Stars






The Sun



The Sun basic facts:

Mass: 1.99 X 1030 kg (332,000 times Earth’s)
Equatorial Radius: 696,000 km (109 times Earth’s)
Mean density: 1410 kg/m3 (0.255 times Earth’s)
Surface gravity: 274 m/s2 (28 times Earth’s)
Escape speed: 618 km/s
Sidereal rotation period: 25.1 solar days (equator)
   30.8 solar days (60 degrees latitude)
   36 solar days (poles)
   26.9 solar days (interior)
Axial tilt: 7.25 degrees (relative to ecliptic)
Surface temperature: 5780 K (see general information)
Luminosity: 3.84 X 1026 W

The Sun from the Inside Out:

Core – The site of powerful nuclear reactions that generate the Sun’s enormous energy output. The radius is about 200,000 km. Within the core, nuclear fusion (the combining of light nuclei into heavier ones) creates the Sun’s energy. See below for discussion of nuclear fusion.
Radiation Zone – Between the core and convection zone is the radiation zone. Solar energy is transported toward the surface by radiation rather than by convection. Along with the convection zone, makes up the solar interior.
Convection Zone – The area extending downward about 200,000 km below the photosphere. The Sun’s material is in constant convective motion. Solar energy is transported toward the surface by convection rather than radiation. Along with the radiation zone, makes up the solar interior.
The visible surface of the sun is granulated with regions of bright and dark gas known as granules. Each is about 1000 km across and last about 5 to 10 minutes. Each granule forms the top part of a convection cell. Supergranulation is similar to granulation, except that the cells measure about 30,000 km across. With both granulation and supergranulation, upwells of material at the center of the cell flows across the surface, and then sinks down again at the edges.
Photosphere – The “surface” of the sun; emits the radiation that we see. This is not a solid surface, as the sun contains no solid material. It has a radius of about 696,000 km. The thickness is about 500 km – less than 0.1% of the Sun’s total radius. Because it is so thin, this is why the Sun is perceived to have a sharp well-defined edge.
The surface of the Sun oscillates, or vibrates. The vibrations are the result of internal pressure waves that reflect off the photosphere and repeatedly across the solar interior. These oscillations can be used to study conditions below the Sun’s surface, just as seismologists study the Earth’s interior with sound waves. Because of this, the study of the Sun’s surface is called helioseismology, even though there is no such thing as solar seismic activity.
Chromosphere – The area of lower atmosphere just above the photosphere, about 1500 km thick. It emits very little light of its own and cannot be observed visually under normal conditions. During an eclipse, when the photosphere is blocked, the chromospheres can be seen. It is a reddish hue, with the coloration due to the red hydrogen alpha emission line of hydrogen, which dominates the chromospheric spectrum.

Every few minutes, small solar storms erupt, expelling jets of hot matter known as spicules into the Sun’s upper atmosphere. They leave the Sun’s surface at about 100 km/s and go several thousand km above the photosphere. They are not spread evenly across the solar surface, and cover only about 1 percent of the total area. They tend to accumulate around supergranules. The Sun’s magnetic field is stronger than average in these regions. Spicules appear dark against the Sun because they are cooler than the underlying photosphere.
Transition Zone – The area of atmosphere from 1500 km to 10,000 km above the top of the photosphere. This area is right above the chromospheres. Temperature rises dramatically in the transition zone.
Corona – Above 10,000 km and stretching far into space is the corona. It is the thin, hot upper atmosphere. This can be seen during an eclipse when the photosphere and chromospheres are both blocked by the moon.

At one time, scientists thought the spectral lines from the corona were caused by a new element that they called coronium. This has been disproven, and we know the spectral lines exist because atoms in the corona have lost more electrons than atoms in the photosphere – in other words, they’re more highly ionized. The extensive electron loss is due to the high coronal temperature. Astronomers believe that the higher temperature in the corona is caused by magnetic disturbances in the photosphere.

Unlike the photosphere that emits most strongly in the visible spectrum, the coronal gas radiates at higher frequencies, primarily in the x-ray range.
Solar Winds – At greater distances, the corona turns into solar wind. Solar wind flows away from the Sun and permeates the entire solar system. They are fast moving particles (not quite at the speed of light, but still comparable to the speed of about 500 km/s). The material reaches Earth in a matter of a few days (light reaches Earth in 8 minutes). They result from the high temperature of the corona. At about 10 million km above the photosphere, coronal gas is hot enough to escape the Sun’s gravity. The wind carries away about 2 million tons of solar matter each second. However, less than 0.1 percent of the Sun’s mass has been lost since the solar system formed 4.6 billion years ago.

Solar wind escapes mostly through solar “windows” called coronal holes. These are not really “holes” but are areas that are deficient in matter, vast regions of the Sun’s atmosphere where the density is about 10 times lower than the normal corona.

General information:

The sun rotates in about a month, but does not rotate as a solid body. It rotates differentially – faster at the equator, slower at the poles.

Sunspots are never seen above 60 degrees latitude north or below 60 degrees latitude south. Sunspots are cooler regions of the photosphereic gas. They are dark areas on the sun, typically measuring 10,000 km across (about the size of Earth). At any given time, the Sun may have hundreds of sunspots, or may have none at all. Sunspots have a dark center called an umbra, surrounded by a grayish area called a penumbra. They typically form in groups. Sunspots almost always form in pairs (roughly the same latitude), with magnetic field lines leaving one sunspot and going back into another. The magnetic field in a sunspot is about 1000 times greater than the field in nearby undisturbed photosphereic regions. They are not randomly oriented, but are roughly perpendicular to the Sun’s surface.

The polarity of a sunspot indicates which way its magnetic field is directed relative to the solar surface. Where field lines emerge from the surface is labeled “S” and where the lines go back in is labeled “N”. Field lines above the surface always run from South to North, as on the Earth. All the sunspots pairs in the same solar hemisphere have the same magnetic configuration. In addition, the sunspots in the other hemisphere have the opposite configuration. So if (reading left to right) the northern hemisphere orients S to N, then the southern hemisphere orients N to S.

