Timing the Neutrino Signal of a Galactic Supernova

We study several methods for timing the neutrino signal of a galactic supernova for different detectors via Monte Carlo simulations. We find that, for the methods we studied, both Hyper-Kamiokande and IceCube can reach precisions of $\sim1\,$ms for the neutrino burst, while a potential IceCube Gen2 upgrade will reach sub-ms precision. In the case of a failed SN, we find that detectors like SK and JUNO can reach precisions of $\sim0.1\,$ms while HK could potentially reach a resolution of $\sim 0.01\,$ms so that the impact of the BH formation process itself becomes relevant. Two possible applications for this are the triangulation of a (failed) SN as well as the possibility to constrain neutrino masses via a time-of-flight measurement using a potential gravitational wave signal as reference.


I. INTRODUCTION
Massive stars above ∼ 8M end their life in a great explosion outshining an entire galaxy for a short period of time. For such Core-Collapse Supernovae (CCSNe), it is predicted that ∼ 99% of the released gravitational binding energy is emitted via neutrinos [1]. State of the art multidimensional simulations model the supernova explosion mechanism as well as the neutrino emission properties [2][3][4].
In the case of a galactic CCSN, current and near future neutrino detectors will be able to detect thousands of events in a time period of ∼ 10 seconds. The detection of such SN neutrinos offers interesting possibilities. In contrast to photons, neutrinos travel freely through the outer shells of the SN. Therefore in the case of a galactic CCSN, the neutrino signal will reach us long before any optical signal can be detected. This way it can serve as an early warning system (see SNEWS [5]). Besides other methods like studying the statistics of neutrino-electron scattering [6,7], the precise timing in multiple neutrino detectors can also be used to locate the SN via triangulation [7][8][9]. This is not only important to enable early astronomical observations of the SN, but also to locate it in the case of a failed SN which would not result in any optical signal. In the latter case, locating the SN will allow us to search for and study the SN remnant, potentially observe the progenitors collapse to a black hole as well as to include and study the impact of Earth-matter effects that can only be included if the direction of the neutrino signal is known. Furthermore, combining neutrino and gravitational wave signals might allow us to determine the mass of neutrinos. This is another application which needs a very precise timing of the neutrino signal. In this work, we present several methods on how characteristic structures of the neutrino signal can be * rshansen@phys.au.dk † lindner@mpi-hd.mpg.de ‡ scholer@mpi-hd.mpg.de  [10] . Note that νe and νx are scaled up. One can clearly see the three different phases of emission namely the large νe-burst during the first ∼ 10 ms, the following accretion phase, and the cooling of the neutron star at the end up to ∼ 10 s. used for precise timing. This is based on simulations of neutrino signals for different detectors using a set of both successful and failed supernova neutrino simulations from the Garching group [10,11]. This paper is structured as follows: In sec. II, we give a short overview on the general neutrino emission properties. In sec. III, we study the neutrino signal in several detectors. In sec. IV, we use a Monte Carlo simulation based on the results of sec. III to study several methods for timing the neutrino signal using characteristic structures. Finally, we study two possible applications namely triangulation and the neutrino mass determination in sec. V. Throughout the paper we use natural units c = = k B = 1.  [11]. The shaded areas show the 1σ deviation. The blue dots in the upper panel show one realization in HK assuming normal ordering. Note that the rates for IC are given per bin i.e. per 1.6384 ms. The black horizontal line in the right panel represents the constant background noise of 280 Hz per module in IC. A sample MC realization for IO as well as more details on the timing methods are displayed in fig. 4.

A. Phases of Emission
Typically, the neutrino emission from a supernova can be separated into three different phases as can be seen in fig. 1 1. ν e -Burst: During collapse, vast amounts of ν e are produced via electron capture. When the collapsing core exceeds a certain density, the neutrinos get trapped inside. Shortly after core bounce, they are suddenly released resulting in a characteristic sharp ν e -Burst with a typical luminosity of ∼ 3.5·10 53 erg s .

