Supernova Neutrino Signal Detection in Nova Experiment

Introduction Signal detection Results and outlook

Supernova neutrino signal detection in NOvA experiment

Andrey Sheshukov

DLNP JINR, Dubna

24.01.2019

Andrey Sheshukov SN detection in NOvA experiment 1 / 21 Supernova neutrino signal Introduction Coincidence network Signal detection NOvA detectors Results and outlook Detecting supernova neutrinos Supernova triggering system Supernova neutrino signal

Neutrino signal from core-collapse supernova:

1057 M = 9.6 M e e x M = 27 M 1058 e e x 1056

1055

1057 1054 Neutrinos per second Neutrinos per second MeV

1053 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 0 10 20 30 40 50 60 Time since bounce, s E , MeV

The models predict diﬀerent ﬂuxes. Also depends on the mass of the progenitor star. 58 Nν ∼ 10 neutrinos Can provide valuable information about supernova E ∼ 10 − 60 MeV ν physics, neutrino physics. T ∼ 10s Very rare: 1-3/century in our galaxy. Models from arXiv:astro-ph/0604300

Andrey Sheshukov SN detection in NOvA experiment 2 / 21 Supernova neutrino signal Introduction Coincidence network Signal detection NOvA detectors Results and outlook Detecting supernova neutrinos Supernova triggering system Coincidence network

Many neutrino experiments sensitive to the SN neutrino signal.

Experiments capable of detecting this signal in real time are united in SNEWS coincidence network. Current mode: combining SN trigger signals from experiments. A better approach: combine signal signiﬁcance from various experiments and do meta-analysis. Plans for SNEWS v.2.0

Work towards uniﬁed network with GW detectors. SNEWS: SuperNova Early Warning System

Andrey Sheshukov SN detection in NOvA experiment 3 / 21 Supernova neutrino signal Introduction Coincidence network Signal detection NOvA detectors Results and outlook Detecting supernova neutrinos Supernova triggering system NOvA detectors

Main goal of the NOvA experiment: study neutrino oscillations in the muon (anti-)neutrino beam, with hEν i = 2 GeV.

NOvA detectors are not ideal for the supernova signal detection (high background! designed for higher neutrino energies) but can still make a valuable contribution to SNEWS. Similar structure ⇒ almost the same reconstruction and data processing, Diﬀerent size and overburden ⇒ very diﬀerent BG conditions, statistics.

Andrey Sheshukov SN detection in NOvA experiment 4 / 21 Supernova neutrino signal Introduction Coincidence network Signal detection NOvA detectors Results and outlook Detecting supernova neutrinos Supernova triggering system Detecting supernova neutrinos

+ Main detection channel:ν ¯e + p → e + n.

NOvA Simulation NOvA Preliminary 40 Candidates from 9.6Msun SN @ 10 3.0 35 Candidates from 27Msun SN @ 10

30 2.5

25 2.0

20 1.5 299.46 15 1.0 Efficiency ,% Candidates/5ms

10 0.5 86.91 5 0.0 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 0 time, s 0 10 20 30 40 50 60 NOvA Preliminary Pe + , MeV Candidates from 9.6Msun SN @ 10 0.04 Candidates from 27Msun SN @ 10

Nbg Nsg @10kpc 0.03 FarDet 2483.21 86.91 0.02 NearDet 0.52 1.28 4.30 Candidates/5ms 0.01 Table: Expected number of candidates 1.28 from the ﬁrst second of SN, after the 0.00 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 reconstruction and selection procedures time, s

Andrey Sheshukov SN detection in NOvA experiment 5 / 21 Supernova neutrino signal Introduction Coincidence network Signal detection NOvA detectors Results and outlook Detecting supernova neutrinos Supernova triggering system Supernova triggering system

A dedicated triggering system was deployed on NOvA detectors. Characterized by: False trigger rate α Detection eﬃciency for particular supernova signal (model, distance) Reaction time.

We need to process the data ﬂow on-line: Reconstruction of neutrino interaction candidates performed in real time: more than 1800 parallel processes for 5ms data slices. Statistical analysis of interactions rate: algorithms should be computationally simple and robust.

