1. Centre for Astrophysics Space- and time-dependent heating of solar coronal loops S. W. Higgins & R. W. Walsh e-mail: SWHiggins@uclan.ac.uk RWWalsh@uclan.ac.uk http://www.star.uclan.ac.uk/~swh/loop2

2. 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?

3. Wide range of temperatures : 20000 K (SOHO/CDS HeI & OV) —6.10 6 K (Yohkoh/SXT) Spatial scales : Bright points? 2000 — 3000 km, Trans-equatorial loops Short timescales ≈ 1 m TRACE EUV movies show that plasma is not static but possibly has a time-dependent component associated with its heat input (Schrijver et al. 1999).

4. 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

5. ● One-dimensional, first-order, inviscid, hydrodynamic code, neglecting gravity ● Loop length 60 Mm, mean heat input 2.0x10 18 J/s ● Cooling by piecewise fit, function of temperature (Cook et al 1989) ● Time-dependent heating by H = H 0 (1 + sin w 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.

6. 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

7. 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.

8. 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

9. 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

10. CONCLUSIONS Different 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, 2 nd order scheme, viscosity and gravity (larger loops). Run extended parameter set on UKAFF and/or UCLAN beowulf.