Astron. Astrophys. 324, 11-14 (1997)

4. Discussion

To be a viable heating mechanism, the time to maximum heating must be less than typical radiation cooling timescales (about 3,000 seconds). Following Hood, Ireland and Priest (1996), we can write as

where S is the Lundquist number and L is the loop length, which we will take as ranging from to . If we substitute this into the expression for assuming further that and (Karpen et al. 1994) then the time to maximum Ohmic dissipation is

For , we obtain which indicates that phase mixing can supply heating at large Lundquist number at timescales shorter than or comparable with the radiative cooling timescale. However, this is the result for one initial disturbance.

A further test for phase mixing will be to include the ohmic heating term into the time dependent simulations of coronal loops of Walsh et al. (1995) to see if repeated pulses can maintain a hot corona. Two possibilities may occur. Firstly, it may be that phase mixing is the main mechanism responsible for keeping coronal loops hot, provided that the disturbances are repeated every 1,000 seconds or so. One pulse is not enough. Walsh et al. (1995) will be able to provide an estimate of the period of the pulses. Secondly, it may be that the time to reach the maximum of the ohmic dissipation, while comparable to the coronal radiative timescale is too long to maintain a hot corona and so some other heating mechanism will be required. Even in this case, it is likely that phase mixing will contribute to a background level of heating.

© European Southern Observatory (ESO) 1997

Online publication: May 26, 1998

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