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Trivia about the Sun... Beer & Red Giant eyes!

The Sun is the star of the day, a nuclear furnace that converts every second 4 million tons of hydrogen into energy, while at the same time it fuses 600 million tones of hydrogen into helium. The composition of the Sun is 73% hydrogen and 25% helium. Modern studies, with instruments on Earth or with satellites in space (such as in orbit around the Earth or at the so called Lagrange points or even missions that have approached the Sun) have revealed to us some amazing secrets of this main sequence star. A major turning point was in the middle of the 19th century and the development of methods for the analysis of the solar spectrum (the beginning of Astrophysics). The Sun does not emit only visible light, but also radio waves, UV, infrared radiation as well as X-rays. The γ-rays which are produced inside the solar core from the nuclear fusion reaction, eventually reach the surface mainly as the less energetic radio waves, UV & infrared radiation, as they lose energy every time they collide with a particle. The Sun constitutes more than 99.86% of the total mass in the solar system, however it has only 0.3% of the total angular momentum of the Solar System (notably Jupiter has 60% of it). The Sun is 1,400,000 km wide and is a perfect sphere. With 109 times the diameter of the Earth, we would need more than 1000 spheres like the Earth to cover this distance. The light and gravity need 8 minutes and 20 seconds to cover this distance. If devil (existed) and could make the Sun to disappear we would know about his decision only after 8 minutes and 20 seconds, as no signal can propagate faster than the speed of light, not even gravity itself. The average distance between the Earth and the Sun is called 1 astronomical unit or 1 AU, and is practical unit of distance inside our Solar System.It is equal to 149,597,870 km. The mass of the Sun is 330,000 times the mass of the Earth.




The Sun is a lemon on the left with a diameter of 15 cm and 1500 cm away there is a sand grain with a diameter of 0.15 cm which represents the Earth. In 5 billion years, the Sun will expand and it will become a red giant. The Sun will eventually literally devour the Earth as its diameter will become about 100 times larger!



The Source of Solar Energy

We have discussed previously how radioactive nuclides can decay to stable daughters. This

is the progress of nuclear fission. The opposite progress is nuclear fusion, which powers the

Sun. In this case protons and neutrons collide forming a new nuclides. The main energy producing process in the Sun is the proton-proton chain where 2 protons collide to form deuterium (consisting of a single nucleus with one proton and one neutron) plus one free positron e+, and one free neutrino ν. The positron will annihilate with an electron from the local environment. The total energy produced from this reaction will be 1.442 MeV. The deuterium reacts with a proton to give hellium-3 plus 5.49 MeV energy. Finally two hellium-3 nuclei collide together to give one hellium nuclei plus two protons plus 12.86 MeV energy.

Problem: Calculate the total energy released with the proton proton chain

Answer:

Given that we would need 4 protons in order to have two helium-3 nuclei the total energy released from the complete proton-proton chain reaction is about 26.7 MeV.

(1.442+1.442+5.49+5.49+12.86) MeV= 26.7 MeV

(What a coincidence: the magnitude of the apparent magnitude of the Sun is also [-26.7]= 26.7!)

In the diagram above you can see highlighted the proton-proton I reaction which is the main source of solar energy. There are also two other chains which occur less often, they involve heavier elements but at the end of the day they also produce helium, plus energy, plus positrons, plus neutrinos of the electron (PP II and PP III chains).

The process is called nucleosynthesis. Nucleosynthesis refers to the formation of nuclides by fusion reaction. Only at the middle of the 20th century scientists (using Albert Einstein's newly discovered formula of E=MC^2, which explains the large amounts of energy being produced with nuclear fusion), were able to gradually figure out the details of stellar nucleosynthesis. A key publication was: "The synthesis of elements in stars" by Burbidge, Burbidge, Fowler and Hoyle in Rev. Mon. Phys. 129, page 547-560 in October 1957.