B. Neutrino Spectra
The neutrino spectrum can be well described by a normalized gamma distribution function [13,14] with the pinching parameter and the mean neutrino energy E . Typically, the pinching parameter is in the range of 2 < α < 3 except for the initial ν e -burst which has a stronger pinching of α ∼ 6 [12]. We will mostly focus on the first 100 ms of the signal i.e. the initial burst and the rise of the signal during the accretion phase. We used a set of 18 spherically symmetric SN simulations from [10] and [11] based on the Lattimer & Swesty EOS with a bulk incompressibility of 180 MeV and 220 MeV. However the different choices of this parameter do not influence the neutrino signal that we are interested in. The models span from SN progenitors with 11.2M up to 40.0M . Multidimensional effects seem to not change the general shape during the first 100 ms post bounce as e.g. [13] and [15] indicate. Also the influence of different EOS on the early signal is very small [15,16] and should therefore not change our results for timing the onset of the burst significantly. For the black hole forming case however the EOS could have a significant impact. Besides influencing the BH formation probability, a stiffer EOS can shift the formation time further away from core bounce [16]. This would result in a change in the event rate for late time collapses and thereby impact our results.

III. DETECTION
We focused on 3 different types of detectors: a liquid scintillator detector (JUNO) [17], two Water-Cherenkov detectors Super-Kamiokande (SK) and Hyper-Kamiokande (HK) [18] and Ice Cube [19]. JUNO will be a liquid scintillator detector filled with 20 kton of linear alkylbenzene (LAB). The expected threshold for e ± detection is and due to quenching for proton detection [20]. Super-Kamiokande is a Water-Cherenkov detector with a fiducial mass of 22.5 kton and a threshold for electron and positron energies of [21] T min e, SK/HK = 4.5 MeV .
In the case of a galactic supernova, however, the detection rate will be much higher than the background so that it will be possible to use the full inner detector volume of 32 kton for detection. Therefore following the Hyper-Kamiokande design report [18], we use the entire inner detector mass of 32 kton for SK and presumably 220 kton for HK in our calculations. Although HK is expected to have a lower electron kinetic energy threshold of ∼ 3 MeV, we keep the more conservative SK threshold for HK too.

A. Calculating Event Rates
In general, the event rate for a certain interaction process x can be calculated from the differential cross-section ∂σ ∂T and the spectral flux given in terms of the flavor dependent luminosity L ν with ν ∈ (ν e , ν e , ν x ) and the distance D as Here, N t is the number of target particles, and T t is the kinetic energy of the directly detected particle. The sum ν runs over all neutrino flavors relevant for the considered interaction. T t, min is given by the detector threshold and E ν, min is the corresponding minimal neutrino energy. The mean energy of the detected neutrinos is given by where R = x R x . To calculate the signal for each detector, we included up to three different detection channels namely the inverse beta decay (IBD), neutrino-electron scattering, and, in the case of JUNO, also neutrinoproton scattering which accounts for a significant fraction of the overall signal in JUNO due to its lower threshold. Also, we assume the SN to be at a distance of 10 kpc.
In the case of IBD, the recoil energy of the proton can be ignored so that the energy of the detected positron is given by For IBD we implement a low energy approximation of the cross-section valid for E ν < 300 MeV [22] with The differential cross-section for neutrino-electron scattering at tree level is given by [23,24] ∂σ ν,e ∂T e = σ 0 m e (g ν with and For the neutrino-proton scattering, we implement the differential cross-section [20] ∂σ with the neutral current axial and vector couplings

B. Neutrino Flavor Conversion
To convert the individual fluxes and spectra of each neutrino flavor at the supernova to the observed signal at Earth, neutrino flavor conversion must be taken into account. A recent study suggests that in the case of a failed supernova, collective oscillations can be ignored [25] such that only matter effects need to be considered. In general, however, collective effects could play an important role in determining the final fluxes [26,27]. In the following we will only consider MSW conversion. Also we assume the SN and the detectors to be within the same hemisphere so that we can ignore any Earth-matter effects.
In the high density neutrinosphere, the Hamiltonian becomes effectively diagonal in flavor space such that pure Hamiltonian eigenstates ν 1m , ν 2m and ν 3m are produced [28]. Those propagate outwards through the SN . For NO, the expected peak at the νeburst is still very small, while for IO, one can see a larger peak reaching ∼ 1σ = √ R above the following plateau.
Normal ordering (NO) Inverted ordering (IO) and are converted to the vacuum eigenstates ν 1 , ν 2 and ν 3 . Depending on the mass hierarchy, one finds the final fluxes in terms of the initial flavor fluxes F 0 α as it is shown in table I. Consequently, the final fluxes of the different flavors at Earth are given by with U being the PMNS-Matrix. Correspondingly, the final normalized spectra are given by Since the difference in the mean energies of the different neutrino mass eigenstates are small compared to the width of the initial spectra, these final neutrino spectra for the different flavors at Earth are also described well by a gamma like distribution. Note that this only works if the initial spectra overlap strongly.

