Why is the Sun Yellow?

This classic childhood question actually has the same answer as, "Why the sky is blue?'', which is actually not the same answer as many teachers give when teaching introductory Astronomy courses, including myself.  This was pointed out in an article, written by Jonathan M. Marr and Francis P. Wilkin at Union College, which appeared on arXiv today.

The usual explanation for why the Sun is yellow is given by the use of Wien's Law which describes where the peak of a blackbody spectrum is given the temperature of the body.  Using Wien's Law and the surface temperature of the Sun, 5800 K, we end up with a wavelength of 500 nm, which we perceive as green.  However, the Sun isn't green by yellow.  Thus the explanation goes that the sky preferentially scatters blue light, via Rayleigh scattering, which shifts the color towards yellow.  Plus the way the human eye perceives the light and the shape of the blackbody curve naturally favor a yellow color rather than green.

This explanation turns out to be partially correct.  While Wien's Law does give the peak emission for a blackbody curve, it only does so for the intensity, B_{\lambda}, and only when done in wavelength.  If one does the emission in frequency, which is inversely related to wavelength one ends up with the blackbody peak being at 880 nm, which is red.  One can't have two peaks so what is going on here?

This ends up being a pretty subtle, but power piece of radiative transfer (I apologize in advance this gets a little technical).  It turns out what matters is the units one looks at.  If one looks at the proper units for the emission, the peaks line up.  The proper units to look at are not intensity but what is termed the spectral energy distribution (SED).  Whereas intensity, B_{\nu} in this case, is in ergs/sec/cm^2/str/Hz, the SED is measured in \nu B_{\nu} which is ergs/sec/cm^2/str.  With the per frequency dependence gone, the peak now lines up properly with the peak gotten from doing the analogous thing with \lambda B_{\lambda}.  This is because the frequency and wavelength are inversely related.  This shifts the respective intensities in different ways.  The wavelength version shifts the intensity down to smaller wavelength, higher frequency.  The frequency version does the opposite by shifting the frequency down and increasing the wavelength.  The SED formulation removes this dependency, reconciling the two.

Using the SED version of the Planck function, another name for a blackbody distribution, the peak is now in between the two at around 633 nm, which is red.  The Sun isn't red though so what's the deal?  It turns out that astronomers have been abusing Wien's Law.  The Planck function isn't sharply peaked around its peak.  Rather it slowly falls off in the immediate region surrounding the peak wavelength.  Over the visual range, which is actually quite small in terms of wavelength space at 390-750 nm, the SED of light between the red and blue end only varies by about 1% which is less than the eye can discern.  Thus the eye would see the unmodified light of the Sun as white, and not any color.

Then why does the Sun look yellow?  Well the atmosphere preferentially scatters blue light via Rayleigh scattering as noted before.  This gives the sky its blue color.  All the blue light that comes from the sky has to be removed from the light coming directly coming from the Sun.  As a result this leaves only the red and green light, which our eyes perceive as yellow.

Thus from now on whenever I, or any other astronomer for that matter, are asked why the Sun is yellow or why the sky is blue, we can give the same answer from now on.

SDO Views an Eclipse

One might think it weird to position a Sun observing telescope such that it would experience an eclipse of that celestial body.  However, that is what is happening now to the Solar Dynamics Observatory (SDO) as the Earth moves towards the Autumnal Equinox on September 23rd.  For the next 3 weeks around the equinox the Earth will block out the Sun for the SDO for up to 72 minutes.

So why did NASA decide to do that?  Well it was to put the SDO in a convenient position to be able to transmit data to Earth constantly to the same ground station.  This was deemed to be more important than the ability to monitor the Sun 24/7, especially since the eclipses are not very long.

Similar to many communications satellites, weather satellites and the GPS system, the SDO sits in geosynchronous orbit (GEO).  At that orbit you go around the Earth at the same speed as the Earth rotates which makes you appear stationary with respect to the Earth's surface.  The orbit is at a radius of 42,164 km from the center of the Earth, which is much closer than the Moon.  In order to be truly geosynchronous the orbit has to be inclined the same amount as the Earth's tilt (24.3 degrees) such that it hovers over the equator.

This is tilt means that for most of the year the Earth will not block out the Sun for the SDO. The Earth has only an apparent angular size of 17 degrees from the point of view of the satellite.  Since the inclination of the SDO's orbit follows the Earth's tilt, it is usually far enough away the ecliptic, the plane of the orbit of the Earth around the Sun, when it is behind the Earth not to have the Earth block its view.  This is due to the Earth's north pole tilting towards the Sun in the northern hemisphere's summer, which moves the orbit behind the Earth above the ecliptic, and away during the winter, which moves the orbit behind the Earth below the ecliptic.  This is the same reason why we don't get Lunar and Solar eclipses all the time, because the orbit Moon is inclined with respect to the ecliptic.

However if one is at GEO there are two times of year when the Earth's axis is not tilted away or towards the Sun, the equinoxes.  At those points the orbital section behind the Earth is in the ecliptic and the shadow of the Earth falls on the satellites in that orbit.  Thus the SDO is eclipsed for a short period of time during these sections of the Earth's orbit.  Not that the SDO can't do interesting science during these times. It will have to opportunity to look at the Earth and its surroundings during this time, not to mention that eclipses give a great chance to study the corona of the Sun.

In other news the US Senate has proposed an appropriations bill for NASA which continues funding for JWST.  Thank you to all those who contacted their representatives and senators.  The bill is not final however and still needs to be reconciled with the House version as well as voted on.  So continued support is appreciated.

New Maunder Minimum?

