Arunn's Notebook

Solar Convection and Sun Spots

Arunn Narasimhan

We all have encountered the phenomenon of convection. Simply put, hot gases raise against gravity. Like smoke from a lighted candle, a heated broth and the shimmering of air currents over a paved road on a hot day.

Convection is also responsible for the transfer of heat from the core to the surface in a main sequence Star -- like our Sun -- the flow of water in the water-wall-panels of the steam generator of a coal or gas fired thermal power plant, the winds over the Earth, the currents in the Oceans...the list is endless. This type of convection is called Free or Natural Convection. Let us do a brief introduction on natural convection using an animation and then shall highlight few convection patterns observed in our Sun.

In Natural Convection there is no external force necessary for the movement of the fluid involved in the above examples. The buoyancy force originating from the density difference between the hot fluids/gases (lower density) and the relatively colder surrounding fluids/gases (higher density) is sufficient to cause the movement of the fluids.

Here is a graphic representation of “natural” convection I made some fifteen years back. The vertical temperature difference (with top cold) against the gravity vector acting downward, sets up the buoyancy driven flow of the two highlighted fluid packets.

It would seem from the above explanation that natural convection will be observed in a fluid region even when there is a small temperature gradient. Such sensitive dependence of the initiation of the flow on the temperature gradient is not observed. It is the buoyancy force that causes the fluid packet to move up and down (see animation). For the fluid to convect, this buoyancy force must be more than the combined magnitude of the 'fluid brake' (via viscosity) and 'heat diffusion'. Because, viscosity impedes fluid motion, while heat diffusion results in reduction in local temperature causing a corresponding reduction in the buoyancy force.

This requirement for natural convection is expressed using the Rayleigh Number, a non-dimensional governing ratio of buoyant force divided by the product of the viscous drag and the rate of heat diffusion. It is named after Lord Rayleigh who came up with the explanation for this convection behavior of an enclosed fluid subjected to a temperature differential. Read this write-up for how Rayleigh number governs convection.

Can you guess what would be the order of Rayleigh number for convection pattern observed in the Sun? Around 10^{20}; 10 raised to 20 and above. For comparison, Rayleigh-Benard type convection rolls that we observe when water is heated on a kitchen stove on Earth, happens just around Ra of order 10 raised to 3.

Natural phenomena abound with such “natural” convection. Here are some natural convection highlights in different regions of the Sun under various circumstances.

1) Solar Dynamo

Convective patterns in a computer simulation of solar convection. Shown is a horizontal surface near the top of the convection zone in a Mollweide projection. Bright colors denote plasma flowing upward and dark colors denote plasma flowing downward.

Convection in a rotating star not only transports energy, it also transports momentum, establishing global circulations and shearing flows. Such mean flows work together with turbulent convection to amplify, organize, and transport magnetic fields, converting kinetic energy to magnetic energy. This is the solar dynamo, where the chain of events that gives rise to space weather begins. More information is available at the High Altitude Observatory webpage.

Once can even think of constructing a convection engine with a propeller that is made to rotate by the convection rolls, but their utility is limited by their inefficiency. Read "Convection Carnot Engine" note [PDF Download] for details on this aspect.

2) Solar Tachocline

Solar Tachocline is the sharp transition region between the differentially rotating convective envelope in the Sun and the uniformly rotating radiative interior.

The solar tachocline is a rotating, stratified, magnetized shear layer and it exhibits a complex array of physical phenomena including turbulent penetrative convection, internal gravity waves, and a variety of MHD instabilities.

When a longitudinal band of magnetic flux is embedded in a region where the rotation rate varies with latitude, the band will tend to tip under certain conditions. The images above show a computer simulation of such a tipping instability. The left image shows the magnetic field after an initially east-west oriented band has tipped, with orange and blue denoting eastward and westward magnetic flux. The center and right panels show the velocity in the longitudinal direction and the vorticity variation associated with the tipping of the bands.

Read more from the source: Solar Convection and Internal Rotation, University Corporation for Atmospheric Research, High Altitude Observatory.

3) Sunspot Convection

Here is the latest video from NASA SDO satellite on the formation and traveling of Sun spot clusters.

The video is a summation of two weeks of data, half the rotation of the Sun covering side to side passing of an active region and the movement of sunspots. Observe the spectacular surface view when the video turns the corner towards the end.

Want to know what a sun spot is, read at the Universe Today (Wikipedia hand waves). Want to know about how a sun spot is formed, here is my attempt to explain it simply.

Just as hot air rises against gravitational pull due to buoyancy, plasma made of ionic substance in the Sun also rises from its interior to the surface. When they reach the surface they cool off by releasing heat to space by radiation — a ray of which reaches out in about eight minutes to heat us on Earth. Since these solar plasma don’t escape the Sun’s gravitational pull, for every local rise of a certain mass of such plasma, some of the relatively cooler plasma near the surface sinks back to the solar interior. This local circulation, as we discussed above, is called Solar Convection. A similar circulation of hot water can be observed inside the vessel on our kitchen stove, but the solar convection renders the Sun with an average surface temperature of 5800 K.. But then, the kitchen convection can do The Boiling Song (do check out that grunge music).

The Sun also emanates strong magnetic fields, the flux lines of which sprout out of the Sun much like it does from the poles of a magnet. When these magnetic flux tubes go through the aforementioned convection region, the magnetic field tangles up inside the charged plasma field to slow down their convection. Due to this slowing down of the upcoming convection column, the already relatively cooled plasma on the surface is prevented from sinking down. In other words, magnetic activity inhibits convection. The cooler region trapped on the Sun surface is our Sun Spot. Here is a close up.

The picture above shows granules and a sunspot in the sun's photosphere, observed on 8 August 2003 by Goran Scharmer and Kai Langhans with the Swedish 1-m Solar Telescope operated by the Royal Swedish Academy of Sciences. This is a dramatic example of turbulent convection patterns in the photosphere of the Sun. By turbulent convection we mean the Rayleigh number that we talked about earlier is higher than 10 raised to 10, which is obviously true in the Sun. Observe the irregular and continuously changing polygonal pattern of bright areas surrounded by darker boundaries. These granules are convection cells with a width of typically 1000 kilometers and a lifetime of only about 10 to 20 minutes.

The above picture source is the excellent web write-up on turbulent convection by Guenter Ahlers.

Although the relatively “cooler” sun spot is also around 5000 K ( can vary between 3500 to 5500 K it seems), the relative temperature difference with the surrounding surface temperature on the Sun (~ 5800 K) is sufficient to contrast these spots as dark, when viewed from afar. The trick is due to radiation heat transfer, which varies ass the fourth power of temperature — an effect that gathers substantial magnitude across a temperature difference of about 1000 K.

On Earth, using controlled (cryogenic) conditions, we have managed to reach Rayleigh numbers of the order of 10 raised to 15. More on such experiments in a separate note.

© Arunn Narasimhan | Original version written ~ 2011 | Last revision on Apr 25, 2012