C. IceCube Signal
Unlike low background detectors with a high PMT coverage like SK/HK and JUNO, IceCube will not be able to detect single SN neutrino events. Instead, IC will see a simultaneous increase in Cherenkov light in all of its digital optical modules (DOMs). We calculated the IceCube SN neutrino signal only including the IBD channel [29]   . The (light-)blue dots represent the total binned signal of one specific Monte Carlo realization, the red curve shows the fit resulting from eq. (22), the green squares show the binned events that produce secondary e ± with a kinetic energy Te > 20 MeV, and the (light-)blue stars show the binned scattering event rate. Therefore, the first green square shows the bin with the event that triggers the Energy Threshold method, while the first bin in which the blue dot and star do not match shows the bin in witch the first IBD event is located. The gray area shows the 2.5 ms time period of the first Bulk that was found. Note that the timing of the single events is taken to be the actual time of the event and not the time of the corresponding bin, thus obtaining sub-ms resolution.
both for IC with 5160 DOMs and for a future IC GEN2 with additional 9600 DOMs with a 25% increased dark noise [30,31].

IV. TIMING THE SIGNAL
We have investigated several methods using characteristic structures of the neutrino signal for timing purposes. This is done with a Monte Carlo (MC) simulation of the neutrino signal with 10000 realizations in each detector for each of the 18 SN simulations available to us. Each MC simulation was done both for NO and for IO. For each Monte Carlo run, we use the average detector rates calculated and assume a poissonian distribution. The total time period of the signal is binned into 1 µs bins to produce "single" neutrino events. In the following, we present the investigated methods. The averaged results are summarized in table 2. The results for each single MC simulation can be found in Appendix A.

A. Exponential Rise of the Signal
A method for timing the supernova neutrino burst which was already explored for IC [32] is fitting a function of the form to the measured rate. We further explore this possibility for SK, HK, and JUNO detectors as well as a potential IceCube Gen2 upgrade.
To fit the rate in SK, HK, and JUNO, the signal was rebinned into 1 ms bins. The results only depend weakly on this choice, but tend to be slightly worse for much larger bins.

B. The Initial νe-Burst
Having a look at fig. 1, the characteristic structure of the strong ν e -Burst seems to be a promising candidate for a timing reference. However, looking at the signals in fig. 2, it only leads to a very small bump in the signal. This has mainly two reasons: 1. The cross-section for scattering on electrons is much smaller than the cross-section for IBD 2. The cross-section for scattering on electrons is higher for ν e than for other flavors since both NC and CC elastic scattering can occur. Due to matter effects, the initial ν e flux F 0 νe corresponds to F ν3 in case of NO and F ν2 in case of IO (see table I).
Since the initial ν-burst consists almost only of ν e , the final ν e flux at the detector is suppressed by The small bump in the expected detector rate resulting from scattering events will therefore not be visible in the total signal since it will be dominated by the poissonian fluctuations. JUNO however will be able to distinguish scattering and IBD events via neutron capture [17]. The same might be achieved in SK/HK with the use of Gadolinium [33]. Assuming a (rather optimistic) perfect identification of IBD vs. scattering events, we further explored the possi-bility of detecting the peak by fitting Taking a look at fig. 3 for HK, one would expect to see the peak in some of the MC realizations in the case of IO since it differs from the following plateau by a little more than 1 σ ( √ R), while one would expect to see no peak in most of the MC realizations for NO. To prevent overfitting we only took into account fits with a peak FWHM of 30 ms > FWHM > 3 ms. Our MC simulations (table 2) show that for SK and JUNO there is little to no chance to see the peak as expected, while for HK it might be possible under the given assumptions in some cases. As we mentioned, however, the assumption of a perfect identification is rather optimistic, and in reality, the IBD identification efficiency in a gadolinium filled water Cherenkov detector will be ∼ 50−90% [34] depending on the amount of gadolinium.

C. Identifying the First Neutrino After Core Bounce
Detectors like the Kamiokande detectors or JUNO provide the unique opportunity to identify the timing of single neutrino events therefore eliminating statistical errors that may arise from the above fitting methods. Looking at the two MC realizations in fig. 4, however, it is clear that the first neutrino that is detected, was emitted prior to the neutrino burst itself. Hence a method to exclude pre-burst neutrinos is necessary.

