Astronomy

Why does the Sun deviate from a typical blackbody spectrum in the S band?

Why does the Sun deviate from a typical blackbody spectrum in the S band?


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This is sort of a follow-up to this question, and my answer to it.

The graph I see here details the radio (and other frequencies) emission of the sun. What's most notable and interesting to me is the deviation from the typical blackbody spectrum of a body at around 6000 K. The sun seems much brighter in the S band (and at some larger wavelengths) than a typical blackbody.

My question is: why does this happen? Is there an underlying physical/astrophysical phenomena that we know of that causes this? Or is this something that's undergoing research right now?


There are other ways of getting emissions than just direct thermal radiation. Most of it happens through plasma interactions in the solar corona and atmosphere than in the chromosphere. This review paper names bremsstrahlung, gyroresonance, cyclotronmaser, and plasma radiation as sources, each with their own brightness temperature way above 6000 K. (See also these lecture slides for a bit more in depth math of the sources).

My own summary would be that there is plenty of energy in the magnetic field and plasma, and this can be released through various wave modes producing radio signals. Further, fast charged particles are spinning around field lines or colliding, producing electromagnetic emissions of various types. None of these are blackbody sources, but they add to the blackbody spectrum to produce the observed curve.


How does the Sun send out EM radiation across the spectrum? Doesn't every frequency require a different process to happen?

No, everything with a temperature is emitting black-body radiation with a distinctive Planck distribution of wavelengths:

For things on Earth, like you or me or a wall or whatever, which are at about 300 Kelvin, the peak of this emission is in the infrared, which is why we see no glow with human eyes (can see it fine with an IR camera though, that's what "predator vision" or thermal imaging is). For something like the Sun, whose surface is 6000 K, the peak of thermal radiation is in the visible (it's almost like our eyes evolved to take advantage of that!). That's what sunlight is, blackbody/thermal radiation.

I get that everything with a temperature (so..everything) gives off a broad spectrum of wavelengths. But, since the EM field is quantized wouldn't that mean that if you zoomed in far enough on the blackbody distribution there would be tiny little equally spaced vertical lines due to Planck's constant?

Since the x-axis on the graph you provided is in units of (wave)length, the spaces would be of width ∆(lambda)=hc/E= Planck length, correct?

No, everything with a temperature is emitting black-body radiation with a distinctive Planck distribution of wavelengths

Not every object is a perfect black body. The distribution can be different, and it typically is different. Stars are quite good approximations to black bodies.

So low temperature has peak in infrared and higher and higher temperature eventually peaks at blue. Why? Why is the peak in that band. On intuition I would imagine that as temperature got higher and higher, the frequency would go higher and higher. I get that you can't have a wavelength of 0, but why is it in this small band?

And does not the Sun emit loads of other lower frequencies? How are those created?

Processes like atomic transitions that occur between bound states are discrete, but not all quantum processes are that way. Synchrotron radiation, Bremstrahlung (free-free emission), and Compton emission are processes that occur between two free particles or between one free particle and a photon. For free particles, energy is continuous rather than discrete even on the quantum level, so a continuous blackbody spectrum is easily produced. Note that because the Sun is hot, its hydrogen is mostly ionized. Therefore, there are few bound particles present at all, and continuous emission processes dominate on the Sun.

Yes - a more terrestrial example is a metal, which has free (delocalized) electrons that can absorb light over a broad continuous frequency range.

If continuous processed dominate the sun, then how do we analyse the elements within the stars by looking at spectral lines?

I think all of these answers are good, but way more complicated than they need to be. You are correct that there are discrete frequencies that account for much of the radiation. But not all radiation is produced by an electron changing state from one orbital to another, in the manner that would produce specific bands with gaps in between them. In plasmatized matter, like youɽ find on a star's surface, there are liberated charges all over the place, accelerating every which way, every possible amount, as a result of thermal kinetic motion and collisions. Every time one of them is accelerated, a different wavelength can be emitted. So it is possible to identify certain frequencies in the radiation of stars, but also a continuous spectrum.


Wavelength of the Sun's Peak Radiation Output

The Sun, Earth's closest star, is a source of a vast amount of power in our solar system, emitting a great deal of radiation to its surroundings. Whether this output is in a form recognizable to the naked eye or not, the sun gives off a variety of different waves, including anything from radio waves to gamma rays, varying a great deal in the energy and wavelength of each emission. The various wavelengths of radiation emitted by the sun is largely due to the temperature of the different portions of the sun each zone emitting its own span of wavelengths, depending on its temperature. According to Wien's Law, established in 1893 by Wilhem Franz Wien, the peak wavelength of a continuous spectrum emitted by a blackbody multiplied by its temperature (in kelvin) is equal to a constant (λpeak T = 2.898x10 𕒷 m·K. The formula also shows that peak wavelength is inversely proportional to temperature. Rearranging Wien's law reveals that

λpeak = (2.898 × 10 𕒷 m·K)/(T in kelvin) for a blackbody radiator

The maximum wavelength output from the surface of the sun (originating from the photosphere) is approximately 500 nanometers (varying from exact measurements of 483 to 520 nm, depending on the temperature used to represent the surface of the sun, which is not clearly defined), while wavelength output from the inner zones are as short as (or even shorter than) 2.9 × 10 󔼒 m (0.29 nm, which is located in the gamma ray portion of the electromagnetic spectrum). The max wavelength outputs vary along this wide range because the peak wavelength relies directly on the temperature of the blackbody, where higher temperatures lead to shorter peak wavelengths.


