Astronomy & Celestial Mechanics
the sky, computed
Concept

Modified Newtonian dynamics — where it appears

A proposed modification of gravity in which accelerations below about 1.2 × 10⁻¹⁰ m/s² are stronger than Newton's law gives. It reproduces galaxy rotation curves from the visible matter alone, without dark-matter haloes.

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

Also named here as radial acceleration relation — the same set of essays touches all of them, so they are one junction rather than several.

The observed acceleration against the acceleration the visible matter explains. The acceleration measured from a rotation curve, v²/r, against the acceleration the stars and gas alone would produce at the same radius, both on logarithmic axes in metres per second squared. The solid curve is the fitting function to the measured relation for 153 disc galaxies, g(obs) = g(bar) / (1 − e^(−√(g(bar)/a₀))) with a₀ = 1.2 × 10⁻¹⁰ m s⁻², and the band is its observed scatter of ±0.13 dex, most of which is measurement error. Above a₀ the relation follows the dashed line of equality, where the baryons account for everything; below it, it bends onto the dotted line g(obs) = √(g(bar)·a₀). At ten times a₀ the observed acceleration exceeds the baryonic by a factor of 1.06; at a₀, by 1.58; at a hundredth of a₀, by 10.5. The discrepancy the dark matter is invoked to explain is a function of one variable, and the variable is an acceleration.

One acceleration, and every galaxy's missing mass

Plot the acceleration measured at each radius of a rotation curve against the acceleration its stars and gas would produce there, for every galaxy at once, and the points fall on a single curve. Where the discrepancy begins is set not by a radius or a mass but by an acceleration.

galaxies · Dark matter Two places one tidal dwarf could sit. The radial acceleration relation — observed acceleration against the acceleration the baryons alone produce, logarithmic, in m/s² — with the fitted relation for ordinary disc galaxies (solid) and the line of equality (dashed). The marks are a tidal dwarf galaxy of 10⁹ solar masses of gas and stars in an exponential disc of scale length 1.5 kpc, sampled every half kiloparsec to 6 kpc. If it carries no dark matter, as debris pulled from a disc should not, its points lie on the dashed line (open). If the relation is a law that every galaxy obeys, they lie on the curve (filled), and at the outermost radius the acceleration is 5.6 times the baryons' — a rotation speed 2.37 times higher. Every point is below a₀, where the two predictions are furthest apart.

A galaxy born without a halo

When two galaxies collide, some of the gas flung out along their tidal tails condenses into new dwarf galaxies. Debris launched from a disc cannot take the dark halo with it, so these dwarfs should rotate at the speed their own gas and stars allow and no faster. The relation that predicts every ordinary galaxy's rotation from its baryons says they should rotate twice as fast. One rotation curve decides between a halo and a law — except that the inclination of a lumpy young disc can move the answer by more than the difference.

galaxies · Dark matter

Named alongside it

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

Dark matter haloRadial acceleration relationRotation curveBaryonThe baryonic Tully–Fisher relationDynamical massEscape velocityFeedbackGalaxy interactionInclinationMass discrepancyTidal tail

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