Gadolinium in Water Cherenkov Detectors Improves Detection of Supernova \nu_{e}

Gadolinium in Water Cherenkov Detectors Improves Detection of Supernova

Ranjan Laha Center for Cosmology and AstroParticle Physics (CCAPP), Ohio State University, Columbus, OH 43210 Department of Physics, Ohio State University, Columbus, OH 43210    John F. Beacom Center for Cosmology and AstroParticle Physics (CCAPP), Ohio State University, Columbus, OH 43210 Department of Physics, Ohio State University, Columbus, OH 43210 Department of Astronomy, Ohio State University, Columbus, OH 43210
laha.1@osu.edu,beacom.7@osu.edu
July 18, 2019
Abstract

Detecting supernova is essential for testing supernova and neutrino physics, but the yields are small and the backgrounds from other channels large, e.g., and events, respectively, in Super-Kamiokande. We develop a new way to isolate supernova , using gadolinium-loaded water Cherenkov detectors. The forward-peaked nature of allows an angular cut that contains the majority of events. Even in a narrow cone, near-isotropic inverse beta events, , are a large background. With neutron detection by radiative capture on gadolinium, these background events can be individually identified with high efficiency. The remaining backgrounds are smaller and can be measured separately, so they can be statistically subtracted. Super-Kamiokande with gadolinium could measure the total and average energy of supernova with 20% precision or better each (90% C.L.). Hyper-Kamiokande with gadolinium could improve this by a factor of 5. This precision will allow powerful tests of supernova neutrino emission, neutrino mixing, and exotic physics. Unless very large liquid argon or liquid scintillator detectors are built, this is the only way to guarantee precise measurements of supernova .

pacs:
95.85.Ry, 97.60.Bw, 14.60.Lm, 14.60.St

I Introduction

Supernovae are one of the most spectacular electromagnetic displays in the Universe. Understanding them is essential for many areas of physics and astrophysics. Core-collapse supernovae are massive stars () that, at the end of their burning cycles, collapse under gravity to form a neutron star or black hole Janka and Mueller (1995); Langanke and Martinez-Pinedo (2003); Mezzacappa (2005); Burrows et al. (2007); Janka et al. (2007); Woosley and Janka (2006); Burrows (2013); Janka (2012). These collapses are potential sites for gravitational-wave production Ott (2009); Kotake (2013); Ando et al. (2013), gamma-ray bursts Woosley and Bloom (2006), heavy-element nucleosynthesis Thielemann et al. (2001); Woosley and Heger (2007), and cosmic-ray acceleration Blasi (2010).

It is difficult to learn about the core properties and collapse mechanism using electromagnetic light curves, as the surface of last scattering of photons is in the outer envelope. Neutrinos, on the other hand, being weakly interacting, have their surface of last scattering much deeper inside, within the core. Neutrinos carry about of the binding energy released during the collapse of the star. Precise measurements of all flavors of neutrinos can provide much information about a supernova Thompson et al. (2003); Tomas et al. (2004); Dasgupta and Dighe (2007); Friedland and Gruzinov (2006); Lunardini et al. (2008); Suwa et al. (2009); Marek et al. (2008); Hudepohl et al. (2010); Kneller and Volpe (2010); Muller et al. (2011); Kistler et al. (2013); Lund et al. (2012); Wongwathanarat et al. (2013); Scholberg (2012); Tamborra et al. (2013); Nakamura et al. (2012); Kneller and Mauney (2013a, b); Borriello et al. (2013).

The only supernova neutrinos ever detected were from SN 1987A Hirata et al. (1987); Bionta et al. (1987). Even this modest data has been invaluable for understanding neutrinos and supernovae. Only were detected, through the inverse beta channel, , leading to, e.g., constraints on the total and average energy in this flavor Jegerlehner et al. (1996); Lunardini and Smirnov (2004); Yuksel and Beacom (2007); Pagliaroli et al. (2009). (We assume that the first event was not due to neutrino-electron elastic scattering, which has a very small probability.)

