Neutrinos · D13 · Where did they come from?

Neutrino Sky Search Observatory

Does a neutrino hotspot found by scanning the whole sky count as real evidence? Only if it beats what the search itself would turn up by chance. Run the same scan on many skies that contain background alone and note the brightest hotspot in each. Your hotspot has to stand out against those. Quoting the chance of a fluctuation at one fixed spot overstates the evidence once you have looked everywhere.

Turn a sky map of reconstructed neutrino directions and record a set of events. Follow one event’s uncertainty ring, then test the same hotspot against a short catalog of candidate sources and against a grid of possible locations across the sky.

Frozen directions $0$

Selected direction likelihood $0$

Finite search tail estimate $1$

Search the sky for a neutrino source

Find where the events cluster

Exposure · arbitrary units

t

2\,\mathrm{arb.}

Source mean counts per exposure

r_s

8\,

Recorded angular sigma parameter

\sigma

6\,{}^\circ

Injected source right ascension

\alpha_s

120\,{}^\circ

Injected source declination

\delta_s

0\,{}^\circ

Search the same sky with new settings

Analysis width multiplier

a

1\,

Right-ascension scrambled skies

B

64\,

Choosing the kernel after looking at the sky adds extra trials, and the displayed tail estimate does not count them.

Changes to the acquisition settings take effect on the next new sky. After changing an analysis setting, run the search again. The candidate and the search scope reuse the same paired scrambled skies.

This is a generated teaching sample that contains directions only; it is not IceCube data or raw sensor hits. The background is isotropic, and each event is spread by an exactly normalized spherical kernel. Energy, acceptance and flux are not modeled. The 162-point grid is deliberately coarse and can miss sources. A finite number of right-ascension scrambles calibrates only this fixed search with its chosen kernel. The tail estimates cannot go below a floor set by the number of simulations, and the Lab claims no discovery significance or real source.

Search declared in advanceSelected candidate · same grid

Frozen reconstructed directions

Equal-area direction chart. Every dot is a generated recorded direction. Gold marks the selected grid candidate; white marks the selected event.

Likelihood from those events

Colors scale to this record’s maximum score; cells are nearest-grid display tiles, not interpolated source locations. The fixed coarse grid can miss narrow or off-grid sources. Click a chart or use the candidate selector.

A fairer background comparison

One fixed directionMaximum over searchSelected observed score

Each scramble preserves every declination and angular error, then independently randomizes right ascension. Both histograms use the same scrambled skies.

The local score is only the first question

Candidate RA & declination: $0$
Conditional fitted source count: $0$
Twice log-likelihood ratio: $0$
Local tail estimate: $0$
Finite search tail estimate: $0$
Search exceedances / scrambles: $0$
Candidate positions: $0$
Simulation floor: $0$

The plus-one estimates never reach zero. A local tail means something only for a direction chosen before looking. The search tail accounts for this fixed catalog or grid; it does not cover catalogs, kernels or analyses chosen later. Reaching the simulation floor does not make a discovery.

Each event direction has an uncertainty

Event number 1

Recorded RA & declination: $0$
Distance from candidate: $0$
Assumed 68% kernel radius: $0$

Reveal injected source and event origins

Cyan ring: recorded event kernel. Gold ring: assumed candidate kernel. Exactly 68% spherical containment, not the sigma parameter itself. The celestial sphere and radial guides represent direction space; they are not flight paths or a detector surface.

Accessible candidate likelihood table

Angles in degrees; conditional direction-only fits
Grid	RA	Declination	Fitted count	Score

Full list of recorded directions

Every generated recorded event; angles in degrees
Event	RA	Declination	Sigma parameter

Model, trials & primary sources

Independent Poisson background and source counts grow with arbitrary exposure. Background is uniform in solid angle; source directions follow the normalized von Mises–Fisher kernel. Its concentration is the inverse squared sigma in radians; sigma is a small-angle tangent-plane width, not a containment radius. Source coordinates and component labels are used only for generation and optional truth displays.