First Bulk
After core bounce, the neutrino event rate increases rapidly. It is therefore quite natural to define the first "bulk" of neutrino events as the start of the supernova neutrino burst. To define this bulk more quantitatively, we can use the exponential fit from sec. IV A and integrate it over the first 2.5 ms in HK and 20 ms in SK/JUNO. Then we can search for the earliest neutrino event which is inside such a "bulk" with N > N integrated neutrino events and take it as the timing reference. The results only depend weakly on the integration time as long as it is sufficiently large to catch several events.

Energy Threshold
Another approach to distinguish pre-burst neutrinos from post-burst neutrinos is to look at the energies of the single events that are detected. Looking at fig. 5, one can see that there is a sudden increase in the mean energy of the detected neutrinos at the core bounce. In a detector, we do not measure the neutrino energy directly, but rather the energy of the secondary particle (e − , e + , p ...) which will be lower. Still, it is possible to define the first post-bounce neutrino as the first event with a secondary particle energy above 20 MeV. In our Monte Carlo realizations, the energy of the scattered electrons was simulated assuming that the spectrum of the detected neutrinos follows the gamma distribution of eq. (1) with the pinching parameter fixed by E and E 2 according to eq. (2). This assumption is reasonable since the spectra of the different neutrino flavors are quite similar, and the detector thresholds are well below the mean energy E during the relevant time after core bounce. Since we are only interested in events above 20 MeV, we can define the spectral difference as During the relevant, time this difference is 1% < ∆f < 2%. In general, this approximation overestimates the spectrum near its peak while underestimating the spectrum for higher energies. The energies of pre-burst neutrinos, however, are overestimated by this approximation because the mean neutrino energy is still close to the detector thresholds. However, in the energy range E > 20 MeV relevant for our analysis, the spectra are close to zero during these times such that the overestimation is not relevant for us. The spectrum of the scattered electrons for a fixed neutrino energy is then given by the differential cross-section (12). For IBD events, the energy of the produced positrons is well approximated by (9). For our purpose, we can ignore the scattered protons in liquid scintillator detectors here since their energy is significantly lower than the energy of the secondary particles from IBD and electron scattering due to the higher mass of the proton.

First IBD
Again assuming perfect identification of IBD events, one can define the timing of the first IBD event as the start of the burst since the pre-burst neutrinos consist only of ν e (see fig. 1). Note that this will resemble the IBD event rate at core bounce and therefore our results will directly scale with the IBD identification efficiency (i.e. the neutron tagging efficiency). Also, the deviation in the delay of the neutron capture will play a role for very nearby SN with significantly higher event rates.

D. Black Hole Collapse
Although the exact fraction is still unknown, it is expected that some CCSNe will collapse to a Black Hole (BH). Observationally, the fraction of these so called failed supernovae is estimated to be [35] f failed = 0.14 +0.33 −0.10 (25) at 90% confidence. In the case of BH formation happening while the neutrino signal is still measurably high, the neutrino emission will be cut off abruptly when the neutrinosphere falls inside the horizon of the BH. This characteristic cut-off provides another possibility for timing the neutrino signal. For detectors like SK, HK, or JUNO, it is possible to define the cut-off time as the time of the last detected neutrino event so that the timing resolution is given by the average time between two events i.e. the inverse detection rate at the time of the cut-off Looking at table II, this is O(10) µs. At such small timescales, the formation process of the BH itself will start to play a significant role. Assuming a proto-neutron star radius of 10 km, we can estimate the BH formation timescale with the help of the light-crossing time which in this case will be ∼ 70 µs i.e. more than 4 times larger than the estimated resolution in Hyper-Kamiokande. Early numerical SN simulations show that the collapsing time for an actual observer at Earth will be O(0.5) ms [36]. In the case of a failed SN happening in our galaxy, Hyper-Kamiokande might therefore allow us to observe the process of a proto-neutron star collapsing to a black hole. However, this will strongly depend on the real distance D to the failed supernova since the event rate and therefore the timing resolution scales with D 2 .

