Presupernova Neutrinos: Directional Sensitivity and Prospects for Progenitor Identification

We explore the potential of current and future liquid scintillator neutrino detectors of kt mass to localize a presupernova neutrino signal in the sky. In the hours preceding the core collapse of a nearby star (at distance kpc), tens to hundreds of inverse beta decay events will be recorded, and their reconstructed topology in the detector can be used to estimate the direction to the star. Although the directionality of inverse beta decay is weak (∼8% forward−backward asymmetry for currently available liquid scintillators), we find that for a fiducial signal of 200 events (which is realistic for Betelgeuse), a positional error of ∼60° can be achieved, resulting in the possibility to narrow the list of potential stellar candidates to less than 10, typically. For a configuration with improved forward−backward asymmetry (∼40%, as expected for a lithium-loaded liquid scintillator), the angular sensitivity improves to ∼15°, and—when a distance upper limit is obtained from the overall event rate—it is in principle possible to uniquely identify the progenitor star. Any localization information accompanying an early supernova alert will be useful to multimessenger observations and to particle physics tests using collapsing stars.

Presupernova neutrinos are the neutrinos of ∼ 0.1 -5 MeV energy that accompany, with increasing luminosity, the last stages of nuclear burning of a massive star in the days leading to its core collapse and final explo-sion as a supernova, or implosion into a black hole (a "failed" supernova).These neutrinos are produced by thermal processes -mainly pair-production -that depend on the ambient thermodynamic conditions (Fowler & Hoyle 1964;Beaudet et al. 1967;Schinder et al. 1987;Itoh et al. 1996) -and by weak reactions -mainly electron/positron captures and nuclear decays -that have a stronger dependence on the isotopic composition (Fuller et al. 1980(Fuller et al. , 1982a(Fuller et al. ,b, 1985;;Langanke & Martínez-Pinedo 2000, 2014;Misch et al. 2018), and thus on the network of nuclear reactions that take place in the stellar interior.
Building on early calculations (Odrzywolek et al. 2004a,b;Kutschera et al. 2009;Odrzywolek 2009), recent numerical simulations with state-of-the-art treatment of the nuclear processes (Kato et al. 2015;Yoshida et al. 2016;Patton et al. 2017a,b;Kato et al. 2017;Guo et al. 2019) have shown that the presupernova neutrino flux increases dramatically, both in luminosity and in average energy, in the hours prior to the collapse, and it becomes potentially detectable when silicon burning is ignited in the core of the star.In particular, for stars within ∼ 1 kpc of Earth like Betelgeuse, presupernova neutrinos will be detected at multi-kiloton neutrino detectors like the current KamLAND (see Araki et al. (2005) for a dedicated study), Borexino (Borexino Collaboration et al. 2018), SNO+ (Andringa et al. 2016), Daya Bay (Guo et al. 2007) and Su-perKamiokande (Simpson et al. 2019), and the upcoming HyperKamiokande (Abe et al. 2016), DUNE (Acciarri et al. 2016) and JUNO (An et al. 2016;Li 2014;Brugière 2017).Next generation dark matter detectors like XENON (Newstead et al. 2019), DARWIN (Aalbers et al. 2016), and ARGO (Aalseth et al. 2018) will also observe a significant signal (Raj et al. 2020).Therefore, presupernova neutrinos are a prime target for the SuperNova Early Warning System network (SNEWS, Antonioli et al. 2004) -which does or will include the neutrino experiments mentioned above -and its multimessenger era successor SNEWS 2.0, whose mission is to provide early alerts to the astronomy and gravitational wave communities, and to the scientific community at large as well.The observation of presupernova neutrinos from an impending core-collapse supernova will: (i) allow numerous tests of stellar and neutrino physics, including tests of exotic physics that may require pointing to the collapsing star (e.g.axion searches, see Raffelt et al. (2011)); and (ii) enable a very early alert of the collapse and supernova, thus extending -perhaps crucially, especially for envelope-free stellar progenitors that tend to explode shortly after collapse -the time frame available to coordinate multi-messenger observations.
In this paper, we explore presupernova neutrinos as early alerts.In particular, we focus on the question of localization: can a signal of presupernova neutrinos provide useful positional information?Can it identify the progenitor star?From a recent exploratory study (Li et al. 2020), we know that the best potential for localization is offered by inverse beta decay events at large (O(10) kt mass) liquid scintillator detectors, where, for optimistic presupernova flux predictions and a star like Betelgeuse (distance of 0.2 kpc), a signal can be discovered days before the collapse, and the direction to the progenitor can be determined with a ∼ 80 • error.Several questions remain to be addressed, having to do with the diverse stellar population of nearby stars (including red and blue supergiants, of masses between ∼ 10 and ∼ 30 times the mass of the Sun, and clustered in certain regions of the sky) and with the rich possibilities of improving the directionality of the liquid scintillator technology in the future.
This article is the first dedicated study on the localization question for presupernova neutrinos.In Section 2 we discuss presupernova neutrino event rates and nearby candidates.In Section 3 we present our main results for the angular sensitivity.In Section 4 we discuss progen-itor identification, and in Section 5 we summarize our results.In Appendix A we detail the distance and mass estimates of nearby presupernova candidates.

