Jiamao Lin林佳茂

F ∝ sin²µ · vis,   cos µ = B̂_spot · n̂(φ)

Cyclotron radiation leaves perpendicular to B, so the flux peaks when the field at the footpoint lies across the line of sight. B̂ is the true dipole direction there, not the pole axis — at the footpoint the field is tilted out of the radial by roughly 14°.

Φ = −µ₁/r₁ − µ₂/r₂ − ½[(x−x_cm)² + y²]

The teardrop is the equipotential through L1, found by bisection along 420 directions. Change q and L1 slides, the lobe changes shape, and the stream — integrated with RK4 in the rotating frame — takes a different Coriolis curve. Nothing here is a drawn ellipse.

i_c = arccos [(R_L,proj + R_wd) / a]

There is no eclipse toggle. Raise i and the projected lobe eventually covers the white dwarf on the sky; the shaded window in the light curve appears at the same moment, because both read the same projected silhouette.

λ_n ≈ 1.071×10⁶ / (n · B[MG]) Å

Consecutive humps are spaced by Δλ/λ ≈ 1/n, so the pattern compresses toward the blue. Measuring the spacing, not the absolute position, is what makes B nearly model-independent — provided you have the right n.

I = B_λ(T_e) [1 − e^−Στ_n]

Not a sum of Gaussians. Low harmonics saturate at the source function and merge into a smooth blue continuum; only where τ_n < 1 do separate humps survive. The inset bars show log τ_n and where it crosses 1.

τ_n ∝ Λ n²ⁿ/(2ⁿn!) · βⁿ⁻¹ sin²ⁿ⁻²θ

Raise Λ or kT_e and the turnover moves up, so the same observed humps can be labelled n or n+1 — and B shifts by tens of MG. My fitting code profiles χ²(B) across those branches and reports them, instead of quietly picking one.

v_⊥ = v_orb sin α,   t_ing ≈ 2R_★/v_⊥

A grazing geometry stretches a stellar-diameter crossing into days. Shrink α and the walls flatten further; a point-like occulted source removes R_★ from the numerator entirely and the eclipse becomes a step function.

R_in ≈ 2–3 a ≈ 130 R_⊙

For a ≈ 0.24 AU (Kepler, M_tot ≈ 1.4 M_⊙), tidal truncation (Artymowicz & Lubow 1994) clears the disk inside ~2.5 a. The ring in the figure is drawn at that radius, not at a convenient one.

F_min = 1 − L_occ/L_tot ≈ 0.60

A single star behind an opaque edge cannot produce a 40% flat bottom unless something else is still shining. The near-achromatic depth from the optical through W1, plus a mid-IR excess, is what points to dust rather than a stellar companion.

The critical Roche surfaces meet at L₁. A stream appears only after the donor fills this surface. Its ballistic path is traced to impact or first closest approach, with all structures rotating in the same orbital plane.