The Sun’s differential rotation distorts the magnetic field wrapping it around the solar equator, eventually causing the north-south lines to reorient east-west. At the same time, convection causes the magnetized gas to well up toward the surface, twisting the magnetic field pattern. Occasionally, the field becomes so strong that it breaks free of gravity and bursts out of the surface, looping through the lower atmosphere, forming a sunspot pair.

Not only do sunspots come and go with time, but the numbers and distribution across the Sun also change fairly regularly. The average number of spots reaches a maximum every 11 years, and then falls off almost to zero before the cycle starts fresh again. This cycle is called the sunspot cycle. At the start of each cycle is the solar minimum (only a few spots are seen, generally confined to two narrow zones about 25 to 30 degrees north and south of the equator). About four years into the cycle is solar maximum (the numbers of spots has increased and are found within about 15 to 20 degrees of the equator). By the end of the cycle, at solar minimum, the number has fallen again. At the end of the 11 year cycle, the polarities reverse (the hemisphere that was S-N becomes N-S and the other hemisphere that was N-S becomes S-N). Another 11 year cycle then takes place, with the polarities reversing again at the end. This 22 year cycle (two 11 year sunspot cycles) is called the solar cycle.

The 11 year cycle is not regular. The period of time going back to when the telescope was invented, and the solar cycle tracked, shows that it ranges from 7 to 15 years. In addition, the sunspot cycle disappeared completely from 1645 to 1715. This lengthy period of solar inactivity is called the Maunder minimum. During this time the corona was also less prominent during solar eclipses

The Sun’s surface temperature is generally rounded off to 5800 K. This temperature is known as the Sun’s effective temperature.

The amount of the Sun’s energy hitting a 1 m2 area at the top of the Earth’s atmosphere is known as the solar constant. This amount is 1400 W/m2. About 50 to 70 percent of the Sun’s energy reaches the Earth’s surface with the rest either intercepted by the atmosphere (about 30 percent) or deflected by clouds (about 20 percent). The Sun’s luminosity is calculated by taking the solar constant, and multiplying it out over an imaginary area that is 1 AU in radius – a sphere around the Sun stretching to the Earth’s center.

Every second, the Sun puts out enough energy equivalent to 10 billion 1-megaton nuclear bombs.

The sun is held together by gravity, but is kept from collapsing in on itself (since it is all gas) by the outward pressure of the hot gasses. The balance of outward pressure of hot gasses to gravity is known as hydrostatic equilibrium.

The sun contains 67 elements that have been identified in various states of ionization and excitation. More elements may exist, but they are there in such small amounts that we cannot detect them. The most abundant element is hydrogen, at about 91.2% of the total number of atoms (and 71 percent of the total mass) of the Sun. Next is helium at 8.7% of the atoms, and 27.1% of the total mass. Below these two elements, the remaining elements all clock in at less than a tenth of a percent of the total atoms, and less than a percent of the total mass.

Active regions are areas around a pair of sunspots where large quantities of energetic particles erupt into the corona. Most groups of sunspots have active regions associated with them. They are most frequent and massive during the times of solar maximum.

Prominences are loops or sheets of glowing gas ejected from active regions. Quiescent prominences persist for days or even weeks, suspended by the Sun’s magnetic field high above the photosphere. Active prominences are much more erratic, changing their appearances in a matter of hours or surging from the photosphere and immediately falling back on themselves. Prominences typically measure 100,000 km, nearly ten times the diameter of Earth.

Flares are also the result of magnetic instabilities, and are more violent than prominences. Often they flash across part of the sun in minutes. A major flare can release as much energy as the largest prominence, but do so in minutes or hours rather than days or weeks. The Sun’s magnetic field is unable to hold the particles produced by a flare, so unlike prominences, they are blasted into space by the violent explosion.

Coronal mass ejections are giant magnetic bubbles of ionized gas that separate from the rest of the solar atmosphere and escape into space. They are sometimes, but not always, associated with flares. They appear about once per week at sunspot minimum and up to two or three times a day at solar maximum.

Nuclear Fusion

Nuclear Fusion is the combination of light nuclei into heavier ones. It is responsible for virtually all of the starlight we see. We can represent a typical fusion reaction symbolically as:

nucleus 1 + nucleus 2 -> nucleus 3 + energy

During fusion reaction, the total mass is decreased. The mass of nucleus 3 is less than the sum of nuclei 1 and 2. The remaining mass is converted to energy in accordance with Einstein’s E = mc2. The production of energy in this way is an example of the law of conservation of mass and energy. This states that the sum of the mass and energy (converted into the same units using Einstein’s equation) must always remain constant during any physical process. According to this, an object can literally disappear provided that energy appears in its place.

All atomic nuclei are positively charged so that they repel each other. If two protons (for example) are moving at high enough speeds, one can momentarily plow deep into the other, eventually coming within the exceedingly short range of the strong nuclear force which binds nuclei together. At distances of less than 10 m-15, the attraction of the nuclear force overwhelms the electromagnetic repulsion, and fusion occurs. This would take speeds of a few hundred km/s, which occur at temperatures in excess of 107 K.

When two protons collide, they form a positron, a neutrino, and a deuteron (the nucleus of a special form of hydrogen atom called deuterium, or heavy hydrogen, which differs from normal hydrogen by an extra neutron in the nucleus.). The positron is a positively charged electron. This is the antiparticle of the electron. They interact with electrons violently, annihilating themselves and the electron, producing pure energy in the form of gamma-ray photons. The neutrino carries no electrical charge and is of very low mass. They move at almost the speed of light interacting with almost nothing. They can penetrate several light years think lead. Their interactions with matter are governed by the weak nuclear force.

Because neutrinos travel cleanly out of the Sun interacting with virtually nothing and escaping into space a few seconds after being created makes them difficult to detect her on Earth. However, it is possible to construct neutrino detectors. They generally fall into two categories.

