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How to use
The Sun throws out a supersonic wind. Far away it runs into the plasma that fills the space between the stars and is slowed by a termination shock (teal), flows around the Sun as a hot heliosheath (orange) and is stopped by the heliopause, the boundary where the wind's pressure equals the interstellar pressure. Start with Voyager era: Voyager 1 (yellow) and Voyager 2 (pink) are launched in 1977 and fly out; the page shows what each probe measures and announces every boundary crossing. The Calendar year slider scrubs time.
Try the presets, then change a slider: a stronger wind or a weaker interstellar medium inflates the bubble, the shock and heliopause sizes follow pressure balance; the magnetic field and flow speed of the interstellar medium decide whether a bow shock exists. The graphs show the Parker wind profile, the pressures that fix the boundaries, the spacecraft distances against the shock position over the years, and the spiral magnetic field. Space pauses, R restarts the mission.
The science
1. The supersonic solar wind (Parker 1958). A hot corona cannot stay in hydrostatic equilibrium; the isothermal solution of the momentum equation with c2 = 2kT/mp is
u2/c2 - ln(u2/c2) = 4 ln(r/rc) + 4 rc/r - 3, rc = GM / (2c2)
The wind passes through the sonic point at rc (about 5 to 8 solar radii for a 1 to 2 MK corona) and is supersonic beyond it. The page finds the coronal temperature that gives your chosen speed at 1 AU. Beyond 1 AU the speed is taken as constant and the density falls as r-2, so the dynamic (ram) pressure is Pram(r) = mp n1 u2 (1 AU / r)2.
2. Parker spiral. The Sun rotates (Ω = 2.87e-6 rad/s) while the wind flows radially, so the frozen-in field forms an Archimedean spiral: tan ψ = Ω r sinθ / u (47 degrees at 1 AU for 400 km/s, almost azimuthal beyond 10 AU). Br falls as r-2, Bφ as r-1.
3. Termination shock. Where the wind pressure falls to the pressure of the surrounding heliosheath it must become subsonic through a shock. For a strong shock the Rankine-Hugoniot relations (conservation of mass, momentum and energy) give the downstream pressure P2 = 2 ρ1u12/(γ+1) = 0.75 ρ1u12 for γ = 5/3, a density jump (γ+1)M2/((γ-1)M2+2) which tends to 4, and a speed drop by the same factor:
RTS = 1 AU × √( 0.75 Pram,1AU / (ζ PISM) )
4. Heliopause and the interstellar pressure. The total interstellar pressure is thermal 2nkT plus magnetic B2/2μ0 plus ram ρv2; with n = 0.07 cm-3, T = 7500 K, B = 0.3 nT and v = 26 km/s this is about 1.3e-13 Pa. The heliopause is where the wind's ram pressure matches it:
RHP = 1 AU × √( κ Pram,1AU / PISM )
Without any tuning (ζ = κ = 1) this gives 96 AU and 111 AU, close to the measured 94 and 121.6 AU. The page then calibrates ζ, κ, the tail elongation and a southern dent so that the surfaces pass through the three Voyager crossings (Voyager 1 shock 2004, Voyager 2 shock 2007, Voyager 1 heliopause 2012); these three checks are calibration targets, not independent tests. The surface shape r(θ) = Rnose(1+e)/(1+e cosθ) is a geometric approximation, not a magnetohydrodynamic solution.
5. Why is there no bow shock? A bow shock needs the interstellar flow to exceed the fast-magnetosonic speed vms = √(cs2 + vA2), vA = B/√(μ0ρ). With B = 0.3 nT the Alfven speed is about 25 km/s, so vms is about 28 km/s against a flow of 26 km/s: Mach number 0.92, no shock (McComas et al. 2012). Weaken the field in the preset Weak field and the shock appears.
6. Solar cycle. The shock sits where Pram equals the downstream pressure, so RTS ∝ √Pram; a pressure swing of amplitude A over 11 years makes the shock breathe, delayed by the wind's travel time (about a year to 90 AU).
Checks (run in the page). The Parker solution at its critical point and its Bernoulli residual; the spiral angle at 1 AU; Rankine-Hugoniot conservation of mass, momentum and energy and the strong-shock limit; the untuned pressure balance against the Voyager distances; the three calibration targets; the magnetosonic Mach number of the interstellar medium.
Simplifications. Isothermal corona, constant speed beyond 1 AU, no pickup ions (they take much of the shock energy, which is why the measured density jump at Voyager 2 was about 2.4 instead of 4), no neutral-atom charge exchange, a parametric rather than self-consistent surface shape, and spacecraft distances from published epochs interpolated linearly.