Why does the field spiral?

The Sun rotates while the wind carries field lines radially outward. The footpoint moves in longitude faster than the radial advance can “unwind” the line, so the IMF winds into a spiral.

What is tan ψ = Ωr/v_sw?

At distance r, co-rotation speed Ωr competes with outflow v_sw. Their ratio sets how much azimuthal field B_φ builds relative to radial B_r in the steady Parker picture.

Why is ψ ≈ 45° at Earth?

With v_sw ~ 400 km/s and solar rotation ~27 days, Ωr and v_sw at 1 AU are comparable, giving ψ near 45°.

Latitude dependence, coronal-hole fast/slow streams, radial v_sw(r), polarity sectors, and time-dependent CMEs are not modeled.

Parker Spiral Solar Wind

Rotating Sun plus radial solar wind: interplanetary B spirals with tan ψ = Ωr/v_sw, animated field lines (top view), ψ(r) and |B| falloff.

About this model

The Parker spiral describes how the interplanetary magnetic field (IMF) is wound into a helix by the combination of solar rotation and radial solar-wind outflow. A field line rooted in the photosphere is carried outward at speed v_sw while the Sun rotates at angular frequency Ω, so in the equatorial plane the spiral angle ψ (between the radial direction and the field) satisfies tan ψ = Ω r / v_sw. Equivalently, the longitude of a line increases as φ − φ₀ = Ω (r − R☉) / v_sw, producing the familiar Archimedean-like spirals seen in a top-down view. The radial field component falls approximately as 1/r² from the source surface, while the azimuthal component grows with distance so that |B| exceeds B_r at large r. At Earth (1 AU) with typical v_sw ≈ 400 km/s and a ~27 day rotation period, ψ is near 45°. This simulator draws animated Parker spirals in the equatorial plane, radial wind arrows, sample B vectors, and plots of ψ(r) and a toy |B|/|B|(1 AU) profile with B_r ∝ 1/r². It uses constant v_sw and rigid rotation — no latitude structure, stream structure, or MHD waves.

Who it's for: Introductory space physics or solar-terrestrial courses after dipole fields and before CMEs, sector structure, or spacecraft data analysis.

Key terms

Parker spiral
Solar wind
Interplanetary magnetic field
Solar rotation
Spiral angle
Heliospheric field
AU

How it works

Parker spiral: solar rotation plus radial solar wind creates the interplanetary magnetic field spiral; ψ(r) and animated field lines in the equatorial plane.

Frequently asked questions

Why does the field spiral?: The Sun rotates while the wind carries field lines radially outward. The footpoint moves in longitude faster than the radial advance can “unwind” the line, so the IMF winds into a spiral.
What is tan ψ = Ωr/v_sw?: At distance r, co-rotation speed Ωr competes with outflow v_sw. Their ratio sets how much azimuthal field B_φ builds relative to radial B_r in the steady Parker picture.
Why is ψ ≈ 45° at Earth?: With v_sw ~ 400 km/s and solar rotation ~27 days, Ωr and v_sw at 1 AU are comparable, giving ψ near 45°.
What is left out?: Latitude dependence, coronal-hole fast/slow streams, radial v_sw(r), polarity sectors, and time-dependent CMEs are not modeled.

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