Measuring the distance and mass of galactic core-collapse supernovae using neutrinos
MMeasuring the Distance and ZAMS Mass of Galactic Core-Collapse SupernovaeUsing Neutrinos
Manne Segerlund
Department of Engineering Sciences and Mathematics,Lule˚a University of Technology, SE-97187 Lule˚a, Sweden
Erin O’Sullivan ∗ Department of Physics and Astronomy, Uppsala University,Box 516, SE-75120 Uppsala, Sweden
Evan O’Connor
The Oskar Klein Centre, Department of Astronomy,Stockholm University, AlbaNova, SE-106 91 Stockholm, Sweden (Dated: January 27, 2021)Neutrinos from a Galactic core-collapse supernova will be measured by neutrino detectors minutesto days before an optical signal reaches Earth. We present a novel calculation showing the abilityof current and near-future neutrino detectors to make fast predictions of the progenitor distanceand place constraints on the zero-age main sequence mass in order to inform the observing strategyfor electromagnetic follow-up. We show that for typical Galactic supernovae, the distance can beconstrained with an uncertainty of ∼
5% using IceCube or Hyper-K and, furthermore, the zero-agemain sequence mass can be constrained for extremal values of compactness.
INTRODUCTION
The next Galactic core-collapse supernova (CCSN) willbe one of the most important astrophysical events in ourlifetime. A burst of neutrinos tens of seconds in dura-tion with individual energies O (10 MeV) will be detectedby neutrino experiments around the world. As neutrinosfrom a supernova arrive before the first light, an unprece-dented multi-messenger search campaign to identify thesupernova and observe the photon shock breakout willfollow. However, due to potentially significant dust ob-scuration in the galaxy [1], the search strategy wouldbenefit from any information about the progenitor sys-tem available from the neutrinos. Indeed, key informa-tion about the supernova is imprinted in the neutrinosignal, including localization [2] and the type of remnant(black hole or neutron star) [3]. We present here a fastand novel method to determine the distance and progen-itor star structure along with constraints on the zero-agemain sequence (ZAMS) mass of a Galactic CCSN, whichcan help guide the observing strategy of electromagnetictelescopes, potentially hastening the identification of thehost star as well as allowing for an estimate of the delaytime between the neutrinos and photons.Our method builds from the procedure described in[4, 5], where it was shown that neutrinos could be usedto place constraints on the presupernova structure ofthe progenitor star. Here, we extend and quantify themethod and include predictions of intrinsic propertiesthat are important for electromagnetic follow-up, such asthe distance to the supernova and constraints, when pos- sible, on the progenitor ZAMS mass. We improve on pastwork by [6], which examined how the neutronization peakimprinted in the neutrino signal can be used to determinesupernova distance in a megaton water-Cherenkov detec-tor. Our method obtains a similar sensitivity to distanceas the method described in [6], but using smaller detec-tor masses present in current and near future experimentsand without relying on the separation between neutrinosand anti-neutrinos, which can take valuable time duringa supernova event and adds potential sources of error.We demonstrate our method for the two most sensi-tive current neutrino experiments, as well as three near-future detectors. The two currently operational neutrinodetectors considered are IceCube [7], a cubic-kilometer-scale neutrino detector embedded in the glacial ice at theSouth Pole, and Super-Kamiokande (Super-K) [8], a 32kton inner-volume water-Cherenkov detector located inJapan. By 2027, we expect three other large facilitiesto significantly contribute to this measurement: Hyper-Kamiokande (Hyper-K) [9], the next-generation of Super-K which will have an inner volume of 220 ktons, DUNE,a liquid argon detector in the US that will be 40 ktons[10], and JUNO, a 20 kton liquid-scintillator detector inChina [11].In order to capitalize on the early warning providedby neutrinos, most large-scale neutrino detectors areconnected to the SuperNova Early Warning System(SNEWS) [12, 13]. The fast reporting strategy for dis-tance and progenitor structure described here can be im-plemented in SNEWS to further enhance the informationreported about the supernova event. a r X i v : . [ a s t r o - ph . H E ] J a n
