Why is the Sun's corona hotter than its surface?

The surface of the Sun is about 5,500 degrees Celsius. The corona, the wispy outer atmosphere visible during a total eclipse, sits above that surface and burns at one to three million degrees. Heat should not flow from a cooler body into a hotter one, yet the Sun’s atmosphere is hundreds of times hotter than the Sun beneath it. This has been an open scandal in astrophysics since 1939, when Walter Grotrian and then Bengt Edlén showed that mysterious green and red lines in the corona’s spectrum, once attributed to a hypothetical new element, actually came from iron atoms stripped of half their electrons, something only extreme temperatures can do.

Why it matters

There is no thermodynamic paradox; the corona is not heated by heat. Something carries energy up from below in a form that is not warmth, most likely mechanical or magnetic, and unloads it in the thin outer atmosphere. Identifying that mechanism matters beyond tidiness. The corona is the source of the solar wind and of the flares and mass ejections that disable satellites and power grids, and space weather forecasting is only as good as our model of the atmosphere that produces it. Every Sun-like star has a corona, so the answer is a fact about stars generally.

What has been tried

Two families of explanation have competed for decades. Wave heating proposes that convection churning the surface shakes the Sun’s magnetic field lines, sending waves up into the corona where they dissipate as heat; such waves, called Alfvén waves, have been directly observed, though whether they deposit enough energy in the right places is disputed. Nanoflare heating, proposed by Eugene Parker in 1988, holds that braided magnetic field lines snap and reconnect in countless small bursts, each too faint to see individually, which together keep the corona hot. Spacecraft have taken the question to the source: one probe has repeatedly flown through the corona itself, finding the magnetic field kinked and switchbacked in ways nobody predicted.

Where the edge is

Both mechanisms are real; the unsolved question is bookkeeping. Which one dominates, where, and how the energy actually converts to heat at scales too small to observe remain open, and the measured wave and flare budgets have so far each fallen short of a full accounting on their own.

What would count as an answer

A measured energy budget that closes: observed inputs from waves and reconnection matching the corona’s known losses, region by region, with a model that predicts coronal temperature from surface conditions on the Sun and on other stars.