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## 1. The Brightest Stars

The following table provides some information about the ten stars that are brightest in the sky as seen from Earth (except for the Sun, which is a star, too, but much closer to us than the other stars).

Table 1: Brightest Stars

Name Constellation Magnitude Brightness Spectral Type Distance/lj Month
1 Sirius α CMa Great Dog −1.47 3.87 A1V 8.6 January
2 Canopus α Car Keel −0.72 1.94 F0II 313 December
3 α Centauri α Cen Centaur −0.29 1.31 G2V+K1V 4.4 May
4 Arcturus α Boo Bootes −0.04 1.04 K1.5III 37 April
5 Wega α Lyr Lyre +0.03 0.97 A0V 25 July
6 Capella α Aur Charioteer +0.08 0.93 G5IIIe 42 December
7 Rigel β Ori Orion +0.12 0.90 B8Iab: 773 December
8 Procyon α CMi Little Dog +0.34 0.73 F5IV-V 11.4 January
9 Achernar α Eri River Eridanus +0.50 0.63 B3Vpe 144 October
10 Betelgeuze α Ori Orion +0.58 0.59 M2Iab: 427 December

The "Brightness" is the brightness compared to a star of magnitude 0. The "Month" is the month in which the Sun is at the other side of the sky, so that the star is highest in the sky at midnight. Of these stars, #2, #3, and #9 are not visible from the Netherlands. #5 and #6 are visible every night (weather permitting) from the Netherlands.

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## 2. The North Star or PoleStar or Polaris

The North Star, also called Polaris or α Ursae Minoris, is about 430 lightyears from Earth. In a car going 100 miles per hour that never stops, it would take you about 3 thousand million years to travel that distance.

The North Star is due north in the sky, at a height above the horizon that is equal to your north latitude. The North Star is not visible from the southern hemisphere of Earth.

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All stars move around compared to one another. The Sun is a star, too, and moves compared to the other stars, so if you wait for long enough, then all stars are in different positions compared to the Sun. The distances and speeds of stars are such that even a nearby star takes many tens of thousands of years to move to the opposite side of the sky (relative to the other stars).

The North Star is quite far away and takes about 80,000 years to move one degree in the sky (compared to the other stars).

At the moment the North Star is close to the North Pole of the sky, the point in the sky that all stars seem to rotate around at night, because the rotation axis of the Earth points in that direction. The Earth behaves like a spinning top of which the axis of rotation traces a circle in the sky in about 26,000 years, so in just a few thousand years' time the North Star will be far from the North Pole of the sky, but that is not because the North Star has moved but because the rotation axis of the Earth has moved.

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## 3. The Lifetime of Stars

How long a star lives depends very much on how much mass that star has. A star with more mass emits much more light, so it consumes its store of fuel faster and lives shorter. A star with less mass lives much longer. A star like the Sun lives for on average about 10 thousand million years. A star that has 1.5 times the mass of the Sun lives about 2 thousand million years. A star that has 15 times the mass of the Sun lives only about 11 million years. A star that has 0.8 times the mass of the Sun lives for about 20 thousand million years.

The Sun is now about 5 thousand million years old, so the Sun can last still about 5 thousand million years more.

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## 4. Viewing the Stars the Most Brilliant

The appearance of stars from Earth depends on the condition of the atmosphere. Even if there aren't any clouds, it matters whether the air is dry or humid, whether it contains dust or air pollution or other small particles (other than air molecules), and whether the air currents are placid or turbulent. It also matters whether there are big cities nearby.

Small particles in the air (such as dust or air pollution) scatter part of the starlight, which then appears to come from the sky between the stars, which then does not appear quite pitch black anymore, which makes the stars stand out less. A lot of water vapor in the air has a similar effect.

Big cities in the area tend to send air pollution and other small particles into the air, and also tend to shine a lot of light into the night sky. The extra light can scatter from the extra particles back down to you, which spoils your view of the stars. That's why you cannot see as many stars from a big city as from a rural area.

If the air is turbulent, then the stars twinkle a lot. If the air is placid, then the stars twinkle hardly at all. Air gets turbulent, for example, if there is a very large temperature difference between the ground and the air. In wetter climates, such conditions also produce cumulus (cauliflower-shaped) clouds. During the day, the ground is heated up by the Sun more than the air is, so then the temperature difference increases and the air becomes turbulent. During the night, the ground cools down again, the temperature difference decreases, and the air becomes more placid (assuming that the weather cooperates).

So, for the best viewing of stars, you want to be in a place with very dry air, far away from big cities or other producers of particles in the air and nighttime light. Desert-like areas sound good for this (except when there are sand storms). Any other lightly populated, dry area with a decent climate should be OK as well, and there are lots of those around the world.