PRESUPERNOVA NEUTRINO EVENT RATES AND CANDIDATES
A liquid scintillator is ideal for the detection of presupernova neutrinos, through the inverse beta decay process (henceforth IBD, νe +p → n+e + ) due to its low energy threshold (1.8 MeV), and its timing, energy resolution, and background discrimination performance.The expected signal from a presupernova in neutrino detectors has been presented in recent articles (e.g., Asakura et al. 2016;Kato et al. 2015;Yoshida et al. 2016;Patton et al. 2017a;Kato et al. 2017;Li et al. 2020).
We consider an active detector mass of 17 kt, which is expected for JUNO, with detection efficiency of unity, and we use the IBD event rates in Patton et al. (2017a); Patton et al. (2019).Figure 1 shows the numbers of events and cumulative numbers of events for progenitor stars of zero age main-sequence (ZAMS) masses of 15 M and 30 M (here M = 1.99 10 33 g is the mass of the Sun) at a distance of D=0.2 kpc (representative of Betelgeuse).Results are shown for the normal and inverted hierarchy of the neutrino mass spectrum.Times are negative, being relative to the time of core-collapse.
Figure 1 shows that a few hundred events are expected in the hours before core-collapse.For the 15 M model, the neutrino signal exceeds 100 events at t=−4 hr and has a characteristic peak at t −2.5 hours, which marks the beginning of core silicon burning.For the 30 M model, the neutrino signal exceeds 100 events at t=−2 hr.The number of events then increases steadily and rapidly, leading to a cumulative number of events that is larger than in the 15 M model.
For the detector background, we follow the event rates estimated in An et al. (2016) (see also Yoshida et al. (2016)) for JUNO: r on Bkg 2.66/hr and r of f Bkg 0.16/hr in the reactor-on and reactor-off cases respectively.In addition to reactor neutrinos, other backgrounds are due, in comparable amounts (about 1 event per day each), to geoneutrinos, cosmogenic 8 He/ 9 Li, and accidental coincidences due to various radioactivity sources, like the natural decay chains, etc.For the latter, it is assumed that an effective muon veto will be in place, see An et al. (2016) for details1 .Roughly, a signal is detectable if the number of events expected is at least comparable with the number of background events in the same time interval (N N bkg ).Using the reactoron background rate, the most conservative presupernova event rate in Figure 1, and the fact that the number of signal events scales like D −2 , we estimate that a presupernova can be detected to a distance D max 1 kpc.
What nearby stars could possibly undergo core collapse in the next few decades?To answer this question, we compiled a new list of 31 core collapse supernova candidates; see Appendix A and Table A1. Figure 2 gives an illustration of their names, positions, distances, masses, and colors.Figure 3 shows the equatorial coordinate system positions of the same stars, colored by distance bins, in a Mollweide projection.These candidates lie near the Galatic Plane, with clustering in directions associated with the Orion A molecular cloud (Großschedl et al. 2019) and the OB associations Cygnus OB2 and Carina OB1 (Lim et al. 2019).We find that for the stars in Table A1 the minimum separation (i.e., the separation of a star from its nearest neighbor in the same list) is, on average, ∆θ 10.4 • , and that 70% of the candidate stars have ∆θ 12.8 • (see Table A2).Therefore, a sensitivity of 10 • is desirable for complete disambiguation of the progenitor with a neutrino detector.