This paper mentions: "Except at catastrophic phases a star possesses a self governing mechanism in which the temperature is adjusted so that the outflow of energy through the star is balanced by nuclear energy generation. The temperature required to give this adjustment depends on the particular nuclear fuel available. Hydrogen requires a lower temperature than helium; helium requires a lower temperature than carbon, and so on, the increasing temperature sequence ending at iron since energy generation by fusion processes ends here. If hydrogen is present the temperature is adjusted to hydrogen as a fuel, and is comparatively low. But if hydrogen becomes exhausted as stellar evolution proceeds, the temperature rises until helium becomes effective as a fuel. When helium becomes exhausted the temperature rises still further until the next nuclear fuel comes into operation, and so on. The automatic temperature rise is brought about in each case by the conversion of gravitational energy into thermal energy. In this way, one set of reactions after another is brought into operation, the sequence always being accompanied by rising temperature. Since penetrations of Coulomb barriers occur more readily as the temperature rises it can be anticipated that the sequence will be one in which reactions take place between nuclei with greater and greater nuclear charges. As it becomes possible to penetrate larger and larger barriers the nuclei will evolve towards configurations of greater and greater stability, so that heavier and heavier nuclei will be synthesized until iron is reached."

The paper has today over 4000 citations and discusses in detail many aspects of the stellar nucleosynthesis. In 1983, Fowler received the Nobel Prize in Physics "for his theoretical and experimental studies of the nuclear reactions of importance in the formation of the chemical elements in the universe."

The temperature near the Sun's centre is calculated to be about 15 million degrees Kelvin, adequate enough for hydrogen fusion but not enough to initiate helium burning. However, as more hydrogen is consumed, the density increases and the temperature rises. A core of helium is left. Computer models suggest that the temperatures near the centre of the Sun are 10% higher than they were when the Sun was formed and nuclear fusion started. As the hydrogen burning continues and more helium is produced, the helium will concentrate in the centre of the Sun and the temperature will rise enough to initiate helium burning. The initiation of helium burning will cause the Sun to expand dramatically and to become a red giant. The size of the red giant will extend well beyond the orbit of Venus and almost to the Earth. This process will continue as helium burning produces heavier elements. Heavier elements will again concentrate in the centre and this core will no longer be supported by heat from fusion reaction and will collapse.

Evolution of the Sun on an HR diagram. The mass of a nebula builds up over 0.1-1 Ma and collapses under its internal gravity. The gravitational energy is converted to heat and the temperature becomes high enough to initiate nuclear fusion. The protostar has a slightly higher luminosity than the present Sun. After 10 Ma the protostar reaches the Main Sequence where it burns its hydrogen up for a period of 10 Ga. During this period the Sun experiences a luminosity increase of 50%. As the hydrogen is burned, the Sun expands and becomes more luminous. During this period He is building up in the solar core. This build up increases temperature because of the transformation of gravitational energy to heat during core formation. The increased density increases pressure in the central core and helium ignites. After the initial He flash, the Sun settles down as a red giant to burn He for around 100 Ma. The He is used up and the Sun flares up violently as a nova, losing much of its outer layers and creating a planetary nebula in the centre of which lies an extremely hot, white dwarf without any further nuclear fuel. A white dwarf is a star with the size of the Earth, but with a huge density. A cubic centimetre of the materials of a white dwarf would have a typical mass of 1000 kg! It consists of a plasma of unbound nuclei and electrons. Electron degeneracy pressure is enough to resist gravity, and therefore there is no further compression of matter. Heavier stars don't form planetary nebulae at the end of their lives, neither white dwarfs. They instead become supernovae explosions, leaving behind either a neutron star or a black hole (the gravity of a neutron star or a black hole is too strong for the electron degeneracy pressure and matter compresses even further to more exotic configurations). White dwarfs cool slowly over 10 Ga to brown dwarfs. White dwarfs have a very high amount of energy trapped in a small volume, therefore it takes a long time of billions of years for the internal energy to be released into space. The study of the Sun, informs us about other stars, since it is a perfect example of how stars of similar mass behave. By studying, and observing other stars we can also know the evolution of the Sun. An HR (Hertzsprung–Russell) diagram is a useful modelling of stars based on their luminosity and surface temperature. Stars tend to occupy different positions on the diagram based on their mass and age, and an HR diagram helps us "map" the stellar evolution.