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## 5. White Dwarves

A white dwarf is what is left when a star such as the Sun runs out of fuel. When that happens, then the core of the Sun consists of carbon and oxygen and is squeezed by the weight of the higher layers until it becomes a sort of giant crystal. The outer layers fly away into space, and the part that used to be the core is left over, and that is the white dwarf.

Such a white dwarf is still as massive as a star, but has been squeezed so severely that it is only as large as a planet. A cubic centimeter of a white dwarf weighs about 300,000 times as much as a cubic centimeter of water. A white dwarf does not generate energy in its center but is yet very hot in the beginning because it used to be the center of a star when that star was generating energy and heat. A white dwarf doesn't do a lot, except slowly cool down.

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## 6. Red Giants

As the Sun grows older, it is expected to get slightly brighter, which means the Earth (and the other planets) will get hotter. When the Sun starts to run out of hydrogen in its core, in about five thousand million years, then it will swell into a red giant star, about 40 times larger than it is today, so then it will reach about halfway to the orbit of Mercury, and will have an apparent diameter of about 20 degrees in the Earth's sky.

The Sun then also increases in brightness to about 1000 times the brightness it has today, and that means that the Solar System gets much hotter than it is today. At the distance where the Earth is today, the average temperature of a pitch-black sphere that the Sun shines on will increase from about room temperature to about 1850 degrees Celsius. The zone where life can exist will shift from the Earth's orbit out to about the orbit of Neptune.

When the Sun has become a red giant, then it will likely start to shed part of its outer layers: great clouds of gas will fly away from the Sun, and these will disrupt the orbit of the Earth because of their friction. I don't know whether they'll make the Earth lose speed and fall into the Sun, or whether they'll push the Earth away from the Sun.

In any case, the Earth will not be a good place to live when the Sun turns into a red giant in about four thousand million years or so. This won't be a big problem, because it is estimated that the Earth will not be able to sustain life anymore after the next two thousand million years or so, because of natural chemical and geological processes in the Earth and the atmosphere.

The inside of the Earth is still cooling down from its formation, and eventually it will cool down so much that volcanoes stop working and the molten material inside the Earth stops moving around.

The Earth continuously loses oxygen and water vapor and other gases from the atmosphere, because they escape into space. The loss of these gases is today made up for by new gases that come from below the surface of the Earth, through volcanoes. So, when volcanoes stop working, then the loss of oxygen and water vapor is no longer balanced, and the Earth will slowly dry out and the atmosphere will change.

The Earth is currently shielded from harmful particles in the Solar Wind by the magnetic field of the Earth, and this magnetic field is generated by molten magma moving around under the surface of the Earth. If the magma stops moving around, then the magnetic field will disappear (or at least get much weaker), so then these harmful particle will be able to reach the surface of Earth and cause trouble for living things.

If humans still exist at that time, then they'd better find another planet to live on.

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## 7. Exploding Stars

Stars tend to blow up when they run out of fuel. The size of a star is determined by the balance between the force of gravity, which tries to make the star shrink, and the pressure of the gas in the star, which tries to make the star expand. For most of the existence of the star, these two forces are balanced, so that the star has a (reasonably) fixed size.

The star loses energy, in the form of heat and light that the star emits into space. The balance between gravity and pressure inside a star could not remain unless the energy that the star loses was made up for somehow. During most of its lifetime, a star generates energy through nuclear fusion in the center of the star where the temperature and pressure is great enough for fusion to happen. This energy compensates for the energy that is lost to space as light and heat, so that the star can stay the same size.

If the fuel inside the star runs out completely, then the star cannot make up for the energy loss anymore, so then gravity wins from pressure and makes the central parts of the star shrink. The outermost layers of the star are then launched into space.

In the case of a very massive star, the ejection of the outer layers happens suddenly in a big explosion. For a few months, the star then gets millions of times brighter than before, and is then called a supernova. The outer layers expand into space and form a so-called supernova remnant, of which the Crab Nebula (M 1, //www.seds.org/messier/m/m001.html) is a good example. The central part of the original star may turn into a neutron star, which has a mass of a star but a diameter of only about 10 km (6 mi), or a black hole, which has the mass of a star inside a region that is even smaller than a neutron star.

In the case of a fairly light-weight star such as the Sun, the outermost layers are launched into space more gradually and form a so-called planetary nebula, of which the Ring Nebula (M 57, //www.seds.org/messier/m/m057.html) is an example. The central part of the original star then forms a white dwarf, which has the mass of a star but the diameter of an earth-like planet.

