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Comments on the Stability of Winds, Breezes and Accretion Marco Velli Dipartimento di Astronomia e Scienza dello Spazio

Comments on the Stability of Winds, Breezes and Accretion Marco Velli Dipartimento di Astronomia e Scienza dello Spazio, Universita` di Firenze Jet Propulsion Laboratory, California Institute of Technology. How does a hot corona expand?

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Comments on the Stability of Winds, Breezes and Accretion Marco Velli Dipartimento di Astronomia e Scienza dello Spazio

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  1. Comments on the Stability of Winds, Breezes and Accretion Marco Velli Dipartimento di Astronomia e Scienza dello Spazio, Universita` di Firenze Jet Propulsion Laboratory, California Institute of Technology

  2. How does a hot corona expand? • g= GMs/Rs, r=R/Rs ∂p/∂r = -mp n g/ r2p=nkT • nkT= nkT0exp (-∫ dr mp g/ (kT r2) ) • If T( r ) falls slower than 1/r a finite pressure at infinity is required to confine the atmosphere • In a hot plasma atmosphere thermal conduction is proportional k~ T5/2 and therefore T( r ) ~ r - 2/7 • STATIC SOLUTION IMPOSSIBLE (PARKER 1958) • Chamberlain did not agree - debate until the 70s (theoretical)

  3. Original Parker- Chamberlain debate cut-off by observations!

  4. Hot Corona Expands Coronal holes Fast wind Streamers Slow wind

  5. 1959Soviet Luna observe the solar wind 1961 Explorer Satellites 1962 Mariner 2 Venus rendez vous. Plasma and magnetometer experiments (M. Neugebauer, Ed Smith JPL, CIT)

  6. However Mestel, quoted in Roberts and Soward (1972) first remarked that “were the temperature at the base of the solar corona 105 K rather than the generally accepted 106 K the total pressure far from the sun would suffice to suppress the solar wind entirely” • Pism = 1.24 10 -12 dyne/cm2 sufficient to confine a corona at 105 K

  7. Stationary, spherically symmetric flows, isothermal approximation Introducing the Mach number M = U/c Integrate to

  8. I Breezes II ? III Supersonic IV? Transonic

  9. Among flows which are subsonic at the atmospheric base the accelerating transonic has the special property that density and pressure tend to zero at large distances: because of the small but nite values of the pressure of the ambient external medium a terminal shock transition connecting to the lower branch of the double valued solutions filling region II will in general be present (McCrea 1954, Holzer and Axford 1970)

  10. Parker - Bondi diagram

  11. Schock position is determined by the pressure at infinity via the jump conditions.

  12. As p∞ increases the shock moves in (obvious and algebra is simple).

  13. Breezes have a finite pressure at infinity Which varied between

  14. So for intermediate pressures at infinity there are two solutions: a wind and a breeze. We now proceed to show that breezes are UNSTABLE, introducing fluctuations We then look for solutions with vanishing pressure perturbations at R0 and infinity

  15. Usually one derives an equation for wave action From which a growth rate estimate may be obtained on integration For subsonic flow, asymptotics is trivial

  16. Parker to Bondi and Back Velli, 1994

  17. Numerical simulation: Del Zanna et al. 1998

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