Computer simulations of supernova explosions have detailed predictions about the neutrino emission, but, due to the lack of a high-statistics Galactic supernova, it is not possible to adequately test these Muller et al. (2010); Brandt et al. (2011); Mueller et al. (2012); O’Connor and Ott (2013); Kotake et al. (2012); Ott et al. (2012); Kotake et al. (2012); Muller et al. (2012); Bruenn et al. (2013). It is important to detect all flavors of neutrinos to measure the total and average energy in each. Because the differences between flavors may be modest, large numbers of events must be detected to ensure adequate precision.

Galactic supernovae occur only once every years. It is essential that a variety of detectors be ready to detect all flavors of neutrinos well to understand the physics and astrophysics of core-collapse supernovae. Using present detectors, it will be easy to measure supernova and , via inverse beta and elastic scattering on protons, respectively Vogel and Beacom (1999); Strumia and Vissani (2003); Beacom et al. (2002); Dasgupta and Beacom (2011). Unless very large liquid argon Raghavan (1986); Gil Botella and Rubbia (2004) or liquid scintillator detectors Wurm et al. (2012); Li et al. (2013) are built, or other techniques become experimentally viable Haxton and Johnson (1988); Fuller et al. (1999); Haxton and Robertson (1999); Ianni et al. (2005); Lazauskas et al. (2009); Suzuki et al. (2012), there is presently no way to guarantee the clean detection of supernova in adequate numbers. The difficulties of measuring the spectrum well enough have long been known; e.g., see Refs. Haxton (1987); Minakata and Nunokawa (1990); Qian and Fuller (1994); Lunardini and Smirnov (2001, 2003); Beacom and Strigari (2006); Skadhauge and Zukanovich Funchal (2007); Skadhauge and Funchal (2008).

Here we show how this problem could be solved by using gadolinium (Gd) in Super-Kamiokande (Super-K) and other large water Cherenkov detectors. The addition of Gd to Super-K was proposed to improve the detection of . Ironically, this would also improve the detection of . We add new ideas to those briefly noted in Ref. Beacom and Vagins (2004) and perform the first detailed calculations, showing how supernova could be measured precisely.

The principal technique is to use neutrino-electron scattering, . These events are forward-peaked, so a narrow cone contains the majority of them. The largest background is from inverse beta events. The use of Gd to detect neutrons will help in individually detecting and removing these events with high efficiency. The spectrum of will be measured precisely so that the remaining inverse beta and scattering events can be statistically subtracted from the forward cone. Liquid scintillator detectors can detect (= ) well enough through scattering, so the scattering events can be statistically subtracted.

In addition, we show how gadolinium will improve the prospects for measuring charged-current interactions with oxygen. This channel is only important if the average energy of is large, either intrinsically, or due to efficient mixing with sufficiently hot . Recent supernova simulations suggest that none of the flavors has a large average energy, and that the differences between flavors are modest, so that these interactions with oxygen may not be important. In contrast, the neutrino-electron scattering events would be measured well in all scenarios if Gd is used to reduce backgrounds.

Detecting supernova will be helpful in constructing the initial spectrum of these neutrinos, testing neutrino mixing scenarios, and probing exotic physics. We concentrate on detecting the emitted during the full duration of the burst; however, this technique could also help in detecting the short neutronization burst in Mton water Cherenkov detectors Kachelriess et al. (2005).

The outline for this article is as follows. In Sec. II, we discuss the various theoretical and experimental inputs required to isolate supernova . In Sec. III, we discuss how this can constrain the spectrum parameters, and we conclude in Sec. IV.

Ii Calculation inputs

We first discuss the neutrino spectra from a supernova, followed by the various detection channels in a water Cherenkov detector. We then outline the detection strategy that we propose to use to detect supernova in a water Cherenkov detector with gadolinium.

ii.1 Supernova Neutrino Spectra

A supernova neutrino burst lasts for 10 sec and includes all flavors of neutrinos. The total binding energy released in the explosion is erg. We assume that the total energy is equipartitioned between the 6 species so that the total energy carried by each (or ) flavor is erg. The supernova is assumed to be at a distance of 10 kpc, the median distance of core collapse progenitor stars in our Galaxy, which is slightly farther than the distance to the Galactic Center Adams et al. (2013).

