Pieter Bruegel the Elder (1525-1569)

Why Do We Study Stars?

  • Stars are interesting
  • Stars are very luminous, LSun = 4x1023 kWatts
    • indirect energy source
    • direct energy source
  • Solar-Terrestrial climate connections
  • Stars are High-Energy Physics Laboratories
  • Stars are useful probes of the properties of the Universe
  • ....


World-Wide Energy Consumption

1 TW (terraWatt) = 1 TWatt = 109 kWatt (kiloWatt) ===> 10 TW = 2.5x10-14 of the Solar luminosity (power output)!

Note that out of the energy sources listed, four (oil, coal, gas, hydro) are from the Sun. The only one which is not is nuclear.

Note: What's a Watt? A Watt is an energy expenditure of 1 Joule per second. Okay, so what is a Joule? Let's see, mosquitos are 1-2 milligrams (~2-4 millionths of a pound) and fly at speeds of ~1-2 km per hour. So, a flying mosquito has kinetic energy ~ 4x10-7 Joule, or a swarm of 2.5 million mosquitos carries kinetic energy of ~1 Joule!

There is more to the story than this, however. Because of the large distance to the Sun (150,000,000 km), we intercept only ~2.2x10-5 of the Sun's power per unit area (its energy Flux). The brightness of the Sun (its flux) falls off as 1/D2, where D is the distance to the Sun. Although the amount of energy we intercept because of this effect (the inverse square fall-off of the brightness of the Sun) is tiny, the fraction of the Solar power we absorb is large in the sense that the Earth easily intercepts enough energy from the Sun to satisfy our energy needs. Even allowing for cloud cover (Albedo effects) and the absorption of light in our atmosphere (our atmosphere is not transparent because of opacity effects), the energy which reaches the ground is substantial, ~0.34 kWatts per square meter, A Solar collector ~100 miles x 100 miles in size is capable of capturing enough Solar energy to satisfy the current energy needs of the Earth.


Sunspot Cycle and Solar Activity

The Sun exhibits cool blemishes on its surface known as Sunspots. The average temperature of the surface of the Sun is ~5,800 Kelvin, Sunspots are ~4,500 Kelvin. Their lower temperatures makes Sunspots appear darker than the surrounding regions of the Sun (see comments after Stefan-Boltzmann Law [Lecture 3]. Sunspots were discovered by Galileo in the 1600s. In and of themselves, Sunspots are not that significant; they are symptomatic of the activity of the Sun, however.

Sunspot Number

The Sun goes through an activity cycle, The Solar Activity Cycle with the most obvious manifestation of the varying number of Sunspots on its surface. The number varies with a period of 7-15 years with an average length of 11 years. There are other effects which we shall describe later, such as increases in coronal activity, increases in flaring activity, increases in the Solar Wind, and increases in magnetic activity. The cycle is fairly regular having been traced back hundreds of years using tree ring studies and nearly 2,000 years using coral reefs. Although regular, the Sunspot cycle has shown disruptions. For example in 1645-1715, the cycle may have halted during what is known as the Maunder Minimum. Interestingly, at this time, Northern Europe and North America were in the middle of what is referred to as the Little Ice Age (see Discovery 16-2, p. 434 ).

Solar Constant

The vexing thing is that although there are measurable changes in the Solar output during the Solar Activity Cycle, the change in the Solar luminosity (as measured by the Solar Constant, see the figure to the left) is small. The Solar Constant varies over the course of the Solar Activity Cycle from 1,367 to 1,365 Watts per square meter, as measured at the top of the Earth's atmosphere. The Sun (somewhat paradoxically) is the brightest at the peak of the Solar Activity Cycle, when the greatest number of sunspots are seen.

Faint Young Sun Paradox

The luminosity of the Sun has increased as it has aged; 3.8 billion years ago the Sun was ~25 % fainter than today. This is a conundrum because there was liquid water on the Earth at least 3.7 billion years ago and a simple argument leads to a prediction for what is referred to as the Equilibrium Temperature, Te for the Earth which at that time, would be below the freezing point of water, Te = -40 C!. Note that Te is determined by simply finding the temperature for the Earth where it radiates exactly the same amount of energy per second as it receives from the Sun in the absence of clouds and an atmosphere. Further, if we were to include an atmosphere with the composition of our current atmosphere, the temperature would rise but would still be less than the freezing point of water.

The answer to the question of then, why do we have liquid oceans? requires that our atmosphere in the past had a much different chemical composition than today so that the Greenhouse Effect could maintain liquid oceans or, perhaps, the Sun was much brighter in the past than we now believe.


The Sun and normal stars are powered by nuclear fusion reactions. In the Sun, the energy is produced through the Proton-Proton Chain, the fusion of four hydrogen nuclei into a helium nucles, plus some other fundamental particles, and energy (see More Precisely 16-2, p. 442). As a byproduct of the proton-proton chain reactions, a ghostlike particle known as the neutrino is also produced; several are produced every time an energy generating reaction occurs. Thus, if we truly understand how the Sun (and stars) shine, we expect that a certain number of neutrinos must also be produced and so, if we design an experiment to detect Solar Neutrinos it must succeed in that it must detect the appropriate number of neutrinos. There is no wiggle-room (or so we thought in the 1960s).

Solar Neutrino experiments were started in the 1960s by Brookhaven scientist, Ray Davis (see Section 16.7, pp. 442-445) to verify that we understood how the Sun worked. No one thought that the experiment would that interesting; it would be difficult but the result would not be surprising. It came as a rude surprise when Davis's experiment detected fewer neutrinos than predicted by the best models of the Sun, throwing doubt onto whether we really did understand our Sun. Follow-up experiments also found ~1/3-1/2 of predicted neutrinos. This conundrum persisted for ~35 years until the early 2000s when, first, the Super-K (Super Kamiokande) experiment showed neutrinos were chamaeleon-like in nature. Neutrinos, once produced, could change into forms undetectable by the early experiments. The SNO (Sudbury Neutrino Observatory) experiment, able to detect transmuted neutrinos, then came online and detected the predicted number of Solar neutrinos. The amusing result was that a simple observation of the Sun led us to a deeper understanding of how the Universe works on the sub-nuclear scale!

Comment: The Davis experiment was a remarkably difficult experiment. The vat contained ~400,000 liters of cleaning fluid (tetrachloroethylene). This vat contains ~2x1030 chlorine atoms. The neutrinos interact with the chlorine (on rare occasions) transforming the chlorine to radioactive argon which is subsequently detected. A huge number of neutrinos passes through the vat every second, 400 billion neutrinos flow through the detector per square inch per second. Remarkably, one expects to build up only a few tens of Argon atoms every month! This exceedingly difficult experiment was performed accurately enough by Davis to show that there were roughly 1/3 the number of neutrinos passing through his experiment as was predicted. Davis received the Nobel Prize (along with Dr. Koshiba of the Super-K experiment) in Physics in 2002 for this remarkable work.


Big Bang, Solar, and Terrestrial Chemical Abundances

At left is shown the chemical make-up of the Sun. In terms of the number of atoms, the Sun is ~91 % hydrogen, ~8.9 % helium, and a little bit of everything else. Also, more interestingly, when the Universe began, Big Bang created primarily hydrogen and helium with essentially nothing heavier. How does this compare to the Earth? Well, the chemical abundance of the Earth is groslly different. Most of the elements found in the Earth had to have been at one point in the interior of a star. The heavy elements of which we are made were, for the most part, produced in stars through fusion reactions.