Concept

Binary pulsar — where it appears

A pulsar in orbit with a compact companion, whose pulse arrival times turn the orbit into a measurement good to nanoseconds. The measurement is made by counting pulses rather than by resolving anything, and it works because the clock at the far end is stable to a part in a thousand million million.

Named by 5 essays across 2 fields — each of them below, with the objects they name alongside it.

Mercury's perihelion, term by term. The observed advance of Mercury's perihelion is 5600 arcseconds per century against the equinox. Almost all of it is the equinox: the coordinate frame itself turns, and removing it leaves 574. Subtracting the perturbations of the other planets — computed by Le Verrier in 1859 and refined many times since — leaves 42.98 arcseconds a century that nothing in Newtonian gravitation accounts for. The bars are logarithmic in nothing; they are the real proportions, which is why the residual is barely visible beside the frame term.

Forty-three arcseconds, after everything else

Mercury's perihelion moves through 5,600 arcseconds a century. Nearly all of that is the coordinate system turning, and almost all of the rest is the other planets. What was left over was 43 — under one per cent of the raw number, and the most consequential residual in the history of the subject.

gravitation · Relativistic orbits

PSR B1913+16: 45 years of periastron arriving 88 seconds early. The cumulative shift of periastron passage for PSR B1913+16, Δt = ½(Ṗ_b/P_b)T², over 45 years from its discovery in 1975. The orbital period is 0.322997449 days and is measured to be shortening at 2.423e-12 seconds per second — a change in the twelfth decimal place, which over a career accumulates to 87.5 seconds. That is the whole reason the effect is measurable. Ṗ_b is taken here as a measured quantity and no radiated power is derived from it; the parabola is the general-relativistic prediction as published, and the points are that prediction scaled by the published ratio of observed to predicted decay, 0.997 ± 0.002 (Hulse & Taylor 1975; Weisberg & Huckins 2016), which is how the agreement is quoted. The error bars are drawn: at the last point the bar is 1.25 px tall against a dot 9 pixels across, so they are invisible, and their invisibility is the result. The campaign has run 45 years.

An orbit measured to be shrinking

A 7.75-hour orbital period that shortens by 68 nanoseconds each turn is beyond any single measurement, and unmissable after fifty thousand of them, because the shift accumulates as the square of the elapsed time. Forty-five years of pulse arrival times have made it 87.5 seconds, which is why the rate is a measured quantity rather than an inferred one.

gravitation · Relativistic orbits

A corner of the diagram that has to be earned

A pulsar spinning a thousand times a second cannot have been born that way and stayed that way, because its own radiation would have slowed it in a few million years. It got there by being fed, and the line it cannot lie above is where the accretion torque balances the magnetic one.

stars · Pulsars

The delay a companion's gravity puts in a pulsar's pulses, over one orbit. The Shapiro delay of a pulsar's pulses against orbital phase, for a companion of 0.5 solar masses and orbital inclinations of 89.17°, 85°, 70°, from Δ = −2r ln(1 − sin i · sin Φ), where r is the companion's mass times G/c³ = 2.46 µs. Superior conjunction, when the pulsar is behind its companion, is at 90°. For the orbit nearly edge-on (89.17°, the inclination measured for PSR J1614−2230) the delay rises in a narrow spike 48.5 µs high as the pulses graze the companion; at 85° the spike is 30.8 µs and broad, at 70° 17.1 µs and nearly a sinusoid. The height is set by the companion's mass and the sharpness by the inclination, which is how one curve returns two numbers the orbit alone cannot give.

The part of a delay no orbit can imitate

A binary pulsar's pulses are delayed by up to fifty microseconds as they pass its companion, and most of that delay is invisible — a timing fit folds it into the orbit. What survives is the third orbital harmonic and above, whose size goes as the cube of the tangent of half the inclination, and that cube, not the delay, decides which neutron stars can be weighed.

gravitation · Relativistic orbits

Two critical mass ratios that move with where the mass goes. The logarithmic response of the donor's Roche lobe to its own loss of mass, ζ, against the mass ratio donor over accretor, for conservative transfer (dashed) and for all of the transferred mass lost from the accretor, from the donor and to a ring. The horizontal lines are two donors' own responses: −1/3 for a deep convective envelope, which swells as it is stripped, and +2 for a radiative one, which shrinks. Transfer is stable where the donor's line lies above the lobe's curve, so each crossing is a critical mass ratio — conservatively 0.63 and 1.72. Re-emission from the accretor moves them to 0.96 and 2.25, a wind from the donor to 1.24 and beyond the range drawn; and with everything fed to a ring the convective donor is unstable at every mass ratio drawn and the radiative one only below 0.19. Nothing about the donor has changed between the curves; only the question of where a gram that is not accreted leaves from.

Mass that leaves takes the orbit's spin with it

Most of the gas a star pours onto its companion never stays there. Where it leaves from decides how much angular momentum it carries, and that one bookkeeping entry moves the largest donor that can transfer stably by a factor of two — without anything about either star having changed.

stars · Mass transfer

Named alongside it

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

Neutron star General relativity Apsidal precession Eccentricity Eddington limit Mass function Mass transfer Pulsar timing Residual Accretion Accretion disc Angular momentum

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