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## 8. Supernovas

A supernova is a short phase in the life of a very massive star. Only stars that start their life with more than about eight times the mass of the Sun can become a supernova. The Sun cannot turn into a supernova. Such a star becomes a supernova when the nuclear reactions inside the star cannot compensate anymore for the loss of energy to light and other radiation and neutrinos. Then the inner parts of the star collapse and the outer parts explode into space. The star then appears much (up to about 15 magnitudes or one million times) brighter for a few weeks. The outer layers that are launched into space form a so-called supernova remnant, of which the Crab Nebula is an example. It may be that the inner parts of the star explode as well, and that nothing is left of the star. It is also possible that a neutron star or a black hole is left.

The brightest stars in the sky that might turn into a supernova have magnitudes near 0, so if such a star goes supernova, then it can briefly get as bright as magnitude −15, which is just brighter than the Full Moon, but the Sun is about 25,000 times brighter still.

These stars are all quite far away, so there is no danger of the Earth being caught up in the explosion, or anything like that.

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## 9. Can One See Stars Outside of our Milky Way Galaxy?

We cannot see ordinary stars outside of our own galaxy if we don't use a telescope. A really bright ordinary star can be seen without a telescope out to about 30,000 lightyears from Earth, if dust and gas do not absorb the light on its way to us, and such a star at 30,000 lightyears would be barely visible even if you saw it under the best of circumstances. Our galaxy has a diameter of at least 100,000 lightyears, so any star at 30,000 lightyears still belongs to our own Galaxy.

The only stars outside of our own galaxy that we could possibly see at night without using a telescope are supernovas. Supernovas are very massive ordinary stars that have come to the end of their life and are transforming into a neutron star or a black hole. During this transformation they get about 10,000 times brighter than they were before, and then they are visible from about 100 times farther than they were before. After a few weeks, the supernova fades again.

You may be able to see a supernova outside of our galaxy without using a telescope if it is no further from you than about 3 million lightyears and if there are no obscuring clouds of dust or gas between it and you. Only the closest members of our own Local Group of galaxies are within 3 million lightyears, including the Andromeda Nebula (M 31) and the Small and Large Magellanic Clouds. Only two supernovas have been seen in any of these galaxies: One in the Andromeda Nebula in 1885, and one in the Large Magellanic Cloud in 1987.

The supernova in the Andromeda Nebula got up to magnitude 6, which means it was right at the limit of visibility without a telescope, so you would probably have doubted that it was even there, and it would most definitely not have stood out.

Supernova 1987a in the Large Magellanic Cloud reached magnitude 3, which means that it was quite easily visible to the unaided eye, if you knew where (and when) to look. It faded and became invisible to the unaided eye after a few weeks.

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## 10. Moving Stars

All stars move, but some move more quickly than others. Even if they didn't move to begin with, the force of gravity from all of the other stars and things would make them move (but perhaps only very slowly).

There are no kilometer or mile markers in space, so you always have to pick some star or some other thing in space to compare the motion to. For example, the Sun moves at about 20 kilometers (12 miles) per second compared to the average of the other nearby stars. All of those stars (and the Sun) move around the center of the Galaxy at about 250 kilometers (160 miles) per second. And the Galaxy moves compared to the other galaxies.

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## 11. Fixed Stars

A fixed star is a point of light in the night sky that does not move from day to day or from year to year, relative to the other fixed stars in the sky. Nowadays we call something like that just a star.

A long time ago, astronomers called every point of light that they could see in the sky a star, because you could not tell from the point of light what kind of thing it really was. Some of those stars moved (slowly) compared to one another, but most did not. The stars that always kept the same place compared to one another and formed fixed patterns (constellations) were called the "fixed stars". The stars that moved slowly between the fixed stars were called the "moving stars". Our word "planet" for these things derives from the Greek words for "moving star".

Nowadays we know that "fixed stars" and "moving stars" don't differ just in how they move along the sky, but also greatly in other things such as their size (fixed stars are much larger) and temperature (fixed stars are much hotter). For this reason, a planet is not regarded any longer as a special kind of star but as a completely separate thing.

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## 12. Hot Stars

Stars produce a lot of heat. All the light that you see from a star was made by that star, and the kind of light that comes from a star comes from the heat of that star. Most stars generate heat in their center by transforming hydrogen into helium there in nuclear reactions. Only stars that have retired (white dwarves, neutron stars, black holes) do not generate heat anymore, though they can still heat up by getting energy from outside.

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## 13. The Closest Stars

The closest star by far is the Sun. The closest star system beyond the Solar System is called alpha Centauri, which holds the brightest star of the constellation Centaurus. Alpha Centauri is a system with three stars. In such systems, each star gets a capital letter, starting with the A for the brightest one. Of the three stars, alpha Centauri C is now the closest one to us (at 4.3 lightyears), and that star is therefore also called Proxima Centauri (proxima = Latin for near). You can find a picture and information about this system at //antwrp.gsfc.nasa.gov/apod/ap960526.html.