10 20 30 40 distance [kpc] N ( m s ) N (0 50 ms) f d=10kpc IceCube, normal mass ordering f error barsfor d=10kpc8 10 121000015000 2.002.252.502.753.003.253.50 f FIG. 1. Progenitor dependence of the early neutrino signal in the IceCube detector assuming a normal mass ordering for theneutrinos. In the left panel we show the expected number of interactions detected by IceCube in the first 50 ms vs. distancefor 149 different progenitor models. The color of each line denotes f ∆ , a directly measurable intrinsic (although detectordependent) property of the core-collapse event. We show this distance independent f ∆ vs. the number of counts in the first50 ms for a supernova at 10 kpc (middle) and vs. the progenitor compactness (right). The one-to-one relationships between f ∆ and these quantities allows a distance and ZAMS mass estimate from a galactic supernova event. The 1 σ error bars shown arebased on the expected Gaussian counting statistics, background level, and systematic errors from the fit to the 149 progenitormodels (only for the error bar on the compactness). METHODSTools
We base our analysis on the early CCSN neutrino sig-nal generated from the evolution of 149 progenitor mod-els from [14]. These models are single-star evolutions ofsolar-metallicity massive stars with ZAMS masses from9 . M (cid:12) to 120 M (cid:12) . The presupernova structures of thesemodels span the range expected for iron-core collapse andtherefore make a complete set for this systematic study.For the core-collapse evolutions we use the FLASH [15–17] hydrodynamics package with an energy-dependentneutrino transport. We use the SFHo nuclear equationof state [18] and neutrino interactions from NuLib [19].In order to capture important processes which impactthe neutrino signal at early times [20], in addition to thestandard neutrino rates used in [17], we utilize the mi-crophysical electron captures rates from [21, 22], inelasticneutrino-electron scattering [23] and inelastic neutrino-nucleon scattering for heavy-lepton neutrinos based on[24]. Using the time evolution of the neutrino luminos-ity, mean energy, and the mean squared energy from oursimulations, we utilize SNOwGLoBES [25, 26] to gener-ate expected count rates in current and near-future neu-trino detectors [27]. Where stated, we use a GalacticCCSN spatial distribution from [1] and a Salpeter ini-tial mass function (IMF) [28], i.e. N ( m ) dm ∝ m − . dm extending from 8 . M (cid:12) to 130 M (cid:12) . Parameter extraction methods
The number of observed supernova neutrinos is relatedto distance via an inverse square law. If the early signalwas progenitor-independent, then we could calculate thedistance by comparing the number of observed events tothe predicted signal at a known distance, a so-called stan-dard candle approach. Indeed, this is the method utilizedin [6] with electron neutrinos that, during the first 10s ofms after the protoneutron star (PNS) forms, do showthis behavior. However, the bulk of the early neutrinosignal in many detectors consists of electron antineutrinointeractions. These neutrinos do not show this univer-sal behavior, rather the early (within the first ∼
50 ms)interaction rates can vary up to a factor of ∼ f ∆ = N (100 −
150 ms) N (0 −
50 ms) , (1)from Horiuchi et al. [5]. f ∆ is the ratio of the numberof neutrino interactions occurring between 100 ms and150 ms ( N (100 −
150 ms)) to the number of interactionsoccurring in the first 50 ms ( N (0 −
50 ms)) [30]. In middlepanel of Fig. 1, we explicitly show the key relationshipwe are exploiting. f ∆ , which is a distance-independentquantity, has a one-to-one mapping with the expectednumber of interactions in the first 50 ms. The error barsshown in this figure are the expected 1 σ error bars for a d = 10 kpc supernova based on Gaussian counting statis-tics and also taking into account the background noise inthe IceCube detector.The combined distance estimate is achieved by averag-ing both of the above methods with weights correspond-ing to the statistical and systematic measurement error.For the statistical errors, Gaussian counting statistics isassumed with the addition for the IceCube detector of abackground component [31]. The systematic error is