Assorted References

Blackbody radiation refers to the spectrum of light emitted by any heated object common examples include the heating element of a toaster and the filament of a light bulb. The spectral intensity of blackbody radiation peaks at a frequency that increases with the…

…spectrum is referred to as blackbody radiation, which depends on only one parameter, its temperature. Scientists devise and study such ideal objects because their properties can be known exactly. This information can then be used to determine and understand why real objects, such as a piece of iron or glass,…

…spectrum is identical to the radiation distribution expected from a blackbody, a surface that can absorb all the radiation incident on it. This radiation, which is currently at a temperature of 2.73 kelvin (K), is identified as a relic of the big bang that marks the birth of the universe…

Work of

…that Max Planck’s formula for blackbody radiation necessarily implies a fundamental postulate of discontinuous energy—the existence of discrete quantum energy levels—which classical physics proved incapable of explaining. In 1911 Ehrenfest also pointed out that Albert Einstein’s light quanta differ from classical particles in being statistically indistinguishable, and he explicitly constructed…

…emitted by the perfectly efficient blackbody (a surface that absorbs all radiant energy falling on it).

…wavelength or frequency distribution of blackbody radiation in the 1890s. It was his idea to use as a good approximation for the ideal blackbody an oven with a small hole. Any radiation that enters the small hole is scattered and reflected from the inner walls of the oven so often…


Types of Spectra

In these experiments, then, there were three different types of spectra. A continuous spectrum (formed when a solid or very dense gas gives off radiation) is an array of all wavelengths or colors of the rainbow. A continuous spectrum can serve as a backdrop from which the atoms of much less dense gas can absorb light. A dark line, or absorption spectrum, consists of a series or pattern of dark lines—missing colors—superimposed upon the continuous spectrum of a source. A bright line, or emission spectrum, appears as a pattern or series of bright lines it consists of light in which only certain discrete wavelengths are present. Figure 3 shows an absorption spectrum, whereas Figure 4 shows the emission spectrum of a number of common elements along with an example of a continuous spectrum.)

When we have a hot, thin gas, each particular chemical element or compound produces its own characteristic pattern of spectral lines—its spectral signature. No two types of atoms or molecules give the same patterns. In other words, each particular gas can absorb or emit only certain wavelengths of the light peculiar to that gas. In contrast, absorption spectra occur when passing white light through a cool, thin gas. The temperature and other conditions determine whether the lines are bright or dark (whether light is absorbed or emitted), but the wavelengths of the lines for any element are the same in either case. It is the precise pattern of wavelengths that makes the signature of each element unique. Liquids and solids can also generate spectral lines or bands, but they are broader and less well defined—and hence, more difficult to interpret. Spectral analysis, however, can be quite useful. It can, for example, be applied to light reflected off the surface of a nearby asteroid as well as to light from a distant galaxy.

The dark lines in the solar spectrum thus give evidence of certain chemical elements between us and the Sun absorbing those wavelengths of sunlight. Because the space between us and the Sun is pretty empty, astronomers realized that the atoms doing the absorbing must be in a thin atmosphere of cooler gas around the Sun. This outer atmosphere is not all that different from the rest of the Sun, just thinner and cooler. Thus, we can use what we learn about its composition as an indicator of what the whole Sun is made of. Similarly, we can use the presence of absorption and emission lines to analyze the composition of other stars and clouds of gas in space.

Such analysis of spectra is the key to modern astronomy. Only in this way can we “sample” the stars, which are too far away for us to visit. Encoded in the electromagnetic radiation from celestial objects is clear information about the chemical makeup of these objects. Only by understanding what the stars were made of could astronomers begin to form theories about what made them shine and how they evolved.

In 1860, German physicist Gustav Kirchhoff became the first person to use spectroscopy to identify an element in the Sun when he found the spectral signature of sodium gas. In the years that followed, astronomers found many other chemical elements in the Sun and stars. In fact, the element helium was found first in the Sun from its spectrum and only later identified on Earth. (The word “helium” comes from helios, the Greek name for the Sun.)

Why are there specific lines for each element? The answer to that question was not found until the twentieth century it required the development of a model for the atom. We therefore turn next to a closer examination of the atoms that make up all matter.

The Rainbow

Rainbows are an excellent illustration of the dispersion of sunlight. You have a good chance of seeing a rainbow any time you are between the Sun and a rain shower, as illustrated in Figure 5. The raindrops act like little prisms and break white light into the spectrum of colors. Suppose a ray of sunlight encounters a raindrop and passes into it. The light changes direction—is refracted—when it passes from air to water the blue and violet light are refracted more than the red. Some of the light is then reflected at the backside of the drop and reemerges from the front, where it is again refracted. As a result, the white light is spread out into a rainbow of colors.