The “faint early Sun” paradox

Estimates of the solar radiation on the early Earth vary down to as little as 30% of the present solar radiation. This gives rise to the “faint early Sun” paradox about the Earth. We know that the Earth has had a fairly controlled temperature for at least 3.8 Ga. At least the temperature has been controlled enough that liquid water has been present on the surface of the Earth for all this time. The problem with the faint early Sun is that insufficient radiation was apparently available for water to remain liquid on the surface of the Earth. The Earth should have been much colder. Mars also appear to have had surface water during its early development. One solution is that the atmospheres of Earth and Mars contained more “greenhouse gases” (i.e carbon dioxide, methane) which helped retain the heat.

Solar magnetism and Sun Spots

The Sun does not have an iron core, and therefore its total magnetic field is relatively weak.

However, it is characterised by extreme concentrations of charged particles. The

movements of these charged particles in a rotating sphere give rise to locally intense

magnetic fields by the dynamo effect. The Sun rotates once in about 27 days. The equator rotates in about 24 days and the poles in 30 days. This differential rotation is caused by the fact that the outer solar layers are not rigid. Because the equator the Sun rotates much faster than the poles, extreme turbulence occurs beneath the surface of the photosphere.

The axis of rotation of the Sun is tilted about 7.25 degrees from the ecliptic. From

Earth we therefore see the Sun's north pole in September of each year and its south pole in

March. The Sun has a granular surface which reflects the turbulence in the subsurface. The

upwelling hotter zones are brighter than the down-welling cooler zones, producing the

granular effect. The location of these granules are controlled by the local magnetic fields.

When the hotter upwelling is extremely dynamic it can break through the surface and be

ejected into space as solar flares, the form of which is controlled by the magnetic fields. Groups of large scale cooler areas are darker and known as sunspots. Observations of

sunspots allow measurements of differential rotation of the Sun to be made. The opposite

brighter areas are called plaques. Sunspots were discovered by Galileo, and were an important contribution to the development of scientific thought. The previous Aristotelian thought and proposed that the heavenly spheres, especially the Sun, were perfect. The discovery of sunspots suggested that they had imperfections. Sunspots are associated with intense local magnetic fields. As with the Earth, the total solar magnetic field flips at intervals. The global flips in the solar field are associated with changes in the polarity of the sunspot magnetic fields. These changes in polarity, where the leading spot in any sunspot group changes its field, are associated in turn with the development of large numbers of sunspots. The increase in sunspots occurs on a cycle of about 22 years, which appears to be related to the magnetohydrodynamics of the interaction between the Sun’s magnetic field and the differential rotation. Although the increase in darker spots on the Sun might intuitively be thought to decrease its luminosity, the opposite is the case. The sunspots are symptomatic of extreme solar magnetic storms which lead to an increase in solar radiation. During the sunspot maxima, vast fiery prominences of hot gas burst out from the photosphere into space as solar flares. These enormous bursts of energy cause an intense stream of charged particles to flow out into space. Sunspot numbers have been counted systematically since 1750. The plot of sunspot number versus time clearly shows the cyclical nature of their appearance. Very few sunspots were seen on the Sun from about 1645 to 1715. This period is called the Maunder Minimum, after Edward Walter Maunder (1851-1928), one of the first modern astronomers to study the long-term cycles of sunspots. The Maunder Minimum is also known as the Little Ice Age. There is a substantial body of evidence that the Sun has had similar periods of sunspot inactivity in the more distant past. Detailed measurements of the Sun’s luminosity have only been made systematically for the last few years. However, the Earth’s climate is highly sensitive to changes in the flux of electromagnetic radiation from the Sun. A 1% decrease in solar luminosity leads directly to a cooling of the Earth’s average temperature by 1°C. It requires an increase of similar magnitude to increase the Earth’s temperature by 1°C. The problem lies in the amplification of these effects by (a) the superimposition of solar variability on other climate drivers (b) the reinforcement of solar variability by terrestrial feedback processes.

The sunspot number R for a given day is computed according to the Wolf Sunspot Number formula:


R = k (10 g + s)


where g is the number of sunspot groups (regions), s is the total number of individual spots in all the groups and k corrects for observing conditions. The formula takes into account tat we can observe only a part of the Solar surface from the Earth.

Problem: Device a method to calculate the height of the Sun from the horizon.

