Astronomy & Celestial Mechanics
the sky, computed
Concept

The Roemer delay — where it appears

The extra time light takes to cross a changing distance, which makes a periodic event appear early or late. It is how Rømer measured the speed of light from Io's eclipses, and it shifts transit and pulsar times when the source or observer moves along the line of sight.

Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.

Three ways for a timing model to be wrong, and three shapes that say which. Timing residuals over 6 years for the Crab pulsar, one curve per kind of error in the model, in microseconds. A position error of 1.2 mas leaves a sinusoid of period exactly one year — measured off the drawn curve as 1.000 — with amplitude (a/c)·δθ·cos β = 2.7 μs, because the error is being projected onto a baseline that is the Earth's own orbit and nothing about the pulsar. An unmodelled proper motion of 0.9 mas/yr leaves the same sinusoid with an envelope growing linearly: twice as large at 6 years as at 3. An error of one part in 10⁹ in Ṗ leaves a parabola, the second integral of a frequency drift, whose second derivative is constant to 4e-12 across the span — and that fractional error is deliberately minute, because anything larger produces a residual thousands of times the other two and draws them as flat lines. The shapes do not resemble each other, which is the whole reason a pulsar is an instrument rather than a clock: fitting them simultaneously delivers a position, a proper motion and — from the annual curvature term, not drawn here — a parallax, all from the arrival times of pulses and no image of anything. What is left when every known shape has been removed is the science: glitches, red noise, and the correlated residual between pairs of pulsars that a timing array exists to find.

A clock read against a model of everything in between

A pulsar delivers arrival times and nothing else. Everything else is a model, and what is measured is the difference between the model and the arrivals — a residual whose shape says which term is wrong, and whose annual sinusoid is a position measured from pulses rather than from an image.

stars · Pulsars One parabola, two causes. Transit times of a planet on a 1.0914-day orbit over 12 years, minus the best straight-line ephemeris, with timing errors of 30 seconds — the shape a period shrinking by 29 milliseconds a year produces, a parabola 116 seconds deep. The curve is drawn once because it is the same curve for both explanations: an orbit decaying at that rate, or a star accelerating towards the observer at 2.9e-6 m/s², which shortens the light-travel time to each successive transit by the same steadily growing amount. Nothing in the transit times can tell them apart.

A clock that slows, or a star that falls

Transit times that curve away from a straight line can mean a planet's orbit is shrinking — the tides draining it into its star — or that the star itself is accelerating along the line of sight under a distant companion's pull. Both draw the same parabola, and the transit times cannot choose. The star's velocities can, but only for the shortest orbits: the acceleration that would fake a given decay grows as one over the period, and beyond a day or two an unseen Saturn can mimic more decay than the tides produce.

exoplanets · Transit timing

Named alongside it

The objects these essays reach for when they reach for this one.

Timing residualApsidal precessionBarycentric correctionDispersion measureGlitchHot jupiterLight-travel timeOrbital decayProper motionA pulsar timing arrayRadial-velocityRed noise

All concepts