponding gamma-ray flux above 100 MeV evaluated by means of the AGILE maximum likelihood (ML) algorithm (Bulgarelli et al. 2012).

The first AGILE/IceCube event in Table 1 is AGL J1418+0008, whose detection was already reported in Lucarelli et al. (2017b). AGILE Source B is reported here for the first time: this detection, with a gamma-ray flux above 100 MeV of F = (1.5 ± 0.6) × 10⁻⁶ ph cm⁻² s⁻¹, is temporally close (2 days prior) to the IceCube event that occurred on 2017 March 21 (Blaufuss 2017a). The last one, Source C, corresponds to the most recent IceCube-170922A event and is consistent with the gamma-ray activity from the blazar TXS 0506+056 as reported in Aartsen et al. (2018a).  We notice that all three events with an AGILE nearby source detection belong to the EHE event class with track-like characteristics (Aartsen et al. 2017c) (see also Table 4 in Appendix B).

All three QL detections are confirmed using the standard AGILE analysis (Bulgarelli et al. 2012), applying additionally a more stringent cut on the Earth albedo contamination.²¹  Figure 1 shows: in the left panel, the AGILE-GRID gamma-ray lightcurves above 100 MeV around T₀ for each of the three sources; in the right panel, the gamma-ray intensity maps above 100 MeV corresponding to the detection found near T₀.

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The standard AGILE data analysis indicates that in all cases the peak gamma-ray emission is similarly observed within 1–2 days from T₀. For Sources B (IC-170321) and C (IC-170922), weak gamma-ray emission is also observed over longer integration timescales that include T₀. In particular, for the new Source B an integration of 15 days, starting from 2017 March 15 (12:00 UT), shows a detection above 4σ with a flux $F(E\gt 100\,\mathrm{MeV})=(4.6\pm 1.6)\times {10}^{-7}\,\mathrm{ph}\,{\mathrm{cm}}^{-2}\,{{\rm{s}}}^{-1}$. The AGILE centroid has Galactic coordinates (l, b) = (224.59, −10.53) ± 0.42 (deg) (95% stat. c.l.) ± 0.1 (deg) (syst.) (R.A., decl. (J2000) = (98.58, −15.08) (deg)), and is fully compatible with the IceCube centroid (see Figure 2).

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2.1. Post-trial False Alarm Probability

To evaluate the probability that each of these three gamma-ray sources is associated with the neutrino events by chance, we first evaluated the FAR for an AGILE QL detection per unit time δt and per unit solid angle δΩ. As the unit time δt, we assumed the standard integration time of the QL maps (δt = 2 days). For δΩ, we assumed the solid angle subtended by a cone with half-aperture matching the standard circular radius of 15 used in the database search (δΩ ≃ 2.15 × 10⁻³ sr).²²  We then estimated the post-trial false alarm probability P_i of a random occurrence in space and time of a neutrino and a gamma-ray transient event separated by an interval Δt and  by the solid angle ΔΩ (corresponding to the angular distance Δθ) as (Connaughton et al. 2016)

$$\begin{eqnarray}&&\begin{array}{l}{P}_{i}={N}_{i}\ast \mathrm{FAR}(\geqslant \sqrt{\mathrm{TS}})\ast {\rm{\Delta }}{\rm{t}}\ast (1\\ \quad +\ \mathrm{ln}({\rm{\Delta }}T/\delta t))\ast \,{\rm{\Delta }}{\rm{\Omega }}\end{array}\end{eqnarray} \tag{ 1 }$$

where N_i is the number of trials for a symmetric time window, $\mathrm{FAR}(\geqslant \sqrt{\mathrm{TS}})$ is the FAR per 2 day map and per unit solid angle for AGILE detections above a given significance $\sqrt{\mathrm{TS}},$ ²³ Δt is the absolute time difference between the QL detection centroid and T₀, and ΔT is the one-sided time interval over which the search is done (set beforehand to ΔT = 4 days). We have assumed a spatial coincidence whenever the centroids of the AGILE/IceCube detections are within an angular distance Δθ = 15, so that in our case ΔΩ ≡ δΩ.  

Since the gamma-ray detection strategy we adopted is fully automated,²⁴ and there is no refined analysis around T₀ , the trial factor N_i takes into account only the choice of the symmetric window around T₀ and is thus equal to 2.