The first star beyond the distance of alpha Centauri is called Barnard's Star, at 5.9 lightyears from the Sun. For a list of the closest stars, you can go to (among other places) //www.astro.wisc.edu/~dolan/constellations/extra/nearest.html.

You have to be a little careful with such lists, because once in a while another nearby star is discovered which isn't yet in the list, though such newly discovered stars are always dim, because the bright ones were easier to spot.

There are quite a few websites that refer to Barnard's Star, including, for instance, Wikipedia at //www.wikipedia.org/wiki/Barnard's_star.

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## 14. Planets near Proxima Centauri

In principle, it is possible that there are planets orbiting around Proxima Centauri (the nearest neighbor star to the Sun), but we would not be able to live on such planets. Proxima Centauri is the smallest member of the Alpha Centauri system. Proxima Centauri is a red dwarf star that is much dimmer, smaller, and cooler than the Sun is. The orbit around that star that yields the same temperature as the Earth's orbit around the Sun is only 7 million kilometers from the star (compared to 150 million kilometers for the Earth). Proxima Centauri is a so-called flare star, which means that the brightness of the star occasionally increases dramatically for a while because something like a super solar flare happens, much larger than the solar flares of the Sun. That is bad news for life on planets close to such a star, because solar flares come with a lot of harmful radiation. On Earth, the atmosphere and Van Allen radiation belts keep most of that radiation away from us, but so close to Proxima Centauri that radiation is presumably much stronger.

The other members of the Alpha Centauri system are called Alpha Centauri A and Alpha Centauri B (Proxima Centauri is also called Alpha Centauri C) and especially Alpha Centauri A looks much more like the Sun. The members A and B orbit around each other at an average distance of 23 Astronomical Units, which is less than the distance between the Sun and the planet Neptune. It is possible that there are planets orbiting around Alpha Centauri A or B, and those have a better chance of harboring life than planets around Proxima Centauri have. See //homepage.sunrise.ch/homepage/schatzer/Alpha-Centauri.html for more information about Alpha Centauri.

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## 15. Measuring Distances to Stars

The distance to nearby stars can be measured most accurately using their parallax. Parallax is the effect whereby an object seems to shift relative to its background if you observe it from a slightly different location. For example, if you hold your finger in front of your face and then look at your finger first with just your left eye and then with just your right eye (without moving your finger), then it seems as if your finger has moved compared to its background. That shift gets greater if your finger gets closer or if the distance between the locations of observation (in this case your eyes) increases.

If you want to determine the distance to really far-away things using the parallax, then you must try to get as large a distance between the locations of observation as possible. The greatest distance that we on Earth can get is the diameter of the orbit of the Earth around the Sun, which is about 300 million kilometers or 200 million miles. If we want to measure the distance to a nearby star, then we regularly take pictures of that star and its surroundings throughout the year, and then after one year (or more) we look at those pictures to see if the star has shifted compared to the other stars in the picture.

If the star is sufficiently close by, then it will have shifted. Part of that shift is because of the real (or proper) motion of the star, and another part is because of the to-and-fro motion because of the parallax and the orbit of the Earth around the Sun. The proper motion of the star is almost always along a straight line, so we can separate it from the to-and-fro motion tied to the parallax. The reach of the to-and-fro motion in the sky is as great as the diameter of the Earth's orbit would appear to be at the distance of the star.

The stars turn out to be at such stupendously great distances that the parallax is measured in seconds of arc, or in small parts of a second of arc. A second of arc is the 3600th part of a degree. For comparison: a stick of 1 meter (1.1 yards) long perpendicular to the line of sight covers 1 second of arc in the sky if it is at 206 km (129 mi) distance.

By definition, the distance at which a star has a parallax of 1 second of arc is called the "parsec". (For this, the parallax is defined not as the full width of the to-and-fro motion, but only half as much -- which is the greatest deviation from the average.) A parsec is equal to about 3.26 lightyears.

The nearest star (Proxima Centauri) has a parallax of 0.772 seconds of arc, so it is at a distance of 1/0.772 = 1.29 parsec or 1.29*3.26 = 4.2 lightyears.

The first parallaxes of a small number of nearby stars were measured around 1830. It remained difficult work until the launch of the Hipparcos satellite in 1989. That satellite could determine much smaller parallaxes than before, down to about 0.001 seconds of arc. With that, one could determine distances to about 500 parsec or 1500 lightyears (but of course with ever decreasing accuracy for ever farther stars). With this, we have now directly measured the distance to a couple of tens of thousands of stars. See //www.rssd.esa.int/Hipparcos/.