de-tector specific and is based on the variance of the modelsto the fit (cf. the middle panel of Fig. 1 for the IceCubedetector with normal mass ordering).Not only does f ∆ relay the expected number of eventsin the first 50 ms, it is also directly related to the com-pactness [5, 32], a measure of the progenitor structure ofthe star at the end of its life. The compactness is definedas ξ M = M/M (cid:12) R ( M ) / , (2)where M is some chosen mass scale (taken here to be M = 2 . M (cid:12) following [5]) and R ( M ) is the radius thatencloses that mass at the point of core collapse. Thisrelationship between f ∆ and compactness is seen in theright panel of Fig. 1. This particular relationship is dis-tance independent, however we show the expected 1 σ error bars for a d = 10 kpc supernova detected in Ice-Cube. A measurement of f ∆ allows a direct constrainton the compactness. It can be related to the ZAMS massof the progenitor star through stellar evolution models, although the mapping is non-monotonic and can changerapidly with changing ZAMS mass [33]. Given the non-monotonic relationship, for a measurement of a particu-lar value of f ∆ , along with an assumption of a progenitormodel series, we can determine a probability distributionfor the ZAMS mass of the exploding star. RESULTSDistance
Following the method to determine distance outlinedabove, we perform a large number of mock observationsto determine the precision. For distances up to 25 kpcin increments of 1 kpc, for each of the five considered de-tectors and for each neutrino mass ordering we perform80000 mock core-collapse events. For each event, we ran-domly choose a mass based on a Salpeter IMF. The mockobservations are randomly determined based on a Gaus-sian distribution about the mean expected events in eachwindow. As mentioned above, for IceCube a backgroundnoise component is added using a modified Gaussian dis-tribution taking the spread to be 1 . √ µ where µ is theaverage detector background rate equal to 286 Hz/DOM,then the mean is subtracted. The factor of 1.3 is toaccount for correlated hits from muons [31]. The dis-tance is estimated for each realization and the resulting1 σ value of the distribution of relative errors on distance( | d − d estimate | /d ) is shown in the top panel of Fig. 2.For nearby distances (which varies detector to detec-tor, but generally (cid:46) few kpc), the error is dominated bythe systematic variation of the models from the fit shownin the middle panel of Fig. 1. It is worth noting thatthis systematic error is smallest with DUNE or in theinverted mass ordering, highlighting the fact the elec-tron neutrinos and to some extent heavy-lepton neutri-nos, are more progenitor-independent then electron an-tineutrinos, especially at early times. This was the orig-inal motivation for the work of [6]. As the distance in-creases, the errors begin to become dominated by statis-tics and the relative error grows linearly with distance.For IceCube, the presence of the constant backgroundnoise floor causes the error to grow faster than linear atlarge distances. Marginalizing over a Galactic distancedistribution [1] we obtain 1 σ relative errors of 5.4%, 8.9%,5.1%, 8.3%, and 8.7% for IceCube, Super-K, Hyper-K,DUNE, and JUNO, respectively for the normal neutrinomass ordering [34]. Changes in the spatial distribution ofCCSN events, for example, using the neutron star distri-bution explored in [35] gives similar (but (cid:46) Distance [kpc] R e l a t i v e D i s t a n c e E rr o r [ % ] IceCubeHyper-KSuper-KDUNEJUNO0 5 10 15 20 25
Distance [kpc] C o m p a c t n e ss E rr o r NOIO
FIG. 2. Estimated 1 σ errors derived from trial observations onthe distance (relative; top panel) and compactness (absolute;bottom panel) marginalized over the IMF as a function ofdistance for each detector and the normal (NO; solid line)and inverted (IO; dashed line) neutrino mass ordering. Compactness