The last two columns of Table 1 show, respectively, the FAR (per 2 day map and per unit solid angle) and the corresponding post-trial false alarm probability P_i of a random coincidence with the IceCube neutrinos for each of the three QL detections. For each AGILE source, the post-trial chance correlation is of the order of 10⁻³.

Given this basic information, we then proceed to calculate the joint post-trial probability to observe three gamma-ray sources out of 10 neutrino alerts over the period of the active IceCube alert system, as

$$\begin{eqnarray}&&\begin{array}{l}{P}_{\mathrm{joint}}(\mathrm{post} \mbox{-} \mathrm{trial})=1-\left(1\right.-\ {\left.{P}_{A}\ast {P}_{B}\ast {P}_{C}\right)}^{{\text{}}N}\end{array}\end{eqnarray} \tag{ 2 }$$

where the number of global trials N is given by the product of two contributions: the total number of IceCube HESE/EHE events considered (equal to 10), and the number (equal to three) of optimizations of the search radius of the gamma-ray error boxes. We therefore determine the joint post-trial chance probability to be

$$\begin{eqnarray}&&{P}_{\mathrm{joint}}(\mathrm{post} \mbox{-} \mathrm{trial})=1.7\times {10}^{-6}\end{eqnarray} \tag{ 3 }$$

which corresponds to a number of Gaussian equivalent one-sided standard deviations of approximately 4.7σ.

Alternatively, assuming an average post-trial false alarm probability p = 4.0 × 10⁻³ for a typical gamma-ray source, we can use a binomial probability distribution to estimate the probability to observe three AGILE gamma-ray counterparts out of 10 IceCube events in the whole sky. This results in a probability of the order of 7.5 × 10⁻⁶ (one-sided 4.3σ).

3.1. AGILE Source A/IC-160731 Event

The first IceCube HESE/EHE event, compatible and temporally close to an automatic AGILE QL detection, occurred on 2016 July 31 (T₀ = MJD 57600.079). The event and the possible AGILE gamma-ray counterpart (AGL J1418 +0008) were extensively studied in Lucarelli et al. (2017b). The EM follow-up of the event did not reveal any transient sources within the IceCube error circle. Using the online SSDC SkyExplorer tool²⁵ and the ASI Open Universe web portal,²⁶ in this work we have performed a new search for possible known EM counterparts within the common AGILE/IC-170321 confidence error regions. Figure 3, left panel, shows the result of a query for cataloged radio, X-ray, and gamma-ray sources within 60 arcmin from the IceCube centroid, placed at R.A., decl. (J2000) = (214.544, −0.3347 deg). The 60 arcmin search radius encompasses the whole IC-160731 error circle and also covers most of the 95% c.l. error circle of the AGILE Source A detection (see Figure 1, upper panel).

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The sky region within the gamma-ray and neutrino error regions does not show any obvious EM counterpart, in particular, neither known gamma-ray sources nor known AGN blazars appear within the search radius chosen for the query. The X-ray source 1RXS J141658.001449 (labeled as 1 in Figure 3) was suggested by Lucarelli et al. (2017b) as a potential high-peaked BL Lac (HBL) AGN blazar. Nevertheless, a dedicated Swift-XRT observation taken some months after the neutrino event time T₀, did not confirm any steady X-ray emission from this position, thus the former hypothesis could not be confirmed.

Five uncataloged X-ray sources were detected during the previous Swift target of opportunity (Lucarelli et al. 2017b): their positions are indicated by the blue crosses in Figure 3. One of them (source labeled as 2) is positionally consistent with the radio source NVSS J141746-001151 and the object SDSS J141746.65-001149.8, which is actually cataloged as star.

Interestingly this region shows the presence of several galaxy clusters (indicated by the black circles in Figure 3), which could host a possible AGN or a different class of powerful active sources that could be the origin of the IceCube neutrino and the gamma-ray transient emission detected by AGILE. In particular, based on its radio/X-ray positional association and flux intensity, one of the most interesting neutrino source candidates within this sky region is that labeled as 3 in Figure 3 (R.A., decl. (J2000) = 213.74038, −0.34967 deg). The radio and X-ray emissions are positionally consistent with the elliptical galaxy SDSS J141457.72-002058.6, whose broadband spectral properties resemble those typical of a high synchrotron peaked (HSP) blazar (see Figure 3, right panel).²⁷

3.2. AGILE Source B/IC-170321 Event

The second IceCube HESE/EHE event, compatible and temporally close to an automatic AGILE QL detection, occurred on 2017 March 21 (T₀ = MJD 57833.314). The ML significance of the QL detection is slightly lower than the others but it is again confirmed through the standard AGILE analysis using a longer integration window around T₀, applying additionally a more stringent cut on the Earth albedo contamination.

