How does the sun's surface conduct thermal energy from the convective zone to the corona?

How does the surface of the photosphere conduct thermal energy from the convective zone to the corona, while remaining at such a relatively low temperature itself?

It seems odd to me that the photosphere is wedged between the convective zone and the corona, both of which are millions of degrees in temperature, while the photosphere itself is observed to be much colder by comparison - approx. 5-10 thousand degrees.

Based on my understanding of convection, this would require thermal energy to jump from the convective zone directly to the corona, and somehow skip the photosphere surface material in-between.

Is there a different model of convection that explains this?
Or is there a type of matter with thermal conductive properties that could accomplish this?

EDIT: Perhaps the convective zone is emitting heat as a different form of energy, such as electromagnetic - thereby allowing the outer layers to cool and sink in standard convection, but without directly heating up the surface of the photosphere.

Based on my understanding of the standard model of the sun, the following layers should be present:

Predicted:

• The core
A central area with pressures high enough to induce hot fusion of atomic nuclei
A spinning ball of somewhat solid material surrounding the core, through which energy is conducted via radiation

Semi-observable:

• The convective zone
A layer of plasma surrounding the radiative zone, through which energy is conducted thermally via convection flows - millions of degrees in temperature
This is the subject of some 2012 studies by NASA in coordination with various other reputable institutions, which observed that the sun's convection appears to be "anomalously weak"
http://arxiv.org/pdf/1206.3173.pdf

Observable:

• The surface of the photosphere
The border between the convective zone and the corona - temperature in the ballpark of 5-10 thousand degrees
• The corona
The outer plasma atmosphere, where flares take place - millions of degrees in temperature
• I'm not educated enough on this to give it a real answer, but in general I don't think the heat is conducted at all. I think it's more an effect of magnetism. This seems a pretty good article on how it happens: nasa.gov/content/goddard/… – userLTK Apr 25 '15 at 0:01
• If you can get access, here is the full paper. iopscience.iop.org/0004-637X/790/2/112 – BowlOfRed Apr 25 '15 at 0:32
• @userLTK Yeah, I tend to agree with the electro-magnetic force being a key driver here - however, it's easy to start spiraling down the Electric Universe model of the "electric sun" if you follow that train of thought too far. – Giffyguy Jan 27 '16 at 18:16
• The solar convection zone does not show much convection, and the convection it shows indicate it is heated from above. (physics.stackexchange.com/questions/315321/…) – Enos Oye Feb 28 '17 at 11:20

You've actually identified a key area of ongoing research known as the coronal heating problem.

First, let's get one thing out of the way. You ask:

Or is there a type of matter with thermal conductive properties that could accomplish this?

There can be no such material. Any material that passively diffuses heat from a cooler region to a warmer one would be in violation of the laws of thermodynamics.

But indeed, the temperature profile of the Sun is not monotonic, reaching a minimum near the photosphere (the surface from which a typical photon is last scattered/emitted before reaching us). In order for temperature to increase away from the source of heat, there must be some nonthermal process.

It helps somewhat to note that the corona is extremely diffuse. Thus we are not necessarily looking for a large amount of nonthermal heat transport compared to the amount of heat transported via thermal radiation through the corona. Wikipedia gives the fraction as one part in $40{,}000$. Moreover, temperature inversions in thin atmospheres are nothing new.

There are two mainstream ideas that are discussed in solving the problem, both involving magnetic fields in plasmas.

In wave heating, the idea is that waves are launched from somewhere below the corona, travel to the appropriate height, and then shock, heating the plasma. In ideal magnetohydrodynamics (MHD, the theory of perfectly conducting perfect fluids, which sounds like a lot of assumptions but is in fact quite applicable to many astrophysical plasmas), there are entropy waves (also found in plain hydrodynamics, HD), slow and fast magnetosonic waves (somewhat analogous to sounds waves in HD), and Alfvén waves (a purely magnetic phenomenon). Like in HD, a smooth MHD traveling wave (think of a sinusoid) will eventually steepen into a shock (where various quantities become discontinuous), and shocks can increase entropy/temperature as they pass.