Figure 5. Rainbow Refraction: (a) This diagram shows how light from the Sun, which is located behind the observer, can be refracted by raindrops to produce (b) a rainbow. (c) Refraction separates white light into its component colors.

Note that violet light lies above the red light after it emerges from the raindrop. When you look at a rainbow, however, the red light is higher in the sky. Why? Look again at Figure 5. If the observer looks at a raindrop that is high in the sky, the violet light passes over her head and the red light enters her eye. Similarly, if the observer looks at a raindrop that is low in the sky, the violet light reaches her eye and the drop appears violet, whereas the red light from that same drop strikes the ground and is not seen. Colors of intermediate wavelengths are refracted to the eye by drops that are intermediate in altitude between the drops that appear violet and the ones that appear red. Thus, a single rainbow always has red on the outside and violet on the inside.

Key Concepts and Summary

A spectrometer is a device that forms a spectrum, often utilizing the phenomenon of dispersion. The light from an astronomical source can consist of a continuous spectrum, an emission (bright line) spectrum, or an absorption (dark line) spectrum. Because each element leaves its spectral signature in the pattern of lines we observe, spectral analyses reveal the composition of the Sun and stars.


Other Series

The results given by Balmer and Rydberg for the spectrum in the visible region of the electromagnetic radiation start with (n_2 = 3), and (n_1^2=2). Is there a different series with the following formula (e.g., (n_1=1)?

The values for (n_2) and wavenumber (widetilde< u>) for this series would be:

Table (PageIndex<3>): The Lyman Series of Hydrogen Emission Lines ((n_1=1))
(n_2) 2 3 4 5 .
(lambda) (nm) 121 102 97 94 .
(widetilde< u>) (cm-1) 82,2291 97,530 102,864 105,332 .

These lines are in the UV region, and they are not visible, but they are detected by instruments these lines form a Lyman series. The existences of the Lyman series and Balmer's series suggest the existence of more series. For example, the series with (n_2^2 = 3) and (n_1^2) = 4, 5, 6, 7, . is called Pashen series.

The spectral lines are grouped into series according to (n_1) values. Lines are named sequentially starting from the longest wavelength/lowest frequency of the series, using Greek letters within each series. For example, the ((n_1=1/n_2=2)) line is called "Lyman-alpha" (Ly-&alpha), while the ((n_1=3/n_2=7)) line is called "Paschen-delta" (Pa-&delta). The first six series have specific names:

  • Lyman series with (n_1 = 1)
  • Balmer series with (n_1 = 2)
  • Paschen series (or Bohr series) with (n_1 = 3)
  • Brackett series with (n_1 = 4)
  • Pfund series with (n_1 = 5)
  • Humphreys series with (n_1 = 6)

The spectral series of hydrogen based of the Rydberg Equation (on a logarithmic scale).

Example (PageIndex<2>): The Lyman Series

The so-called Lyman series of lines in the emission spectrum of hydrogen corresponds to transitions from various excited states to the n = 1 orbit. Calculate the wavelength of the lowest-energy line in the Lyman series to three significant figures. In what region of the electromagnetic spectrum does it occur?

Given: lowest-energy orbit in the Lyman series

Asked for: wavelength of the lowest-energy Lyman line and corresponding region of the spectrum

  1. Substitute the appropriate values into Equation 1.5.1 (the Rydberg equation) and solve for (lambda).
  2. Locate the region of the electromagnetic spectrum corresponding to the calculated wavelength.

We can use the Rydberg equation to calculate the wavelength:

A For the Lyman series, (n_1 = 1).

Spectroscopists often talk about energy and frequency as equivalent. The cm -1 unit is particularly convenient. The infrared range is roughly 200 - 5,000 cm -1 , the visible from 11,000 to 25.000 cm -1 and the UV between 25,000 and 100,000 cm -1 . The units of cm -1 are called wavenumbers, although people often verbalize it as inverse centimeters. We can convert the answer in part A to cm -1 .

[lambda = 1.215 imes 10^<&minus7> m = 122 nm ]

This emission line is called Lyman alpha. It is the strongest atomic emission line from the sun and drives the chemistry of the upper atmosphere of all the planets producing ions by stripping electrons from atoms and molecules. It is completely absorbed by oxygen in the upper stratosphere, dissociating O2 molecules to O atoms which react with other O2 molecules to form stratospheric ozone

B This wavelength is in the ultraviolet region of the spectrum.

Exercise (PageIndex<2>): The Pfund Series

The Pfund series of lines in the emission spectrum of hydrogen corresponds to transitions from higher excited states to the (n_1 = 5) orbit. Calculate the wavelength of the second line in the Pfund series to three significant figures. In which region of the spectrum does it lie?

Answer: 4.65 × 10 3 nm infrared

The above discussion presents only a phenomenological description of hydrogen emission lines and fails to provide a probe of the nature of the atom itself. Clearly a continuum model based on classical mechanics is not applicable.


How much of the electromagnetic spectrum does the Sun emit?

From high-energy X-rays to long-wavelength radio waves, what electromagnetic radiation does the Sun emit and where in the Sun does this radiation come from?

Asked by: Karen Olsen, Leicester

The Sun emits radiation right across the electromagnetic spectrum, from extremely high-energy X-rays to ultra-long-wavelength radio waves, and everything in-between. The peak of this emission occurs in the visible portion of the spectrum.