The EM follow-up of the event did not reveal any transient source within the IceCube error box: in the high-energy gamma-ray band, Fermi-LAT placed a 95% c.l. upper limit (u.l.) above 100 MeV for point-like emission at the IceCube position over different time intervals near and before T₀, with the most stringent found to be 5.5 × 10⁻⁸ ph cm⁻² s⁻¹ in one week of exposure prior to T₀ (Buson et al. 2017).

In the hard X-ray/gamma-ray band, INTEGRAL and Konus-Wind reported an u.l. on burst-type emission over short time periods around T₀ (Savchenko et al. 2017; Svinkin et al. 2017). The Swift-XRT follow-up, with a seven-tile mosaic covering only 21% of the 90% error box on the refined IceCube localization, detected only one known X-ray source (1SXPS J063214.5-143300) at a flux level consistent with the cataloged value (Keivani 2017). Archival data from Swift-BAT²⁸ did not show any transient hard-X-ray emission at this position. No optical follow-up was reported for the event. We explored the All-Sky Automated Survey for SuperNovae transient web page²⁹ and the Palomar Transient Factory catalog³⁰ but did not find any transient optical emission within 1° from the IceCube centroid.

Using the online SSDC SkyExplorer tool (see footnote 25) and the ASI Open Universe web portal (see footnote 26), we searched also for this event a possible common EM counterpart for the IC-170321 neutrino and AGILE Source B. Figure 4 shows the result of a query for cataloged radio, X-ray, and gamma-ray sources within 90 arcmin from the IceCube centroid,  which fully contains the AGILE Source B error circle. Labels from 1 to 10 in Figure 4  indicate the most interesting neutrino/gamma emitter candidates found in the search, based on their radio/X-ray positional association and flux intensity. Among them, we found two flat spectrum radio quasars (FSRQs), one 3FGL source, 3FGL J0627.9-1517, and three possible blazars of the HBL sub-class. Details of each of the 10 sources are reported in Table 2.

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Table 2.  Possible EM Candidate Counterparts for IC-170321 and the AGILE Source B Detected in the Days around T₀

ID	Catalog Name	R.A. (J2000)	Decl. (J2000)	Other Association	Source Class	Distance from IC-170321 Centroid
		(deg)	(deg)			(arcmin)
1	5BZQ J0631-1410	97.83429	−14.1755	CRATES J063119-141030	FSRQ	58
2	CRATES J063148-143042	97.94638	−14.50844	⋯	Possible IBL	37
3	PSZ2 G224.01-11.14	97.75250	−14.83520	⋯	Cluster of Galaxies	34
4	NVSS J063535-151813	98.89838	−15.30361	1RXS J063533.5-151817	Possible HBL	39
5	NVSS J063556-154038	98.98450	−15.67736	1RXS J063558.2-15410	Possible HBL	56
6	3FGL J0627.9-1517	96.9853	−15.29782	WHSP J062753.2-151956	HSP BL Lac	79
7	CRATES J063428-160239	98.6191	−16.0519	⋯	Flat spectrum radio source	65
8	CRATES J063053-155929	97.7306	−15.9829	⋯	Flat spectrum radio source	67
9	CRATES J063329-163020	98.38046	−16.5201	⋯	Possible HBL	89
10	PMN J0635-1415	98.95842	−14.25011	⋯	Flat spectrum radio source	60

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Assuming the HBL sub-class of blazars as one of the most promising neutrino emitter candidates (Padovani et al. 2016; Resconi et al. 2017), one of the most interesting source within the SkyExplorer search radius appears to be the 3FGL J0627.9-1517 source (#6 in Figure 4), which has been recently classified as the HSP blazar 2WHSP J062753.2-151956 (Chang et al. 2017). The steady average 3FGL flux above 100 MeV for this source is below 2 × 10⁻⁸ ph cm⁻² s⁻¹. The gamma-ray light curve above 1 GeV produced with the Fermi-LAT online data analysis tool available at SSDC,³¹ with a 7 day binning, did not show any relevant activity in the six months around the neutrino event T₀, except for one small peak, appearing some days later it was not confirmed by a further analysis made with the official Fermi Science Tools (v10r0p5).³²