The questions are if such waves actually propagate into the corona at all, when they would shock, and how much heat would actually be dissipated.

The other theory is that of magnetic reconnection. This is a non-ideal process, in which so-called flux-freezing is no longer valid. For background, in ideal MHD, magnetic field lines can be thought of as advecting with the motion of the fluid -- magnetic fields cannot drift relative to the fluid, since its conducting nature would have a 100% backreaction restoring the field (think Lenz's law). However, at some point, our assumptions must break down (due e.g. to the discrete nature of matter).

Reconnection can be visualized as opposing magnetic field lines cancelling each other out. Conservation of energy, though, demands the missing magnetic energy be turned into something, heat in our case. We know reconnection must happen at some level, but again it is a question of details as applied to the corona. For example, naive estimates of the rate of reconnection that simply place an electrical resistivity term into the equations are observed to be wrong by orders of magnitude.

• Chris, the temperature inversion of our atmosphere is caused by different effects than that of the corona and it is a very different system (i.e., the corona's energy source comes from within and the Earth's atmosphere's energy source comes from the sun). In addition, there are a few other ideas about coronal heating, namely micro and nano flares (I personally do not like this proposal, as it just inserts another black box as an explanation). In any case, the leading idea at the moment is that microturbulence causing wave-particle interactions plays a significant role... – honeste_vivere Apr 26 '15 at 11:02
• That is, interactions occurring at much smaller scales and shorter times than allowed for within MHD. Not to mention that the tenuous nature of the corona makes it nearly collisionless, and thus, not a fluid. It should be treated kinetically. – honeste_vivere Apr 26 '15 at 11:03
• Magnetic reconnection densify plasma and create counter flowing currents, the Themis satellites discovered this in earths plasma tail. Helioseismology neither observe any convection in the convection zone to support a solar MHD generated magnetic field, or any convectionally driven heat transfer. A wild suggestion is, what if we put all fusion in the corona, and make room for a solid solar core that can be remagnetised? That is topsy turvey, but might it solve the problems without creating new ones? – Enos Oye Feb 28 '17 at 12:04

I think I'm in a bit over my head, but I don't think it's convection. The Corona, because of the sun's high gravity, thins out very quickly.

http://sunearthday.gsfc.nasa.gov/2008/TTT/58_hotcorona.php

from the article:

It would be like standing in your kitchen far away from the open oven, but feeling temperatures almost 100 times higher than what was inside the oven!

That's not convection. Convection doesn't do that. It's probably some kind energy conversion. Magnetic energy turns into heat energy.

http://en.wikipedia.org/wiki/Nanoflares

According to Parker a nanoflare arises from an event of magnetic reconnection which converts the energy stored in the solar magnetic field into the motion of the plasma. The plasma motion (thought as fluid motion) occurs at length-scales so small that it is soon dumped by the turbulence and then by the viscosity. In such a way the energy is quickly converted into heat, and conducted by the free electrons along the magnetic field lines closer to the place where the nanoflare switches on. In order to heat a region of very high X-ray emission, over an area 1" x 1", a nanoflare of $10^{17}\ \mathrm{J}$ should happen every 20 seconds, and 1000 nanoflares per second should occur in a large active region of $10^5 \times 10^5\ \mathrm{km^2}$. On the basis of this theory, the emission coming from a big flare could be caused by a series of micro-nanoflares, not observable individually.

It's worth pointing out that this is just one of 3 main theories and there's not absolute certainty on how it works, but the first article I posted suggested there's some evidence that micro-flares are the primary cause.
( https://www.nasa.gov/content/goddard/best-evidence-yet-for-coronal-heating-theory and http://iopscience.iop.org/0004-637X/790/2/112/ )

• Thanks for the clarification! I think it's generally healthy to jump outside your comfort zone. They say the best way to learn about something is to try teaching it to someone else. ;-) – Giffyguy Apr 25 '15 at 0:54