Different wavelengths of light generally come from different regions of the Sun’s atmosphere or are due to particular atoms radiating at specific wavelengths (spectral emission lines). Visible light, for example, comes from the photosphere (or surface) whereas most infrared light comes from the lower chromosphere just above. Much of the high-energy UV and X-ray photons come from the Sun’s outer atmosphere (called the corona). This gives astronomers the ability to explore different solar features, constituents or processes simply by selecting a particular wavelength of light to observe. That is why NASA’s Solar Dynamics Observatory, for example, has an array of instruments that cover a wide range of wavelengths simultaneously.

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The Multispectral Sun

Your eyes tell you that the Sun obviously delivers energy to Earth in the form of visible light. If you think about it a bit, especially in terms of the choices you make about UV-A and UV-B protection when you shop for sunscreen or sunglasses, you'll also realize that you know that the Sun also bathes our planet in ultraviolet "light" or radiation. The Sun, in fact, emits radiation across most of the electromagnetic spectrum. from high-energy X-rays to ultra-long wavelength radio waves. Let's take a look now at this multispectral Sun and the energy it emits. Later in this week we'll see what happens to these different types of energy when they reach Earth. Electromagnetic radiation from the Sun is the main source of energy that drives Earth's climate system.

Review: The Electromagnetic Spectrum

Before we look at the multispectral Sun, let's review some key ideas about the electromagnetic (EM) spectrum. If you are very familiar with the EM spectrum (most chemistry and physics teachers are), feel free to skim this section. If this is an area that you are less comfortable with, we've provided some links to further readings that you might want to browse.

Visible light is the most familiar form of a type of energy called electromagnetic radiation. Light is actually rather strange stuff. In some ways it behaves like a stream of particles (which we call "photons"), and in other ways it acts like a series of waves. Light travels at a finite, albeit absurdly high, speed of 299,792 km/sec (186,282 miles per second) a beam of light could circle the globe more than seven times in a single second!

Light comes in different colors, spread across the rainbow of hues we call the visible spectrum. Each color corresponds to waves with different wavelengths. Red waves are the longest, purple the shortest. Since all colors of light (and all types of EM waves, for that matter) travel at the same speed, wavelength is inversely proportional to frequency (frequency is how often the "crest" of a wave passes by a given location). Long wavelength red waves have low frequencies short wavelength purple waves have high frequencies. Different colors of light also carry differing amounts of energy. High frequency, short wavelength purple light carries the most energy low frequency, long wavelength red light carries the least energy.

The visible light spectrum ranges from short-wavelength violet to long-wavelength red. Photons of light from violet end of the spectrum have the highest energies and the highest frequencies, while red photons have lower energies and lower frequencies. Beyond the range of our vision are the longer wavelengths of the infrared and the shorter wavelengths of the ultraviolet regions of the electromagnetic spectrum.
Credit: Artwork by Randy Russell .

Visible light is not, however, the whole story by any means. Visible light is but one small segment of the entire electromagnetic spectrum. Waves that have wavelengths slightly shorter than purple light, and thus have slightly higher frequencies and higher energy levels, are called ultraviolet ("beyond violet", from the Latin ultra = "beyond") or UV "light" or radiation. We cannot see UV "light", though some animals, like honeybees, can. Likewise, just beyond the other end of the visible spectrum lie waves with wavelengths slightly longer that red light waves. These waves, which have even lower frequencies and carry somewhat less energy than red light, are called infrared ("below red", from the Latin infra = "below") or IR "light" waves.

Of course, IR and UV and visible light are not the whole story either. Beyond the UV portion of the spectrum lie the still shorter waves (with higher frequencies and greater energies) of X-rays. Beyond X-rays lie the extremely short wavelength gamma rays, which have exceptionally high energies and frequencies. Moving in the other direction, out beyond the infrared portion of the EM spectrum, we find various types of radio waves. All radio waves have longer wavelengths than infrared waves, and thus carry less energy and have lower frequencies. Microwaves (yes, the kind employed in microwave ovens) are relatively short wavelength (and thus relatively high energy) radio waves. Back when broadcast television signals were common, the waves that carried TV signals to our antennas were a type of radio wave. Of course, radio signals, both AM and FM, are also carried by radio waves.

This depiction of electromagnetic spectrum shows several objects with size scales comparable to the wavelengths of the waves of different types of electromagnetic radiation. Note that the range of wavelengths vary by many orders of magnitude, while the waves shown in this "cartoon" do not. For example, visible light waves are typically 100 time shorter than infrared waves, not just slightly shorter as depicted pictorially.
Credit: Image courtesy of NASA's "Living With a Star" program and the Center for Science Education at Space Sciences Laboratory, University of California at Berkeley .

Click here to view a QuickTime movie titled "Infrared - More Than Your Eyes Can See". This is a very large file (38 megabytes), so it will probably take quite a while to download! (Source: The CoolCosmos Project).