The future Gaia satellite, which is now expected to be launched in 2011, is going to be much more accurate still than Hipparcos, and will be able to measure the distance to about a thousand million stars. See //gaia.esa.int/science-e/www/area/index.cfm?fareaid=26.

For stars that are so far away that we cannot (yet) measure their distance using parallax we have to use a different method, such as the "standard candle method". A candle seems brighter when it is closer by and dimmer when it is further away. If you know that two candles are identical (i.e., they are according to the same standard), then the dimmer-seeming candle must be further away than the brighter-seeming candle. This general method can be used also for stars, if you can estimate how much light the star really emits. And you can estimate that if you look carefully at how the light of the star is distributed among the differen colors (and spectral lines), because that is different for a giant star than for a dwarf star, and different for a hot star than for a cool star.

For example, assume that you want to know the distance to a very far-away star. If based on the distribution of light across the different colors you can find an identical star that looks much brighter in the sky than the far-away star, then you can calculate the ratio of their distances from the ratio of their apparent brightness. And if you already know the absolute distance to the bright star (for example because Hipparcos could measure it using parallax), then you can use that ratio to calculate the distance to the very far-away star.

The parallax of stars was invented long before people could really measure it. That parallax was used in the 16th century as an argument in the fight between the geocentric world view (where the Sun orbits around the fixed Earth) and the heliocentric world view (where the Earth orbits around the fixed Sun). That so far nobody had been able to measure the parallax of any star was easiest explained, or so the argument went, if you assumed that the geocentric world view was correct, because then you don't expect any parallax of stars, because then the Earth is always in the same location. The proponents of this argument could not imagine that the stars would turn out to be so enormously far away that they would not show a then-measurable parallax even when the Earth does orbit around the Sun.

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## 16. Information about Particular Stars

You can find all kinds of information about individual stars at //simbad.u-strasbg.fr/simbad/sim-fbasic. For example, type "alpha CMa" or "Sirius" to get information about the brightest star in the constellation of the Great Dog, including

Parallaxes mas:379.21 [1.58]

This says that the parallax of Sirius is equal to 379.21 milli-arcseconds ("mas"), with an uncertainty of 1.58 milli-arcseconds. The distance to a star, measured in parsec (pc), is equal to 1000 divided by the parallax measured in "mas", so the distance to Sirius is equal to 1000/379.21 pc = 2.63 pc.

1 pc = 3.26156 lightyears, so the distance to a star is also equal to 3261.56 lightyears divided by the parallax in "mas". The distance to Sirius is then 2.63 * 3.26 = 3261.56/379.21 = 8.6 lightyears.

Another option is to install the free software "Stellarium" (from //www.stellarium.org). Then you can point at the stars of interest on your screen and see some information about them, including the parallax and distance. (That program also gives a very realistic picture of the starry sky as seen from a dark location.)

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## 17. What Stars Are

Stars are giant glowing balls of gas that emit light that was formed in nuclear reactions deep inside the stars. Stars are just like the Sun, but are much further away than the Sun. Because they are so much further away, they look much smaller and much less bright than the Sun, just like the headlights of a car at the end of your street look smaller and dimmer than the headlights of a car that drives past your house.

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A star is not the same as a nebula. A star looks like a point of light, but a nebula looks like a fuzzy patch of light. Some nebulas (or nebulae) are big clouds of gas and dust (such as the Orion Nebula), and some are very large groups of stars that are close together (such as the Andromeda Nebula).

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Stars die when their fuel runs out. Stars send out energy in the form of light and heat. To make up for this energy that is lost, the star generates new energy in its center by using up fuel (mostly hydrogen gas). Stars are born with a limited (but very large) amount of fuel, so that fuel eventually runs out, and then the star dies. It is expected that the Sun will die (turn into a white dwarf) in about five thousand million years.

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## 18. Nuclear Fusion

Stars generate energy because of nuclear fusion that happens inside them, and part of the energy leaves the star in the form of light. Nuclear fusion occurs only at very great temperatures and pressures. The simplest fusion reaction that can occur is the reaction in which four hydrogen nuclei or protons are changed into a helium nucleus, two positrons, two neutrinos, and some photons. This reaction occurs in stars in several different ways, which are known as the proton-proton reaction and the CNO cycle. These reactions are described further below. The symbols that occur in the formulas are:

 Symbol Meaning $${q}$$ $${m}$$ H = ¹H hydrogen-1 nucleus (proton) +1 1 D = ²H hydrogen-2 nucleus (deuterium nucleus) +1 2 ³He helium-3 nucleus +2 3 ⁴He helium-4 nucleus +2 4 ⁷Be beryllium-7 nucleus +3 7 ⁸Be beryllium-8 nucleus +3 8 ⁷Li lithium-7 nucleus +4 7 ⁸B boron-8 nucleus +5 8 ¹²C carbon-12 nucleus +6 12 ¹³C carbon-13 nucleus +6 13 ¹³N nitrogen-13 nucleus +7 13 ¹⁴N nitrogen-14 nucleus +7 14 ¹⁵N nitrogen-15 nucleus +7 15 ¹⁵O oxygen-15 nucleus +8 15 γ photon 0 0 ν neutrino 0 0 e⁺ positron +1 0 e⁻ electron −1 0

In the preceding table, $$q$$ stands for the electrical charge of the particle (measured in units of the charge of an electron) and $$m$$ stands for the mass number (measured as the number of nucleons, which are protons and neutrons).

