Centre for Astrophysics

Space- and time-dependent Space- and time-dependent heating of heating of

solar coronal loopssolar coronal loops

S. W. Higgins & R. W. Walshe-mail: SWHiggins@uclan.ac.uk

RWWalsh@uclan.ac.uk

http://www.star.uclan.ac.uk/~swh/loop2

SUMMARY• Coronal heating, nature of loops – dynamic and heterogeneous• Interpretation of observations of dynamic loops• Different heating mechanisms can produce different forms of spatially

varying heating• Physical model: 1-D hydrodynamics (‘pipeline’ flow) with simple heating &

cooling• Results – observational consequences: apex temperature variation

– Standing wave driven in the loop– Although in each case the loop is receiving the same total amount of

heat per cycle, the total variation on the apex temperature depends on the spatial distribution.

– The apex dominant case has the largest variation in temperature and the footpoint dominant case the smallest for all values of frequency

• Conclusions – possible diagnostics of heating mechanisms?

Wide range of temperatures: 20000 K (SOHO/CDS HeI & OV)—6.106 K (Yohkoh/SXT)

Spatial scales: Bright points? 2000 — 3000 km, Trans-equatorial loops

Short timescales ≈ 1 mTRACE EUV movies show that plasma is not static but possibly has a time-dependent component associated with its heat input (Schrijver et al. 1999).

Different heating mechanisms can produce different forms of spatially varying heating:

APEX HEATING: Alfvén waves dissipated by phase-mixing (Heyvaerts and Priest 1983) or resonant absorption (Ionson 1978); flux braiding (Parker 1988) in a loop broadened at its apex

UNIFORM HEATING: loops with uniform cross-sections (Klimchuk 2000) could give a more uniform braiding profile

FOOTPOINT HEATING: agitation of the at the base of the loop

Heating mechanisms

● One-dimensional, first-order, inviscid, hydrodynamic code, neglecting gravity

● Loop length 60 Mm, mean heat input 2.0x1018 J/s

● Cooling by piecewise fit, function of temperature (Cook et al 1989)

● Time-dependent heating by H = H0 (1 + sin t)

● Space dependent-heating by hyperbolic function

● Begin with loop in equilibrium, then apply heat input with periods from about 4 seconds to 5.4 hours.

PLASMA DYNAMICS

Standing wave: during the heating phase plasma at the apex (x = 0) expands and drives flow down the loop; during cooling phase compressed plasma rises back up

Figure 3: variation in the apex temperature Figure 4: variation in the apex temperature with time for low frequency with heat input for low frequency

Apex temperature variation

As the plasma has time to respond to the heating changes, each case has approximately the same apex temperature minimum ~0.9 MK.Temperature variation: ~1.8 MK for apex heating, ~1.2 MK uniform heating, ~0.9 MK footpoint heating.

Apex temperature range

The variation of the apex temperature range is consistently highest for apex heating, and lowest for the case when heat is deposited at the base

Apex temperature amplitude

observed loop with measured length and temperature variation amplitude and frequency can be placed on one of these diagrams – its position above or below the uniform heating curve indicates its heating profile

CONCLUSIONSDifferent spatial heating profiles show significant differences in observable behaviour; similarly the timescale of any variation can affect the amplitude of observable variations. The frequency variation in apex temperature is approximately the same as the driving frequency. For lower frequencies coronal plasma in the loop has time to respond to the changes in the energy input and follows that variation in time quite closely.

For any given frequency the amplitude and maximum of apex temperature depends on the distribution of heat input.

Thus it should be possible to use estimates of loop length along with frequency and range of temperature variation at loop apex, in conjunction with these theoretical results, as a diagnostic of the location and frequency of dominant heat input.

Further work: Refine simulations with a finer, irregular grid, 2nd order scheme, viscosity and gravity (larger loops).Run extended parameter set on UKAFF and/or UCLAN beowulf.