Interactive · Pedagogical tool

What does dark matter look like in a detector?

Dark matter is streaming through you right now — billions of particles a second. The hard part was never getting it into the detector; it's getting a single particle to recoil hard enough, often enough, above threshold, to notice. Slide the controls and watch what actually arrives — the flux through your hand, the spread of halo speeds, and the recoil spectrum a real detector records.

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Swipe: Velocity distribution · Recoil spectrum · σ–mass

What does this plot show?

Lab-frame velocity distribution. The probability that a halo particle is moving at a given speed past you on Earth — the rotation of the galaxy plus the Sun's orbit show up as a shifted Maxwellian, cut off at the galactic escape speed. Only particles in the fast tail (highlighted) carry enough energy to produce a recoil above the detector threshold; everything to the left of the dashed line is too slow to register.

Drag the WIMP mass slider down and the dashed line moves right — light particles need to be moving faster to deposit the same energy, and there are fewer of them out in the tail. That's the threshold cliff.

WIMP mass 100

How heavy each dark-matter particle is. At fixed local density, heavier WIMPs are rarer (fewer per cm³) but each carries more momentum. 40 MeV – 10 TeV

“WIMP” is used here as shorthand — the slider extends to 40 MeV, well outside the canonical thermal-relic weakly-interacting massive particle range. Below ~1 GeV the page is best read as exploring a generic spin-independent contact-interaction dark-matter particle, not a textbook WIMP.

How this control works

Mass enters in three distinct places: it sets the number density n = ρ/m (so light particles are far more numerous at fixed energy density), the WIMP–nucleus reduced mass μ which controls how much energy each collision can transfer, and the minimum halo speed needed to produce a recoil above threshold (lighter particles need to be moving faster).

Cross-section is not in that list — moving mass changes the shape of the recoil spectrum; moving cross-section only changes the vertical scale.

WIMP–nucleon cross-section 10⁻⁴⁵ cm²

How likely a single dark-matter particle is to actually strike a nucleus. This scales the whole recoil spectrum vertically — it doesn't change its shape. Current limits reach ~10⁻⁴⁷ – 10⁻⁴⁸ cm²

How this control works

The per-nucleon cross-section is the simplest knob in the model: the entire dR/dE curve moves up or down by the same factor. The shape — set by mass, target and halo — is unchanged.

That means cross-section only trades expected events against itself. To gain reach you almost always have to do something harder: lower threshold, more exposure, or change targets.

Target nucleus Argon (A=40)

Heavier nuclei get a stronger A² coherent boost for spin-independent scattering, but a light WIMP can't make a heavy nucleus recoil much — like a marble hitting a bowling ball. Light targets (He, Si) catch low-mass WIMPs better.

How this control works

Target changes everything about the recoil spectrum: the kinematic ceiling (heavier nuclei accept smaller maximum recoil energies from a light projectile), the coherent A² enhancement (heavier wins for heavy WIMPs), the Helm form factor (heavier nuclei lose coherence faster as recoil energy rises), and the realistic detector acceptance turn-on shape (loaded per target in beginner mode).

The "right" target depends on what mass you want to catch. There is no universally best choice — which is why argon, xenon, silicon and germanium experiments coexist.

Lower energy cutoff 1 keV

Where the detector's selection efficiency switches on. Below it, nothing is recorded; just above it, acceptance is still climbing (see the ε curve on the plot's right axis). The single sharpest lever on low-mass reach. DS-50 ≈ 13 keV ‖ LZ ≈ 5 keV ‖ cryogenic ≈ 0.05 keV

How this control works

The lower energy cutoff is where events first become selectable — efficiency is zero below it. The separate halfway-to-plateau energy (advanced mode) controls how fast the detector then becomes efficient: a lower halfway means a sharper turn-on, a higher one means the detector wakes up gradually. The two together define the shape of the acceptance ε(E) curve you see on the recoil plot.

In beginner mode they move together so the per-target acceptance shape stays realistic. Advanced mode lets you separate them, e.g. to model a detector with a soft turn-on tail extending below the nominal threshold.

Halfway-to-plateau energy 8 keV

Energy at which the acceptance reaches half its plateau — it sets how gradually the turn-on rises from the cutoff. Must stay above the cutoff. Selecting a target loads its real turn-on; drag to explore.