Supernova neutrinos are emitted in a quasi-thermal distribution. For concreteness, we take a particular modified Maxwell-Boltzmann spectrum Keil et al. (2003); Tamborra et al. (2012),

(1)

where this is normalized to unity. Using a regular Maxwell-Boltzmann or a Fermi-Dirac spectrum with the same average energy gives more neutrinos at high energies. For the electron-scattering and inverse-beta channels, the increased number of events is 5%. For the oxygen channel, which depends very sensitively on neutrino energy, the number of events can increase by 50%. Our choice of spectrum is conservative and our results can only improve if other neutrino spectra are appropriate.

For the average energies of the initial spectra, we take 11 – 12 MeV, 14 – 15 MeV, and 15 – 18 MeV; the hierarchy follows from the different strengths of interaction in the supernova core. Neutrino mixing effects in the supernova Dighe and Smirnov (2000); Dighe (2008); Dasgupta et al. (2009); Dasgupta (2010); Duan et al. (2010, 2011); Friedland (2010); Pehlivan et al. (2011); Sarikas et al. (2012); Cherry et al. (2012) or in Earth Lunardini and Smirnov (2001); Dighe et al. (2003, 2004) can have a dramatic effect on the final spectra, even exchanging them. Then the (or ) spectrum could have an average energy of 15 – 18 MeV, increasing the yields of charged-current detection channels. (The yields of neutral-current detection channels do not change for active-flavor mixing.) To tell how efficient the mixing is, we need to measure the detection spectra precisely.

A model independent neutrino signal from a supernova is the neutronization burst, which consists of a short pulse ( 25 msec) of initially pure before the 10 sec emission of neutrinos of all flavors Kachelriess et al. (2005). Depending on the neutrino mixing scenario, the number of neutronization detected in a Mton water Cherenkov detector for a Galactic supernova is 30 – 100 Kachelriess et al. (2005); Cherry et al. (2013). Our detection strategy will also be useful in this case. In Super-Kamiokande (fiducial volume 32 kton), the number of events due to neutronisation is only (1).

ii.2 Neutrino Detection Interactions

All flavors of neutrinos and antineutrinos can be detected with the channel. The recoil kinetic energy of the scattered electron varies between 0 and . The forward-scattered electron makes an angle with the incoming neutrino given by cos , where is the kinetic energy of the recoil electron.

The differential cross section for neutrino-electron elastic scattering is Vogel and Engel (1989)

(2)

where is the Fermi coupling constant, sin for and , respectively, and for and , respectively. For anti-neutrinos, . When integrated over , the total cross section .

Only were detected from SN 1987A, via the inverse beta reaction, , where denotes free hydrogen (protons) in water and the positrons are emitted almost isotropically. The cross section for this process is cm where is the proton mass, the energies are in MeV, the threshold of the reaction is MeV, and MeV Vogel and Beacom (1999); Strumia and Vissani (2003).

The neutron thermalizes by elastic collisions and is captured on protons as in about 200 . The emitted gamma ray has an energy of 2.2 MeV, which cannot be reliably detected in Super-K due to low-energy detector backgrounds Zhang et al. (2013). To unambiguously detect the emitted neutron, it has been proposed to add Gd to large water Cherenkov detectors. Then the neutron will be thermalized and captured on Gd in about 20 , leading to a 3 – 4 gamma rays with a total energy of about 8 MeV, which is easily detectable in Super-K Beacom and Vagins (2004).

Electron neutrinos can also be detected in water Cherenkov detectors by O F Haxton (1987), where most of the final-state decay products of the excited F nucleus are not detectable. The threshold for this reaction is 15 MeV, and the electron kinetic energy is MeV. In the energy range MeV, the cross-section is given by cm, for energies in MeV Haxton (1987); Tomas et al. (2003). The angular distribution of the electrons is slightly backward tilted. The steep energy dependence of the cross section means that can only be detected well if the average energy is large, say due to mixing.

