Astronomy & Celestial Mechanics
the sky, computed
Concept

Spallation — where it appears

The breaking of a nucleus into lighter fragments when it is struck by a fast particle such as a cosmic-ray proton. It is how lithium, beryllium and boron are made, and the abundances of its products in cosmic rays record how much matter they crossed.

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

The energy at which the sky begins to point. Gyroradius against energy for a singly charged particle, in three field strengths, with the thickness of the galactic disc and the size of its halo marked. A cosmic ray is not an image of anything: its path is a helix about a field line, and by the time it arrives the direction it came from has been erased. The erasure is quantitative. At 3 µG a proton's gyroradius equals the disc's half-thickness at 4.2·10¹⁷ electronvolts and the halo's radius at 4.2·10¹⁹, so below the first the particle is stored and stirred for tens of millions of years, and only above the second does it travel in something like a straight line. The measured spectrum has a break — the knee — at about 3×10¹⁵ eV, which is within a factor of a few of the first of those; the sky only starts showing structure above 10¹⁹, which is the second. Two features of a spectrum measured on the ground, both located by one straight line on this plot.

The energy at which a sky begins to point

A cosmic ray arrives from a direction that has nothing to do with where it came from. Its path is a helix about a galactic field line, and only above the energy at which that helix is bigger than the galaxy does the arrival direction start to mean anything — which is one particle per square kilometre per century.

galaxies · Cosmic rays The anisotropy each slope of escape predicts. The dipole anisotropy of cosmic rays diffusing out of a halo 4 kpc high, 3D/(cH), against energy, for diffusion slopes of ⅓, 0.5, 0.6, each normalised to the boron-to-carbon grammage at 10 GV — so all three agree at low energy and part above it. The shaded box is the range of dipole amplitudes measured between 1 and 100 TeV, a few parts in ten thousand to about a part in a thousand. At 10 TeV the three predict 0.0043, 0.014, 0.027: the slope that would let shocks inject an index of two overshoots the measurement by 27 times, and even Kolmogorov's ⅓ by 4. The normalisation of the prediction is uncertain by a factor of a few, through the arrangement of the sources and the shape of the halo; its rise with energy is not, because it is the same slope that the spectrum and the secondary ratio require.

One slope read twice, and the reading that disagrees

How fast cosmic rays leak out of the Galaxy depends on their energy through a single power, and that power is measured twice: in the falling ratio of boron to carbon, and in how unevenly the particles arrive across the sky. The first reading says one-third. The second, taken at face value, says the leak must be slower still — and neither leaves room for the spectrum shock acceleration predicts.

galaxies · Cosmic rays

Named alongside it

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

Cosmic raysGyroradiusAnisotropyDiffusion coefficientDiffusive shock accelerationGrammageGreisen zatsepin kuzmin cutoffInterstellar mediumKneeMagnetic confinementResidence timeShock acceleration

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