Neutrino capture detector – These measure the change that occurs when a neutrino is absorbed by the nucleus of an atom, converting the neutron into a proton, and changing the atom to a new element. Chlorine (converts to argon) and gallium (converts to germanium) are more likely than most to interact with neutrinos.

Neutrino scattering detectors – These use large photomultiplier tubes (light-amplification devices) to detect the resultant faint glow when a neutrino collides with (scatters from) an electron in a water molecule.

The number of solar neutrinos detected on Earth is substantially less (by 50% to 70%) than the predicted amount from the standard solar model. This discrepancy is known as the solar neutrino problem. The answer to this problem involves the properties of the neutrinos themselves. If they have even a minute amount of mass, theory indicates that it should be possible for them to change their properties – even to transform into other particles- during the 8 minute flight to Earth. This process is known as neutrino oscillations. In this model, the neutrinos are produced at the correct amount by the Sun as per the solar model. However, some turn into something else – actually, other types of neutrinos – on the way to Earth, and therefore are undetected in the two types of detectors listed above. This was proven using a neutrino scattering device that used “heavy” water (hydrogen replaced by deuterium).

Nuclei of atoms that have the same number of protons but different number of neutrons are called isotopes. Usually atoms will have the same number of protons and neutrons, but the number of neutrons can vary. To avoid confusion, numbers are added to the elemental symbol to indicate the total number of particles (protons plus neutrons) in the nucleus of the atom. Ordinary hydrogen is 1H, deuterium is 2H. Helium (two protons and two neutrons) is 4He (also called helium-4), etc.

The basic set of nuclear reactions powering the Sun is not a single reaction, but a sequence called the proton-proton chain. There are three steps involved.

(I) Two protons combine to form deuterium. (1H + 1H -> 2H + positron + neutrino)
(II) The resulting positrons annihilate with electrons to form gamma rays. The deuterons combine with protons to create an isotope called helim-3 (containing only one neutron), releasing additional energy, again in the form of gamma-rays. (2H + 1H -> 3He + energy)
(III) Two helium-3 nuclei combine to produce helium-4, 2 protons, and more gamma-ray energy.
(3He + 3He -> 4He + 1H + 1H + energy)

Gargantuan quantities of protons are fused into helium by the proton-proton chain in the core of the Sun each second. The energy released ultimately becomes sunlight. The net effect of the proton-proton chain is that four protons create helium 4, two neutrinos, and releasing gamma-ray energy.

4 protons -> helium-4 + 2 neutrinos + energy
Or
4 (1H) -> 4He + 2 neutrinos + energy

To fuel the Sun’s present energy output, hydrogen must be fused into helium in the core at a rate of 600 million tons per second. The Sun can sustain this rate of core burning for about another 5 billion years.

The Sun’s energy is produced in the core as gamma rays. As it passes through the cooler layers of the solar interior and photons are absorbed and reemitted, the radiation’s blackbody spectrum shifts toward lower and lower temperatures. The energy eventually leaves the photosphere mainly in the form of visible and infrared radiation.

Four Fundamental Forces
Gravitational force – The best known force. It binds galaxies, stars and planets together. Its magnitude decreases with distance according to an inverse-square law. The strength is also proportional to the masses of each of the two objects involved.
Electromagnetic force – Another of nature’s basic forces. Any particle having a net electric charge, such as an electron or proton, exerts an electromagnetic force on other charged particles. The strength decreases with distance according to an inverse-square law. For subatomic particles, electromagnetism is much greater than gravity. Like charges repel, and opposites attract.
Weak nuclear force – This force is much weaker than electromagnetic force. It does not obey the inverse-square law, and has an effective range much less than the size of an atomic nucleus – about 10-18 m.
Electroweak force – It is now known that electromagnetic and weak nuclear forces are not separate forces, but two different aspects of a more basic force. At low temperatures such as those found on Earth or in stars, the electromagnetic and weak forces have quite distinct properties. At very high temperatures, however, such as those that prevailed in the universe when it was less than a second old, the two are indistinguishable. Because of this, the two are said to be unified, and the universe really only has three fundamental forces, not four.
Strong nuclear force – This is the strongest of all the forces. This binds atomic nuclei and subnuclear particles together. It operates at very close range. It is unimportant outside of a distance of 10-15 m. However, within that range, it binds particles with enormous strength.

The Stars

The Milky Way contains more than 100 billion stars spread throughout a volume of space nearly 100,000 light years across. The galactic center is about 25,000 light years from Earth. Despite the incredible numbers of stars, the essential properties of stars (appearance in the sky, births, lives, deaths, and interactions with their environment) can be understood in terms of just a few basic physical stellar quantities – luminosity (brightness), temperature (color), chemical composition, size and mass.

As distances between objects increases, it becomes harder to measure parallax as it becomes smaller. The closest stars are so far away, no baseline on Earth can be used to measure the parallax. By observing a star at different times of the year, and then comparing the observations, the baseline can be extended to the diameter of Earth’s orbit – 2 AU. A star’s parallactic angle (parallax) is determined to be half the apparent shift relative to the background as we move from one side of Earth’s orbit to the other.

Stellar parallaxes are so small, astronomers use arc seconds to measure parallax instead of degrees. The distance a star must lie to have a parallax of 1” is 206,265 Aus, or 3.1 X 1016 m. This distance is known as a parsec (parallax per arc seconds), shown as 1 pc. Parallax decreases as the distance increases. The formula for parsecs is:

Distance (in parsecs) = 1 / parallax (in arc seconds)

A star with a parallax of 1” lies 1 pc from the Sun. An object with a parallax of 0.5” lies 2 pc. An object with a parallax of 0.1” lies 10 pc, etc. One parsec is approximately 3.3 light years. There is an uncertainty of +/- .01”.

