Astronomy & Celestial Mechanics
the sky, computed
Series

Stellar winds — the series

2 essays on one idea, from the one that introduces it to the one that assumes the rest.
  1. A wind that writes its own terminal speed on the blue edge, at 2017 km/s. A P Cygni profile, computed by integrating a spherical wind on a grid rather than drawn. The wind accelerates outward as one minus the inverse radius to the power 0.8, reaching 2000 kilometres a second, and its density falls as the inverse square of the radius over its own speed; the horizontal axis is the Doppler shift in units of that terminal speed, with blue to the left. The column directly in front of the stellar disc is moving toward the observer at every speed from nearly nothing near the surface up to the terminal value far out, so it takes light out of the beam across that whole range and the absorption trough runs from the rest wavelength to the blue edge at -1.01 of the terminal speed. That edge is the measurement: no model of the star, its distance or its mass enters it, only the geometry of a column seen end-on. The emission comes from everywhere else, where the wind moves across the line of sight and can only add photons; it is Infinity times stronger to the red than to the blue, because the part of the shell receding directly away is hidden behind the star and its blueshifted counterpart is not. Two features, one shell, and between them a velocity and a mass-loss rate.

    A speed read off an edge

    A hot star drives material off itself at thousands of kilometres a second, and the profile that wind prints on the star's own spectrum has a sharp blue edge. That edge is the terminal velocity, measured with no model of the star, no distance, and no calibration — one of the few numbers in stellar astrophysics obtained from geometry alone.

    part 1 · starlight
  2. A radial wind from a rotating star draws a spiral. The interplanetary field out to 5 astronomical units, drawn as the Archimedean spiral it is. Nothing here rotates: the plasma moves radially outward at 400 kilometres a second and the field is frozen into it, so each parcel remembers the longitude it left from and the pattern winds up while the material does not. The pitch angle is arctan(Ωr/v), which is 47° at one astronomical unit — the radius where the star's rotation has carried the footpoint through one radian in the time the wind takes to arrive. The practical consequence is a matter of hours: a flare's particles follow the field rather than the line of sight, so the ones that reach a given planet left a longitude about 61° to the west of it. A magnetically well-connected flare on the western limb delivers a particle storm and a larger one at disc centre does not, and the difference is this geometry rather than anything about the flare.

    The flare that arrives from somewhere else

    The solar wind blows radially outward and the Sun rotates, so the field frozen into the wind is wound into a spiral making forty-five degrees to the radius at the Earth. Energetic particles follow the field rather than the line of sight, which is why the flares that deliver particle storms are the ones on the western limb rather than the ones facing the planet.

    part 2 · sky

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