Gravitational-Wave Detector Noise Budget

Interferometer Parameters

Laser arm power 800 kW

End-mirror mass 40 kg

Seismic isolation cutoff 10 Hz

Readout frequency cursor 100 Hz

Noise Sources (toggle)

Shot noise Radiation pressure Thermal (suspension) Seismic Reference BNS chirp

Live Readouts

Total strain noise at cursor

— ×10⁻²³ /√Hz

Dominant source at cursor

—

SQL crossing f

— Hz

Est. BNS inspiral SNR

—

How it works

A gravitational-wave interferometer measures a strain h = ΔL/L in two perpendicular kilometre-scale arms. Its sensitivity is set by a noise budget — several independent noise processes added in quadrature into one amplitude spectral density (ASD):

h_total(f) = √( h_shot² + h_rp² + h_th² + h_seis² )

Shot noise — photon-counting statistics at the output port: h_shot ≈ (1/L)·√(ħcλ / 2π²P). Higher laser power P narrows this floor — it dominates at high frequency.
Radiation-pressure (back-action) noise — the same photons randomly kick the mirrors: h_rp ≈ √(8ħP/(cλ)) / (M·L·(2πf)²). It grows with power and falls off as 1/f², and shrinks with heavier mirror mass M — it dominates at low frequency.
Standard Quantum Limit (SQL) — because shot noise falls with power while radiation-pressure noise rises with it, there is one frequency f_SQL where the two are equal; no fixed laser power can beat both at once there. This sim marks that crossing live as you move the power and mass sliders — it is the same quantum trade-off that motivates squeezed-light injection in real detectors (LIGO, Virgo, KAGRA).
Thermal noise — Brownian motion of the mirror-suspension fibres, roughly h_th ∝ 1/(√M·√f); it fills the mid-band "bucket" of the curve.
Seismic noise — ground motion the isolation stack cannot filter below its cutoff frequency f₀; it rises steeply (∝ f⁻⁴) below f₀ and walls off the usable band at low frequency.

The pink dashed curve is a reference binary-neutron-star inspiral's characteristic strain (h_c ∝ f^−7/6, GW170817-like amplitude). Wherever it sits above the total noise curve, that frequency band contributes signal-to-noise; the readout integrates (h_c/h_total)² over the plotted band as a rough SNR estimate — the same principle used to forecast whether a detector design can see a given merger.

All prefactors here are simplified for a single, non-power-recycled Michelson cavity — the shapes and trade-offs are physically real, but real detectors (Fabry-Pérot arm cavities, power/signal recycling, squeezed vacuum) push the curve roughly 2–3 orders of magnitude lower than this teaching model.

Laser / beamsplitter Photon pulses in cavity Mirror jitter (amplified)

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