Proxima Centauri (part of the Alpha Centauri Complex triple-star system) is the closest star to the Earth other than the Sun. It has the largest stellar parallax of 0.77”, which makes it about 1.3 pc away – about 4.3 light years. The next nearest Sun outside of the Alpha Centauri complex is Barnard’s Star. It has a parallax of 0.55”, making it 1.8 pc (6 light years) away from Earth. Turbulence in Earth’s atmosphere smears out ground-based images into a disk of radius 1”. However, astronomers can routinely measure stellar parallaxes of 0.03” or less, which correspond with stars 30 pc (100 light years) of Earth. High resolution adaptive optics can allow even more accurate measurements to over 100 pc.

In addition to apparent motion caused by parallax, stars have actual motion through the galaxy. Relative to the Sun (as seen by astronomers on Earth as we travel through space along with our Sun), stellar motion has two properties. Radial velocity (movement along the line of sight) is measured using the Doppler effect. Transverse velocity (perpendicular to our line of sight) can be determined by careful monitoring of the star’s position in the sky. Proper motion is the annual movement of a star across the sky, as seen from Earth, and corrected for parallax. It describes the transverse component of a star’s velocity relative to the Sun. Both the star and the Sun are moving through the galaxy. However, only their relative motion causes the star’s position in the sky to change, as seen from Earth. Like parallax, it is measured in degrees. Since the degrees are very small, it is usually expressed in arc seconds per year. Barnard’s Star moved 228” in 22 years, so its proper motion is 228”/22 = 10.4”/yr.

Once you have proper motion in arc seconds per year, the transverse velocity (in km/s) can be calculated. 10.4” is a physical displacement of 0.000091 pc or 2.8 billion km. Barnard’s Star takes a year (3.2 X 107 s) to travel this distance. Dividing 2.8 billion km by 3.2 X 107 s gives 89 km/s. Although the transverse velocities of stars is quite large (tens or even hundreds of km per s), the great distances make the proper motion small, and it usually takes years for us to calculate their movement across the sky.

With the transverse velocity and the radial velocity calculated, the two can be put into Pythagorean’s theorem (a2 + b2 = c2) to find the true space motion.

A star’s luminosity is sometimes referred to as its brightness. When we look at a star, we see its apparent brightness. Apparent brightness is not a measure of the star’s luminosity, but of its energy flux as seen from Earth. The brightness depends on the distance between the Earth and star. Apparent brightness is inversely proportional to the square of the distance from the star. Doubling the distance makes it appear 4 times dimmer. Tripling the distance makes it appear 9 times dimmer, and so forth. Apparent brightness is directly proportional, however, to the luminosity of the star. The higher the luminosity, the brighter the star appears to be.

Apparent brightness (energy flux) is proportional to luminosity / distance2

Astronomers measure apparent brightness in terms of a magnitude scale. The scale dates back to 2nd century BC. It works backwards with a bright object such as the Sun having a magnitude of -26.7, and a darker object such as the moon having a magnitude of -12.5. The original scale categorized the stars seen by naked eye into six groups. 1 was for the brightest, and 6 for the faintest. Since the numbers on this scale are apparent brightness, it is called the apparent magnitude scale.

A star’s absolute magnitude is its apparent magnitude when it is placed 10 pc away from the observer. Because this puts all stars at an equal distance, absolute magnitude is a measure of a star’s absolute brightness, or luminosity. When a star that is more than 10 pc away is moved to the 10 pc position, the apparent brightness increases and apparent magnitude decreases. Stars greater than 10 pc away have apparent magnitudes greater than their absolute magnitudes.

Astronomers determine a star’s surface temperature by measuring its apparent brightness at several frequencies and matching the observations to the appropriate blackbody curve. Because blackbody curves are so well understood, astronomers only have to use two measurements at selected wavelengths. This is done with telescopic filters that block all radiation except that within specific wavelength ranges. A B (blue) filter rejects all but a certain range between violet and blue light (380 to 480 nm). This range corresponds to wavelengths that photographic film is most sensitive. A V (visual) Filter passes only 40 to 590 nm (green to yellow) range – the part of the spectrum human eyes are most sensitive. By comparing the measurements from these two points, a blackbody curve can be drawn. As only one blackbody curve can be drawn that will relate to these two points, the blackbody curve for the star can be found, and thus yield the surface temperature. This type of non-spectral line analysis is called photometry. The ration of B flux to V flux is called the color index, or color, of the star. The higher the ratio (B over V) the hotter the temperature, and more blue the star. The lower the number, the cooler the temperature, and more red color is the star.

Stellar spectroscopy is a powerful tool for measuring the temperature of a star. The main determinant of a star’s spectral appearance is its temperature.

There are seven main spectral classes. These are:
Class (Surface Temperature (in K))
O (30,000)
B (20,000)
A (10,000)
F (7,000)
G (6,000)
K (4,000)
M (3,000)

These seven classes were subdivided into 10 subdivisions denoted by 0-9. By convention, the lower the number, the hotter the star. The series runs as follows:
… A8, A9, F0, F1 …
Our Sun is a G2 star (a little cooler than a G1, and a little hotter than a G3).

Speckle interferometry uses many short-exposure images of a star (each too brief for Earth’s turbulent atmosphere to smear) which are combined to make a high resolution map of the star’s surface. This allows astronomers to measure a star’s size directly. Once the star’s angular size has been measured, if its distance is also known, the radius can be calculated with geometry.

Many stars are too distant or too small for direct measurements to be made. Their sizes must be inferred by indirect means using radiation laws. The radius-luminosity-temperature relationship demonstrates that knowledge of a star’s luminosity and temperature can yield an estimate of its radius. It’s important to remember that this formula must be in solar units (T). This is expressed in number of times compared to the Sun. So an object with twice the luminosity of the Sun would have 2LT. When the numbers are in solar units, the following formula can be used.

LT = RT2 X TT4

This formula can be rearranged to find the radius (if luminosity and temperature are known), or temperature (if radius and luminosity are known).

Stars come in different sizes. Stars with a radius of between 10 and 100 times that of the Sun are called giants. A giant with a reddish color (one of about 4000 K surface temperature) is known as a red giant. Stars that are even larger, up to 1000 times that of the Sun, are known as supergiants. A dwarf refers to any star of radius comparable to or smaller than the Sun (including the Sun itself). A dwarf star that glows white hot is a white dwarf.