Plateau efficiency 90 %

The best acceptance the detector ever reaches, well above the turn-on. Cuts, fiducialisation and reconstruction losses keep this below 100%. Xenon TPCs ≈ 90% ‖ argon (DS-50-style) ≈ 30%

Exposure 1 t·yr

Detector mass × running time. Sets how many recoils you expect to count. DS-50 ≈ 0.05 t·yr ‖ LZ ≈ 4.2 t·yr ‖ DS-20k ≈ 200 t·yr

Background rate 0.1 /(keV·t·yr)

Events that look like a WIMP recoil but aren't — radio-impurities, neutrons, neutrinos. Feeds the "run the experiment" toy below.

Local dark-matter density 0.3 GeV/cm³

The mass of dark matter per cm³ near the Sun. Number density follows as n = ρ / m, so this sets the flux. Measured ≈ 0.3–0.4 GeV/cm³

Halo speed (v₀) 220 km/s

The width of the Maxwell-Boltzmann speed distribution (the rotation speed of the galaxy here). Faster WIMPs carry more energy, raising the recoil tail.

Galactic escape speed 544 km/s

The fastest a bound WIMP can move — the distribution is cut off here. It sets the highest recoil energy possible at a given mass.

Nuclear structure On

At high recoil energy the WIMP's de Broglie wavelength resolves the nucleus, so the coherent A² enhancement fades (the Helm form factor). Turn it off to see the idealised point-nucleus spectrum.

How much is passing through you

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Number density

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Reduced mass μ

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Max recoil energy

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Recoils detected (acceptance-weighted)

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Mass matching — WIMP vs nucleus

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Would this detector see it?

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What each control changes

A glance-table connecting the sliders to the physics. The shape of the recoil spectrum is set by mass, target and halo; cross-section is just a vertical scale. Threshold and exposure act on the detected counts, not the underlying spectrum.

Control	What it changes
WIMP mass	Spectrum shape: kinematic ceiling, peak position, low-energy fall-off. Plus the flux per kg of dark matter.
Cross-section	Vertical scaling only. Up or down by the same factor at every energy — never the shape.
Target nucleus	Everything kinematic: the A² coherent boost, the form-factor falloff, the maximum recoil energy, and the realistic acceptance turn-on shape.
Recoil threshold	The detected fraction only. The underlying spectrum is unchanged; the threshold just decides where ε(E) switches on.
Exposure (advanced)	Counts only. Total events scale linearly. Background and statistical noise scale with it too — see the toy below.
Background (advanced)	Discovery significance only. Doesn't change signal at all; only how easy the signal is to see against noise.
Local density ρ (advanced)	Overall normalisation: sets flux and rate. Doesn't affect spectrum shape at all.
Halo speeds v₀, v_esc (advanced)	Spectrum shape at the tail. Faster halo widens the velocity distribution, fattens the recoil tail, and raises the kinematic ceiling.

Run the experiment

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What does 3σ / 5σ mean?

Significance Z measures how far the observed event count sits above what background alone would produce, in units of the background's own statistical noise: Z = (N_obs − N_bg) / √N_bg. The bigger Z, the harder the observation is to explain as a fluctuation.

Particle physics uses two conventions: Z ≥ 3σ ("evidence" — roughly a 1-in-740 fluctuation, looking only at this measurement) and Z ≥ 5σ ("discovery" — roughly 1-in-3.5 million). Even a 5σ excess is only saying something is producing events beyond background. Telling a WIMP from a mis-modelled background or another rare process needs the recoil energy spectrum to match the prediction, and ideally a second independent experiment.

Press Run once to draw one experiment with this exposure.

Jump to a scenario

Companion tool

How do we hunt for dark matter? →

This page shows what arrives. The sensitivity explorer shows how deep a detector can reach — slide thresholds, exposure, background and depth against the world's leading limits.

The story in six parts

01An enormous flux

With the local density fixed at ~0.3 GeV/cm³, a light WIMP means billions of particles streaming through your hand every second. The challenge was never getting dark matter into the detector — it's already everywhere — it's getting one particle to interact.

02Only the fast tail counts

The velocity-distribution plot shades the part of the halo fast enough to produce a recoil above your threshold. Raise the threshold or lower the WIMP mass and that shaded sliver shrinks — sometimes to nothing. That is why low-mass dark matter is so hard.