3.3. AGILE Source C/IC-170922 Event

The first AGILE detection of a gamma-ray counterpart above 100 MeV consistent with the position of the neutrino event IC-170922 was first reported in Lucarelli et al. (2017a). Again, the detection initially appeared as result of the automatic QL daily processing, and was confirmed afterwards using the standard AGILE analysis. The EM follow-up triggered by the GCN Notice and the GCN Circular announcing the identification of an EHE neutrino event by IceCube (Kopper & Blaufuss 2017) allowed the identification of the blazar BL Lac TXS 0506+056 (also known as 5BZB J0509+0541; Massaro et al. 2015) as the likely counterpart of the IceCube event (Aartsen et al. 2018a).

Using GRID data with energies above 400 MeV in a time interval of three days close to the neutrino event T₀, we obtained a better positional agreement of the AGILE detection with the TXS 0506+059 source, contained within the IC-170922 error box (see Figure 5, left panel), which thus confirms the gamma-ray activity observed from the source during this period (Tanaka et al. 2017; Aartsen et al. 2018a).

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As reported in Aartsen et al. (2018a), the source has been active in gamma-rays since a time several months before 2017 September. Figure 5, right panel, shows the AGILE gamma-ray lightcurve above 100 MeV from the beginning of 2017 August until the end of September, estimated on the TXS 0506+056 position. Superimposed is the corresponding Fermi-LAT curve (red points) obtained with the public analysis tool available at SSDC (see footnote 31), which shows a good agreement with the flaring activity detected by AGILE.³³

A recent IceCube paper claimed a second excess of VHE neutrinos observed from the direction of TXS 0506+056 in the period from 2014 September to the beginning of 2015 (Aartsen et al. 2018b). The analysis of the AGILE-GRID data over this period around the TXS 0506+059 position shows a strong gamma-ray contribution from the near FSRQ source PKS 0502+049 (12 away), which was in a high flaring state at that epoch (Lucarelli et al. 2014; Ojha et al. 2014). Using Fermi-LAT data, Padovani et al. (2018) show that the gamma-ray emission from the TXS is particularly hard compared to the softer emission from the FSRQ, and becomes predominant only by selecting gamma-rays above the GeV. Indeed, our analysis also shows that the contribution from PKS 0502+049 above a few GeV becomes negligible but, due to the limited AGILE gamma-ray sensitivity above 1 GeV, we can set a flux u.l. < 3.8 × 10⁻⁸ ph cm⁻² s⁻¹ for E > 1 GeV (for a 95% c.l.) over the emission from the TXS 0506+056 during this period.

We reported the results of the AGILE gamma-ray observations of the error regions of 10 IceCube HESE/EHE neutrino events announced since 2016 April through the GCN/AMON system.

Mining the database of automated AGILE-GRID QL detections, determined on predefined 2 day integration maps, we found three significant gamma-ray detections above 100 MeV within 15 from the IceCube best-fit centroids, and within 2 days from the neutrino event time T₀. The AGILE automatic detections, each of them with a significance at the level of 4σ estimated using the AGILE ML algorithm, are compatible in position and time with the three IceCube events IC-160731, IC-170321, and IC-170922, all of them classified as EHE.

We dubbed the three AGILE Sources A, B, and C. The global post-trial probability found in our study for the AGILE/IceCube chance correlation for three out of 10 events is quite low (around 4.7 Gaussian standard deviations), and significantly hints toward an astrophysical connection between the AGILE detections and the observed IceCube single-track events.