The Hertzsprung-Russell Diagram, or H-R Diagram, uses luminosity along with surface temperature to chart the stars. The Y axis is the Luminosity in solar units (with the Sun at 1). The X axis is the temperature scale O B A F G K M. This reads left to right in decreasing units as opposed to the standard increasing units we’re used to using on a chart.

As more and more stellar objects are plotted on the H-R diagram, you can see that there is a relationship between the stars. Stars are not uniformly scattered across the diagram. Instead, most are confined to a fairly well-defined band called the main sequence. Using the radius-luminosity-temperature relationship, astronomers find that the stellar radii also vary along the main sequence. Faint, red M type stars at the bottom right are only about 1/10th the size of the Sun, but bright blue O type stars in the upper left are about 10 times larger than the Sun.



At the very top are bright, hot, big stars called blue giants. The largest are called blue supergiants. At the other end are small, cool, faint stars called red dwarfs. Red dwarfs are the most common type of star in the sky, accounting for about 80%. In contrast, O and B type supergiants are extremely rare, with only about 1 in 10,000 falling into these categories. About 90% of stars in our solar neighborhood fall on the main sequence. About 9% are white dwarfs, and the remaining 1% are red giants. Big bright objects have larger habitable zone, but they don’t’ last very long (10’s of millions of years). Small stars like red dwarfs last a long time, but have small habitable zones.

Spectroscopic parallax is the process of using stellar spectra to infer the distance of the star. There are three key steps:
1. Measure the star’s apparent brightness and spectral type without knowing how far away it is.
2. Use the spectral type to estimate the star’s luminosity.
3. Apply the inverse-square law to determine the distance to the star.

Distances obtained in this way have a margin of error, and are generally accurate to no better than 25%.

By studying the width of a star’s spectral lines, astronomers can tell whether the star is on the main sequence or not. The luminosity class is a way for astronomers to classify stars according to the width of their spectral lines.

Luminosity classes:
Class (Description)
Ia (Bright supergiants)
Ib (Supergiants)
II (Bright Giants)
III (Giants)
IV (Subgiants)
V (Main-sequence stars and dwarfs)

Spectral type and luminosity class define a star just as surely as do temperature and luminosity. The full specification of a star’s spectral properties include its luminosity class. Our Sun, for example, is a G2V – indicating it is a G2 star with luminosity class V.

Mass and composition of a star determine a star’s position on the main sequence.

Most stars are part of multiple star systems. These are groups of two or more stars in orbit around each other. The majority are found in binary star systems which consist of two stars in orbit around a common center of mass, held together by their mutual gravitational attraction. Astronomers categorize binaries according to their appearances from Earth. Visual binaries are widely separated members that are bright enough you can see two stars. The more common is the spectroscopic binaries. With these, they are too distant to see the separate stars. However, the spectral lines shift back and forth indicating that there are two different stars. In the much rarer eclipsing binaries, we observe a periodic decrease in starlight as one star passes in front of another. The intensity of the light curve goes up and down.

The table below summarizes the various observational and theoretical techniques used to measure the stars listing the quantities that are assumed known, those that are measured, and the theory that is applied to turn the observations into the desired result.



On the H-R Diagram, the higher up the main sequence, the more massive the stars. The further down, the less massive the stars. With few exceptions, main sequence stars range from 0.1 to 20 times the mass of the Sun. The mass of a star at the time of its formation determines the star’s location on the main sequence. In general, the stellar mass distribution of the main sequence stars is: 41% red dwarfs (less than .25 Mass of Sun); 28% dwarfs (.25 to .5 M); 19% (.5 to 1 M); 8% (1-2 M); 3% (2 to 4 M); Giants and above rest.

We can estimate a star’s lifetime by dividing the amount of fuel available (the mass of the star) by the rate at which the fuel is being consumed (the luminosity of the star).

Stellar lifetime is approximately stellar mass/stellar luminosity

Also, since mass-luminosity relation tells us that a star’s luminosity is roughly proportional to the fourth of its mass. So the expression can be rewritten as:

Stellar lifetime is approximately 1 / (stellar mass)3

When placed in solar units, the expression becomes (this is the one used in class):

Stellar lifetime = (1/Solar Mass2) X 10 billion years

Interstellar Medium

The dark areas in the sky are not “holes” in the stellar distribution. They are regions of space where interstellar matter obscures, or blocks, the light from stars beyond. Interstellar matter is distributed very unevenly throughout space. The matter among the stars is collectively termed the interstellar medium. It is made up of two components: gas and dust. The gas is mainly individual atoms, of average size 10-10 m (1 nm), and small molecules no larger than about 10-9 m across. Interstellar dust is more complex consisting of clumps of atoms and molecules.

Gas alone does not block radiation to any great extent. The obscuration of light is caused by the dust. Light from distant stars cannot penetrate the densest accumulations of interstellar dust.

A beam of light can only be absorbed or scattered by particles having diameters comparable to or larger than the wavelength of the radiation involved. A range of dust particle sizes will block shorter wavelengths most effectively. The size of a typical interstellar dust particle or dust grain is 10-7 m, comparable in size to the wavelength of visible light. Therefore, dusty regions of space are transparent to long wavelength radio and infrared radiation, but opaque to optical and ultraviolet radiation. The overall dimming of starlight by interstellar matter is called extinction.

Because the interstellar medium is more opaque to short-wavelength radiation than longer wavelengths, light is robbed of high frequency (blue) components. Therefore, in addition to being diminished, the light is also made to appear redder than it really is. This process is called reddening.

The density of interstellar medium is extremely low. Overall, gas averages roughly 106 atoms per cubic meter – just 1 atom per cubic centimeter. Densities ranging from 104 to 109 atoms per meter cubed have been found. The best vacuum on Earth that has been attained is 1010 molecules per meter cubed.