Condition on the recorded event total. Fit only a nonnegative source fraction at each fixed direction using a uniform background. No energy, spectral index, time, declination acceptance, atmospheric composition, Earth absorption or real telescope response. Event error estimates are ideal and known. An incorrect analysis width still receives its own conditional scramble calibration; that does not calibrate a fitted flux or source count uncertainty.

The right-handed frame has north upward, zero right ascension along the first horizontal axis and 90-degree right ascension along the negative third axis. The 18 by 9 grid is uniform in right ascension and sine declination, with the poles omitted. All scans and scramble scores are retained in CSV; estimates use one plus the exceedance count divided by one plus the trial total. Limited permutations give noisy estimates and a hard floor, not a Gaussian significance or a confidence interval. Repeated exposure or post-hoc search choices add uncounted trials.

First: reconstruct one track →Explore the worldwide history →

Start with the essentials

Focus question: Would a sky with only background look at least this interesting somewhere?
One-sentence intuition: If you pick a direction after scanning, compare it with the best spot the same search finds in background-only skies.

Core mathematical model

Spread of one event’s direction on the sphere

S(\mathbf n\mid\mathbf s)=\frac{\kappa e^{\kappa(\mathbf n\cdot\mathbf s-1)}}{2\pi(1-e^{-2\kappa})}

The kernel integrates to one over the whole sphere. Its concentration is one over the square of the angular spread, measured in radians.

Likelihood for a source plus background

\mathcal L(f)=\prod_i\left[fS_i+(1-f)B_i\right]

The total number of events is taken as given. Only the source fraction, which cannot be negative, is fitted; the background is uniform in solid angle.

Test statistic for one direction

T=2\ln\frac{\mathcal L(\widehat f)}{\mathcal L(0)}

The score is computed at every grid position declared in advance. A large score is not by itself a calibrated probability of discovery.

Chance probability for the whole search

\widehat p_{\mathrm{search}}=\frac{1+\sum_{b=1}^{B}\mathbf1[T_{b,\max}\geq T_{\mathrm{selected}}]}{B+1}

The same right-ascension scrambles also give the local tail at each spot. With a finite number of scrambles the estimate has a floor, and kernel or catalog choices made later are not accounted for.

Common difficulties

Reconstructed directions are not raw data

Typical misconceptionThese points are original IceCube sensor hits.

Better mental modelThey are generated estimates of reconstructed directions. The earlier track Lab shows how the detector gets from sensor hits to a direction.

Hitting the simulation floor is not a discovery

Typical misconceptionIf no scrambled sky beats the observed score, the significance must be enormous.

Better mental modelWith a finite number of scrambles, the plus-one estimate cannot go below its floor, and it gives no significance in Gaussian sigmas.

Run the experiment

01
Follow one direction
Select an event, turn the sphere and open the candidate view.
What to observe: The event’s kernel is drawn as a ring on the sphere that encloses 68% of its probability. A reconstructed direction is not an exact source position.
02
Search more places
Keep candidate 78 and switch between the three candidates and the 162-point grid.
What to observe: The local score and local tail stay the same. Searching more places can only raise the chance, at that same threshold, that background beats it somewhere.
03
Find a background hotspot
Choose Background only, then go to the hottest point.
What to observe: That spot can have a small local tail while the tail for the whole search is ordinary, because the spot was picked after looking.
04
Test the grid and the kernel width
Try Between grid points or Wide directions. Then change Analysis width multiplier and run the search without acquiring again.
What to observe: A coarse grid or the wrong kernel can miss a source. If you make those choices after looking at the data, they count as extra trials.

Neutrino Sky Search Observatory

How lucky is this sky?

Frozen reconstructed directions

Likelihood from those events

A fairer background comparison

The local score is only the first question

Each event direction has an uncertainty

One hotspot, many opportunities

Core mathematical model

Spread of one event’s direction on the sphere

Likelihood for a source plus background

Test statistic for one direction

Chance probability for the whole search

Common difficulties

Reconstructed directions are not raw data

Hitting the simulation floor is not a discovery

Run the experiment

Follow one direction

Search more places

Find a background hotspot

Test the grid and the kernel width

Related experiments and articles

How detectors see a neutrino

Build a new way to observe the sky

Read evidence, data and worldwide contributions