Answer:

A basic unit of astronomical distances is 1 parsec (pc). The parsec gets its name form the

method of estimating stellar distances of parallax. If parallax is measured in seconds of degrees, then 1 parsec is defined as the distance of the star, when the parallax is equal to 1" (or 1 arc second). The picture below clarifies this idea:


Below you can see a plot for the temperature of the solar core (measured in millions of degrees Kelvin as a function of time (measured in billions of years).

Solar Structure

The sun consists of a thin photosphere at the surface, that emits the light we receive

on Earth. Below that surface layer, there is a convective layer and a thick radiative layer. The convective and radiative layers transmit the heat generated by nuclear fusion in the core. The solar atmosphere consists of the chromosphere and the corona which extends into space.

The Sun’s core is about 17000 km in radius, with a temperature 15 million degrees K. It is composed of 62% helium and 38% hydrogen. The next layer is called the Radiative Layer . The Radiative Layer is 420,000 km thick and has a temperature of 1.7 to 5.9 x 10^6 K. These temperatures are too low for nuclear fusion to occur. The proton/proton chain reactions of nuclear fusion in the core produce gamma radiation. The gamma rays collide with material in the radiative layer to produce energy at longer wavelengths. The energy is transported with radiation in this layer. Since the photosphere is about 1000 times cooler than the Radiative Layer, intense convection occurs. The layer in which this occurs is about 105,000 km thick. It is called the Convective Layer. Its temperature ranges from 5.9 x 10^6 K to 6.95 x 10^3 K. The

composition of the Radiative and Convective Layers is 72% hydrogen, 26% helium and 2%

of the heavy elements by mass. The intense gamma radiation emanating from the core keeps

the radiative and convective layers from collapsing. The visible surface of the Sun is about 450 km thick and has a temperature of 4,000- 8,000K. This zone is called the Photosphere and emits the radiation into space. The solar atmosphere consists of two layers :the Chromosphere and the Corona. The Chromosphere is a low density layer of very hot gas about 2,500 km thick. Temperatures reaches 10^6K only 3 km above the solar surface. The Corona is a zone of lower density gas which grades into space. The Chromosphere and the Corona are visible from Earth and spacecrafts have revealed that the Sun constantly emits a

stream of particles into space. These particles include protons, electrons and charged ions

and constitute the solar wind. On Earth, the solar wind is evidenced by the auroras. The solar

wind has a velocity of several hundred kilometres per second. The solar wind is attenuated

as it increases in distance form the Sun. The Voyager 1 space mission, at a distance of about 121 AU from the Sun detected heliopause (i.e the solar wind had attenuated significantly compared to the interstellar plasma). During the peak of the sunspot cycle , the Sun emits charged particles with energies of several hundred MeV. These are solar cosmic rays and cause disturbances to terrestrial electrical systems and satellite communication.


Below you can see some sunspots. They appear dark only because of their lower temperature (3800 K) as compared with the temperature of 6000 K of the surrounding region (photosphere).



Below you can see two pictures from NASA's space instruments: Matter in the solar chromosphere is following strong magnetic field lines. It demonstrates of how important is the local magnetic field in regulating the solar "weather".

Flares occur locally, in contrast with (Coronal mass injections) CMEs which are much larger eruptions of the corona. Solar flares are energetic explosions in the low solar atmosphere which can heat the surrounding material to millions of degrees in just a few seconds or minutes. Solar flares typically occur near sunspots where magnetic field is concentrated in the active regions on the photosphere. Flares emit radiation in visible light, ultraviolet, x-rays, gamma rays and are observed by ground based and space based telescopes. In addition to emitting large amounts of radiation, solar flares also accelerate particles which are ejected into space. Solar flares are classified based on their x-ray intensity. The letters used are: A, B, C, M and X, with A being the weakest and X being the strongest. The full classification of an x-ray flare is composed of a letter followed by a number, i.e A5.1 . The number indicates the specific intensity of the flare.