Andrey Sheshukov SN detection in NOvA experiment 6 / 21 Analyzing time series Introduction Hypothesis testing, signiﬁcance Signal detection Simple example: using number of candidates in 1s Results and outlook Using signal shape: log likelihood ratio Analyzing time series

Input data from the candidates selection: time series

ni = bi + si

NOvA Preliminary Sg+Bg candidates 25 Signal from 9.6M SN @ 5.0 kpc Bg candidates 20 Sg candidates

15 Average background 10

candidates/5ms 5

0 0 5 10 15 20 25 30 35 40 45 Time, s

The triggering system needs to distinguish between the ”background only” H0 and ”background+signal” H1 hypotheses, using data within a sliding time window n~ = {ni }

Andrey Sheshukov SN detection in NOvA experiment 7 / 21 Analyzing time series Introduction Hypothesis testing, signiﬁcance Signal detection Simple example: using number of candidates in 1s Results and outlook Using signal shape: log likelihood ratio Hypothesis testing, signiﬁcance

In general: use some test statistics function X (n~) to discriminate between the hypotheses. We then need to know how the X (n~) is distributed in case of each hypothesis is true: P(X |H0), P(X |H1) The signal signiﬁcance is characterized by p-value:

∞ Z p(X (n~)) = P(x|H0)dx X (~n)

We convert signiﬁcance in ”sigmas” for convenience:

1 − p(x) z(x) = erf−1 2

Trigger fires if significance exceeds threshold (whatever definition we use):

−9 α = 1/week ⇐⇒ pthr = 8.267 · 10 /5ms ⇐⇒ zthr = 5.645σ

Andrey Sheshukov SN detection in NOvA experiment 8 / 21 Analyzing time series Introduction Hypothesis testing, signiﬁcance Signal detection Simple example: using number of candidates in 1s Results and outlook Using signal shape: log likelihood ratio Simple example: using number of candidates in 1s

We can use number of candidates in 1s 200 P Nbg Nsg @10kpc time window: N = ni i=0 FarDet 2483.21 86.91 Assuming N to have Poisson distribution around the average numbers from table, Table: Expected number of candidates from the we can have the distributions fortest ﬁrst second of SN statistics P(X |H0,1)

0 NOvA Preliminary 0 NOvA Preliminary 0 NOvA Preliminary 10 thr=2770 10 thr=8.27e-09 10 thr=5.662 H0: Bg only H0: Bg only H0: Bg only

H1: Bg+SN @ 5kpc H1: Bg+SN @ 5kpc H1: Bg+SN @ 5kpc 10 2 10 2 10 2

10 4 10 4 10 4

10 6 10 6 10 6 p.d.f p.d.f p.d.f

8 10 8 10 8 10

10 10 10 10 10 10

12 12 10 12 10 10 46 40 34 28 22 16 10 4 2200 2400 2600 2800 3000 3200 10 10 10 10 10 10 10 10 5 0 5 10 15 N candidates p-value significance,

Probability to detect the SN @ 5kpc distance in FarDet is 86.46%, with α =1/week

Andrey Sheshukov SN detection in NOvA experiment 9 / 21 Analyzing time series Introduction Hypothesis testing, signiﬁcance Signal detection Simple example: using number of candidates in 1s Results and outlook Using signal shape: log likelihood ratio Simple example: using number of candidates in 1s

We can use number of candidates in 1s 200 P Nbg Nsg @10kpc time window: N = ni i=0 NearDet 0.52 1.28 Assuming N to have Poisson distribution around the average numbers from table, Table: Expected number of candidates from the we can have the distributions fortest ﬁrst second of SN statistics P(X |H0,1)

0 NOvA Preliminary 0 NOvA Preliminary 0 NOvA Preliminary 10 thr=8 10 thr=8.27e-09 10 thr=5.743 H0: Bg only H0: Bg only H0: Bg only

H1: Bg+SN @ 5kpc H1: Bg+SN @ 5kpc H1: Bg+SN @ 5kpc 10 2 10 2 10 2

10 4 10 4 10 4

10 6 10 6 10 6 p.d.f p.d.f p.d.f

8 10 8 10 8 10

10 10 10 10 10 10

12 12 10 12 10 10 46 40 34 28 22 16 10 4 0 5 10 15 20 25 30 10 10 10 10 10 10 10 10 0 2 4 6 8 10 12 14 N candidates p-value significance,

Probability to detect the SN @ 5kpc distance in NearDet is 11.66%, with α =1/week

We can gain more sensitivity, if we use the information about the expected signal shape vs time.