At the annual meeting of the Solar Physics division of the American Astronomical Society, Frank Hill, Matt Penn, William Livingston, Richard Altrock and collaborators presented data indicating that the Sun may be heading that direction after Solar Cycle 24 is complete. So what does this mean?

Well first lets go over what the Maunder Minimum was. Humans have been observing sunspots regularly since Galileo first turned his telescope towards the Sun. (WARNING: DO NOT DO THIS UNLESS YOU HAVE A SOLAR FILTER FOR YOUR TELESCOPE!!!) Since that time a record has been kept of the number of sunspots on the Sun. This one of the longest scientific observing records to date, with over 400 years of data. It was discovered that the number of sunspots rises and falls over a period of 11 years. However, something strange happened to this pattern between 1645 and 1715, known as the Maunder Minimum. During this time the Sun showed few if any sunspots.

Since that time heliophysicists have discovered the cause of sunspots and the sunspot cycle. Sunspots are caused by regions of intense magnetic field on the Sun. This magnetic field keeps the region of the sunspot cooler than the surrounding plasma, thus the sunspot looks dark. The cycle of the sunspots is related to the cycle over which the magnetic field on the Sun reconfigures. Every 11 years, the magnetic field of the Sun flips its direction so that the North pole becomes the South and visa versa. During a minimum in Solar activity the magnetic field is stable in its orientation. However, as solar activity increases, indicated via the proxy of an increasing sunspot number, the magnetic field becomes chaotic as it flips direction. This chaotic field is the seed for the solar activity. Thus the Sun flips its magnetic field every 11 years, leading to the 11 year sunspot cycle.

Helioseismologists have recently uncovered more detail about this process. It all relates to the different flows with in the Sun's convection zone. In this region, particularly the region known as the tachocline, the magnetic field for the Sun is thought to be generated. Scientists have discovered large scale flows which control the motion of sunspots on the Sun. They have also discovered jet streams, similar to the ones found on Earth, which can be used to predict when new sunspot cycles begin. This was used to predict the late onset of the current sunspot cycle labelled Cycle 24.

Current data from Frank Hill's group shows that the jet streams for Cycle 25, the next cycle, have not formed yet which is unusual. If they don't form at all Cycle 25 probably won't happen. Penn and Livingston presented data that indicated that the sunspots have been weakening over the past 2 cycles. Altrock presented data showing that the field accumulation at the poles of the Sun has slowed as well. The combined data indicates that Cycle 25 will either be weak or not occur at all. If Cycle 25 doesn't happen it may be the start of another Maunder Minimum (aka grand minimum).

So what would be the implications for us here on Earth if another Maunder Minimum were to occur? Well there would be less activity from the Sun. A lower number of solar flares and Coronal Mass Ejections. This would lead to lower auroral activity. It would also make it safer for people out in space as the chances of being exposed to harmful radiation from the Sun would decrease. It would also lower the danger activity from the Sun poses to electronics in space and on Earth. The Sun would also put out less radiation making it slightly cooler here on Earth. In fact the Maunder Minimum coincided with the middle Little Ice Age in the 17th century. While the minimum certainly contributed to the Little Ice Age, the main cause was vulcanism here on Earth, so don't expect the cooler Sun from a minimum to counter act global warming. In fact the Sun would have to get 10 times cooler than it would become during a grand minimum to make up for the net effect of greenhouse emissions, so no worries of a new Ice Age yet.

A grand minimum would also be extremely interesting to heliophysicists. This is because we don't know what caused the original Maunder Minimum. Also while we have a pretty good idea about how the magnetic field on the Sun works, we still know very little about its generation. Observing another grand minimum would help us to understand both of these topics.

So will the Sun go into another grand minimum or not? Only time will tell if the predictions from the recent data hold true. As more data is accumulated better models will be generated and we will get a better idea of how Cycle 25 will likely play out. Ultimately, as with weather forecasting, you will never know for sure until you get to the actual date of the event to see if it happens.

Cool Solar Flare

This has been making the rounds and its pretty cool so I figure I would mention it as well. On June 7th the Sun let off a rather impressive solar flare which was observed by the satellites which observe the Sun, the Solar Dynamics Observatory (SDO), Solar and Heliospheric Observatory (SOHO), and Solar Terrestrial Relations Observatory (STEREO) to name a few. While this explosion wasn't out of the ordinary in terms of size or power, it was interesting because a lot of the material that was originally ejected fell back onto the surface of the Sun. This made for a rather spectacular movie by the SDO of material being shot up by the flare and then falling back to burn up on the surface.

So what is going on in the movie? Well a solar flare occurs because of magnetic fields on the Sun. Normally the magnetic fields on the Sun allow for material to flow off the Sun and form the Solar Wind. However if the fields get tangled that can stop that material from leaving the Sun and pressure begins to build up. Think of the Sun as a pot of boiling water and the Solar Wind as the steam rising off of the water to release energy. Tangled magnetic fields act like a very tight lid, which turns the Sun into a pressure cooker. The pressure builds and builds and builds until something gives way. In the case of the Sun, the magnetic field lines end up breaking in an event called reconnection. The reconnection event triggers the release of energy and material. This release is seen as a solar flare

In the case of this particular case the flare material didn't have enough energy to escape the Sun's gravity so it fell back on to the Sun. The material looks dark because it is cooler than the surface of the Sun. You will also notices that the material doesn't fall the way one expects. Rather it falls more slowly and is twisted around as it goes. This is the magnetic fields of the Sun at work again. The fields a strong enough to counter the force of gravity and channel the flow of material on the Sun.

The material from the flare that escaped was directed towards the Earth but only delivered a glancing blow to the Earth's magnetosphere. This caused a boost in auroral displays. We will be seeing more of these types of events from the Sun in the years to come as solar activity increases to its projected peak in 2013.