Constraining high-energy neutrinos from choked-jet supernovae with IceCube high-energy starting events
Different types of core-collapse supernovae (SNe) have been considered as candidate sources of high-energy cosmic neutrinos. Stripped-envelope SNe, including energetic events like hypernovae and super-luminous SNe, are of particular interest. They may harbor relativistic jets, which are capable of explaining the diversity among gamma-ray bursts (GRBs), low-luminosity GRBs, ultra-long GRBs, and broadline Type Ib/c SNe. Using the six-year IceCube data on high-energy starting events (HESEs), we perform an unbinned maximum likelihood analysis to search for spatial and temporal coincidences with 222 samples of SNe Ib/c. We find that the present data are consistent with the background only hypothesis, by which we place new upper constraints on the isotropic-equivalent energy of cosmic rays, , in the limit that all SNe are accompanied by on-axis jets. Our results demonstrate that not only upgoing muon neutrinos but also HESE data enable us to constrain the potential contribution of these SNe to the diffuse neutrino flux observed in IceCube. We also discuss implications for the next-generation neutrino detectors such as IceCube-Gen2.
Prepared for submission to JCAP
Constraining high-energy neutrinos from choked-jet supernovae with IceCube high-energy starting events
Departamento de Física, Pontifícia Universidade Católica do Rio de Janeiro, Rio de Janeiro 22452-970, Brazil
Department of Physics; Department of Astronomy & Astrophysics; Center for Particle and Gravitational Astrophysics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
Yukawa Institute for Theoretical Physics, Kyoto, Kyoto 606-8502, Japan
The recent discoveries of high-energy cosmic neutrinos [1, 2] and gravitational waves [3, 4] have opened the new era of multi-messenger astroparticle physics. Powerful explosive phenomena such as gamma-ray bursts (GRBs) and supernovae (SNe), including low-luminosity GRBs and transrelativistic SNe, are among the candidate sources of IceCube neutrinos [5, 6, 7, 8, 9], and expected to have bright electromagnetic counterparts at different wavelengths. In particular, gamma-ray emission of long-duration GRBs is thought to originate from relativistic jets launched at the death of massive stars. The jet has to successfully break out from is progenitor star for the gamma-ray emission to be observed. However, it is also natural for the jet to fail to penetrate the progenitor star, if the jet power is not high enough or the star has an extended structure [10, 11]. Such failed GRBs could be seen as low-luminosity (LL) GRBs or energetic SNe Ib/c with a relativistic component of the SN ejecta [12, 13, 14]. Such choked-jet SNe are likely to possess a key link between GRBs and SNe, and the relativistic jet may play an important role in making the diversity among Type Ib/c SNe, including broadline Type Ib/c SNe and super-luminous Ic SNe [15, 16, 17, 18].
Non-thermal properties of observed GRBs suggest that particles can be accelerated by a jet up to high energies. However, the electromagnetic emission cannot be directly observed if it is choked. High-energy neutrino observations provide a unique opportunity to probe the choked jet hidden inside a star [6, 19], and enable us to study particle acceleration mechanisms in a photon-rich environment . In addition, not only the jet emission but also subsequent shock breakout emission may lead to high-energy neutrino and gamma-ray signatures in the presence of a dense circumstellar material [21, 22, 23, 24].
The main origin of high-energy cosmic neutrinos observed in IceCube is unknown (see a review ). LL GRBs and choked-jet SNe are suggested as the main candidate sources of IceCube neutrinos [7, 20], and their contribution to the diffuse neutrino flux have been extensively studied [26, 27, 28, 29, 30, 31, 32]. They are among the classes of gamma-ray dark or hidden neutrino sources, and seem necessary to explain the diffuse neutrino flux in medium-energy (10-100 TeV) range . Contrary to canonical GRBs whose contribution to the background flux is strongly constrained [34, 35, 36, 37], these classes of SNe and GRBs are not accompanied by bright gamma-ray emission, so the existing stacking analyses do not give any strong constraint. The absence of clustering in the arrival distribution of neutrinos gives a limit on the rate density, [38, 39], but LL GRBs and SNe with long durations of s are allowed by this constraint. More dedicated searches focusing on these SNe are necessary. Ref.  recently provided a new constraint on high-energy emission from Type Ib/c SNe, by searching for spatial and temporal correlations between through-going muon neutrinos and these SNe. In this work, for the first time, we present results of a stacking analysis for SNe, using six-year high-energy starting events (HESEs) observed in IceCube. Although the angular resolution of HESE events is not as good as that of the muon track events, thanks to the temporal information, we can still obtain a useful limit on the energy of cosmic rays produced in SNe. This limit can be translated into a constraint on the SN contribution to the diffuse neutrino flux, which is useful for us to address the question about the origin of high-energy cosmic neutrinos.