A direct correlation between gamma-rays and neutrinos from astrophysical sources is expected whenever hadronic emission mechanisms are at work. In a hadronic source scenario, we do expect comparable values of the gamma-ray/neutrino observed luminosities (Gaisser et al. 1995). We thus estimate the AGILE gamma-ray luminosities for each of the three Sources A, B, and C, and compare them with the corresponding neutrino luminosities, assuming a typical timescale of six months for neutrino production as a product of an underlying hadron acceleration and interaction (Aartsen et al. 2018a). With Sources A and B unidentified, we assume two values for their possible distance: 10 kpc (typical of a Galactic object), and redshift z = 1 (for an extragalactic object). For Source C, we make use of the TXS 0506+056 redshift, z = (0.3365 ± 0.0010), recently estimated by Paiano et al. (2018). For the calculation of the neutrino luminosities, we adopt the muon neutrino fluence value of 2.8 × 10⁻³ erg cm⁻² estimated in Aartsen et al. (2018a), for which we would expect to detect one high-energy neutrino event with IceCube over its entire lifetime.³⁴

Table 3 displays the gamma-ray energy density fluxes and luminosities above 100 MeV, estimated in a time interval of about ±1 week around T₀, and the neutrino luminosities estimated assuming a source active period of six months. Interestingly, for each of the three events we obtain similar values of the luminosities in gamma-ray and neutrinos. The observed power for the two adopted distances (assumed to be emitted isotropically), is typical of Galactic and extragalactic compact objects in the range of 10³⁶ erg s⁻¹ or 10⁴⁷ erg s⁻¹, respectively.

In case of IC-170922A (Source C) we observed a significant temporal correlation between the neutrino event and the almost simultaneous gamma-ray activity in HE and VHE bands from the IBL/HBL BL Lac type of blazar TXS 0506+056 (Aartsen et al. 2018a). This is suggestive of this AGN sub-class of blazars being one of the main VHE neutrino emitters from hadronic processes. In the other two cases (A and B) there is no clear evidence of flaring activity from any known EM source inside the AGILE/IceCube common error circles. A search for possible EM counterparts within the common AGILE/IceCube error regions, initially focusing on the identification of unknown HBL/HSP blazar candidates, found no obvious blazar candidates for Source A, as discussed in Lucarelli et al. (2017b). A further investigation made in this work has identified a new possible HBL candidate, the elliptical galaxy SDSS J141457.72-002058.6. Regarding the gamma-ray Source B, presented in this paper for the first time, some potential HBL blazars are found within the uncertainty neutrino/gamma regions. Moreover, a Fermi-3FGL source, 3FGL J0627.9-1517, recently associated with an HSP blazar, is at the boundary of the 90% IceCube error box, although well outside the smaller AGILE error circle obtained on the longer integration around T₀ (see Figure 4).

Given the lack of clear blazar counterparts for Sources A and B, we are led to explore alternative explanations. Different classes of extragalactic sources, potentially hosting hadronic processes (bursts from radio galaxies, starburst galaxies, eruptions from AGN cores, etc.) might be invoked to explain the gamma/neutrino correlations for A and B. Furthermore, IceCube neutrino fluxes can be produced also by gamma-ray hidden sources for which the high matter/radiation density surrounding a central engine enhances the target matter for the p–p or p–γ absorption processes. This would result in an observable neutrino flux with a highly suppressed gamma-ray flux from neutral pion decay. The AGILE detections of gamma-ray sources near IC-160731 (Source A) and IC-170321 (Source B) indicate the possibility that, from time to time, under particularly favorable conditions the neutrino source may become transparent to MeV/GeV gamma-rays. Taking into account the optimized AGILE sensitivity to soft gamma-ray emission in the 100–400 MeV energy band, sources with softer spectra can also be considered. For example, in such a case of enhanced target density, we might expect to observe a soft gamma-ray component peaking at MeV/sub-GeV due to the reprocessing of the VHE photons emitted by pion decay.

The detection of the gamma-ray Source B within the IC-170321 error box is interesting. Its position is close to the Galactic plane with no clear extragalactic known gamma-ray counterpart. This source might be considered to belong to a class of neutrino sources associated with a sub-dominant population of IceCube events apparently aligned near the Galactic plane (Halzen et al. 2017). Future observations will explore this very interesting possibility related to hidden compact objects in our Galaxy. We note that Fermi-LAT placed only a 95% c.l. u.l. on the gamma-ray emission above 100 MeV over an interval of one week just before T₀ (Buson et al. 2017). Similar cases of AGILE sources, both transient and steady, not confirmed by Fermi-LAT have been detected in the past (Pittori et al. 2009; Verrecchia et al. 2013; Bulgarelli et al. 2018). Several reasons can explain these discrepancies: source variability; different spectral response of the instruments; source visibility/exposure due to the different observing modes; event classification algorithms; background model (especially important for sources near the Galactic plane). All these factors may become important for relatively short gamma-ray transients (with duration of a few days) at the level of 4σ above the background.³⁵

This is the first time that evidence of multiple gamma-ray sources in close spatial and temporal coincidence with cosmic neutrinos has been presented. AGILE continues to monitor the gamma-ray sky and to react to IceCube alerts. More simultaneous neutrino and gamma-ray events are needed to strengthen the correlation indicated in the current AGILE data analysis. From our analysis, different classes of neutrino sources should be considered. Continuous blazar monitoring is needed to confirm the association of BL Lac-type sources as in the case of our Source C and, in principle, Galactic sources should be also taken into account and included in future searches.