E. Timing Results
The averaged timing results are shown in table II. One important aspect to further inspect is how the different neutrino energies will affect these results if the neutrinos have non-negligible masses. The main effect of massive neutrinos is to shift the total signal a few ms away from the core bounce. In addition to that, there could be some influence on the shape of the signal due to ToF differences resulting from different energies of the detected neutrinos. Looking at fig. 5, we see that with time evolving, the mean neutrino energy increases such that for massive neutrinos, we would expect the total signal to be compressed slightly. In the case of a black hole formation, however, the hard cut-off at the end of the signal could (depending on the mass scale) become a smooth transition.
To inspect the effect of non-zero neutrino masses, we take the current upper limit on the effective (anti-) electronneutrino mass from tritium decay experiments [37] m max ν = 2 eV (27) and simulate the signal shift resulting from differences in the time of flights (ToF) for different neutrino masses down to the theoretical lower limit for the heaviest mass eigenstate in the three flavor mixing scheme This is done for HK and the two models ls180s12.0 and BH ls220s40s7b2c and 1000 Monte Carlo realizations each. The results of these MC simulations are shown in Appendix B. As expected, the timing methods at core bounce are only affected by the inclusion of neutrino masses through a shift in the mean arrival times. The BH formation cut-off, however, is significantly influenced by the energy dependent ToF in such a way that the abrupt hard cut-off in the detection rate becomes a rather smooth transition depending on the absolute mass scale. This effect is well known and already discussed in e.g. [38]. Taking the most stringent cosmological limits on the sum of all neutrino masses [39] i m i < 0.17 eV (29) into account, constrains the absolute neutrino masses to be below 0.1 eV. For this mass range, the BH timing resolution would grow at most by a factor of ∼ 2. All in all this supports the conclusion that the timing accuracy is not reduced significantly when considering massive neutrinos.

A. Triangulation
First, we apply our results to estimate the angular resolution that could be achieved via triangulation. Locating the SN is not only relevant to allow for early astronomical observations, but it is especially important in the case of a failed SN where there is no strong optical signal. In general, by measuring the arrival time of the neutrino signal, two detectors separated by a distance D can determine the position of the SN via the measured time difference ∆t to be on a cone along their axis with an opening angle θ. We can easily calculate θ using the law of cosines as Consequently, the uncertainty in the angular resolution is To exemplify which angular resolution the above timing results can achieve, we calculate it for the combination of IC GEN2 and HK in the non-BH case as well as HK and JUNO in the case of BH formation. Applying the above eq. (31), we find δ(cos θ) IC,HK = 0.03 , (32) δ(cos θ) HK,JUNO,BH = 0.01 .
While the latter is limited by the relative proximity of both detectors and JUNOs relatively small size compared to HK, triangulating a SN in reality takes 4 different detectors. Thereby other promising candidates such as NOνA [40] or DUNE [41] (located in the US) which both will reach similar event rates as JUNO [9] come into play.
The combination of the first HK tank with a possible second tank in Korea ∼ 800 km away would also reach resolutions similar to the HK-JUNO combination in the BH case despite the very short distance between the detectors. The actual angular resolution δθ will depend on the real angle θ. For large and moderate angles up to θ ∼ 90 • , the angular resolution is given by while for small angles around θ ∼ 0 • , it is given by [7] δθ = 2δ(cos θ) .
Taking the above results on the resolution of cos θ, we can constrain the angular resolution for these examples to