The paper is organized as follows. In Sec. 2, we describe the neutrino and SN data used in our likelihood analysis as well as the details of the method. Sec. 3, based on the results of the likelihood analysis, shows the constraints on the amount of cosmic-ray energy. In Sec. 4, we compare our results to other limits obtained in the literature. In Sec. 5, we summarize our findings and discuss prospects for future observations.
2 Data Selection and Analysis Method
2.1 Neutrino and SN data
The 6 years of HESE data consists of events***The total number of the events in the 6-yr HESE dataset is 82 where two events, events #32 and #55, are coincident events and are not considered in our analysis. where 22 events are muon-tracks, with median angular resolution , and the rest are cascades with larger () resolution in the reconstruction of the direction of the incoming neutrino. During the same period SNe Ib/c have been registered by several telescopes†††Data are available from Open SNe catalog: https://sne.space. There are two date stamps for each SN event: the detection date and the date of its maximum optical brightness. The known correlation between the GRBs and SNe Ib/c suggests the date difference of days between the GRB’s explosion (without emerging jet) and the SN’s date of maximum brightness . We will consider this date difference as a Poisson distributed random parameter with mean value days. The 90% confidence interval from Poisson distribution defines a time window for each neutrino event which is given by: , where is the date of SN maximum optical brightness and is the date of neutrino event. Notice that we are neglecting the exact detection time of both neutrino and SNe and assume the observation date as a discrete parameter given by the Modified Julian Day of the corresponding event. Figure 1 shows the time distribution of the neutrino and SNe events. The blue line segments show the time windows for each neutrino event (the event number is shown above the time window) and the red stars show the SNe. The time correlation of the neutrinos and SNe can be seen as the number of stars within the time window of each neutrino event. Notice that the depicted SNe are all the SNe regardless of their relative directions to the neutrino event.
As can be seen, out of the 80 neutrino events, 62 neutrino events have at least one SN happening within their corresponding time window. However, out of these 62 events, there are two neutrino events, #27 and #33, that have a SN within their median error circles. Figure 2 shows the skymap of these two events in the galactic coordinate. In this figure the red shows the neutrino event, with the error circle depicted in brown, and the green stars show the SNe occurred within the time window of the neutrino event. The neutrino event #27 is a cascade with the deposited energy TeV and the moderate median angular resolution of , and the accompanied SN is type Ic LSQ12bqn with the luminosity distance Mpc. The neutrino event #33 also is a cascade with the deposited energy TeV and large median angular resolution , and the correlated SN is the type Ic SN2012gi with Mpc.
The luminosity distances, , of the observed SNe are of crucial importance since the fluence of each SN scales as . Using the optical data, the majority of SNe’s redshifts are precisely determined. In our sample just for 5 SNe the redshifts (and so the ) are not measured. For our analysis we will randomly assign luminosity distances to these SNe, chosen from the measured s. Figure 3 shows the distribution of the luminosity distances of SNe that will be used in our analysis. Notice that the binning of the histogram in Figure 3 is not uniform: the bin-width of the first four bins is 50 Mpc, followed by three bins of width 100 Mpc and three bins with the width 500 Mpc.
2.2 Analysis method
In order to quantify the contribution of the choked-jet stripped-envelope SNe to the HESE data set, we perform a stacking analysis on the neutrinos. The analysis is very similar to the one performed by the IceCube and Auger collaborations in the search for correlation between the arrival directions of IceCube neutrino events and ultrahigh-energy cosmic rays . In the following we summarize the details.
The correlation between HESE and SNe events is quantified by the following likelihood function (in terms of one parameter ):
where is the number of observed SNe Ib/c during the July/2010 to July/2016. The and are the signal and background PDFs for the SN, respectively, and can be written as:
where the first and second terms in each equation are, respectively, the directional and temporal contributions to the signal and background PDFs.
The temporal signal PDF for the SN, that is , can be written as the sum over the mutual signal PDFs of the neutrino event and the SN:
where . For the SN, just the neutrinos falling in the time window are considered. For these neutrinos the PDF is given by the Poisson probability mass function:
Similarly, the temporal background PDF, , can be written as:
We assume a uniform distribution within the time window, such that:
Figure (a)a shows the ratio of as function of the day-difference between and . As can be seen from the figure, the ratio of is larger than one for .