NOvA Preliminary Number of candidates n in each of 5ms Candidates from 9.6Msun SN @ 10 i 3.0 Candidates from 27Msun SN @ 10 time bins should have Poisson distribution: 2.5

2.0 ni −B P(ni |H0) =B · e /ni ! 1.5

1.0 299.46

n −(B+S ) Candidates/5ms (B + Si ) i · e i P(n |H ) = 0.5 i 1 86.91 ni ! 0.0 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 time, s The average background rate per 5ms B is The average signal candidates rate per 5ms constant. Si , varying with the time bin i (FD). BFD = 12.42 cands/5ms.

Log likelihood ratio P(n~|H1) X Si X `(n~) ≡ log = ni · log 1 + − Si P(n~|H ) B 0 i i

Andrey Sheshukov SN detection in NOvA experiment 10 / 21 Analyzing time series Introduction Hypothesis testing, signiﬁcance Signal detection Simple example: using number of candidates in 1s Results and outlook Using signal shape: log likelihood ratio Log likelihood ratio (contd)

We can use ` as test statistics for hypothesis testing. P The constant shift Si is not important and can be omitted:

Log likelihood ratio X Si `(n~) = ni · Ai , where Ai = log 1 + B i

Very convenient for real-time computation: A linear combination of the data in considered time window. For trigger we want a sliding time window - this becomes a convolution of incoming data ni with the kernel Aˆ.

Next, we need to know the distributions: P(`|H0,1) But a linear combination of Poisson random numbers ni is not Poisson (in general). We still can calculate the distribution P(`|H) in two speciﬁc cases.

Andrey Sheshukov SN detection in NOvA experiment 11 / 21 Analyzing time series Introduction Hypothesis testing, signiﬁcance Signal detection Simple example: using number of candidates in 1s Results and outlook Using signal shape: log likelihood ratio Log likelihood ratio distributions: high background

If the background B in the time bin is high enough, ni can be considered normally distributed: p P(ni |H1) =N (µ = B + Si , σ = B + Si )

and linear combination of normal random variables is also normal:   s X X 2 P(`|H1) = N µ = (B + Si ) · Ai , σ = (B + Si ) · Ai  i i

This case can be applied to Far Detector, if we make the time bins large enough: for δt = 50ms, B = 124.2

H0: Bg only

0.003 H1: Bg+SN @ 5kpc

0.002 p.d.f

0.001

0.000 175 180 185 190 195 200 205 210 Log Likelihood Ratio,

Andrey Sheshukov SN detection in NOvA experiment 12 / 21 Analyzing time series Introduction Hypothesis testing, signiﬁcance Signal detection Simple example: using number of candidates in 1s Results and outlook Using signal shape: log likelihood ratio Log likelihood ratio distributions: low background P Consider total number of candidates in time window N = ni .

B 1.5 / i S

+ 1.0 1 = i 0.5 A

0.0 P( |1) 0 500 1000 time bin number, i

P(`|N + 1): ` = `N + Ai ⇒ P(`|N + 1) = P(`|N) ∗ P(`|1)

Andrey Sheshukov SN detection in NOvA experiment 13 / 21 Analyzing time series Introduction Hypothesis testing, signiﬁcance Signal detection Simple example: using number of candidates in 1s Results and outlook Using signal shape: log likelihood ratio Log likelihood ratio distribution: low background (continued) ) 0 | ( P

Log Likelihood Ratio, ) 1 | Summing up with correct Poisson probability P(N|H ) we get

( 0 P the result distribution. Log Likelihood Ratio, ) 2 |

( This is the mode for the Near Detector. Average background P rate is 0.5 candidates/sec. Log Likelihood Ratio, ) 3 | (

P This procedure is rather fast. It is done every time the

Log Likelihood Ratio, background level is measured (every 10 minutes) ) 4 | ( P

0 1 2 3 4 5 6 7 Log Likelihood Ratio,

H0: Bg only 0.06 H1: Bg+SN @ 5kpc

0.04 p.d.f

0.02

0.00 0 5 10 15 20 25 30 Log Likelihood Ratio, Andrey Sheshukov SN detection in NOvA experiment 14 / 21 Example: triggering on Far Detector Introduction Signiﬁcance vs. distance Signal detection Combining detectors Results and outlook Summary Example: triggering on Far Detector

