Energy goes up... but doesn't come back down! Coronal heating?
From RHESSI Wiki
Nugget | |
---|---|
Number: | 236 |
1st Author: | Brian Welsch |
2nd Author: | |
Published: | September 22, 2014 |
Next Nugget: | Balmer continuum! |
Previous Nugget: | Which detectors? |
List all |
Contents |
Introduction
As noted here recently, it was recognized more than 70 years ago (Ref. [1]) that the temperature of the solar corona is over a million Kelvin, much hotter than underlying photosphere, which is near 6000 Kelvin. This is the crux of the coronal heating problem: How is the outer atmosphere of the Sun heated to much higher temperatures than its photosphere? From RHESSI's point of view, this question relates the quiet-Sun emission studied in this earlier Nugget and still earlier ones cited therein.
The second law of thermodynamics implies that the energy required to maintain coronal temperatures cannot flow outward as heat. (Hot material might flow upward to heat the corona from below --- but this energy transport must be non-thermal, e.g., spatially coherent jets of heated plasma like those reported by Ref. [2]). The situation is similar for the 104 K chromosphere, which is also substantially hotter than the photosphere. Consequently, non-thermal energy transport is required to move energy from the energy reservoir of the solar interior past the photosphere before it is deposited as heat in the chromosphere and corona.
E. N. Parker proposed three decades ago that turbulent convective motions in the near-surface plasma could "braid" the footpoints of coronal magnetic fields, thereby inducing electric currents in the corona; and that the magnetic energy stored in the coronal field due to these currents could then be dissipated to heat the chromosphere and corona. The obligatory cartoon:
![](/~tohban/wiki/images/thumb/9/97/Parker_winding_nanoflares.png/300px-Parker_winding_nanoflares.png)
The induced currents might be characterized as either steady or rapidly varying (e.g., wave-driven) relative to the timescales of the atmospheric response, and the dissipation of each has been referred to as "DC" (direct-current) or "AC" (alternating-current) heating (e.g., Ref [3]).
Can we observe the upward transport of magnetic energy that drives heating in the outer solar atmosphere?
The Poynting Flux
The flux of magnetic energy across the photosphere --- in a local Cartesian approximation, the vertical component Sz of the Poynting vector, S --- can be estimated from the observed magnetic evolution in sequentially measured vector magnetograms (2D maps of the photospheric magnetic field vector, B Assuming that the photospheric magnetic field, B, is frozen to the plasma --- a valid assumption in quite general circumstances (see, e.g., Ref. [4]), then the photospheric electric field, E, is given by the ideal Ohm's law,
c E = - (v × B).
Then
Sz = [vz Bz2 - (vh ⋅ Bh)Bz]/ 4 π ,
where the h subscripts refer to horizontal components of vectors. This expression for total vertical Poynting flux has been conceptually divided into an "emergence" term, which contains vz, and a "shear" term, which contains vh (e.g., Ref [5]). In fact, a positive (upward) value for the shearing term also implies the emergence of magnetized plasma across the photosphere. This is because a positive value implies a non-zero component of the photospheric velocity perpendicular to B that is upward. Flows parallel to B can be ignored, since they cancel out in the equation for Sz. Upward transport of a tilted magnetic field does not increase the total unsigned magnetic flux threading the photosphere. (This is in contrast to the emergence of new, or additional, magnetic flux, which must occur at a polarity inversion line).
An Observational Estimate
Plage magnetic fields are unipolar, nearly-vertical fields associated with active regions that are more coherent and typically stronger than quiet-sun fields, but weaker than sunspot (umbral) fields; see, e.g., Ref. [6]. Plage fields are ideal observational targets for estimating energy injection by convection, because they are: (i) strong enough to be measured with relatively small uncertainties; (ii) not so strong that convection is heavily suppressed (as within umbrae); and (iii) unipolar, so Sz in plage is not influenced by flux emergence, which cannot explain steady heating in stable, active-region fields. For observations of B in plage regions that include an estimate of the filling factor f, the upward flux of magnetic energy is approximately given by (Ref. [7])
Szplage ≈ - (vh ⋅ Bh)Bz/ 4 π
Hence, estimating Szplage requires both a vector magnetic field measurement and an estimate of vh. Welsch et al. (2012) used local correlation tracking (LCT) to estimate vh from a sequence of line-of-sight magnetograms of NOAA AR 10930 observed by the Narrowband Filter Imager (NFI), part of the Solar Optical Telescope (SOT) aboard the joint Japanese/U.S./U.K. Hinode satellite. From simultaneous observations recorded by the SOT's SpectroPolarimeter (SP), B. Lites and the late T.R. Metcalf estimated the vector magnetic field and filling factor. Yeates et al. (2014) and Welsch (2014) combined these results to estimate the Poynting flux in two small regions of plage, and found upward (positive) fluxes of energy. The left panel of Fig. 2 shows a map of B and vh from the region studied by Welsch (2014), and the right panel shows the corresponding Poynting flux map. The user-set "windowing" parameter used by the LCT code was set to 4 pixels to produce this flow field, corresponding to about 1.3 arcsec (or roughly 1 Mm in this near-disk-center region). The average upward energy flux from the region shown in Fig. 2 is near 5 x 107 erg cm−2 s−1, higher than the combined chromospheric and coronal energy demands estimated by Withbroe & Noyes (1977) nearly 40 years ago.
