The Sun's outer corona - stretching millions of kilometers out into space from the surface - reaches temperatures of up to 4 million °C.. This contrasts sharply with the surface of the sun which has been measured at around 6 thousand °C.

A number of possible mechanisms have been proposed to explain why it's so hot. They include:

• Slow and fast magneto-acoustic surface waves
• Current (or magnetic field) dissipation
• Microflares/transients
• Mass/particle flows
• Magnetic flux emergence
• Alfvén body wave heating
• Magnetic re-connections
• 'Spicule' conduction

As yet, none has been definitely confirmed as the cause. See Wikipedia for details.

Further reading Stanford Solar Center

Note: In 1997 the Goddard Space Flight Center issued a press release regarding a new 'Magnetic Carpet' theory.

Also see : Solar spiculesplugin-autotooltip__plain plugin-autotooltip_bigSolar spicules

"Spicules comprise one of the most fundamental components of the solar chromosphere. They appear to be jets of gas seen at the limb of the Sun in chromospheric spectral lines, and have been observed in Hα and other chromospheric spectral lines for over 100 years. They have an upward mass flux 100 times that of the solar wind, and therefore are an important consideration in the mass balance of the solar atmosphere.

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