ANGULAR RESOLUTION AND SENSITIVITY
Here we discuss the angular sensitivity of a liquid scintillator detector for realistic numbers of presupernova neutrino events.We consider two cases: a well tested liquid scintillator technology (henceforth LS) based on Linear AlkylBenzene (LAB), as is used in SNO+ (Andringa et al. 2016) and envisioned for JUNO; and a hypothetical setup where a Lithium compound is dissolved in the scintillator for enhanced angular sensitivity (henceforth LS-Li), as discussed for geoneutrino detection (Tanaka & Watanabe 2014).As a notation definition, let us assume that the total number of events in the detector is N = N S + N Bkg , where N S is the number of signal events and N Bkg is the number of background events.
The IBD process in LS is illustrated in Figure 4. Overall, the sensitivity of this process to the direction of the incoming neutrino is moderate, with the emitted positron (neutron) momentum being slightly backward (forward)-distributed, see Beacom & Vogel (1999) and Vogel & Beacom (1999) for a detailed overview.Here, C e le s t ia l E q u a to r δ = 0 º 0.6 kpc 0.4 kpc  we follow the pointing method proposed and tested by the CHOOZ collaboration (Apollonio et al. 2000), which we describe briefly below.
Let us first consider a background-free signal, N Bkg = 0.For each detected neutrino ν i (i = 1, 2,. . ., N ), we consider the unit vector X(i) pn that originates at the positron annihilation location and is directed towards the neutron capture point.Let θ be the angle that X(i) pn forms with the neutrino direction (see Figure 4).The unit vectors X(i) pn carry directional informationalbeit with some degradation due to the neutron having to thermalize by scattering events before it can be captured -and possess a slightly forward distribution.The angular distributions expected for LS and LS-Li are given by Tanaka & Watanabe (2014) (in the context of geoneutrinos) in graphical form; we find that they are well reproduced by the following functions: (1) Using these, one can find the forward-backward asymmetry, which is a measurable parameter: Here N F and N B are the numbers of events in the forward (θ ≤ π/2) and backward (θ > π/2) direction respectively.We obtain a 0 0.16 for LS, which is con- . The geometry of Inverse Beta Decay in liquid scintillator.Shown are the incoming anti-neutrino (brown), proton (black), outgoing positron and its annihilation point (blue), outgoing neutron, its subsequent scattering events and its capture point (red), and the outgoing photon (orange).The vector pn originates at the positron annihilation location and points in the direction of the neutron capture point.θ is the angle between X (i) pn and the incoming neutrino momentum.sistent with the distributions shown in Apollonio et al. (2000), and a 0 0.78 for LS-Li.
Let us now generalize to the case with a non-zero background, and define the signal-to-background ratio, α = N S /N Bkg .For simplicity, the background is modeled as isotropic and constant in time.Suppose that N S , α, and a 0 are known.In this case, the total angular distribution of the N events will be a linear combination of two components, one for the directional signal and the other for the isotropic background The two distributions have a relative weight of α, which yields the forward-backward asymmetry as (5) In the small background limit, N Bkg → 0, then α → ∞ and a → a 0 .In the large background limit N Bkg → ∞, then α → 0 and a → 0.
Figure 5 shows the angular distribution for different signal-to-noise ratios α (see Table 1 for the corresponding values of a).For LS the α = ∞ curve (blue solid) is taken from Equation (1), and for LS-Li the α = ∞ curve (red solid) is taken from Equation (1).For LS-Li, an enhancement in the directionality is achieved as a result of an improved reconstruction of the positron annihilation point and a shortening of the neutron capture range.Enhancement in the directionality decreases for LS and LS-Li as the background becomes larger.
To develop an intuitive understanding of the angular sensitivity, for all cases we adopt an approximate distribution for the N events in the detector, which is linear in cos θ: f We have checked that this simple form yields results that are commensurate with those obtained using the more accurate distributions in Figure 5.
Table 1.Values of a for the curves in Figure 5. Rigorously, a depends on the neutrino energy.We investigated the uncertainty associated with treating a as a (energy-independent) constant, and found it to be negligible in the present context where larger errors are present from, for example, uncertainties associated with modeling of the presupernova neutrino event rates.In addition, the values of a used in the literature for supernova neutrinos, reactor neutrinos and geoneutrinos (e.g., Apollonio et al. 2000;Tanaka & Watanabe 2014;Fischer et al. 2015) vary only by 10-20% over a wide range of energy.The values of a in Table 1 for the backgroundfree α = ∞ cases are used in Tanaka & Watanabe (2014) and Fischer et al. (2015) for geoneutrinos, which have an energy range (E 2-5 MeV) and spectrum that is similar to those of presupernova neutrinos.