We neglect other neutrino interactions with oxygen ( charged-current Haxton (1987) and all-flavor neutral-current Langanke et al. (1996)), as they are not our focus and their yields are small compared to that from the inverse beta channel.

Detection channel 12 MeV 15 MeV 18 MeV
188 203 212
56 64 70
60 64 68
48 54 56
O F 16 70 202
5662 7071 8345
Table 1: Expected numbers of events in Super-K for a Galactic supernova at a distance of 10 kpc for different values of the neutrino average energy (we do not round the numbers so that small differences remain visible). The total energy of the supernova is assumed to be erg, equipartitioned among all flavors (here ). The detection threshold during a burst is assumed to be MeV. Other interactions with oxygen are neglected because their yields are small compared to that of inverse beta decay.

The time-integrated flux for single neutrino flavor is

(3)

where denotes the total energy in that flavor and is the distance to the supernova. The observed event spectrum in the detector is

(4)

where is the appropriate number of targets. For a larger average energy, the thermally-averaged cross section is larger, but the flux is smaller (because the total energy is taken to be fixed). For neutrino-electron scattering, these effects nearly cancel, making the total number of events almost insensitive to the average energy. The shape of the electron recoil spectrum does change, which provides sensitivity to the average energy.

Table 1 shows the expected number of events in Super-K for these reactions under different assumptions about the neutrino average energy. For additional details about the detection of neutrinos from a Galactic supernova in water Cherenkov detectors, see the references already cited as well as Refs. Beacom and Vogel (1998a, b); Ikeda et al. (2007).

ii.3 Proposed Detection Strategy

Figure 1: Electron spectra for the detection channels for a supernova in Super-K. These are just the events in the forward 40 cone ( of the total). We take MeV, MeV, and MeV; the other assumptions are listed in Table 1.
Figure 2: Detectable electron (or positron) spectra in Super-K without or with Gd. The two panels consider different cases for after neutrino mixing. Other parameters, including MeV, are as in Fig. 1. Left Panel: For Case (A) with MeV, we focus on the signal (solid line) in the forward 40 cone. The dotted line shows the large inverse beta background without Gd, and the dashed lines show the most important backgrounds with Gd. Right panel: For Case (B) with MeV, we focus on the O signal (solid line) in the region complementary to the forward 25 cone (note the different angle). The inverse beta background without Gd is too large to show, and dashed line shows this background with Gd. Here the signal and background are both due to the Galactic supernova.
Figure 3: Detectable electron spectra in Super-K, ignoring backgrounds, for different assumed average energies for (12, 15, and 18 MeV) to show variants of the signals in Fig. 2. All spectra scale linearly with changes in the assumed total energy in . Other assumptions as above. Note axis changes from Fig. 2. Left Panel: For the channel in the forward 40 cone. Right Panel: For the O channel in the region complementary to the forward 25 cone.
Figure 4: Allowed regions (90% C.L. contours) for the spectrum parameters determined from the and O channels separately. The combined constraints (not shown) closely follow what would be expected visually. The two panels are for different cases (fiducial parameters marked by an x), matching those of Fig. 2. Dashed lines indicate the contours when Gd is not used, and solid lines show the improvements when Gd is used. Left Panel: When the average energy is small, here 12 MeV, the channel gives a closed allowed region but the O channel only defines upper limits. Right Panel: When the average energy is large, here 18 MeV, both channels give closed allowed regions.
Figure 5: Allowed regions (90% C.L. contours) for the spectrum parameters determined from the and O channels jointly. Two examples of fiducial parameters ( MeV and MeV) are each marked with an x. The corresponding fit regions are shown without and with Gd.

We focus on Super-K, the largest detector with low intrinsic backgrounds Abe et al. (2011). We assume that supernova events can be detected in the full inner volume of 32 kton. Super-K measures the energy, position, and direction of charged particles with very high efficiency. During a burst, detector backgrounds can be ignored. There is extensive ongoing research on employing Gd in Super-K Beacom and Vagins (2004); Watanabe et al. (2009); Vagins (2012). The efficiency of neutron capture on Gd will be known from calibration data.