Nuclear reactions cannot occur at will, but have to obey certain conservation laws. For example, the total (net) amount of electrical charge $$q$$ must remain the same during the reaction, and the total number of nucleons $$m$$ must also remain the same. Another conservation law ensures that whenever a nucleus ejects a positron, then a neutrino is also ejected. There is no conservation law for the number of photons that are emitted.

In ordinary stars (dwarf stars, stars on the main sequence, stars of brightness class V), with central temperatures between about 1 million and 20 million kelvin, energy is generated only using the proton-proton reaction and the CNO cycle. In the Sun, less than 1 percent of the energy is generated using the CNO cycle, and more than 99 percent with the proton-proton reaction.

### 18.1. Proton-Proton Reaction

The proton-proton reaction or pp-reaction converts hydrogen nuclei (protons) into helium without needing other elements to be present. There are three different proton-proton reactions, which are known as PP I, PP II, and PP III. In the Sun, about 70 percent of the energy is generated using the PP I reaction, 29 percent using the PP II reaction, and 0.1 percent using the PP III reaction.

#### 18.1.1. PP I Reaction

The PP I reaction works as follows:

 2 H + 2 H →  2 D + 2 e⁺ + 2 ν 2 D + 2 H →  2 ³He + 2 γ ³He + ³He →  ⁴He + 2 H + γ net: 4 H →  ⁴He + 2 e⁺ + 2 ν + 2 γ

#### 18.1.2. PP II Reaction

The PP II reaction goes as follows:

 H + H →  D + e⁺ + ν D + H →  ³He + γ ³He + ⁴He →  ⁷Be + γ ⁷Be + e⁻ →  ⁷Li + ν ⁷Li + H →  ⁸Be ⁸Be →  2 ⁴He net: 4 H + e⁻ →  ⁴He + e⁺ + 2 ν + 2 γ

#### 18.1.3. PP III Reaction

The PP III reaction goes as follows:

 H + H →  D + e⁺ + ν D + H →  ³He + γ ³He + ⁴He →  ⁷Be + γ ⁷Be + H →  ⁸B + γ ⁸B →  ⁸Be + e⁺ + ν ⁸Be →  2 ⁴He net: 4 H →  ⁴He + 2 e⁺ + 2 ν + 2 γ

### 18.2. CNO Cycle

The CNO cycle uses carbon (C), nitrogen (N), and oxygen (O) as catalysts: those elements are not used up, but if none of them is present, then the CNO cycle cannot proceed.

 ¹²C + H →  ¹³N + γ ¹³N →  ¹³C + e⁺ + ν ¹³C + H →  ¹⁴N + γ ¹⁴N + H →  ¹⁵O + γ ¹⁵O →  ¹⁵N + e⁺ + ν ¹⁵N + H →  ¹²C + ⁴He net: 4 H →  ⁴He + 2 e⁺ + 2 ν + 3 γ

### 18.3. Other Nuclear Reactions in Stars

The greater the temperature and pressure are, the heavier the elements are that can be formed by nuclear fusion reactions. At temperatures of at least about 100 million kelvin, a carbon-12 nucleus can be formed from three helium-4 nuclei (via beryllium-8), and an oxygen-16 nucleus from four helium-4 nuclei (via carbon-12). You cannot find these temperatures inside dwarf stars such as the Sun is today, but you can find them in the center of red giant stars (stars of brightness class III), such as the Sun will be in about five thousand million years.

At temperatures of at least about 600 million kelvin, carbon and oxygen nuclei can be combined to form sodium (Na), neon (Ne), magnesium (Mg), silicon (Si), phosphorus (P), and sulfur (S), as is shown schematically in the next table (from which non-nucleons have been omitted). These temperatures can be found only in supergiant stars (stars of brightness class I) and in supernovae.

 2 ¹²C →  ²⁰Ne + ⁴He 2 ¹²C →  ²³Na + ¹H 2 ¹²C →  ²⁴Mg 2 ¹⁶O →  ²⁸Si + ⁴He 2 ¹⁶O →  ³¹P + ¹H 2 ¹⁶O →  ³²S

If a supergiant star at the end of its life briefly turns into a supernova, then yet other types of nuclear reactions can occur which can form yet heavier elements, such as iron and uranium.