Pointing to the progenitor location
For a signal of N IBD events in the detector from a point source on the sky, and therefore a set of unit vectors X(i) pn (i = 1, 2, . . ., N ), an estimate of the direction to the source is given by the average vector p (Apollonio et al. 2000;Fischer et al. 2015): This vector offers an immediate way to estimate the direction to the progenitor star in the sky.The calculation of the uncertainty in the direction is more involved (Apollonio et al. 2000), and requires examining the statistical distribution of p, as follows.
Consider a Cartesian frame of reference where the neutrino source is on the negative side of the z-axis.In the limit of very high statistics (N → ∞), the averages of the x-and y-components of the vectors X(i) pn vanish.The average of the z-component can be found from Equation ( 6), and is z = a/3.Thus, the mean of p is: For a linear distribution such as Equation ( 6), the standard deviation is σ = 1/ √ 3.For N 1, the Central Limit Theorem applies, and the distribution of the three components of p are Gaussians centered at the components of p m , and with standard deviations Hence, the probability distribution of the vector p is The angular uncertainty on the direction to the supernova progenitor is given by the angular aperture, β, of the cone around the vector p m , containing a chosen fraction of the total probability (e.g., I = 0.68 or I = 0.90): or, in spherical coordinates: The latter form reduces to: where k = 3N/2 | p| = a N/6, and the error function is Erf(z) = 2/ √ π z 0 e −t 2 dt.For a fixed value of I, Equation ( 12) can be solved numerically to find β = β(k, I), and therefore to reveal the dependence of β on N and a. • in the two cases respectively.The degree of improvement in performance with increasing a is shown in Figure 7, where N = 200 is kept fixed.
In the case of isotropic background the mean vector, p m , still points in the direction of the progenitor star.That is no longer true in the general case of anisotropic background, which would introduce a systematic shift  1.
in the direction of p m , in a way that depends on sitespecific information and is beyond the scope of the present paper.Another source of potential uncertainty is in the sitespecific number of accidental coincidences in the detector (e.g., a coincidence between a positron from a cosmic muon decay and a neutron capture from a different process).Although here we assume a strong muon veto (An et al. 2016), the actual performance of the veto in a realistic setting may be different and contribute to larger background levels that would negatively affect the presupernova localization.