Future studies of neutrino and gamma-ray sources need sensitive detectors and space missions able to reveal transient episodes occurring in the MeV/sub-GeV energy band. The e-ASTROGAM space mission (De Angelis et al. 2017) has been proposed as well as the mission AMEGO, which is in an advanced state of development (McEnery 2017). They can accomplish this task in the 2030s along with the upgraded neutrino experiment IceCube-Gen2 (The IceCube-Gen2 Collaboration et al. 2015) and the new generations of gamma-ray and neutrino telescopes such as CTA and KM3NET (Acharya et al. 2013; Adrián-Martínez et al. 2016).

AGILE is an ASI space mission developed with scientific and programmatic support from INAF and INFN. Research partially supported through the ASI grant No. I/028/12/2. We thank ASI personnel involved in the operations and data center of the AGILE mission. Part of this work is based on archival data, software or online services provided by the Space Science Data Center (SSDC)—ASI. It is also based on data and/or software provided by the High Energy Astrophysics Science Archive Research Center (HEASARC), which is a service of the Astrophysics Science Division at NASA/GSFC and the High Energy Astrophysics Division of the Smithsonian Astrophysical Observatory. This research has also made use of the SIMBAD database and the VizieR catalog access tool, operated at CDS, Strasbourg, France.

Software: AGILE scientific analysis software (BUILD 21 Chen et al. 2011), XIMAGE.

To evaluate the probability of finding an AGILE gamma-ray detection above 100 MeV in random coincidence with a candidate IceCube HESE/EHE astrophysical neutrino, we have estimated a FAR for the AGILE-GRID data using the whole database of QL detections hosted at the AGILE Data Center.

Every day an automatic AGILE QL procedure searches for gamma-ray transients above 100 MeV over the whole accessible sky (Bulgarelli et al. 2014). The AGILE QL has run since 2009 November, the start of the spinning observation mode, over predefined data time intervals of 48 hr. Given the AGILE effective area and sensitivity, these collecting time intervals are the most appropriate to accumulate enough statistics and to maximize the signal-to-noise ratio in spinning mode.

A blind search for gamma-ray transients is first applied to the data either using the XIMAGE detect algorithm or the so-called spotfinder method (Bulgarelli et al. 2014). Then, counts, exposure and diffuse background model maps, centered at the excess positions found previously, are produced using the tasks of the AGILE software, and eventually the count excess is evaluated against the expected background counts using the AGILE ML fit procedure (Bulgarelli et al. 2012).³⁶ All the gamma-ray detections and their ML best-estimate parameters (source significance as the square root of the ML test statistic ($\sqrt{\mathrm{TS}}$), gamma-ray flux and source location) of each candidate source are then stored in the QL detection database.

Bulgarelli et al. (2012) assessed the AGILE ML method, computing the chance probability to get a gamma-ray detection with a significance above a certain threshold, both for an empty extragalactic field and crowded Galactic fields. In our study, we need to extend that work in order to statistically determine the chance probability to have an AGILE detection above a certain threshold of $\sqrt{\mathrm{TS}}$ (over a 2 day time interval) in temporal and spatial coincidence with an IceCube neutrino event, having a localization error of the order of 1° in radius.

Practically, to determine the FAR for the AGILE-GRID data integrated over a 2 day interval, we proceed as follows:

• 1.  
  a sky position in a relatively empty region of the AGILE gamma-ray sky is considered and, using the QL database, the number of gamma-ray detections above a certain value of $\sqrt{\mathrm{TS}}$ within a circular region of 20° in radius, centered at the chosen position, is counted;
• 2.  
  the observed $\sqrt{\mathrm{TS}}$ counting frequency is divided by the number of 15-radius pixels³⁷ contained in the sky region under evaluation;
• 3.  
  the $\sqrt{\mathrm{TS}}$ counting frequency per pixel is divided by the AGILE livetime computed from the beginning of the spinning mode (MJD = 55139.5).