We employ the reaction to detect the and look for the forward-scattered electrons. Knowing the direction of the Galactic supernova, if we make an angular cut of half-angle 40 (appropriate for the lowest energy events Abe et al. (2011)), then 68% of the electron-scattering events will be in that cone. The forward-scattered electrons can also locate the supernova to within a few degrees Beacom and Vogel (1999); Tomas et al. (2003); Antonioli et al. (2004); Adams et al. (2013).

Fig. 1 shows the recoil spectra for neutrino-electron scattering for all flavors. (We use kinetic energy, but Super-Kamiokande conventionally uses the total energy, ). Because the energy range is so broad, the effects of energy resolution smearing ( near 10 MeV) were found to be modest, and are not included. As can be seen from the figure, has the largest number of events. This is important, because the other flavors of neutrino-electron scattering events are an irreducible background to the events.

The largest number of events will be due to the inverse beta reaction, which is almost isotropic. Neutron detection on Gd will individually identify 90 of these events. The very large number of events will determine the parameters precisely ( with events), which will be used to statistically subtract the remaining inverse beta events. Events from other detection channels can also be statistically subtracted.

Iii Supernova detection and constraints

We first discuss the typically-assumed range of supernova neutrino spectrum parameters and show spectra for some representative neutrino mixing scenarios. We then calculate fits for the neutrino spectrum parameters and show the results for these and other cases.

iii.1 Calculated Detection Spectra

Several cases can be considered for the initial spectra and how they are changed by neutrino mixing. Our focus is on testing the sector. We first note the two extreme cases that we want to differentiate and then mention some other possibilities. There are also cases intermediate between the extremes we note. We do not try to identify these cases in terms of active-flavor neutrino mixing scenarios, given the large uncertainties in the problem, especially in the initial neutrino spectra. Our focus on improving the measurements, and the interpretation in terms of supernova emission and neutrino mixing will come once there is a detection.

Case (A) has MeV and 15 – 18 MeV, i.e., there is a hierarchy of average energies between the flavors initially and neutrino mixing has not interchanged them (other assumptions are as above).

Case (B) has 15 – 18 MeV and one flavor of has MeV (the other flavors of have 15 – 18 MeV), i.e., there is a hierarchy of average energies between the flavors initially and neutrino mixing has interchanged them.

If the average energy of were large and mixing was effective at exchanging the spectra of antineutrinos instead of neutrinos, this would be evident in the spectrum; this is disfavored by the SN 1987A data. If all flavors had a low average energy, this would be evident in the and spectra (because the channel is a neutral-current interaction, its yield is not changed by active-flavor mixing). The yields of these and other channels can decide everything except the differences between Cases (A) and (B). That’s the open problem: What is the spectrum?

When the average energy is high, O is a good detection channel; otherwise, it gives no useful signal because the yields are too small to be detected in the presence of backgrounds. Typical average energies from supernova simulations are markedly lower than the values assumed a decade or two ago, so O is now a much less favorable channel. Besides in Super-K, there is no other detection channel in any existing detector that produces enough identifiable events when the average energy is low. The yield of barely changes with changes in the average energy. Another important change from a decade or two ago is that much lower energies can be detected, which improves the spectrum shape tests.

The main background for these reactions is the inverse beta events. Some of these numerous events can be removed using an angular cut, but they still pose a formidable background. This is shown in the left panel in Fig. 2 for the same average energies as in Fig. 1. There are 128 events in the 40 cone, but this is swamped by inverse beta events. In the absence of neutron tagging, it will be difficult to extract the signal from this background.