Interstellar dust is even rarer. There are 1012 atoms of gas for one atom of dust. Despite the rarity of dust particles in space, it is relatively a dirty place. Earth’s atmosphere is about a million times cleaner than interstellar space.

About 90% of interstellar gas is atomic or molecular hydrogen; about 9% is helium, and the remaining 1 percent is heavier elements. This is comparable to the elemental abundances found in the Sun and other stars. In contrast to interstellar gas, the composition of interstellar dust is not very well known. Astronomers do know the shape of interstellar dust particles, however. Individual grains are apparently elongated or rod like. We can infer this elongated structure because light emitted by stars is dimmed and partially polarized by the dust. Polarization is the alignment of the electric fields of emitted photons, which are generally emitted with random orientations. Unpolarized light waves have randomly oriented electric fields. When light passes through aligned dust particles in interstellar space, they polarize radiation, only waves whose electric fields are oriented in a specific direction are transmitted and the resulting light is polarized.

The alignment of the interstellar dust is the subject of ongoing research. The current view is that the dust particles are affected by a weak interstellar magnetic field (perhaps a million times weaker than Earth’s field). Measurements of the blockage and polarization of starlight thus yield information about the size and shape of interstellar dust particles, as well as magnetic fields in space.

Emission nebulae are glowing clouds of hot interstellar matter. Astronomers have historically used the term nebula to refer to any “fuzzy” patch (bright or dark) on the sky; any region that was clearly distinguishable through a telescope, but not sharply defined, unlike a star or a planet. Many, but not all, of these nebulae are clouds of interstellar dust and gas.

If a cloud obscures the stars behind it, it appears as a dark patch – a dark nebula. If something within the cloud, such as a group of hot young stars, causes it to glow, then we see a bright emission nebula instead. As a newly formed hot O or B type star produces huge amounts of ultraviolet light, the photons travel outward and ionize the surrounding gas. As electrons recombine with nuclei, they emit visible radiation, causing the gas to glow. The reddish hue of these nebulae results when hydrogen atoms emit light in the red part of the visible spectrum. Because hydrogen is so plentiful, its emission usually dominates that of any other elements in the nebulae.

Throughout the glowing nebular gas are lanes of dark, obscuring dust. These are called dust lanes, and are part of the nebulae.

Another type of nebula is the reflection nebula. These are bluish nebula caused by starlight scattering from dust particles in an interstellar cloud located just off the line of sight between Earth and a bright star. They appear blue because short wavelength blue light is more easily scattered by interstellar matter back toward Earth and into our detectors.

Photoevaporation is the process in which a cloud in the vicinity of a newborn hot star is dispersed by the star’s radiation. As photoevaporation continues, it eats away the less dense material first, leaving behind delicate sculptures composed of the denser parts of the original cloud.

The ionization state of an atom is referred to by attaching a roman numeral to the chemical symbol for the atom. I for the neutral (non-ionized) state, II for singly ionized atom (missing one electron), III for doubly ionized atom (missing two electrons), etc. Because emission nebulae are composed mainly of ionized hydrogen, they are often referred to as HII regions. Regions of space containing neutral hydrogen are known as HI regions.

Because at least one hot star resides near the center of every emission nebula, we would think that the combined spectrum of the star and the nebula would be confused. However, they are not. We can easily distinguish nebular spectra from stellar spectra because the physical conditions in stars and emission nebulae differ greatly.

Unlike stars, nebulae are large enough for their actual sizes to be measured by simple geometry. Taking the information on size with estimates of the amount of matter along our line of sight as revealed by the nebula’s total emission of light, we can find the density. Generally, emission nebulae have only a few hundred particles, mostly protons and electrons, in each cubic centimeter. This is a density some 1022 times lower than that of a typical planet. Spectral-line widths indicate that the gas atoms and ions have temperatures around 8000 K.

In addition to the dominant red coloration, many nebulae emit light with a green color. The greenish tint eluded scientists for a long time, as they defied explanation in terms of the properties of spectral lines known at the time. With a fuller understanding of the working of the atom, astronomers realized these lines did result from electron transitions within the atoms of familiar elements, but under unfamiliar conditions that could not be reproduced on Earth. We now understand it is caused by a particular electron transition in doubly ionized hydrogen. In order for this to be achieved, and ion has to be left undisturbed (sometimes for hours) before dropping back to the lower state and emitting a photon. Because even a “low density” laboratory gas on Earth has many trillions of particles per cubic meter, the result is millions of collisions per second. The result is that an ion in the particular energy state that produces the peculiar green line in the nebular spectrum never has time to emit its photon in the lab. These are therefore called forbidden lines, even though it violates no law of physics – it simply can’t be reproduced on Earth.

The average temperature of a typical dark region of interstellar matter is about 100 K. Within these vast, dark interstellar voids lurks another astronomical object – the dark dust cloud. Dark dust clouds are colder than their surroundings with temperatures as low as a few tens of kelvins, and thousands or even millions of times denser. Their densities can range from 107 atoms/m3 to more than 1012 atoms/m3. Even the densest regions of dark dust clouds are barely denser than the best vacuum achievable on Earth. However, it is because they are denser than the average value of 106 atoms/m3 in interstellar space that we can distinguish these clouds from the surrounding expanse of interstellar medium.

Most interstellar clouds are much bigger than our solar system, and some are many parsecs across. These clouds are primarily gas. However, their absorption of starlight is due to the dust they contain. Emitting no visible light, they are generally undetectable to the eye, except by the degree to which they dim starlight. Interstellar clouds are the regions that spawn emission nebulae and stars.

The local bubble is a particular low-density intercloud region surrounding the Sun. It contains about 200,000 stars and extends for nearly 100 pc.

Hydrogen atoms have one electron and one proton. In addition to the orbital motion around the proton, the electron also has a spin. The proton has a spin as well. This is similar to a plant spinning on its axis as it rotates around a star that is also spinning. However, unlike a planet that is free to move in any orbit and spit at any rate, within an atom all physical quantities are quantized – they are permitted to take on only specific, distinct values. Law of physics dictates that there are only two possible spin configurations for a hydrogen atom in its ground state. They can spin in the same direction (parallel spins) or in opposite directions (antiparallel spins). The antiparallel state has slightly less energy than the parallel state.