Since our minimum "time unit" is the 2 day integration time of the QL detections, the AGILE livetime is expressed as the number of 2 day "good" maps generated since MJD = 55139.5, i.e., having sufficient and uniform exposure to allow a reliable ML source parameter estimation.

In this way, we basically end with a FAR for an AGILE QL detection normalized to the solid angle subtended by a cone with half-aperture of 15 (i.e., the database search radius) and to the duration time of the QL maps. This FAR, expressed in units of 2 day maps and unit solid angle, can be then used to evaluate the probability of an accidental detection closed both in time and in space with an external event like the IceCube neutrinos.

The number of 2 day good maps varies according to the sky position considered, due both to the spacecraft rotation mode, in which the solar panels have to be kept fixed toward the Sun, and the seasonal variation of the Sun/anti-Sun exclusion regions due to the Earth orbital motion.³⁸ Figure 6, left panel, shows a Hammer–Aitoff projection in Galactic coordinates of the overall AGILE exposure (in cm² s), covering the period 2009 November–2017 September (MJD = 55139.5–58026.5). The regions around the ecliptic poles are the most exposed, while the exposure along the ecliptic plane is affected by the apparent motion of the Sun/anti-Sun exclusion regions.

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The total AGILE livetime for the whole spinning period of almost 8 yr, expressed in terms of total number of 2 day good maps, ranges from around 1000 for the regions near the ecliptic poles down to around 200 for the less exposed sky positions on the ecliptic plane.³⁹ For the FAR calculation, we considered a relatively empty region of brilliant gamma-ray sources placed near the south ecliptic pole (position 1 in Figure 6, left panel). For this position, the number of 2 day good maps amounts to 1000. The value of FAR estimated on position 1 can be applied to the estimation of the false alarm probability in case of an AGILE QL detection consistent with an IceCube HESE/EHE event lying well above the Galactic plane (with Galactic latitude $| b| \geqslant 20^\circ$).

Since AGILE Sources B and C described in the main text are consistent with two IceCube events located nearer the Galactic plane (b = −10.75 and −19.56 (deg), respectively), to estimate the chance correlation for this region we considered a 20° region centered at Galactic coordinates l, b = (217.0, −15) (deg) (position 2 in Figure 6, left panel). Due to higher diffuse gamma-ray emission near the plane, the FAR for this region resulted to be roughly 30% higher than the value obtained at higher or lower Galactic latitudes, ending in a slightly higher value of the post-trial false alarm probability P_i for the two events, as shown in Table 1.

We notice that the FAR (and the false alarm probability) can be overestimated by 20%–30% due to the presence of an un-subtracted non-Poissonian component of real gamma-ray transients from unknown sources occurring in the extraction sky region.

Table 4 shows all the IceCube HESE/EHE events published up to 2018 August. Since 2016 April, these events have been announced through the GCN/AMON notice circuit (Aartsen et al. 2017c), usually followed by a GCN Circular reporting the results of a further refined data analysis which provides improved reconstructed neutrino arrival directions and position uncertainties.

Along with the IceCube event ID, the table shows:

• 1.  
  the neutrino event time (in UT and MJD date);
• 2.  
  the event classification (HESE or EHE);
• 3.  
  the best-fit reconstructed neutrino arrival direction in equatorial coordinates (J2000) and its uncertainty;
• 4.  
  the corresponding Galactic coordinates l and b;
• 5.  
  the GCN Circular number reporting about the refined analysis (if available).

Where available, the table shows the refined arrival direction published in the GCN Circular.

Event numbered 34032434 has been rejected after refined analysis (IceCube Collaboration 2017) while events 65274589 and 32674593 were considered consistent with rare atmospheric muon background events (Blaufuss 2017b, 2017c) and, thus they were not considered in our analysis.

Figure 6, right panel, shows the distribution of all IceCube events in a Hammer–Aitoff projection of the sky in Galactic coordinates. All events appear well above the Galactic plane, except for one case (IC-170321) which shows a Galactic latitude of −1075. The three neutrino events with an AGILE possible transient counterpart, A, B, and C, are shown in orange.