![](/~tohban/wiki/images/thumb/b/b9/Joint_poynt_map.png/700px-Joint_poynt_map.png)
Fluke positive fluxes?
Essentially all models of coronal heating assume that energy stored in magnetic fields is the ultimate source of the energy later observed as heat. And this energy must originate in the solar interior, so there must be a net positive (outward) Poynting flux. But the spatial and temporal scales on which the bulk of this energy crosses the photosphere are not known.
So it is possible that the two regions of positive Poynting flux found by Yeates et al. (2014) and Welsch (2014) might be flukes of sampling: at the spatial and temporal scales on which they estimated B and vh (about 1 Mm, and about 8 minutes, respectively), the Poynting flux might be negative in just as many areas as it's positive. To test this, we identified all "plage-like" pixels in AR 10930, defined to be pixels for the filling-factor-weighted |Bz| was between 100 and 1500 Mx cm−2 and inclinations were less than 30 degrees from vertical. Contours in Fig. 3 outline areas identified as plage-like.
We then compared the distributions of Poynting fluxes in the upward- and downward-Poynting-flux sub-populations of plage-like pixels. As can be seen in Fig. 4, the upward-flux pixels outnumber the downward-flux pixels across most of the range of Poynting flux values. Consequently, we conclude that, at the spatial and temporal scales of our observations, the Poynting flux appears to be systematically positive.
This is a notable result, because it is plausible that a lot of energy is supplied to the outer atmosphere on smaller spatial scales and faster time scales. It might be the case, however, that much of the energy input occurs on scales we can now resolve. This can only be settled, of course, with (cue the choir, to recite the well-known observer's chorus...) observations at higher resolution! So we are happy that construction of DKIST is underway, and hope that the Japanese-led Solar-C mission concept will be realized!
The future
What do the chromosphere and corona do with the magnetic energy that goes up, but doesn't come back down?
Conversion to heat is a plausible answer, but can we observe this? We plan to compare Poynting flux maps with observations of emission from the overlying atmosphere with IRIS, and AIA, to search for correlations in space and time. We might be stymied, though: energy can both be stored within and propagate along magnetic fields, so the times and locations at which energy is injected might differ significantly from when and where energy is released as heat.
(It should also be mentioned that this energy flux might not actually play any significant role in coronal heating: perhaps this energy cascades to some unobservably small or fast scale, but then returns to the solar interior without significant dissipation! And the corona might be heated by energy flowing outward on yet a different scale.)
Also, the oft-cited estimates for the chromospheric and coronal energy demands made by Withbroe & Noyes (1977) are now quite dated. Given that excellent instruments such as IRIS, EVE, AIA, and XRT are aloft, more precise estimates can surely be made, and should be.
References
[1] "Zur Frage der Deutung der Linien im Spektrum der Sonnenkorona"; "Die Deutung der Emissionslinien im Spektrum der Sonnenkorona"
[2] "The Origins of Hot Plasma in the Solar Corona"
[3] "On Solving the Coronal Heating Problem"
[4] "Depth of origin of solar active regions"
[5] "Magnetic Energy and Helicity in Two Emerging Active Regions in the Sun"
[6] "Active Region Magnetic Fields. I. Plage Fields"
[7] "Magnetic Properties at Footpoints of Hot and Cool Loops"
RHESSI Nugget Date | 22 September 2014 + |
RHESSI Nugget First Author | Brian Welsch + |
RHESSI Nugget Index | 236 + |