However, adding Gd to Super-K has a dramatic effect. Assuming that the efficiency of neutron detection in a Gd-loaded Super-K is , the inverse beta background will decrease to 83 events. This strongly improves the detection prospects of . The spectrum will be well measured by cleanly-identified inverse beta decay events using neutron detection by Gd. This will allow statistical subtraction of the backgrounds due to and the remaining events. Liquid scintillator detectors will measure the spectrum of from the channel, which is most sensitive to the flavors with the highest average energies. This will allow statistical subtraction of the backgrounds due to the channel. These subtractions only lead to modest increases in the uncertainties of the spectrum shown in the left panel of Fig. 2.

The O channel is only useful if the average energy is large, as otherwise the yield is too small. Even for a average energy of 18 MeV, the backgrounds are still important. There are signal events in the whole detector. Excluding a forward cone of 25, events remain. (The different choice of angle for the forward cone is because now we focus on higher energies, for which the angular resolution is better.) In a detector without Gd, these would be overwhelmed by the 7071 inverse beta events, but neutron tagging by Gd will dramatically reduce this background. This situation is shown in the right panel in Fig. 2. Again assuming an efficiency of 90% in neutron tagging in a Gd-loaded Super-K, only 707 of the inverse beta events will remain. This enormous reduction in background will greatly help in isolating the O signal.

Fig. 3 shows how the detection spectra for and O change with different assumptions about the average energy. The yield for elastic scattering depends only weakly on the average energy but that for O reaction changes dramatically. See also Table 1. Both channels also have characteristic spectrum changes as the average energy changes, as shown in Fig. 3.

iii.2 Fits for Neutrino Spectrum Parameters

The detection spectra in Fig. 2 show that adding Gd to Super-K will greatly reduce backgrounds for supernova . We quantify the improvement in the determination of the spectrum parameters, and , by constructing a and performing fits. We use

(5)

where are the numbers of events in each bin assuming the fiducial values of the parameters, are the same allowing different values, and are the uncertainties on the fiducial numbers.

Because all spectra except will be well measured separately, here we only need to fit for the spectrum parameters. That is, we fit spectra like those in Fig. 3 after the remaining backgrounds shown in Fig. 2 have been statistically subtracted. In the calculation, the numbers of events in the numerator are only those of the signals; the backgrounds affect the results by increasing the uncertainties in the denominator, which depend on the numbers of signal plus background events.

Put another way, if we set up a for the data before the statistical subtractions (Fig. 2 instead Fig. 3), then the contributions from flavors besides would cancel in the numerator but not the denominator. More precisely, those cancelations would occur only on average if typical statistical fluctuations were included.

To determine the allowed regions of parameters when a supernova is detected, we calculate relative to various assumed best-fit cases (using for two degrees of freedom to obtain the C.L. regions).

Our results indicate the likely size and shape of the allowed regions once a supernova is detected. We make some reasonable approximations. The uncertainties on the initial spectra and the effects of neutrino mixing are large, and the uncertainties on the neutrino cross sections are moderate. In addition, we are considering only the time-averaged emission, whereas the average energies may vary during the burst. The widths of the bins were chosen to have approximately equal numbers of events in each bin (at least events per bin). The numbers of events are then large enough that the Poisson uncertainties can be treated as Gaussian.

In Case (A) from above, there is a hierarchy between the average energies of different flavors, but their spectra are not interchanged by mixing, so the average energy of is low. We take = 12 MeV and erg as fiducial parameters for this case.

If these are the true parameters of the supernova, then the left panel of Fig. 4 shows the likely precision with which the parameters would be reconstructed from the measured data in Super-K without or with Gd. In this case, the primary constraint comes from the channel. The O channel does not have enough events relative to the backgrounds, though large values of can be excluded by the non-observation of a significant number of events. The presence of Gd reduces the size of the allowed region significantly. With both channels together, the allowed region would be centered on MeV and would range from roughly 9 to 14 MeV. Thus, with Gd, it would be possible to say that is different from (which could be 15 MeV with precision). This would not be possible without Gd, so this is an important difference.

In Case (B) from above, there is a hierarchy between the average energies of different flavors, and their spectra are interchanged by mixing, so the average energy of is high. We take = 18 MeV and erg as fiducial parameters for this case.