The Sun's Emissions of Electromagnetic Radiation

The Sun emits EM radiation across most of the electromagnetic spectrum. Although the Sun produces gamma rays as a result of the nuclear fusion process (see the diagram of the proton-proton chain on "The Solar Furnace" reading page), these super high energy photons are converted to lower energy photons before they reach the Sun's surface and are emitted out into space. So the Sun doesn't give off any gamma rays to speak of. The Sun does, however, emit x-rays, UV, light (of course!), IR, and even radio waves.

The peak of the Sun's energy output is actually in the visible light range. This may seem surprising at first, since the visible region of the spectrum spans a fairly narrow range. And what a coincidence, that sunlight should be brightest in the range our eyes are capable of seeing! Coincidence? Perhaps not! Imagine that our species had "grown up" on a planet orbiting a star that gave off most of its energy in the ultraviolet region of the spectrum. Presumably, we would have evolved eyes that could see UV "light", for light of that sort is what would be most brightly illuminating our planet's landscapes. The same sort of reasoning would apply to species that evolved on planets orbiting stars that emit most of their energy in the infrared they would most likely evolve to have IR sensitive eyes. So it seems that our eyes are tuned to the radiation that our star most abundantly emits.

The graph below shows a simplified representation of the energy emissions of the Sun versus the wavelengths of those emissions. The y-axis shows the relative amount of energy emitted at a given wavelength (as compared to a value of "1" for visible light). The x-axis represents different wavelengths of EM radiation. Note that the scale of the y-axis is logarithmic each tick mark represents a hundred-fold increase in amount of energy as you move upward.

This graph shows (approximately) the distribution of the EM energy emitted by the Sun vs. the wavelength of that energy. Long-wavelength radio waves are to the right, short wavelength X-rays are to the left. The units of energy along the vertical axis are relative to the peak in the Sun's EM energy output in the visible light part of the spectrum, which is arbitrarily given the value of "1". Note that the vertical scale is logarithmic, so that each tick mark represents a hundred-fold increase/decrease in energy.
Credit: Image courtesy of the COMET program and the High Altitude Observatory at NCAR (the National Center for Atmospheric Research) .

Physicists use a concept called a "blackbody radiator" to explain how hot objects emit EM radiation of different wavelengths. Although a blackbody radiator is a mental construct, not a real object, many real objects behave almost like a blackbody radiator. As an example, imagine a piece of iron that is heated in a furnace. At first, when the iron is not especially hot, it will not glow at all but if you put your hand near it, you could feel the heat it was giving off. At this relatively low temperature the iron radiates most of its energy in the IR portion of the spectrum, which we cannot see but which we can feel as heat. As the iron gets warmer, it begins to glow deep red the peak of its radiation has just moved into the lowest energy, longest wavelength portion of the visible spectrum just above the infrared. As the iron grows hotter, its glow becomes orange and then yellow, as its peak emissions creep up the spectrum to higher energies and shorter wavelengths.

So what does this have to do with the Sun? An iron bar made of solid metal and a giant ball of gas-like plasma made of hydrogen and helium don't seem very similar, and you might not expect them to behave at all alike. Nevertheless, the visible "surface" of the Sun behaves pretty much like an idealized blackbody radiator. Recall that the temperature of the photosphere is around 5,800 K. The graph below shows the theoretical radiation curve for a blackbody radiator with a temperature of 5,800 K. Notice that over much of the EM spectrum the Sun looks very much like a blackbody radiator. Notice also that the Sun emits many more high-energy photons in the UV and X-ray regions of the spectrum than a blackbody radiator would. So what does all of this mean?

This graph shows the distribution of the EM energy emitted by a "blackbody radiator" having a temperature of the surface of the Sun (approximately 5,800 kelvin). Compare this with the energy distribution of the Sun shown above. Note how the two curves are virtually identical from the near ultraviolet to the radio wave regions, but are quite different in the far ultraviolet and X-ray regimes. The radiation emitted from the Sun's atmosphere causes the Sun to behave differently than an ideal blackbody radiator.
Credit: Image courtesy of the COMET program and the High Altitude Observatory at NCAR (the National Center for Atmospheric Research) .

The Sun's photosphere behaves pretty much like a blackbody radiator. If we look at the Sun in visible or IR light, we will pretty much be observing the photosphere. However, the Sun emits more high energy UV and X-rays than a blackbody radiator would. These high energy photons are mainly emitted from the Sun's atmosphere. Recall how the temperature of the Sun gradually declined from 15 million K at the core to 5,800 K at the photosphere, but then surprisingly rose again to 3 million K in the Sun's outer atmosphere (the corona). The high temperatures of the solar atmosphere, along with explosive phenomena like solar flares that further energize this region of the Sun, generate high energy UV and X-ray photons. Furthermore, different wavelengths of UV and X-ray emissions come from different heights in the solar atmosphere, so we can view different levels of the Sun's atmosphere by looking at specific wavelengths of these UV and X-ray emissions. Let's examine some of these multispectral views of the Sun now.

The Multispectral Sun

The Sun emits electromagnetic radiation at many wavelengths across the EM spectrum. These images show the Sun in the infrared, visible light, four different ultraviolet wavelengths, and in X-rays. Images taken in very narrow bands have the wavelengths of the associated waves noted (in nanometers). The photosphere is most prominent in the visible light images, while UV and X-ray views show details of the solar atmosphere. Note that almost all of these images are "false color" representations, since your eyes cannot see X-rays or ultraviolet or infrared "light".

