A gravitational-wave detector's sensitivity curve looks like a property of the machine. It is closer to a laboratory result: produced by a calibration chain, quoted with uncertainties, and revised when the chain changes. The noise budget behind that curve rests on choices about how strain is inferred from light, and those choices carry error bars that propagate into every astrophysical number downstream.

The Noise Floor Is a Calibration Artifact

Detector sensitivity is usually quoted as an intrinsic figure, a strain amplitude per root hertz at which signals become distinguishable from noise. That figure is not read off a dial. It is reconstructed from a model that converts a measured differential arm-length signal into strain, dividing by the arm length and correcting for the response of the mirrors, suspensions, and readout electronics.

Change the actuation model, the timing reference, or the treatment of a cross-coupled auxiliary channel, and the same raw data yields a slightly different strain curve. The shift is small, typically at the level of a few percent in amplitude across the sensitive band, but gravitational-wave inference is sensitive to exactly that scale. A distance estimate scales roughly linearly with strain amplitude, so a calibration offset of a few percent moves a quoted luminosity distance by a comparable amount.

Two conventions get conflated in casual reading. Displacement noise is what the interferometer physically measures, in metres per root hertz. Strain noise is displacement noise divided by arm length, and it is the quantity compared against theoretical waveforms. The division looks trivial. It is not, because the effective arm length in a folded cavity is not simply the physical length, and the calibration must account for the optical response.

How Interferometers Turn Light Into Strain

A laser interferometer splits light into two perpendicular arms and recombines it. In the current generation, each arm holds a Fabry-Perot cavity so the light traverses the arm many times, amplifying the phase shift a passing wave induces. The readout is differential: a gravitational wave stretches one arm while compressing the other, and the photodiode sees the beat between the two returning fields.

Power recycling adds a mirror between the laser and the beam splitter to build up circulating power; signal recycling tunes the response near the frequencies of interest. KAGRA, the underground Japanese detector with 3-km arms, adds cryogenic mirrors to reduce thermal noise. LIGO and Virgo run at room temperature with larger suspended optics. Each configuration produces a different optical response function, which the calibration must model.

The folded-cavity geometry deserves its own note, because it sets how much a passing wave is amplified before the photodiode ever sees it. Light bounces back and forth inside each arm hundreds of times, so the phase accumulated per pass adds coherently while the storage time also low-passes the detector's response: the instrument is more sensitive to slow swings in arm length than to fast ones. That frequency dependence is not a nuisance to be corrected away at the end. It is built into the transfer function the calibration is trying to recover, and an error in the assumed storage time tilts the whole curve rather than shifting it uniformly.

Calibration lines are injected continuously to track that response. A known sinusoidal or swept signal is applied to the mirrors through the actuation chain, and its appearance in the readout measures the transfer function from actuation to strain in real time. The precision of the calibration is therefore bounded by how well the actuation itself is known.

Where the Budget Lines Come From

The noise budget is a stack of contributions plotted against frequency. At high frequency, quantum shot noise dominates: the statistical fluctuation in photon arrival at the photodiode. At low frequency, radiation pressure noise from the same photons pushes the mirrors, and seismic noise enters through the suspension. Between them sit thermal noise sources, including coating Brownian noise in the mirror dielectric stacks and suspension violin modes.

Each line in the stack is a model, not a direct measurement. Coating thermal noise, for instance, depends on the mechanical loss angle of the deposited layers, a parameter measured on witness samples rather than on the actual mirrors. A related piece on this site about fabrication steps accumulating in superconducting qubits makes a comparable point: process detail that never appears in the headline number sets the real limit.

Witness samples are the quiet vulnerability in that stack. A coating deposited on a small test substrate in the same chamber as the mirror is assumed to share its loss angle, and usually it does to within the measurement scatter. The assumption holds only as long as the process is reproducible run to run, and coating chambers are not perfectly repeatable instruments. A small drift in deposition conditions can move the loss angle by an amount comparable to the uncertainty the witness measurement was meant to pin down, and nothing in the published budget flags that the sample and the optic diverged.

Auxiliary channels complicate the picture further. Hundreds of sensors monitor alignment, laser frequency, and environmental conditions, and some of that information leaks into the main readout. The budget must account for cross-coupling, and the coupling coefficients are themselves estimated with uncertainty.

Calibration Choices That Move the Budget

Actuation function uncertainty dominates the calibration error budget in most published analyses. The photon calibrator, a separate laser whose radiation pressure is calculable from measured power, provides an independent reference, but its own power measurement and beam profile carry uncertainty. Timing reference drift adds a smaller but non-negligible term.

The photon calibrator is worth dwelling on because it is the closest thing the field has to an absolute standard. Its force on the mirror follows from the laser power and the mirror's reflectivity, both of which can in principle be measured to high precision outside the interferometer. In practice the beam profile at the mirror surface, the fraction of light absorbed rather than reflected, and the alignment of the calibrator beam against the arm axis all enter the systematic budget. The calibrator reduces dependence on the actuation chain without eliminating dependence on metrology.

The choice of calibration standard matters when detectors are combined. A network analysis assumes the individual strain curves are consistent, and a shared systematic between two detectors does not average down the way independent noise does. Long-baseline comparison across LIGO, Virgo, and KAGRA therefore requires an explicit statement of which calibration version was used for each instrument.

There is a real trade-off here. Tighter calibration priors reduce statistical error but risk baking in a systematic that later revisions must undo. Looser priors are more honest but widen every downstream error bar, including the ones that decide whether a marginal event clears a detection threshold.

Ask which calibration standard and version a paper used, and whether the sensitivity curve is the one valid for the analysis segment or an averaged run figure. The two differ, and the difference is usually larger than the statistical error the paper spends most of its words on. Check whether the quoted error bars are marginalized over calibration nuisance parameters or fixed at central values; a fixed calibration is a choice, and it should be stated. Compare the result against an independent detector where one exists, since a signal seen in two instruments with separate calibration chains is stronger evidence than the same signal in one. Treat any quoted sensitivity as conditional on the calibration model, and read the astrophysical error bar as a floor rather than a ceiling.

What the Error Bars Do Not Cover

Quoted calibration uncertainties are typically estimated for stationary noise. Real observing runs are not stationary: scattered light, microseism, and instrumental glitches come and go. A calibration valid on average can be wrong during the minutes that matter, and the published error bar does not usually capture that time dependence.

Glitch populations and the vetoes used to remove them introduce another layer. Vetoes are tuned on the same data used for detection, and the tuning choices affect which events survive. A related piece on this site about code repositories preserving the software results depend on is relevant here: the analysis pipeline version is part of the result.

Calibration priors are also shared across events in a catalogue. Individual event papers may quote marginalized error bars, but the underlying calibration model is common, so the catalogue's errors are not fully independent. Astrophysical inference that treats them as independent will be overconfident, and the effect compounds as catalogues grow: a hundred events with a shared few-percent systematic do not buy a hundredfold improvement in the population-level number.