NOvA Preliminary Signal from 9.6M SN @ 5.0 kpc Sg+Bg candidates Bg candidates 20 Sg candidates Average background 10 candidates/5ms

0 Maximum = 7.69 Expected signal Model independent

, Threshold e

c 5 n a c i f i n g

i 0 S

10 Maximum = 8.36 Expected signal SN from 9.6M star

e Threshold c

n 5 a c i f i n g i 0 S

10 Maximum = 8.24 Expected signal SN from 27M star

e Threshold c

n 5 a c i f i n g

i 0 S

0 5 10 15 20 25 30 35 40 45 Time, s

Andrey Sheshukov SN detection in NOvA experiment 15 / 21 Example: triggering on Far Detector Introduction Signiﬁcance vs. distance Signal detection Combining detectors Results and outlook Summary Signiﬁcance vs. distance

10 Expected signal Model independent 1s 8

e 6 5.53 kpc 10.27 kpc c

n 1/week

a 1/day c i

f 1/hour i

n 4

g 1/minute i S 1/second 2

Diﬀerent expected signal shapes Si . 0 10 Expected signal SN from 9.6M star And we can get the unexpected signal 8

˜ , Si , diﬀerent from Si . e 6 6.15 kpc 10.45 kpc c

n 1/week

a 1/day c i

f 1/hour i

n 4

g 1/minute i S Note: when Si is ﬂat, we get 1/second P 2 ` ∼ ni , i.e. get the simple triggering 0 on the Ncands in a time window. 10 Expected signal SN from 27M star 8

e 6 5.86 kpc 11.10 kpc c

n 1/week

a 1/day c i

f 1/hour i

n 4

g 1/minute i S 1/second 2

0 0 2 4 6 8 10 12 14 Distance to SN, kpc Signiﬁcance in the Far detector.

Andrey Sheshukov SN detection in NOvA experiment 16 / 21 Example: triggering on Far Detector Introduction Signiﬁcance vs. distance Signal detection Combining detectors Results and outlook Summary Signiﬁcance vs. distance

10 Expected signal: Model independent 1s 8

e 6 3.75 kpc 6.90 kpc c

n 1/week a 1/day c i f

i 1/hour

n 4 g

i 1/minute S 1/second Diﬀerent expected signal shapes Si . 2

0 And we can get the unexpected signal 10 Expected signal: ˜ SN from 9.6M star Si , diﬀerent from Si . 8

e 6 4.80 kpc 8.01 kpc c

n 1/week a 1/day c i f

i 1/hour

Note: when S is ﬂat, we get n 4

i g

i 1/minute P S 1/second ` ∼ ni , i.e. get the simple triggering 2 on the N in a time window. cands 0 10 Expected signal: SN from 27M star ”Steps” from Poisson distribution are 8

e 6 4.70 kpc 8.18 kpc c visible n 1/week a 1/day c i f

i 1/hour

n 4 g

i 1/minute S 1/second 2

0 0 2 4 6 8 10 12 Distance to SN, kpc Signiﬁcance in the Near detector.

Currently the detectors perform hypothesis test separately. If we can get the synchronized signiﬁcance scores from both detectors, we can perform meta-analysis using these two parameters.

NOvA Preliminary We need to deﬁne a combined ”signiﬁcance”, which can then be

used as test statistics: S(znear , zfar ). 8 The threshold on S deﬁnes a region in 6

(znear , z ) space where the trigger far , 1/week

e 1/day occur. c n 1/hour a 4 c i

The ways to deﬁne this function are f 1/minute i n g inﬁnite, depending on what we want: i 1/second s

2 t

Maximize the efficiency for specific e D signal? r a Keep as model independent as F 0 possible? Minimize the data flow between 2 detectors? 2 0 2 4 6 8 NearDet significance,

Andrey Sheshukov SN detection in NOvA experiment 17 / 21 Example: triggering on Far Detector Introduction Signiﬁcance vs. distance Signal detection Combining detectors Results and outlook Summary Combining detectors: examples