In addition to extracting the distance via the earlyneutrino signal we can extract properties of the progeni-tor star itself. Compactness, as seen in Equation 2, is ameasure of the structure of the star at the point of col-lapse. The original proposal from Horiuchi et al. [5] wasto determine the compactness of the presupernova starvia an observation of neutrinos. We reproduce that anal-ysis here, extend it to IceCube, Hyper-K, and JUNO,and quantify our ability to constrain the compactnessfor a galactic population. As determined by Horiuchi etal.. From the fit of f ∆ = m ξ ξ . + b ξ (see right panelof Fig. 1 for IceCube in the normal mass ordering) andan observation of f ∆ , we estimate the compactness via˜ ξ . = ( f ∆ − b ξ ) /m ξ , where m ξ and b ξ are the fitted slopeand intercept (available in the supplemental informationfor each detector and neutrino mass ordering). In thebottom panel of Fig. 2 we show the expected 1 σ absoluteerror on a measurement of ξ . as a function distance. Wenote the same characteristics as the relative distance er-ror. At small distances ( (cid:46) (cid:46) σ ab- solute errors of 0.11, 0.2, 0.11, 0.17, and 0.20 for IceCube,Super-K, Hyper-K, DUNE, and JUNO respectively forthe normal neutrino mass ordering [36]. Mass
The strong correlation between f ∆ and compactnessgives us an indirect measurement of the presupernovastructure. Stellar evolution–to the extent that the cur-rent modeling of the advanced burning stages, convec-tion, and overshoot can be trusted–complicates the map-ping between the ZAMS properties of the stars and thefinal structure at the time of core-collapse [33]. Further-more, astrophysical factors, such as binarity, rotation,and metallicity will all impact the ZAMS mass to com-pactness mapping. With these caveats in mind, for thesingle-star, solar metallicity, non-rotating model set wehave chosen to use from Sukhbold et al. (2016) [14], wecan invert the ZAMS mass-compactness relation in orderto explore potential constraints on the ZAMS mass of theprogenitor star from a neutrino observation.In Fig. 3, we show the probability distribution of mea-sured f ∆ as a function of the progenitor ZAMS mass fora supernova observed with a reconstructed distance of10 kpc sampled over the IMF. We assume the IceCubedetector and the normal neutrino mass ordering. Thereis some structure in the f ∆ − M ZAMS plane suggesting in-formation on the ZAMS mass may be obtained, at leastin some limiting cases. We show in the bottom panel cu-mulative distributions in ZAMS mass for assumed valuesof f ∆ = 2.0, 2.5, 3.0, and, 3.25. Note, these cumula-tive distributions have the statistical uncertainty of themeasurement of f ∆ built in and therefore will dependon the detector and assumed distance. For an observedvalue of f ∆ =2.0, which corresponds to progenitors of lowcompactness, this model set confidently places an upperZAMS mass limit (95% of the time) of ∼ M (cid:12) . A mea-surement of f ∆ =2.5 would give a lower ZAMS mass limit(95% of the time) of ∼ M (cid:12) . For this model set, ameasurement of f ∆ > . (cid:38)
98% of the time)places a lower limit on the ZAMS mass of 20 M (cid:12) , andisolates potential masses to be near either ∼ M (cid:12) or35 M (cid:12) -50 M (cid:12) . Even with the caveats listed above, thereis general confidence in the statement that low ZAMSmass stars ( M (cid:46) M (cid:12) ) have the lowest compactnessand therefore the lowest values of f ∆ . It is thereforelikely that for such supernovae, a constraint on ZAMSmass is possible. DISCUSSION AND CONCLUSIONS
In the results of this paper we present a compelling casethat current and near-future neutrino detectors have thecapabilities and statistics to make a measurement of the f IceCube, NOd=10kpc
10 20 30 40 50 60 80 100 M [ M ] f =2.0 f =2.5 f =3.0 f =3.25 FIG. 3. Probability distribution of measured f ∆ as a functionof the ZAMS mass of the progenitor stars for a measured dis-tance of 10 kpc for the IceCube detector assuming the normalneutrino mass ordering. The color denotes the logarithm ofthe probability, dark blue values are ∼ f ∆ relays some information on the ZAMSmass of the progenitor star, particularly if the measured f ∆ is small. In the bottom panel we show cumulative distribu-tions for four choices of f ∆ , marked by dashed lines in the toppanel. The grey dashed lines denote cumulative probabilitiesof 5% and 95%. On the right is the marginalized distributionof observed f ∆ over the IMF. distance, compactness, and a constraint on the ZAMSmass of a future Galactic CCSN. However, both stellarevolution modelling and CCSNe evolution are complexmultiphysics problems. There are certainly systematicerrors, both known and unknown, in both of these pro-cesses. We have tried to eliminate many of the potentialmodel dependencies. We explore the full range of iron-core progenitors expected and show that the response weinvestigate is well behaved and linear over this model set.Also, by restricting our measurements to early times, inmany cases we avoid the complex multidimensional ex-plosion dynamics and potentially avoid complex collec-tive neutrino oscillations, that we know are present atlater times. However, we note that very early explosions(prior to ∼