All matter in the universe tens to achieve its lowest possible state. A slightly excited hydrogen atom with the electron and proton spinning in the same direction eventually drops down to the less energetic, opposite spin state as the electron suddenly stops and spontaneously reverses its spin. As with any such change, the transition from high energy to low energy state releases a photon with energy equal to the difference between the two levels.

The energy between the two states is very low, and the energy of the emitted photon is very low. Therefore, the wavelength is long – about 21.1 cm. This wavelength lies in the radio portion of the electromagnetic spectrum. The spectral line that results from the spin flip process is called 21 centimeter radiation. Needing no visible starlight to calibrate their signals, radio astronomers can use this radiation to observe any interstellar region that contains enough hydrogen to produce a detectable signal – even the low density regions between the dark clouds can be studied. The wavelength of this characteristic radiation is much larger than the typical size of interstellar dust particles, so it reaches Earth completely unscatterered by interstellar debris.

A molecular cloud is a cold, dense interstellar cloud which contains a high fraction of molecules. It is widely believed that the relatively high density of dust particles in these clouds plays an important role in the formation and preservation of the molecules. They dwarf even the largest emission nebulae. Molecular Hydrogen is by far the most common constituent of these clouds, but despite its abundance, it does not emit or absorb radio emission. Other molecules (although not as abundant as hydrogen) must be used to probe molecular clouds. These include ammonia, water, and formaldehyde. An unconfirmed report shows that glycine has been detected. Glycine is one of the key amino acids that form the large protein molecules in living cells.

A molecular cloud complex is a collection of molecular clouds that spans as much as 50 parsecs and may contain enough material to make millions of Sun size stars. About a thousand of these are known in our galaxy.

Star Formation

There are about 100 billion stars in each galaxy. There are about 100 billion galaxies in the universe.

Stellar nurseries are scenes of violent outbursts, interstellar shock waves, even actual collisions, as prestellar fragments grow in mass and compete for resources in a newborn cluster. The Sun and planet Earth are survivors of a similarly violent environment, some 4.5 billion years ago. Star formation is a continuing process. Stars are forming all across the Milky Way. Whatever their size, large or small, emission nebulae are the birthplace of all stars in our night sky. Star formation begins when part of the interstellar medium (one of those cold dark clouds) starts to collapse under its own gravity. The cloud fragment heats up as it shrinks, and eventually its center becomes hot enough for nuclear fusion to begin. At that point, the contraction stops, and a star is born.

The most important factor that competes with gravity to determine a cloud’s fate is heat. Gravity makes clouds collapse while heat opposes the inward pull of gravity. Two other factors affecting star formation are rotation and magnetism.

Rotation can compete with gravity’s inward pull. The faster the cloud spins, the more of a bulge it gets (and turns into a disk as gravity tries to pull it in). If the cloud is spinning fast enough, material will be thrown off into space rather than collapse in to form a star. The faster that the cloud is spinning, the more material is required to form a star, as material is lost to space.

Magnetism can also hinder a cloud from forming into a star. Magnetic fields permeate most interstellar clouds just as they do planets and the Sun. Clouds collapse along the magnetic field lines, making the cloud oblong, contracting in a distorted way. The charged particles in the magnetic field are linked, and the field itself follows the contraction of the cloud. Charged particles pull the magnetic field toward the cloud’s center in the direction perpendicular to the field lines. As the field lines are compressed, the magnetic field strength increases.

The temperature of a gas is a measure of the average speed of the atoms or molecules in it. The higher the temperature, the greater the average speed of the molecules, and the higher the pressure of the gas. To overcome this pressure (even for a cool 100 K typical cloud), the amount of mass needed to have sufficient gravitational force requires nearly 1057 atoms of hydrogen.

Star formation begins when gravity begins to overpower heat, causing the cloud to lose equilibrium and contract. Only after radical changes within the cloud does equilibrium stabilize again. There are seven basic evolutionary changes that a cloud goes through on its way to becoming a main-sequence star. The numbers on the following table are valid only for a star about the size of the Sun.



Stage 1: Interstellar cloud. The first stage is the interstellar cloud – the core of a dark dust cloud or molecular cloud. These clouds are vast ,some spanning tens of parsecs across. Stage 1 clouds contain thousands of times the mass of the Sun. The cloud becomes unstable and begins collapsing under its own gravity, eventually breaking down into smaller cloud fragments. This can be caused by many things, including the shockwave from a nearby stellar explosion, or the pressure wave produced when a nearby O and B type star forms and ionizes its surrounding. Once the cloud begins to fragment, gravitational instabilities fragment it into smaller and smaller clumps of matter. A typical cloud can break into tens, hundreds or even thousands of fragments. The whole process, from a single stable collapsing cloud to many collapsing fragments takes a few million years. Because of the fragmentation, a single cloud can produce a few dozen stars, each much larger than the Sun, or a whole cluster of hundreds of stars each comparable to the size of our Sun (or smaller).

Stage 2: A collapsing cloud fragment. A fragment destined to form a star like the Sun contains between one and two solar masses of material. The fragment spans a few hundredths of a parsec across, and is a gaseous blob. Virtually all the energy released in the collapse radiates away as the cloud fragment is still too thin to stop the photons produced. Only in the center where the radiation must traverse the greatest amount of material to escpae, is there any appreciable temperature rise.

The process of fragmentation is eventually stopped by the increasing density within the shrinking cloud. As stage 2 fragments condense, they eventually come so dense that radiation cannot get out of the cloud easily. Trapped radiation causes the temperature to rise, pressure to increase, and fragmentation to cease.

