Astronomy & Celestial Mechanics
the sky, computed
Concept

Cusp core problem — where it appears

The disagreement between the steep central density cusp dark-matter-only simulations give a halo and the flat cores the rotation curves of many dwarf galaxies imply. Whether it is solved by feedback from the ordinary matter, or points at the dark matter itself, is unsettled.

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

Also named here as inner slope, nfw profile, stellar feedback — the same set of essays touches all of them, so they are one junction rather than several.

A cusp and a core in the same halo: 39 times apart in density, 2.34 in rotation. Two dark-matter density profiles for a halo of 10¹⁰ solar masses, drawn on logarithmic axes so a power law is a straight line and its exponent is a slope. The upper curve is the profile cold dark matter simulations produce: density rising inward without limit, with a logarithmic slope tending to -1.01 — a cusp. It is not a fit to observations; it emerges from simulations run by many groups with different codes, and its robustness is what makes it a prediction worth testing. The lower curve is a cored profile with the same virial mass, flat inside a kiloparsec, slope -0.01. What the rotation curves of gas-rich dwarf galaxies prefer is the second. The disagreement is stark where it is drawn — a factor of 39 in density at 0.10 kiloparsecs — and much less stark in what is actually measured, because a rotation speed depends on the mass enclosed rather than on the local density, and integrating a cusp over a small radius does not accumulate very much. At 1 kiloparsecs the two halos differ by a factor of 2.34 in circular speed — a real difference, and a far smaller one than the 39 in density that produced it. That compression is the whole difficulty of the problem. The observable is an integral of the quantity in dispute; integrating a cusp over a small radius does not accumulate much mass, so the sharpest disagreement lives where the instrument is bluntest. And the innermost points of a rotation curve are also the ones most affected by non-circular motions, by beam smearing, and by the inclination assumed — so the measurement is hardest exactly where it matters most. Whether the resolution is astrophysical — supernova feedback moving gas repeatedly and dragging the dark matter outward with it — or a statement about what dark matter is remains open, and the figure deliberately shows only the alternatives rather than choosing.

An argument about the innermost kiloparsec

Simulations of cold dark matter have produced the same halo for thirty years — a density rising inward without limit. The rotation curves of the smallest galaxies say the density flattens off. The disagreement is confined to a region a thousandth of the halo's size, and it has not been settled.

galaxies · Halo profiles A cusp pulled deeper by the disc inside it. The dark-matter density of a halo of 10¹² solar masses and concentration 10 before and after an exponential disc of 5·10¹⁰ solar masses and scale length 3 kpc settles slowly into its centre, computed shell by shell from the adiabatic invariant r·M(r). Far outside the disc the two profiles coincide — 4.8% apart at 83 kpc — because contraction moves mass inward without changing how much there is. Inside, the dark matter is pulled in after the baryons: at half a disc scale length the density is 2.9 times higher, and at 1 kpc the logarithmic slope goes from −1.09 to −1.25. The cusp that dark-matter-only simulations predict is therefore the shallowest the inner halo of a disc galaxy can be before feedback acts, not the profile feedback starts from. The calculation assumes circular orbits and slow settling, and simulations that include gas find the true response weaker than this.

The halo a galaxy drags inward

The cusp that dark-matter simulations predict is a halo with no galaxy in it. When gas cools and settles into a disc at the centre, the dark matter is pulled in after it, and a quantity conserved on slowly changing orbits says by how much. In a large disc galaxy the pull triples the dark matter at the centre and multiplies tenfold the energy needed to dig a core; in a dwarf it barely registers.

galaxies · Halo profiles

Named alongside it

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

Inner slopeNfw profileStellar feedbackAdiabatic contractionAdiabatic invariantBaryon fractionBeam smearingDark matterDark matter haloDisc halo decompositionDwarf galaxyEnclosed mass

All concepts