150 ms) may give smaller f ∆ then predictedhere. We have tested our methods against the parame-terized explosion models of [37] and find no systematic differences as long as the same set of neutrino interactionrates is assumed. On this note, we have found, thoughnot included here, that varying these neutrino interac-tions (such as including and excluding neutrino-nucleonscattering and microphysical electron-capture rates) thatthe quantitative fits shown in Fig. 1 can change, how-ever the qualitative results, such as the expected preci-sion and the ability to measure or constrain compactnessand mass, are robust against these changes. We expectsimilar results for variations in the nuclear equation ofstate [38]. We therefore advocate for efforts to quantifyand ideally eliminate these systematic errors so that thesupernova properties discussed here can be rapidly, reli-ably, and accurately determined during the next GalacticCCSN and allow for optimal multi-messenger followup.These efforts would include the development and imple-mentation of precision neutrino interaction rates and re-fined nuclear equations of state. Unless the core containsa large amount of angular momentum, which is the casein only a small fraction of progenitors, we do not expectrotation to affect the neutrino signal enough to distortthe trends found here.We have not included detailed detector responses,which may change the predicted number of events fora given model, or taken into account in our error esti-mate any uncertainties in the cross sections of neutrinosin these detectors. Furthermore, we have not combinedthe results from the different experiments, which mayimprove the distance, compactness, and mass determina-tions shown here.Neutrinos from the next Galactic CCSN will providea once-in-a-generation warning for the electromagneticcommunity to view the first light from shock breakout.We present a simple method to determine supernova dis-tance and constrain the progenitor mass using the neu-trino signal from current and near-future experiments,with the intention that this information could be used toaid astronomers in localizing the progenitor star, as wellas inform the observing strategy. We hope this methodcan help to ensure we are prepared to fully maximize thedata we can collect from this incredible event.We thank Sean Couch and MacKenzie Warren forFLASH development and access to models from [37], aswell as Olga Botner, Allan Hallgren, Carlos Perez de losHeros, Christian Glaser, Kate Scholberg, and Segev Ben-Zvi for useful discussions. 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Supplemental Information: Measuring the Distance and ZAMS Mass ofGalactic Core-Collapse Supernovae Using Neutrinos
Progenitor dependence for different detectors
In the main article we specifically demonstrate our method using the IceCube detector and assuming the normalmass ordering for neutrinos, with the aid of Figure 1. Here we present the equivalent figures for the inverted massordering and the IceCube detector (Fig. 4; for completeness we reproduce the normal mass ordering figure for IceCubeas well), for both mass orderings for the Super-K detector (Fig. 5), for the Hyper-K detector (Fig. 6), for the DUNEdetector (Fig. 7), and for the JUNO detector (Fig. 8).
10 20 30 40 distance [kpc] N ( m s ) N (0 50 ms) f d=10kpc IceCube, normal mass ordering f error barsfor d=10kpc8 10 121000015000 2.002.252.502.753.003.253.50 f
10 20 30 40 distance [kpc] N ( m s ) N (0 50 ms) f d=10kpc IceCube, inverted mass ordering f error barsfor d=10kpc8 10 121000015000 1.501.752.002.252.50 f FIG. 4. Progenitor dependence of early neutrino signal in the IceCube detector assuming a normal mass ordering (upper panel;repeat of Figure 1 in the main article for completeness) inverted mass ordering (lower panel) for the neutrinos. For details, seethe Figure 1 caption in the main article.