PROGENITOR IDENTIFICATION
Attempts at progenitor identification will involve a complex interplay of different information from different channels.Here, we discuss a plausible, although simplified, scenario where two essential elements are combined: (i) pointing information from a single liquid scintillator detector, using the method in Section 3; and (ii) a rough estimate of the distance to the star, from the comparison of the signal with models2 .Both these indicators will evolve with time over the duration of the presupernova signal, with the list of plausible candidates becoming shorter as higher statistics are collected in the detector.We emphasize that the goal here is not necessarily to reduce to a single star; even reducing the list to a few stars (3 or 4, for example) can be useful to the gravitational wave and electromagnetic astronomy communities.
Consider the two case studies shown in Figure 8 and detailed in Tables 2 and 3.The left column refers to Betelgeuse and the right column to Antares, both with a time distribution of IBD events as in Figure 1 for 15 M .The three panels show how the 68% and 90% C.L. angular errors decrease with time, leading to a progressively more accurate estimate of the position3 .
For the case of LS, at t = −1 hr pre-collapse, as many as ∼ 10 progenitor stars are within the angular error cone, with only a minimal improvement at later times.Therefore, the identification of the progenitor can not be achieved using the angular information alone.It might be possible, however, in the presence of a rough distance estimation from the event rate in the detector.In both examples, a possible upper limit of D < 0.25 kpc (red squares in Figure 8, also see Figure 3) results in a single pre-supernova being favored.For LS-Li, the angular information alone is sufficient to favor 3-4 stars as likely progenitors already ∼4 hours pre-collapse.At t = −1 hr, a single progenitor can be identified in the case of Antares.
A less fortunate scenario is shown in the left panels in Figure 9 (details in Table 4) for σ Canis Majoris (distance D = 0.513 kpc).The number of events was calculated according to the 15 M model in Figure 1.The lower signal statistics (the number of events barely reaches 60), and the larger relative importance of the background result in a decreased angular sensitivity.We find that LS will only eliminate roughly half of the sky if we use the 68% C.L. error cone.When combined with an approximate distance estimate, this coarse angular information might lead to identifying ∼ 10 stars as potential candidates.With LS-Li, the list of candidates might be slightly shorter but a unique identification would be very unlikely, even immediately before collapse.
A 30 M case is represented by the right panels in Figure 9 (and detailed in Table 5) for S Monocerotis A (distance D = 0.282 kpc).An hour prior to the collapse 120 events are expected, allowing LS to shorten the progenitor list to 12 stars within the error cone at 68% C.L. Whereas, LS-Li narrows the progenitor list down to 3 stars with the same C.L. one hour prior to the collapse.When combined with a rough distance estimate, the progenitor might be successfully identified.

DISCUSSION
We have demonstrated that it will be possible to use the neutrino IBD signal at a large liquid scintillator de-    robust, as it has been used successfully for reactor neutrinos, and it is sufficiently simple that it can be im-plemented during a pre-supernova signal detection.For a detector where the forward-backward asymmetry is The method has the potential to become even more sensitive if it is used with LS-Li, and therefore it provides further motivation to develop new experimental concepts in this direction.For example, 200 signal events with forward-backward asymmetry of ∼40% would result in a resolution of about 15 • , and the possibility to uniquely identify the progenitor star.
In a realistic situation, as soon as a presupernova signal is detected with high confidence (a few tens of candidate events), an alert with a coarse localization information can be issued, followed by updates with improved angular resolution in the minutes or hours leading to the neutrino burst detection.
Using the Patton et al. (2017b) presupernova model, we find that (see Figure 8) when the number of events reaches N = 100 ( 1 hour pre-collapse for Betelgeuse), the angular information is already close to optimal, since only a minimal improvement of the positional estimate can be gained at subsequent times.Note, however, that our results are conservative.According to other simulations where the presupernova neutrino luminosity reaches a detectable level over a time scale of days (Kato et al. 2015;Guo et al. 2019), it might be possible to detect a larger number of events, resulting in even better angular resolutions in the last 1-2 hours before the core collapse.
It is possible that, when a nearby star reaches its final day or hours before becoming a supernova, a new array of neutrino detectors will be available.A large liquid scintillator experiment like the proposed THEIA (Askins et al. 2019), which could reach 80 kt (fiducial) mass, could observe more than 10 3 IBD events, with an angular resolution of at least ∼ 30 • .The resolution of THEIA would be improved by using a waterbased liquid scintillator, where the capability to separate the scintillation and Cherenkov light would result in enhanced pointing ability (e.g., Askins et al. 2019) for IBD, and in the possibility to use neutrino-electron elastic scattering for pointing.A subdominant, but still useful, contribution to the pointing effort -at the level of tens of events -will come from O(1) kt liquid scintillator projects like SNO+ (Andringa et al. 2016) and the Jinping Neutrino Experiment (Beacom et al. 2017), for which the deep underground depth will result in very low background levels.Further activities on directionality in scintillators are ongoing (e.g., Biller et al. 2020).Data from elastic scattering events at water Cherenkov detectors like SuperKamiokande (Simpson et al. 2019) and possibly the planned HyperKamiokande (O(100) kt) (Abe et al. 2016), will also contribute, despite the loss of statistics (compared to liquid scintillator) due to the higher energy threshold (∼ 5 − 7 MeV).In these detectors, a possible phase with Gadolinium dissolved in the water, like in the upcoming SuperK-Gd, (Beacom & Vagins 2004;Simpson et al. 2019), will allow better discrimination of the IBD events, resulting in an enhanced pointing potential.
In addition to new experimental scenarios, a different theoretical panorama may be realized as well, and there might be novel avenues to conduct fundamental science tests (e.g., searches for exotic light and weakly interacting particles) using presupernova neutrinos.