The directional signal PDF for the SN can be written as
where is a factor that takes into account the relative direction-dependence of the detector response for SN detection. Since the SNe we are considering are detected by several experiments we can assume that this factor is equal to one. For the neutrinos that fall within the time window of the SN, the is given by (using the Fisher-Bingham or Kent distribution function):
where and . Here is the uncertainty in the direction of the neutrino event and is the angular distance between the neutrino event and SN. For the neutrinos falling outside the observation window the signal PDF is zero. The directional background PDF is assumed to be an uniform distribution from all the directions, that is . Figure (b)b shows the ratio of as function of the angular distance for various angular resolutions . As can be seen, by increasing the resolution, the width of the curves increase. The Kent distribution in Eq. (2.7) assigns significant correlation for . For example, for , the ratio of is larger than one for .
The test statistics (TS) value is defined by:
The best-fit value of can be obtained by maximizing the TS value. Figure (a)a shows the TS as a function of the obtained in our analysis. The TS is maximum at with the value . As can be seen, by increasing the the TS decreases rapidly. The -value of the obtained TS value can be estimated by randomly generating SNe events. We generated sets of 222 SNe with random dates and directions and calculated the distribution of the TS values. Figure (b)b shows the distribution of the maximum TS values obtained in the randomly generated SNe events. As can be seen, the obtained TS has a -value .
3 Upper limits
The large -value obtained in section 2.2 points to almost no indication of the correlation between the SNe and HESE events in the current data set. Using this observation, it is possible to place upper limit on the contribution of the SNe to the HESE data. The contribution of the SNe to the observed neutrino events depends on two parameters: i) the fraction, , of the choked GRBs which have their jets aligned to the Earth; ii) the neutrino fluence of a SN explosion at the Earth, or equivalently the energy deposited into cosmic-rays, , in the SN explosion. The neutrino fluence (per flavor) of a SN can be approximated as :
where and the factor takes into account the relative energy that the produced neutrinos carry from the parent proton. Assuming spectrum for the parent cosmic-rays, the flux of neutrinos per flavor (sum over neutrino and antineutrino) can be written as
Taking into account that in the photomeson interaction of the protons , we obtain:
Knowing the flux of neutrinos from a SN at the Earth (assuming the jet is directed to the Earth), we can calculate the expected number of the events in IceCube by
where is the HESE effective area for flavor  available in the IceCube webpage ‡‡‡https://icecube.wisc.edu/science/data/HE-nu-2010-2012, in the energy range of TeV to PeV. The expected number of neutrinos from a set of SNe, with the fraction of their jets aligned to the Earth, will be (assuming 1:1:1 neutrino flavor ratio at the Earth)
To place the upper limit on the and parameters we proceed as following: fixing the directions and dates of the neutrino events to the observed ones in HESE dataset, we generate SNe with random directions and dates sampled from uniform distributions over the sky and through the six years data-taking period of HESE, respectively, where each SN has deposited energy into cosmic-rays. For a fixed value of , we force out of the SNe to have directions and dates correlated with randomly chosen neutrino events. The directional correlation between each of the neutrinos and SN events is sampled from the Kent distribution with the angular resolution of the corresponding neutrino event. For the temporal correlation the date of each SN sampled from a Poisson distribution with the mean date difference value of 13 days (ahead) with the corresponding neutrino event. This process realized times for each set of the fixed values of and . For each realization we calculate the maximum TS value using the likelihood method described in section 2.2. The rejection confidence level of a set of and values is defined as the percentage of the realizations that have a maximum TS value larger than 90% of the generated TS values in the background only hypothesis; i.e., when no correlation is introduced between neutrino and SN events. This value, denoted by and depicted by the green vertical dashed line in figure (b)b, is .
Figure 6 shows the cumulative distribution of values obtained in the realizations of the process described above, depicted by solid (dashed) curves for (0.6) with colors blue, red and green respectively for , and erg. The gray dotted vertical line shows the . The rejection C.L. of a given set of and is given by the percentage of the values that are larger than ; which can be read from figure 6 as the corresponding fraction value of the intersection between the gray dotted line and cumulative distribution curve. Scanning over the parameter space of and , figure 7 shows the heat plot which gives the rejection C.L. of each point. For example, in figure 7, the top right corner (corresponding to and erg) is rejected at 88% C.L.