The fits shown in Figs. 4-8 are given in Table I. We also include the variance of the models from the fit, which isused as an estimate of the systematic error in our analysis.
Detector, ν mass ordering m N b N σ sys N, b m ξ b ξ σ sys ξ, b IceCube, NO 0.000182 0.779 0.11 1.48 2.1 0.119IceCube, IO 0.000125 0.342 0.0656 1.12 1.42 0.0695Super-K, NO 0.0105 0.894 0.0973 1.22 2.0 0.0996Super-K, IO 0.00815 0.439 0.0529 0.914 1.37 0.0583Hyper-K, NO 0.00152 0.894 0.0973 1.22 2.0 0.0996Hyper-K, IO 0.00119 0.439 0.0529 0.914 1.37 0.0583DUNE, NO 0.0158 -0.0304 0.0641 1.18 1.23 0.0696DUNE, IO 0.00978 -0.706 0.0411 0.893 0.66 0.05JUNO, NO 0.0109 0.746 0.0909 1.18 1.87 0.0952JUNO, IO 0.0088 0.319 0.0515 0.914 1.29 0.0569TABLE I. Fit parameters for the relationship between f ∆ and N (0 −
50 ms) and compactness ( ξ . ) in the middle and rightcolumn, respectively, for the five detectors considered (IceCube, Hyper-K, Super-K, DUNE, and JUNO) and the two neutrinomass orderings (NO: normal mass ordering, IO: inverted mass ordering). The fits are of the form f ∆ = m X X + b X . Thevariance of the 149 progenitor models to the fit are also given, this is taken as a proxy for the systematic error on the fit.
10 20 30 40 distance [kpc] N ( m s )
100 125 150 175 200 N (0 50 ms) f d=10kpc Super-K, normal mass ordering f error barsfor d=10kpc8 10 12100200 2.002.252.502.753.00 f
10 20 30 40 distance [kpc] N ( m s )
100 125 150 175 200 N (0 50 ms) f d=10kpc Super-K, inverted mass ordering f error barsfor d=10kpc8 10 12100150200 1.41.61.82.02.2 f FIG. 5. Progenitor dependence of early neutrino signal in the Super-K detector assuming a normal mass ordering (upper panel)and the inverted mass ordering (bottom panel) for the neutrinos. For details, see the Figure 1 caption in the main article.
10 20 30 40 distance [kpc] N ( m s )
800 1000 1200 1400 N (0 50 ms) f d=10kpc Hyper-K, normal mass ordering f error barsfor d=10kpc8 10 1275010001250 2.002.252.502.753.00 f
10 20 30 40 distance [kpc] N ( m s )
800 1000 1200 1400 N (0 50 ms) f d=10kpc Hyper-K, inverted mass ordering f error barsfor d=10kpc8 10 1275010001250 1.41.61.82.02.2 f FIG. 6. Progenitor dependence of early neutrino signal in the Hyper-K detector assuming a normal mass ordering (upper panel)and the inverted mass ordering (bottom panel) for the neutrinos. For details, see the Figure 1 caption in the main article.
Cumulative Distributions of error on distance and compactness determination
In the main article we provide 1 σ error estimates for the relative error on the distance, and absolution error on thecompactness extracted from our mock observations. For this we marginalized over a galactic spatial distribution [1]and a Salpeter initial mass function [28]. We show, for each detector and neutrino mass ordering, the full cumulativedistribution of this relative error for distance and absolute error on compactness in Fig. 9. We show the resultsfor three different definitions of f ∆ from [5]. These three definitions are the ratio of the number of counts in three0
10 20 30 40 distance [kpc] N ( m s )
80 100 120 140 N (0 50 ms) f d=10kpc DUNE, normal mass ordering f error barsfor d=10kpc8 10 1275100125 1.21.41.61.82.02.22.4 f
10 20 30 40 distance [kpc] N ( m s )
140 160 180 200 N (0 50 ms) f d=10kpc DUNE, inverted mass ordering f error barsfor d=10kpc8 10 12150200 0.60.81.01.21.41.6 f FIG. 7. Progenitor dependence of early neutrino signal in the DUNE detector assuming a normal mass ordering (upper panel)and the inverted mass ordering (bottom panel) for the neutrinos. For details, see the Figure 1 caption in the main article.