Figure 1 .
Figure 1.Top row a) and c): Number of presupernova neutrino events at a 17 kt liquid scintillator detector, in time bins of width ∆t = 0.5 hrs as a function of time before core-collapse.Bottom row or b) and d): Cumulative numbers of events in half-hour increments.Shown are the cases of a ZAMS 15 M (blue histogram) and a ZAMS 30 M (red histogram) progenitor, at a distance D=0.2 kpc, for the normal (left column) and inverted (right column) neutrino mass hierarchy.

Figure 2 .Figure 3 .
Figure 2. Illustration of nearby (D ≤ 1 kpc) core collapse supernova candidates.Each star's spectral type, name, mass and distance is shown in labels.See TableA1for details and references.

Figure 5 .
Figure 5. Normalized distributions of cos θ for LS and LS-Li, for different values of the signal-to-background ratio, α = NS/N Bkg (numbers in legend).Here, α = ∞ means absence of background, N Bkg = 0.

Figure 6 .
Figure 6.The angular uncertainty, β, as a function of the number of events, for LS and LS-Li, two different confidence levels, and three values of the signal-to-background ratio, α (see figure legend).
Figure 6 shows the dependence of β on N , for two confidence levels (C.L.).The figure illustrates the (expected) poor performance of LS: we have β 70 • at 68% C.L. and N = 100, improving to β 40 • at N = 500.For the same C.L. and values of N , LS-Li would allow an improvement in the error by nearly a factor of 4, giving β 18 • and β 10

Figure 7 .
Figure 7.The angular uncertainty, β, as a function of the forward-backward asymmetry, a, for two different confidence levels (see figure legend) and fixed number of events, N = 200.The vertical lines indicate the values of a corresponding to α = ∞, 3 for LS (dashed lines) and LS-Li (dot-dashed), see Table1.

Figure 8 .
Figure 8. Angular error cones at 68% C.L. and 90% C.L. for LS (orange and maroon contours), and LS-Li (indigo and black contours) at 4 hours, 1 hour and 2 minutes prior to the core collapse.The left panels correspond to Betelgeuse (D= 0.222 kpc, M 15 M ); the right panels to Antares (D= 0.169 kpc, M15M ).The presence of background is considered in all cases according toAn et al. (2016).The number of events is based on the model byPatton et al. (2017b).

Table 2 .
Parameters and results for Betelgeuse, Figure8, left panels.
•tector to obtain an early localization of a nearby pre-supernova (D 1 kpc).The method we propose is

Table 3 .
Parameters and results for Antares, Figure8, right panels.

Table 5 .
Parameters and results for S Monocerotis A, Figure9, right panels.

Table A2 .
Minimum Angular Separation Between Pre-supernova Candidates.