Credits: IR image courtesy of the High Altitude Observatory at NCAR UV and visible light images courtesy of SOHO (NASA/ESA) visible light (656 nm) image courtesy of Big Bear Solar Observatory/New Jersey Institute of Technology X-ray image courtesy of Yohkoh.

This animation shows views of the Sun at various frequencies across the electromagnetic spectrum. Note how different features and regions of the Sun are visible in the different views. The visible light view shows the photosphere, including several sunspots. The infrared view shows the lower chromosphere immediately above the photosphere, where temperatures are still relatively cool. Most of the high energy photons that produce the UV and X-ray views come from higher up in the Sun's hot atmosphere. Notice how the areas of the atmosphere above sunspots tend to be especially bright in the X-ray and UV views. Sunspots are visible indicators of magnetic disturbances on the Sun that spawn high-energy phenomena such as solar flares and coronal mass ejections.

Most of the individual views portray the Sun as seen through a very narrow range of wavelengths for example, the IR view is just a narrow band of infrared "light" with a wavelength around 1,083 nanometers (as opposed to the entire IR portion of the spectrum, which ranges across wavelengths from 750 nm to 1 mm), while the first UV image is centered around a wavelength of 30.4 nanometers. These narrow wavelength "windows" in the EM spectrum are actually the "fingerprints" of specific elements at specific temperatures. Hot gases and plasmas emit light (or UV radiation or X-rays) at very specific wavelengths, depending on the element involved and the temperature of that element. For example, the IR image with a wavelength of 1,083 nm is produced by atoms of helium indicative of temperatures of a few thousand kelvin. The 30.4 nm wavelength UV image is also produced by helium, but that helium has been ionized (stripped of one of its two electrons), which indicates that its temperature is somewhere in 60,000 to 80,000 kelvin range, and thus that it is somewhere around the boundary between the upper chromosphere and the hotter corona. The shorter wavelength, higher energy photons that produce the 19.5 nm wavelength UV image indicate an even hotter region higher up in the corona they are emitted by iron (yes, the Sun has vaporized iron in it!) atoms that have had 11 of their electrons stripped away by temperatures around 1.5 million kelvin. The main upshot of all this is that different wavelength images allow us to see material at different temperatures on and above the Sun. In many cases, this means that each different wavelength image provides us with a view of material at a different height within the solar atmosphere. Also, certain features are especially prominent at different wavelengths.

"OK", you may say, "these are indeed pretty pictures. but what does all of this have to do with Earth's climate?". As we'll see in later pages, different wavelengths of EM radiation behave differently when they reach Earth's atmosphere. Fortunately for us, most of the high energy X-rays and ultraviolet radiation are absorbed by our atmosphere far above our heads, preventing them from frying us. They do, however, transfer their energy to the atmosphere at various levels, which has implications for our climate. Also, as we'll see in the very next reading, the amount of radiation emitted by the Sun in various wavelengths is not completely constant over time. Short term events like solar flares can dramatically alter the levels of X-ray and UV emissions from the Sun over the course of a few minutes. Multi-year cycles in solar activity only slightly alter the amount of visible light the Sun emits (to the tune of 0.1%), but can change the levels of X-ray and UV emissions by a hundred-fold.


Introduction to Solar Radiation

Radiation from the sun sustains life on earth and determines climate. The energy flow within the sun results in a surface temperature of around 5800 K, so the spectrum of the radiation from the sun is similar to that of a 5800 K blackbody with fine structure due to absorption in the cool peripheral solar gas (Fraunhofer lines).

Solar Constant and "Sun Value"

The irradiance of the sun on the outer atmosphere when the sun and earth are spaced at 1 AU - the mean earth/sun distance of 149,597,890 km - is called the solar constant. Currently accepted values are about 1360 W m -2 (the NASA value given in ASTM E 490-73a is 1353 ±21 W m -2 ). The World Metrological Organization (WMO) promotes a value of 1367 W m -2 . The solar constant is the total integrated irradiance over the entire spectrum (the area under the curve in Figure 1 plus the 3.7% at shorter and longer wavelengths.

The irradiance falling on the earth's atmosphere changes over a year by about 6.6% due to the variation in the earth/sun distance. Solar activity variations cause irradiance changes of up to 1%. For Solar Simulators, it is convenient to describe the irradiance of the simulator in “suns.” One “sun” is equivalent to irradiance of one solar constant.

Extraterrestrial Spectra

Figure 1 shows the spectrum of the solar radiation outside the earth's atmosphere. The range shown, 200 - 2500 nm, includes 96.3% of the total irradiance with most of the remaining 3.7% at longer wavelengths. Many applications involve only a selected region of the entire spectrum. In such a case, a "3 sun unit" has three times the actual solar irradiance in the spectral range of interest and a reasonable spectral match in this range.

Example

The model 91160 Solar Simulator has a similar spectrum to the extraterrestrial spectrum and has an output of 2680 W m -2 . This is equivalent to 1.96 times 1367 W m -2 so the simulator is a 1.96 sun unit.