10 20 30 40 distance [kpc] N ( m s )
100 125 150 175 N (0 50 ms) f d=10kpc JUNO, normal mass ordering f error barsfor d=10kpc8 10 12100200 1.82.02.22.42.62.83.0 f
10 20 30 40 distance [kpc] N ( m s )
100 120 140 160 180 N (0 50 ms) f d=10kpc JUNO, normal mass ordering f error barsfor d=10kpc8 10 12100150200 1.41.61.82.02.2 f FIG. 8. Progenitor dependence of early neutrino signal in the JUNO detector assuming a normal mass ordering (upper panel)and the inverted mass ordering (bottom panel) for the neutrinos. For details, see the Figure 1 caption in the main article. time windows (50 ms-100 ms, 100 ms-150 ms, and 150 ms-200 ms) to the number of counts in the first 50 ms. For thedetermination of the distance, all three choices are comparable, although with a slight preference for the latest timewindow, 150 ms-200 ms. For the compactness, the latest time window is generally the best, although for IceCube andHyper-K the 100 ms-150 ms time window is comparable or slightly better. We settle on f ∆ = N (100 −
150 ms) N (0 −
50 ms) becausethe multidimensional dynamics (not included here) will impact the latest time window most significantly.1
Demonstration of distance extraction methods
We utilize two methods to extract the distance from the early neutrino signal. One is purely based on the numberof counts in the first 50 ms and compares this observation to the mean progenitor from our model set. The othermethod first constrains the progenitor model with f ∆ in order to more precisely determine the expected number ofthe count. At close distances (or large detectors) we can constrain the progenitor well enough for the latter methodto give better distances estimates. However, at large distances, or smaller detectors, the error introduced by theprogenitor identification is larger than the one introduced by just assuming the mean progenitor. We explicitly showthis in Fig. 10 for IceCube and Super-K (both using the normal mass ordering). As a function of distance, the bluedashed and dashed-dotted lines are the 1 σ relative distance errors for the first (with the mean progenitor model)and the second (via the progenitor constraint with f ∆ ) distance-estimate method, respectively. As argued above,the f ∆ method performs better at close distances and for larger detectors. The cross over point is at ∼
13 kpc forIceCube and ∼ σ values of the estimated error whichare used to weight the distance estimates from the two methods for each mock observation. As can be seen, theytrack the actual errors quite well. The blue solid line is the 1 σ relative distance error achieved when we combine thetwo distance-estimate methods.2 C u m u l a t i v e D i s t r i b u t i o n HK, NO HK, IO f = N (50 100ms) N (0 50ms) f = N (100 150ms) N (0 50ms) f = N (150 200ms) N (0 50ms) Error
Error
JUNO, IO
FIG. 9. Cumulative distributions of the relative distance error (orange) and the absolute compactness error (blue) marginalizedover a galactic population of core-collapse supernovae (i.e. both spatial position [1] and initial mass function [28]). From thetop to the bottom we show the distributions for IceCube, Super-K Hyper-K, DUNE, and JUNO, respectively. The left panelsare for the normal neutrino mass ordering while the right panels are for the inverted mass ordering. The three lines for eachdetector and mass ordering represent three different defintions of f ∆ , see the text. Distance [kpc] R e l a t i v e D i s t a n c e E rr o r [ % ] IceCube, NOcombinedmean only: errorfdelta only: errormean: error estimatefdelta: error estimate 2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0
Distance [kpc] R e l a t i v e D i s t a n c e E rr o r [ % ] SK, NOcombinedmean only: errorfdelta only: errormean: error estimatefdelta: error estimate
FIG. 10. 1 σσ