Ref.  constrained high-energy neutrino emission from choked-jet SNe, using the one-year sample of muon neutrinos in IceCube. For , the 90% C.L. upper limit on the total CR energy is erg, which is comparable to the limit obtained in this work. Because the time coincidence drastically reduces the atmospheric backgrounds, poorer angular resolutions of HESE events do not cause a serious problem for our purpose. The fluence of stacked SNe is naively written as , where is the number of SNe correlated with the neutrino events. Then, for given energy and observation time , the upper limit roughly scales as . The HESE effective area  is worse than the upgoing muon neutrino one , which is compensated by the larger data set used in our analysis ().
Stripped-envelope SNe harboring choked jets have been discussed as possible candidates for the dominant origin of IceCube neutrinos even in the 10-100 TeV range . If these SNe are responsible for 100% of the diffuse neutrino flux, the required CR luminosity density is for the spectrum . Then the upper limit of implies that the rate density is . Note that the local rate densities of stripped-envelope SNe and broadline SNe Ib/c are and , respectively. If only a fraction () of the SNe have jets beamed toward us, the corresponding apparent rate densities are and , respectively. Here is the jet opening angle. Thus these choked-jet SN models can provide viable explanations for the diffuse neutrino flux without violating the stacking limits.
Another piece of important information comes from multiplet and auto-correlation analyses [45, 46, 47, 48, 49]. The number of multiplet sources gives a lower limit on the effective rate density of the dominant neutrino sources as 
where is the luminosity-dependent correction factor, is the observed solid angle, and represents the redshift evolution of the sources . The above limit is also consistent with the latest limits by Ref. . At present, neither stacking nor multiplet search gives a sufficiently strong constraint on the choked-jet SN models as the origin of IceCube neutrinos.
We searched for temporal and spatial coincidences between high-energy neutrino events in the six-year HESE data and SNe Ib/c that occurred in this time period. We did not find any significant correlation, by which we placed upper limits on the total neutrino energy . The 90% C.L. limit for , erg, is comparable to that obtained by the independent stacking analysis based on the one-year muon neutrino data. Our result demonstrates that meaningful constraints for transients with sufficiently short durations can also be obtained by using shower events with poorer angular resolutions.
The current upper limits are not yet sufficient to exclude the relevant parameter space of choked-jet SN models. However, the situation will be drastically improved in near future. First, the number of neutrino events does not have to be restricted to HESE events. One can use the shower data with lower energies for this kind of stacking search. Furthermore, IceCube-Gen2  is expected to have a volume about ten times larger than that of the current IceCube, by which the number of signals can also be about ten times larger with a similar observation time. KM3Net  with a better angular resolution for shower events would also be useful for this kind of study. We have checked that reducing the angular resolution of shower events to can improve the obtained rejection C.L. by . Second, the current catalog of SN Ib/c are highly incomplete, so that is quite limited. The number of SN samples will be increased with future SN surveys via, e.g., Zwicky Transient Factory, Kiso Tomo-e Gozen, and Large Synoptic Survey Telescope. Critical constraints on the choked-jet SN models will be obtained if we can achieve erg in the limit of .
In addition to such stacking analyses, as proposed by Ref. , “’follow-up” searches for electromagnetic counterparts of neutrino events can provide a powerful way to discover the sources of high-energy neutrinos, and choked-jet SNe could be found by optical follow-up observations. The feasibility of such high-energy neutrino triggered campaigns has recently been demonstrated by the measurements of the flaring blazar TXS 0506+056 followed by the discovery of the high-energy neutrino event, IceCube-170922A [52, 53]. Along this line, the Astrophysical Multimessenger Observatory Network  can play a role in the real-time detections of neutrino transients especially when the sources are accompanied by X-ray or gamma-ray emission. Indeed, jet-driven SNe may possess trans-relativistic ejecta, which are expected to naturally cause short-duration X-ray and gamma-ray emission at the shock breakout.
A. E. thanks the partial support by the CNPq grant No. 310052/2016-5 and resources from FAPESP Multi-user Project 09/54213-0. The work of K. M. is supported by NSF Grant No. PHY-1620777 and the Alfred P. Sloan Foundation. This research was supported by the Munich Institute for Astro- and Particle Physics (MIAPP) of the DFG cluster of excellence "Origin and Structure of the Universe".
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