Terrestrial Spectra

The spectrum of the solar radiation at the earth's surface has several components (see Figure 2). Direct radiation comes straight from the sun, diffuse radiation is scattered from the sky and from the surroundings. Additional radiation reflected from the surroundings (ground or sea) depends on the local "albedo." The total ground radiation is called the global radiation. The direction of the target surface must be defined for global irradiance. For direct radiation the target surface faces the incoming beam.

All the radiation that reaches the ground passes through the atmosphere, which modifies the spectrum by absorption and scattering. Atomic and molecular oxygen and nitrogen absorb very short wave radiation, effectively blocking radiation with wavelengths -2 reaching the outer atmosphere is reduced to ca. 1050 W m -2 direct beam radiation, and ca. 1120 W m -2 global radiation on a horizontal surface at ground level.

The Changing Terrestrial Solar Spectrum

Absorption and scattering levels change as the constituents of the atmosphere change. Clouds are the most familiar example of change clouds can block most of the direct radiation. Seasonal variations and trends in ozone layer thickness have an important effect on terrestrial ultraviolet level.

The ground level spectrum also depends on how far the sun's radiation must pass through the atmosphere. Elevation is one factor. Denver has a mile (1.6 km) less atmosphere above it than does Washington, and the impact of the time of year on solar angle is important, but the most significant changes are due to the earth's rotation (see Figure 4). At any location, the length of the path the radiation must take to reach ground level changes as the day progresses. So not only are there the obvious intensity changes in ground solar radiation level during the day, going to zero at night, but the spectrum of the radiation changes through each day because of the changing absorption and scattering path length.

With the sun overhead, direct radiation that reaches the ground passes straight through the entire atmosphere, all of the air mass, overhead. We call this radiation "Air Mass 1 Direct" (AM 1D) radiation, and for standardization purposes we use a sea level reference site. The global radiation with the sun overhead is similarly called "Air Mass 1 Global" (AM 1G) radiation. Because it passes through no air mass, the extraterrestrial spectrum is called the "Air Mass 0" spectrum.

The atmospheric path for any zenith angle is simply described relative to the overhead air mass (Figure 4). The actual path length can correspond to air masses of less than 1 (high altitude sites) to very high air mass values just before sunset. Our Oriel Solar Simulators use filters to duplicate spectra corresponding to air masses of 0, 1, 1.5 and 2, the values on which most comparative test work is based.

Standard Spectra

Solar radiation reaching the earth's surface varies significantly with location, atmospheric conditions including cloud cover, aerosol content, and ozone layer condition, and time of day, earth/sun distance, solar rotation and activity. Since the solar spectra depend on so many variables, standard spectra have been developed to provide a basis for theoretical evaluation of the effects of solar radiation and as a basis for simulator design. These standard spectra start from a simplified (i.e. lower resolution) version of the measured extraterrestrial spectra, and use sophisticated models for the effects of the atmosphere to calculate terrestrial spectra.

The most widely used standard spectra are those published by The Committee Internationale d'Eclaraige (CIE), the world authority on radiometeric and photometric nomenclature and standards. The American Society for Testing and Materials (ASTM) publish three spectra - the AM 0, AM 1.5 Direct and AM 1.5 Global for a 37° tilted surface. The conditions for the AM 1.5 spectra were chosen by ASTM "because they are representative of average conditions in the 48 contiguous states of the United States". Figure 5 shows typical differences in standard direct and global spectra. These curves are from the data in ASTM Standards, E 891 and E 892 for AM 1.5, a turbidity of 0.27 and a tilt of 37° facing the sun and a ground albedo of 0.2.

Table 1 Power Densities of Published Standards

Solar Condition Standard Power Density (Wm -2 )
Total 250 - 2500 nm 250 - 1100 nm
WMO Spectrum 1367
AM 0 ASTM E 490 1353 1302.6 1006.9
AM 1 CIE Publication 85, Table 2 969.7 779.4
AM 1.5 D ASTM E 891 768.3 756.5 584.7
AM 1.5 G ASTM E 892 963.8 951.5 768.6
AM 1.5 G CEI/IEC* 904-3 1000 987.2 797.5

* Integration by modified trapezoidal technique
CEI - Commission Electrotechnique Internationale
IEC - International Electrotechnical Commission

The appearance of a spectrum depends on the resolution of the measurement and the presentation. Figure 6 shows how spectral structure on a continuous background appears at two different resolutions. It also shows the higher resolution spectrum smoothed using Savitsky-Golay smoothing. The solar spectrum contains fine absorption detail that does not appear in our spectra. Figure 7 shows the detail in the ultraviolet portion of the World Metrological Organization's (WMO) extraterrestrial spectrum. Figure 7 also shows a portion of the CEI AM 1 spectrum. The modeled spectrum shows none of the detail of the WMO spectrum, which is based on selected data from many careful measurements.

The spectra we present for our product, and most available reference data, is based on measurement with instruments with spectral resolutions of 1 nm or greater. The fine structure of the solar spectrum is unimportant for all the applications we know of most biological and material systems have broad radiation absorption spectra. Spectral presentation is more important for simulators that emit spectra with strong line structure. Low resolution or logarithmic plots of these spectra mask the line structure, making the spectra appear closer to the sun's spectrum. Broadband measurement of the ultraviolet output results in a single total ultraviolet irradiance figure. This can imply a close match to the sun. The effect of irradiance with these simulators depends on the application, but the result is often significantly different from that produced by solar irradiation, even if the total level within specified wavelengths (e.g. UVA, 320 - 400 nm) is similar.