If these are the true parameters of the supernova, then the right panel of Fig. 4 shows the likely precision with which the parameters would be reconstructed from the measured data in Super-K without or with Gd. In this case, both channels have enough events to define allowed regions. The steep energy dependence of the O cross section gives a precise measurement of the average energy, though the large backgrounds and uncertainties mean that the total energy is not well determined. As before, the presence of Gd improves the precision, especially for the channel. With both channels together, the allowed region would be very small. It would be easy to distinguish Case (A) and Case (B); Gd would greatly improve the significance of this comparison.

The presence of Gd is even more important when the neutrino average energies are closer to each other. This is seen in some simulations, e.g., Ref. Mueller et al. (2012), where 11 MeV, and 15 MeV. Due to the less pronounced hierarchy, it will be much harder to distinguish scenarios like Case (A) and Case (B).

Fig. 5 shows our results (joint constraints using both channels) for the allowed regions of the spectrum parameters. In this case, the presence of Gd does not completely separate the 90% C.L. contours, but it comes very close. Without Gd, the two allowed regions cannot be separated at all, which would significantly degrade the ability to test the physics.

Recent long-term simulations show that the average energy of the neutrinos can change during the 10 sec emission time Hudepohl et al. (2010); Fischer et al. (2012); Nakazato et al. (2013). The average energy of typically changes from 12 MeV to 6 MeV. For a detector like Super-Kamiokande, it might be difficult to detect this change of average energy. For a future detector like Hyper-Kamiokande, which will have better precision the spectral properties (see later), such a difference could distinguished.

Iv Conclusions

When the next Galactic supernova occurs, it is essential that we have a collection of detectors that can measure all neutrino flavors well. Without this, we will be unable to fully address many important questions. What is the total energy emitted in neutrinos and how is it partitioned among flavors? Are the average energies of the various flavors different? What do these results say about neutrino mixing and tests of exotic physics? What do the differences between and emission tell us about the neutron-to-proton ratio of the collapsing core?

At present, the only detector with a relatively large yield of events is Super-K. Even so, this is only events using the channel. If the average energy of is large enough, then the O channel will have a comparable number of events. The problem is the background of events from the inverse beta channel, . This background can be reduced for using an angular cut, but not enough.

We demonstrate in detail a new technique to reduce backgrounds for both the and O channels. If Super-K adds Gd to improve the detection of , then of these events will be individually identified through detection of the neutron radiative capture on Gd in close time and space coincidence with the positron. This would dramatically reduce backgrounds for other channels. The remaining backgrounds can be statistically subtracted using independent measurements.

We show that the spectrum parameters, (average energy) and (total energy), can be measured to or better if Super-K adds Gd. This is a significant improvement over the capabilities of Super-K without Gd. (For comparison, the precision for in existing scintillator detectors is comparable, and the precision for in Super-K will be .) Further, this improvement could be the difference between being able to answer essential questions or not. Unless very large liquid argon or liquid scintillator detectors are built, then we have no other way to adequately measure the spectrum.

Future extremely large water Cherenkov detectors like Hyper-Kamiokande would have a dramatic impact on detecting supernova using this technique. The times larger volume would reduce the uncertainty on the parameters by factor of . This requires using Gd in Hyper-Kamiokande, the prospects of which are prominently considered Kearns et al. (2013). (This would also require a new very large liquid scintillator detector Wurm et al. (2012); Li et al. (2013) to for improved measurements of using the channel.)

This new method of determining supernova would help improve our understanding of supernovae and neutrinos in many ways. It provides yet another motivation for Super-K to add Gd. Given how infrequent Galactic supernovae are, it is essential that the opportunity to measure well not be missed.

Acknowledgments

We thank Andrea Albert, Basudeb Dasgupta, Shunsaku Horiuchi, Kohta Murase, Kenny C.Y. Ng, Sergio Palomares-Ruiz, and the anonymous referee for discussions and helpful suggestions. RL and JFB were supported by NSF Grant PHY-1101216 awarded to JFB.

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