03The recoil spectrum

The central plot is the energy spectrum of nuclear recoils, dR/dE. It falls steeply — most recoils are soft. The grey region sits below threshold and is invisible; the cross-section slider scales the whole curve up and down without changing its shape.

04Mass matching

Energy transfer is governed by the WIMP–nucleus reduced mass. A light WIMP barely nudges a heavy xenon nucleus; a heavy WIMP can recoil anything. The mass-matching meter shows how well your WIMP and target are tuned to each other.

05S1, S2 and what a detector records

A nucleus struck by a WIMP recoils and deposits energy. How that energy is read out depends on the detector: a dual-phase argon or xenon TPC sees prompt scintillation (S1) and delayed ionisation (S2), and their ratio separates nuclear from electron recoils; cryogenic germanium and silicon read phonons plus ionisation instead. The recoil spectrum is the same physics — the signatures differ by technology.

06One event isn't a discovery

Press Run the experiment and the expected counts become a random Poisson draw of signal and background. Run it a hundred times and watch the spread. A single event proves nothing — that statistical fluctuation is why claiming a discovery takes far more than seeing one recoil.

Model & assumptions

Physics model used

Calculations use the Standard Halo Model (a truncated Maxwell-Boltzmann speed distribution with the Earth's motion through the halo and a galactic escape cut-off), Helm nuclear form factors, and standard spin-independent WIMP–nucleus recoil kinematics. The same engine drives the companion sensitivity explorer, so the two pages stay physically consistent.

The differential rate dR/dE, the flux, the number density n = ρ/m, the maximum recoil energy and the acceptance-weighted detected fraction are all computed live from the slider values.

Detector acceptance ε(E)

Each target carries a selection-efficiency turn-on ε(E): zero below a lower cutoff, rising through a halfway energy as a smooth error-function (erf), and flattening to a plateau — the three numbers advanced mode exposes. This is what stops the model from over-counting the soft recoils a real detector never actually selects.

The per-target baselines load automatically in beginner mode (xenon ≈ LZ-like, argon ≈ DarkSide-50-like and reused for DarkSide-20k, He/Si/Ge as cryogenic-style sharp turn-ons). Advanced mode lets you separate cutoff, halfway energy and plateau to study how a soft turn-on tail or a low plateau affect reach.

Normalisation: semi-empirical, not first-principles

The spectral shape dR/dE is computed from standard recoil kinematics and halo assumptions. The absolute normalisation is a calibrated constant (K_RATE in the code), anchored so that an LZ-like configuration on xenon recovers the published 2.1×10⁻⁴⁸ cm² minimum at 40 GeV (arXiv:2410.17036, 4.2 t·yr). Per-target acceptance baselines are tuned in the same spirit.

This is therefore a semi-empirical rate engine, not an independent absolute-rate calculation. Absolute event counts should be read as pedagogical scale estimates. With those anchors in place, the model's recovered 90% C.L. cross-section tracks published limits at key masses: LZ within a factor of 2.3× from 10 GeV to 1 TeV, DarkSide-20k within 1.4× of its projection, and DarkSide-50 within ~2×. Exposure, threshold and target scalings all reproduce the expected trends (limit ∝ 1/exposure when background-free, the low-mass threshold cliff, the A² and light-target preferences).

What this does not include

The page models a single spin-independent contact interaction. Spin-dependent, light-mediator, momentum- or velocity-suppressed operators all give different recoil-spectrum shapes for the same nominal cross-section and are out of scope here.

The recoil pane shows the true recoil-energy spectrum convolved with detector acceptance, but not with energy resolution. The "Run the experiment" toy treats signal and background as Poisson counts in one energy bin — i.e. it ignores spectral-shape information that a real analysis would use to separate signal from background. Profile-likelihood, S2-only / Migdal channels and annual modulation are also outside scope; the sensitivity explorer covers the first two.

Why real analyses differ from this counting model

Published limits and projections use shape-likelihood fits that exploit the full predicted dR/dE versus a background model with its own spectral shape — that distinguishes signal from background per event, not just by counting. At the DS-20k preset the counting model here sits within a factor of ~1.4× of the published projection at high mass; at sub-GeV mass in dedicated S2-only / Migdal analyses the gap can be larger because shape information becomes very powerful.

The qualitative lessons this page is built to convey — the huge flux, the steep recoil spectrum, the acceptance turn-on, the threshold cliff, WIMP–nucleus mass matching, and the role of statistical fluctuation — are robust to these refinements.