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## 19. Convection Zones

Many stars have convection zones where their gas is not at rest but is bubbling as if it is boiling. On average, warmer gas moves upward and colder gas moves downward in such zones, and in that way energy (heat) is transported to the surface of the star. Convection occurs where that is a more efficient way of energy transport than radiation is.

According to [BowersDeeming], main sequence stars with more than about two solar masses have a convective core, because such stars get their energy mostly from the CNO cycle for which the rate of energy production is very sensitive to the temperature, which tends to produce very steep temperature gradients. Main sequence stars with less than about two solar masses get their energy from proton-proton reactions for which the rate of energy production is much less dependent on temperature, which allows for non-convective cores. For stars of less than 1.1 solar masses the core remains non-convective, but for more massive stars it seems to be possible that their core turns convectie after all towards the end of their stay on the main sequence. That is likely connected to the conversion of helium into carbon, which may again have a steep dependence on temperature. If helium is the end product (for less massive stars), then the star ends up with a core that is made almost exclusively of helium in which no more fusion reactions occur, and then that core has the same temperature throughout, and has no convection.

At the other end, cool stars (like the Sun) have an extensive convection zone near the surface, because the relatively low temperature means that there is a wide zone where hydrogen is only partially ionized, and that yield high opacity that makes it more difficult for radiation to get through, which makes convection more effective at transporting energy. For hotter stars the hydrogen is very quickly completely ionized, which means the opacity is a lot lower, and then there is no convection near the surface.

So: In the main sequence, cool, light stars (M < 2) have a convection zone near the surface, and hot, massive stars (M > 2) have a convective core. What happens for medium-type stars is not clear to me. Some people say that an A-type star is completely non-convective, but others refer to two convection zones in an A-type star. I guess it depends a lot on the specific model and on the specific abundances.

After the main sequence, on the way to becoming a red giant, the outer layers of all stars become convection-free, but for lighter stars the surface convection returns eventually, when the outer layers have cooled down enough.

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## 20. The Stars During the Day

The stars are still there in the daytime, but then you don't see them because the sky is then so brightly blue (at least, if it isn't cloudy). The blue of the sky is light that comes from the Sun at that was on its way to a different place from where you are, but that hit an air particle along the way and then came to you after all. Scientists call this "scattering of light". Such collisions go easiest with blue light, and that's why the sky is blue. The sky is much less bright than the Sun itself, but is yet much brighter than the stars, and that's why you can't see any stars during the day.

It does not help if you reduce the amount of sky that you see, for example by looking up a smoke stack, because that does not reduce the brightness of the sky next to the star nor increase the brightness of the star, so it does not make the star more visible by comparison.

You could see the star only if you reduced the amount of sky so much that you could not tell anymore where the sky begins and the star ends, but then there'd be a very good chance that no bright star at all would happen to pass through the tiny window when you were looking, and it would take a star only a second or two to pass through that window. It seems hardly worth the effort to go to all that trouble.

But there is a better way. You can reduce the apparent brightness of the sky by looking at it through a magnifying optical instrument, such as a telescope. If you look at the sky through a telescope, then a particular patch of sky looks bigger, so its brightness seems to be spread over a larger amount of sky and is lower. A star still looks like a point, so its brightness is not spread out. So, if you look at the sky with magnification, then the sky looks less bright compared to the stars. If the magnification is large enough, then you can see stars during mid-day.

I don't know off-hand how large a magnification you need, but it can't be all that large, because it seems that you can sometimes see Venus (at magnitude −4) at midday even without magnification, if you know where to look.

The stars don't all appear at the same time at night, either. You can see the brightest stars first, because then the sky is already darker than the brighest stars, but still brighter than the dimmer stars.

If there weren't any air on Earth, then the sky wouldn't be blue, and then you'd be able to see stars in the sky, if you didn't look at the Sun, at least, because you cannot see a small light well if it is very close to a very bright light.

There is no air on the Moon or in space, so from there you can see the stars during the day.

On Earth, you can still see stars during the day if you use a very big telescope (so there's only a very tiny patch of sky in view next to the star) or if you experience a total eclipse of the Sun. During a total eclipse of the Sun, the Moon blocks nearly all of the sunlight. Then it gets dark as if it is night, and then you can see the brightest stars.

Scattering of light happens also at night. Of the light of streetlights, greenhouses, cars, and houses that goes up into the sky, the air scatters a small part back down again. That's why from a city or an area of greenhouses the dimmest stars or the Milky Way aren't visible even on a clear night. That's also why astronomers take their telescopes to faraway places where there aren't any towns or greenhouses nearby: then the sky is still really dark at night and then you can see many more stars.