X-ray flare intensity is measured in units of power per area, or Watts per meters squared. Each letter (A, B, C, M or X) represents a certain numeric value and the number which follows the letter in the flare classification multiplies that value. The numeric values of the letter classes are listed below:

A = 1.0x10^-8 (W m^-2)

B = 1.0x10^-7 (W m^-2)

C = 1.0x10^-6 (W m^-2)

M = 1.0x10^-5 (W m^-2)

X = 1.0x10^-4 (W m^-2)

For example, an A2.1 flare would have an intensity of 2.1 x 10^-8 W m^-2.


Coronal mass injections also inject plasma into space and can cause serious problems for unprotected astronauts or sensitive systems on Earth. Below you can see an image from SOHO (SOlar and Heliospheric Observatory), that depicts a typical corona mass injection. Both solar flares and CMEs are energetic events which occur on the Sun. These events are both associated with high energy particles. In the case of a CME, coronal material is ejected into space at high speeds, sometimes in the direction of Earth. Both flares and CMEs depend on magnetic fields on the Sun. The most obvious difference between a solar flare and a CME is the spatial scale on which they occur. Flare x-rays can occur as short impulses, gone in minutes, or brightenings that decay over hours to days. The impulsive events usually produce a stream of high energy particles leaving the flare site. The slower events are often accompanied by a CME. A Coronal Mass Ejection (CME) occurs when magnetic forces overcome pressure and gravity in the solar corona. This lifts a huge mass of solar

plasma from the corona and creates a shock wave that accelerates some of the solar wind’s

particles to extremely high energies and speeds.This in turn generates radiation in the form of

energetic particles.

Sun Storm: A Coronal Mass Ejection

Credit: SOHO Consortium, ESA, NASA


Problem: Assuming that the Sun loses half of his mass during the later stages of his life, but also at the same time shrinks to the half of its size, calculate the change in the surface escape velocity.

Answer:

Using the formula for the escape velocity (which we have already derived from the law of conservation of energy), we can see that the escape velocity must remain unchanged, since it is proportional to the mass M, but inversely proportional to the distance from the centre R.


Problem: What is the luminosity of a star that is the twice as big as the Sun but has the same surface temperature? What is the luminosity of a star that is 1/4 as big as the Sun and twice as hot? Estimate the size of a star that has half of the surface temperature as the Sun but produces 10 times as much energy.

Tip: Remember that the formula for the stellar Luminosity is derived from the Stefan-Boltzmann law:

E= σT^4

where σ=5.6703*10^(-8) watt/(m^2 K^4) is Stefan's constant.


Problem: If we could add enough mass inside the Sun we would create a black hole. Calculate the change of gravitational potential energy inside the Sun, as the Sun collapses to create a black hole and explain how much mass do we need to put inside the Sun to create a black hole. Explain where does the lost gravitational potential energy goes in terms of the black hole.

Write the answer in the comment section below.


Question: What is the orbital velocity of planets around the Sun?

Answer: We can find their orbital velocity if we remember that v=v_esc,

For an object to escape from the gravitational pull of the Sun we must have v>v_esc


11 Solar trivia. Did you know that...

  1. Every 42,000,000 years the Sun converts to energy a quantity of materials equal to the mass of Earth.

  2. The solar energy that is received on the surface of Earth by the Sun is 100,000 times larger than the total energy produced in the interior of Earth.

  3. Once created in the core of the Sun, a light ray travels for 20,000 years before it reaches its surface.

  4. In the last hundreds of years the diameter of the Sun shrinks with a speed of about 1.5m per hour, but that means that its diameter is today less than about 1,300 km than it was before 100 years.

  5. If our entire Solar System had the size of a walnut, then our Galaxy would have a diameter of 160,000 km.

  6. If we changed the scale of our solar system of about three million times then it would have the size of one large room.

  7. In the same scale our Sun would have the size of a pin's head, while our nearest star would be 42 km away

  8. The pressure in the solar core is about 450 billion times the pressure on the Earth's surface.

  9. The first photograph of the Sun was taken in 1842.

  10. Sun is a typical main sequence star of spectral type G2, however the spectral type plays a major role in the probability of life appearance, as more massive stars (of spectral types O or B for example) live only for a few million years, giving almost no time for life to evolve.

  11. The first accurate measurement of the distance to the Sun was made by the Greek philosopher Anaxagoras around 450 BC although the vast majority of people continued to think that the Sun orbited the Earth for long after that.

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