Geometry of Solar Radiation

The sun is a spherical source of about 1.39 million km diameter, at an average distance (1 astronomical unit) of 149.6 million km from earth. The direct portion of the solar radiation is collimated with an angle of approximately 0.53° (full angle), while the "diffuse" portion is incident from the hemispheric sky and from ground reflections and scatter. The "global" irradiation, the sum of the direct and diffuse components, is essentially uniform. Since there is a strong forward distribution in aerosol scattering, high aerosol loading of the atmosphere leads to considerable scattered radiation appearing to come from a small annulus around the solar disk, the solar aureole. This radiation mixed with the direct beam is called circumsolar radiation.


The Rayleigh-Jeans Law

Lord Rayleigh and J. H. Jeans developed an equation which explained blackbody radiation at low frequencies. The equation which seemed to express blackbody radiation was built upon all the known assumptions of physics at the time. The big assumption which Rayleigh and Jean implied was that infinitesimal amounts of energy were continuously added to the system when the frequency was increased. Classical physics assumed that energy emitted by atomic oscillations could have any continuous value. This was true for anything that had been studied up until that point, including things like acceleration, position, or energy. Their resulting Rayleigh-Jeans Law was

[ egin d ho left( u ,T ight) &= ho_ < u>left( T ight) d u [4pt] &= dfrac<8 pi k_B T> u^2 d u label end]

Experimental data performed on the black box showed slightly different results than what was expected by the Rayleigh-Jeans law (Figure (PageIndex<5>)). The law had been studied and widely accepted by many physicists of the day, but the experimental results did not lie, something was different between what was theorized and what actually happens. The experimental results showed a bell type of curve, but according to the Rayleigh-Jeans law the frequency diverged as it neared the ultraviolet region (Equation ( ef)). Ehrenfest later dubbed this the "ultraviolet catastrophe".

It is important to emphasizing that Equation ( ef) is a classical result: the only inputs are classical dynamics and Maxwell&rsquos electromagnetic theory. The charge (e) of the oscillator does not appear: the result is independent of the coupling strength between the oscillator and the radiation, the coupling only has to be strong enough to ensure thermal equilibrium. The derivation of the law can be found here.

Figure (PageIndex<5>): Relationship between the temperature of an object and the spectrum of blackbody radiation it emits. At relatively low temperatures, most radiation is emitted at wavelengths longer than 700 nm, which is in the infrared portion of the spectrum. The dull red glow of the hot metalwork in Figure (PageIndex<5>) is due to the small amount of radiation emitted at wavelengths less than 700 nm, which the eye can detect. As the temperature of the object increases, the maximum intensity shifts to shorter wavelengths, successively resulting in orange, yellow, and finally white light. At high temperatures, all wavelengths of visible light are emitted with approximately equal intensities. (CC BY-SA-NC anonymous)

Differential vs. Integral Representation of the Distribution

Radiation is understood as a continuous distribution of amplitude vs. wavelength or, equivalently, amplitude vs. frequency (Figure (PageIndex<5>)). According to Rayleigh-Jeans law, the intensity at a specific frequency ( u) and temperature is

However, in practice, we are more interested in frequency intervals. An exact frequency is the limit of a sequence of smaller and smaller intervals. If we make the assumption that, for a sufficiently small interval, (&rho( u,T)) does not vary, we get your definition for the differential (d&rho(&nu,T)) in Equation ef:

The assumption is fair due to the continuity of (&rho( u,T)). This is the approximation of an integral on a very small interval (d u) by the height of a point inside this interval ((frac<8pi k_bT u^2>)) times its length ((d u)). So, if we sum an infinite amount of small intervals like the one above we get an integral. The total radiation between ( u_1) and ( u_2) will be:

Observe that (&rho( u,T)) is quadratic in ( u).

Example (PageIndex<4>): the ultraviolet catastrophe

What is the total spectral radiance of a radiator that follows the Rayleigh-Jeans law for its emission spectrum?

The total spectral radiance ( ho_(T)) is the combined emission over all possible wavelengths (or equivalently, frequencies), which is an integral over the relevant distribution (Equation ef for the Rayleigh-Jeans Law).

[int_0^infty x^2mathrmx onumber ]

does not converge. Worse, it is infinite,

[ lim_int_0^k x^2mathrmx = infty onumber ]

Hence, the classically derived Rayleigh-Jeans law predicts that the radiance of a a blackbody is infinite. Since radiance is power per angle and unit area, this also implies that the total power and hence the energy a blackbody emitter gives off is infinite, which is patently absurd. This is called the ultraviolet catastrophe because the absurd prediction is caused by the classical law not predicting the behavior at high frequencies/small wavelengths correctly (Figure (PageIndex<5>)).


Watch the video: Distance to the Sun. Myths and reality. How we actually measure it. Crepuscular rays. (June 2022).