The signal (blue distribution) is for 9.6M SN signal at 5 kpc distance. The background (red distribution) integral over the green area is ﬁxed to α =1/week Detectors triggering separately:

NOvA Preliminary NOvA Preliminary FD only: ND only: 66.32% 10.00%

8 8

6 6

, 1/week , 1/week e 1/day e 1/day c c n 1/hour n 1/hour a 4 a 4 c c i i

f 1/minute f 1/minute i i n n g g i 1/second i 1/second s s

2 2 t t e e D D r r a a F 0 F 0

2 2 2 0 2 4 6 8 2 0 2 4 6 8 NearDet significance, NearDet significance,

S = zfar S = znear

Andrey Sheshukov SN detection in NOvA experiment 18 / 21 Example: triggering on Far Detector Introduction Signiﬁcance vs. distance Signal detection Combining detectors Results and outlook Summary Combining detectors: examples

The signal (blue distribution) is for 9.6M SN signal at 5 kpc distance. The background (red distribution) integral over the green area is ﬁxed to α =1/week Trigger signals combined (each detector still makes its own decision, but we combine the results):

NOvA Preliminary NOvA Preliminary FD and ND: FD or ND: 56.60% 65.26%

8 8

6 6

, 1/week , 1/week

e 1/day e 1/day c c

n 1/hour n 1/hour a 4 a 4 c c i i

f 1/minute f 1/minute i i n n g g i 1/second i 1/second s s

2 2 t t e e D D r r a a F 0 F 0

2 2 2 0 2 4 6 8 2 0 2 4 6 8 NearDet significance, NearDet significance,

S = min(zfar , znear ) S = max(zfar , znear )

The signal (blue distribution) is for 9.6M SN signal at 5 kpc distance. The background (red distribution) integral over the green area is fixed to α =1/week Significance combined (significance score collected for every 5ms time bin):

NOvA Preliminary NOvA Preliminary Model Combined: indep.: 92.34% 87.11%

8 8

6 6

, 1/week , 1/week

e 1/day e 1/day c c

n 1/hour n 1/hour a a 4 4 c c i i

f 1/minute

f 1/minute i i n n g g i

i 1/second

1/second s s

2 2 t t e e D D r r a a F F 0 0

2 2 2 0 2 4 6 8 2 0 2 4 6 8 NearDet significance, NearDet significance, q 2 2 S = a · zfar + b · znear S = zfar + znear

Mode S(zfar , znear ) ε for SN @ 6 kpc (9.6M ) Data sent every FD only zfar 66.32% 1 week ND only znear 10.0 % 1 week ND and FD min(zfar , znear ) 56.6% 55 seconds ND or FD max(zfar , znear ) 65.26% 2 weeks q 2 2 Model indep. zfar + znear 87.11% 5 ms Combined a · zfar + b · znear 92.34% 5 ms

Expanding to many experiments network (SNEWS, GWNU): Time synchronization will be worse — larger time windows Need weighted approach, so less sensitive experiments don’t decrease overall sensitivity

Other signals will have a different position in (zfar , znear ). Different detectors sensitive to different signals.

Mode depends on our requirements, and on the range of H1 we want to be sensitive to. It’s hard to stay model independent.

Andrey Sheshukov SN detection in NOvA experiment 19 / 21 Example: triggering on Far Detector Introduction Signiﬁcance vs. distance Signal detection Combining detectors Results and outlook Summary Summary

NOvA detectors require slightly different statistical approaches, because of different conditions. Using the log likelihood ratio to take into account the expected signal shape improves sensitivity. This is model-dependent, but SN neutrino signals have many common features. The calculation of significance is done online. This requires the fast way to calculate P(X |H0,1), NOvA SN triggering system can be considered as a small coincidence network for SN detection. So we can try out various methods of combining the measurements from detectors. We still need to define the most promising strategy. Currently we’re working in the ”OR” mode.

Andrey Sheshukov SN detection in NOvA experiment 20 / 21 SN from 9.6 M star SN from 27 M star 25 = 25% = 25% = 50% = 50% = 99% = 99% 20

Kiloparsec 5

0 NOvA

10 NOvA Preliminary

20 15 10 5 0 5 10 15 20 Kiloparsec