B. Neutrino Mass Determination
Precise timing of the SN neutrino signal also offers a possibility to constrain neutrino masses. A conceptually easy way to constrain or even determine the masses of neutrinos is to use the above mentioned mass induced ToF difference in comparison to the ToF of the SN gravitational wave signal propagating at the speed of light. In general, for a SN at distance D and two signals with masses m i and m j both at energy E, the ToF difference is given by Precise timing of the neutrino signal therefore allows to distinguish even small ToF differences and hence allows for precise constraints on the upper mass limit. With the largest mass squared difference between the neutrino mass eigenstates being at the order of ∆m 2 ∼ 2.5 · 10 −3 eV 2 , ToF differences between the different mass eigenstates will be at the order of ∼ 3 µs for a neutrino energy of 20 MeV. We can therefore safely ignore them since none of the above techniques will reach such resolutions. After LIGO's historical detection of GW150914 [43], gravitational wave astronomy has become reality, and galactic CCSNe are promising candidates for such a measurement. To compare the neutrino signal with the gravitational wave signal, we need correlated structures in both. To first order, gravitational waves are produced by the second time derivative of the energy density quadrupole moment tensor. Although it is null for spherical symmetric objects, SN simulations show that the flattening of the collapsing core due to its own rotation can induce a non-vanishing quadrupole moment high enough to produce a detectable gravitational wave signal (see e.g. [44][45][46]). There are generally two characteristic signals of short timescale that one can expect to see in the gravitational wave signal of a rotating SN. The first is the core bounce and the second is the collapse to a black hole. Luckily, the neutrino signal also shows characteristic structures at both these times namely the onset of the signal rise and the cut-off at BH formation time. To quantify how the above methods for finding and timing characteristic structures in the neutrino signal can be used to constrain neutrino masses, we assume that the model dependent mean timing value for each method is known. In this case, only the methods uncertainty contribute to the overall timing uncertainty. We also assume that the gravitational wave signal will be timed with a high precision such that the neutrino signal is the limiting factor. To determine the constrainable masses for each method, we simulated the time shift induced by different non-zero neutrino masses from 0.05 eV up to 2 eV for all models with each 1000 realizations and determined the lowest mass that could be distinguished from zero at 90% confidence level in at least 90% of the MC realizations. The averaged results for HK are shown in table III. We can compare these mass limits to possible limits resulting from a likelihood analysis [47]. For SK, this analysis allows to constrain masses down to m ∼ 0.8 eV, resulting in a possible limit of m ∼ 0.45 eV for HK taking a scaling factor of m 2 ∝ 1 √ N with N being the number of detected neutrinos [47]. This comparison shows that timing single characteristic structures and their delay only gives reasonable sub-eV limits in the case of a failed SN where the timing is very precise. However, using the time delay of the Expfit also allows IC to constrain the mass from SN neutrinos. The possible limits for IC will be comparable to HK's IBD limits.

VI. CONCLUSION
We investigated six possible methods for timing the neutrino signal of a galactic supernova for three (five for Expfit) existing and future detectors. Our results show that HK will be comparable to today's IceCube detector both being able to achieve ∼ 1 ms precision, while in the case of a failed SN, even the smaller SK and JUNO detectors can reach sub-ms precision. Additionally, we found that the very intuitive idea of timing the characteristic initial ν e -burst shortly after core bounce fails in most of the scenarios. The only candidate that could potentially see the ν e -Burst is Hyper-Kamiokande. However, if the ν e -burst is detected by the future HK experiment, it would be a hint towards an inverted mass hierarchy. In the exciting case that the next galactic supernova will fail and result in the proto-neutron star collapsing to a black hole during accretion or early cooling phase time, Hyper-Kamiokande might be able to actually observe how the formation process proceeds in the neutrino signal. This will depend on the actual distance. Three methods (Expfit, BULK, and Gauss) use a fit over several neutrino events. While the latter does not work in most cases, the Expfit method results in stable timings, and due to the fact that it is using many neutrino events, it is not affected by background events. The same holds for the BULK method. The other methods (IBD, MEV and BH) all use the statistical fluctuations in the timing of single neutrino events making them more background sensitive. However, compared to the event rate during a SN, the background in the relevant energy range is negligible [17,18,42]. Especially the IBD method, due to its characteristic signature of a positron followed by neutron capture, is rather insensitive to backgrounds. Comparing the different detectors, the future IceCube Gen2 update will deliver the most precise timing resolution in the non-BH case while HK, SK and JUNO allow very precise timings in the case of a BH formation. Here IceCube is again limited by the fact that it will detect a SN by noise excess rather than single events. However, with the addition of the HitSpooling system, IC will be capable of resolving the BH collapse with a resolution similar to that of HK and even provide internal triangulation of the location [48,49]. The improved data binning should, however, not influence the timing of the onset of the burst significantly since this is limited by the still existing noise rate rather than the data binning. In the last section, we studied the impact of the timing results on two possible applications, the first being the location of the SN via triangulation. Taking the example of HK+IC, we found that, for a SN that is approximately perpendicular to the connecting axis between the two considered detectors, the angular resolution is comparable to the method of locating the SN via neutrinoelectron elastic scattering. In the case of a failed SN, the HK+JUNO combination can potentially reach subdegree resolution. Similar results can be obtained by combining the Japanese HK tank with a second Korean tank. At last we studied the possibility to constrain neutrino masses via ToF differences in comparison to gravitational waves. In the non-BH case, we found that by timing the onset of the signal, HK can limit neutrino masses to ∼ 1 eV. This improves to ∼ 0.3 eV in the BH forming case considering a SN at 10 kpc. The latter result is comparable to the goal of the KATRIN experiment [50].