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## 21. Spectral Classes

With for example a prism you can break light up into its separate colors, in a so-called spectrum. When astronomers did this to the light of stars, they found that the stars weren't all the same. Some had more blue light, and others had more red light. Also, thin dark lines (spectral lines) could be seen in the spectra and those weren't the same for all stars, but there were groups of stars that had roughly the same spectra. The astronomers started dividing the stars into classes based on their spectra. They began with class A and worked their way down the alphabet. Some of these classes were later combined so eventually only classes A, B, F, G, K, M, N, O, R, and S remained. The Sun is a star of class G.

Many years later it was discovered that most spectral classes depend mainly on the surface temperature of the stars. When you put the classes in descending order of surface temperature, then you get O B A F G K M and that is the order in which they're usually mentioned nowadays. Stars of class O are hottest, and those of class M are coolest. The classes R, N, and S are rare and don't rely on just the temperature (though they contain only cool stars) and are usually placed in that order after M.

This sequence is not easy to remember, so generations of astronomy students have tried to invent mnemonics for them. A very well known one is "Oh, Be A Fine Girl Kiss Me Right Now, Smack".

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## 22. Variable Stars

Most stars aren't always equally bright, but are sometimes a bit brighter and sometimes a bit fainter. For most stars, the variation is so small that you need sensitive equipment to measure it. For some stars, the variation is so large that you can notice it by just looking at them regularly. Those stars are called variable stars.

Stars can be variable for many different reasons. Some vary so regularly that you could set your watch by them, and always vary by nearly the same amount, while the brightness of others changes at unpredictable times and by ever changing amounts.

One kind of variable star is an eclipsing binary star. A binary star is two stars that orbit around each other. An eclipsing binary star is a binary star of which one member periodically eclipses part of the other member, as seen from Earth. When one of them moves in front of the other one, then the closer one blocks part of the light of the more distant one, so then less light reaches us from both of them combined. So, an eclipsing binary star isn't periodically brighter but rather periodically fainter.

It is possible for binary systems to get periodically brighter, but then it's not because of mutual eclipses, but because one of them is periodically capturing gas from the other one. That gas heats up tremendously when it slams into the surface of the capturing star, and that means it gets very bright and emits lots of X-rays. Such a variable star is called a flaring star.

It is quite easy to distinguish these two types of binary stars: flaring stars tend to show enormous periodic increases in X-ray emissions, whereas eclipsing binary stars show hardly any change in X-ray emissions by comparison.

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## 23. The Hertzsprung-Russell Diagram

The Hertzsprung-Russell Diagram (often abbreviated to HR diagram) is a graph with along its horizontal axis a measure of the surface temperature (spectral class, color), and along its vertical axis a measure of the absolute brightness (the brightness as seen from a standard distance). If you put a mark in the graph for each star according to its surface temperature and absolute brightness, then you see that the stars don't show up all over the place but instead prefer certain areas in the diagram.

Most stars in the HR diagram can be found in the Main Sequence, which runs from the top left (bright and hot) to the bottom right (dim and cool) in the diagram.

The (ordinary) Giant Branch is the route that a star like the Sun follows through the HR Diagram when the hydrogen in its core runs out (through transformation into helium) and the star turns into a red giant. Meanwhile that core gets hotter, and in the end (for a star with sufficient mass, including the Sun) gets hot enough to start transforming helium into carbon. Then the star slowly moves to the left in the HR Diagram. Many stars in this phase of their evolution are close together in the HR Diagram in a horizontal cloud, which is called the Horizontal Branch.

Eventually the helium in the core runs out, too, and then the star moves (in the HR diagram) back to the place where the helium burning first started: it then becomes a red giant again. The route that it takes through the HR diagram is near the route that the star took when it became a red giant for the first time, and is called the Asymptotic Giant Branch because in the end it is nearly the same as the earlier (ordinary) Giant Branch.

It is a bit confusing that some names (such as "Main Sequence" and "Horizontal Branch") belong to things that you can see in a HR Diagram of a particular moment that contains information about many stars, and other names (such as "Giant Branch" aand "Asymptotic Giant Branch") belong to things that you can see in the HR Diagram if you follow the evolution of a single star for a very long time.

You can see a recent HR Diagram of many stars at //en.wikipedia.org/wiki/File:HRDiagram.png. You can recognize the Main Sequence and Horizontal Branch in that diagram.

You can see an HR Diagram with some evolutionary tracks of stars at //en.wikipedia.org/wiki/File:Stellar_evolutionary_tracks-en.svg.

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Last updated: 2021-07-19