Neutrinos · D13 · Where did they come from?

Neutrino Sky Search Observatory

Orbit a sky of reconstructed neutrino directions. Freeze the events, follow an angular uncertainty ring and test the same hotspot against a small catalog or a whole grid of possible locations.

Frozen directions $0$

Selected direction likelihood $0$

Finite search tail estimate $1$

ACQUIRE · FREEZE · SEARCH

Find a direction.

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

QUESTION THE SAME SKY

Analysis width multiplier

a

1\,

Right-ascension scrambled skies

B

64\,

A kernel chosen after seeing the sky creates additional trials. These are not included in the displayed tail estimate.

Acquisition changes need a new sky. Run search after changing analysis settings. Candidate and scope reuse the same paired scrambles.

Generated direction-only teaching sample, not IceCube data or raw sensor hits. Isotropic background and an exactly normalized spherical kernel; no energy, acceptance or flux model. The 162-point grid is deliberately coarse and can miss sources. Finite right-ascension scrambles calibrate only this fixed search and its chosen kernel. Tail estimates have a simulation floor; no discovery significance or real-source claim.

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.

Local 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: $0$

Plus-one estimates never equal zero. A local tail is meaningful only for a direction fixed before looking. The search tail accounts for this fixed catalog or grid, not later catalog, kernel or analysis choices. Reaching the simulation floor does not establish a discovery.

One 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

Accessible full recorded direction list

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 →

CONTINUE EXPLORING

From flavor to evidence

Propagation predicts a flavor probability. Which parts of the experiment turn an interaction into a usable record?

Start with the essentials

Focus question: Would a background sky look at least this interesting somewhere?
One-sentence intuition: A direction selected after a scan needs a comparison with the maximum of the same search on background skies.

Core mathematical model

A normalized sphere

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

The spherical kernel integrates to one in solid angle; concentration is the inverse squared angular sigma in radians.

Fit a mixture

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

The total event count is conditioned on. Only the nonnegative source fraction is fitted; background is uniform in solid angle.

One direction at a time

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

Evaluate every predeclared grid position. A large score is not itself a calibrated discovery probability.

Ask about 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 local tails. Finite estimates have a floor; later kernel or catalog choices are not included.

Common difficulties

Reconstructed does not mean raw

Typical misconceptionThese points are original IceCube sensor hits.

Better mental modelThey are generated reconstructed direction estimates; the earlier track Lab covers the detector measurement chain.

The simulation floor is not a discovery

Typical misconceptionZero scrambled exceedances proves an enormous significance.

Better mental modelThe finite plus-one estimate stops at its simulation floor and provides no Gaussian sigma claim.

Run the experiment

01
Follow one direction
Select an event, orbit the sphere and inspect the candidate view.
What to observe: The event kernel has a 68% spherical ring. A direction is not an exact source position.
02
Pay for more places
Keep candidate 78 and switch between three candidates and the 162-point grid.
What to observe: Local score and local tail stay fixed. A larger search can only raise its paired maximum tail at that same threshold.
03
Find a background hotspot
Choose background only, then go to the hottest point.
What to observe: A small local tail can coexist with an ordinary search tail. It was selected after looking.
04
Question the grid and width
Try between-grid-points or wide directions; change analysis width and run search without acquiring.
What to observe: A coarse grid or a misspecified kernel can lose a source. Those choices add trials if chosen after inspection.