Stage 3: Fragmentation ceases. The density in the inner regions has become high enough that the gas is opaque to the radiation it emits, so the core of the fragment begins to heat up considerably. In the outer part, the gas is still able to radiate energy into space, and so remains cool. The fragment begins to resemble a star. The dense opaque region at the center is called a protostar – an embryonic object at the dawn of star birth. The protostar’s mass continues to grow as more material rains down on it, but the radius continues to decreased because pressure cannot overcome gravity at this point. After stage 3, we can distinguish a surface, or photosphere, on the protostar.

Stage 4: A protostar. At this point, electrons and protons are ripped from atoms and whiz around at hundreds of kilometers per second. The temperature, however, is still short of the 107 K needed for proton-proton nuclear reaction to begin. Because there is no nuclear reaction, the luminosity at this point is due to gravitational energy as the protostar continues to shrink and material from the surrounding fragment continues to fall onto its surface. The protostar has a surface temperature only about half the Sun, but is hundreds of times larger than the Sun. The luminosity of the protostar is several thousand times the luminosity of the Sun.

At stage 4, the physical properties of the protostar can be plotted on the H-R diagram, so the protostar enters the H-R diagram at stage 4. At each point here after of the star’s evolution, it can be plotted on the H-R diagram. The motion of the point as the star evolves is known as the star’s evolutionary track. It is a graphical representation of a star’s life. The portion of the path from when the fragment became a protostar in stage 3 to where it lies on the H-R diagram at stage 4 is an approximated path. The early evolutionary track here is known as the Kelvin-Helmboltz contraction pase.

As the stage 3 fragment contracts, it spins faster to conserve angular momentum. The fragment flattens into a rotating protostellar disk about 100 AU indiameter that surrounds the central stage 4 protostar. The protostar is still not in equilibrium. The outward direct pressure has become a powerful counter against gravity’s continued inward pull, but the balance is not yet perfect. The internal heat gradually diffuses out from the hot center to the cooler surface, where it radiates away into space. The overall contraction slows, but it does not stop completely.

After stage 4, the protostar on the H-R diagram moves down (lower luminosity) and slightly to the left (higher temperature). Surface temperature remains almost constant, and it becomes less luminous as it shrinks. The evolutionary path from stage 4 to stage 6 is called the Hayashi track. Protostars on the Hayashi track often exhibit violent surface activity during this phase of their evolution, resulting in extremely strong protostellar winds much denser than the solar wind that flows from our Sun. This is often called the T Tauri phase after T Tauri, the first protostar to be observed in that stage of prestellar development.

Stage 5: Protostar evolution. By stage 5, the protostar approaches the main sequence. It is about 10 times the size of the Sun. Central temperatures reach about 5,000,000 K. The gas is completely ionized by now, but there is still not enough thermal energy to overcome electromagnetic repulsion and begin nuclear fusion. Heat causes the protostar’s evolution to slow down. The contraction slows, luminosity decreases, and escaping radiation slows down.

Stage 6: A newborn star. About 10 million years after its first appearance, the protostar finally becomes a true star. The core temperature finally reaches 10,000,000 K, and nuclear fusion beings. Protons begin fusing into helium nuclei in the core, and a star is born.

Stage 7: The main sequence at last. Over the next 30 million years or so, the stage 6 star contracts a little more. By making this slight adjustment, the central density rises, the central temperature increases, and the surface temperature rises. By stage 7, the star finally arrives on the main sequence. Pressure and gravity are finally balanced (hydrostatic equilibrium), and the rate that nuclear energy is generated in the core exactly matches the rate energy is radiated from the surface.

The evolutionary events just described occur over 40 to 50 million years. This is less than 1% of the Sun’s lifetime on the main sequence.

The numerical values and evolutionary track just described are valid for 1 solar mass stars. Temperatures, densities and radii of prestellar objects of other masses exhibit similar trends, but the numbers and evolutionary tracks are slightly different, in some cases considerably different. The most massive fragments within interstellar clouds tend to produce the most massive protostars and stars. Low mass fragments give rise to low-mass stars. Whatever the mass, the end point of the prestellar evolutionary track is the main sequence.

The below figure compares the pre0main sequence track taken by a 3 solar mass, 0.3 solar mass, and 1 solar mass protostar. Those that form more massive stars follow a track higher on the H-R diagram than that of the Sun. Those that form a less massive star follow a lower track. Time also is affected by the size of the fragment creating the protostar. If the fragment is more massive, it will cause the protostar to heat up more quickly. If it is less massive, it will take more time for the matter to heat up. The 3 solar mass protostar will reach the main sequence faster than the 1 solar mass protostar. The 0.3 mass protostar will take the longest time to travel its evolutionary track.



A star is considered to have reached the main sequence when hydrogen begins burning in the core and the star’s properties settle down to stable values. The main sequence line is called the zero-age main sequence, or ZAMS for short. Stars with more heavy elements tend to be cooler and slightly less luminous than stars that have the same mass, but contain fewer heavy elements. As a result, differences in compostion between stars blur the zero-age main sequence into the broad band we observe.

The main sequence itself is not an evolutionary track – stars do not evolve along it. It is a “way station” on the H-R diagram where stars stop and spend most of their lives. Low mass stars are towards the bottom with high mass stars towards the top. In other words, a star that reaches the main sequence as a G type star can never work its way up to a B or O type star, or move down to an M type star.

Some fragments are too small to become stars. Jupiter is a good example. It formed in the Sun’s protostellar disk, and contracted under the influence of gravity. There was not enough mass for gravity to crus its matter to the point of nuclear ignition. Instead, it became stabilized by heat and rotation before the central temperature became hot enough to fuse hydrogen. Jupiter never evolved past the protostar stage. Low mass fragments lack the mass needed to initiate nuclear burning. Astronomers believe that the minimum mass of gas needed to generate core temperature high enough to begin nuclear fusion is about 0.08 solar mass (80 times the mass of Jupiter).

Brown dwarfs are failed stars. They are fragments of collapsing gas and dust that did not contain enough mass to initiate core nuclear fusion. Such an object is then frozen somewhere along its pre-main sequence contraction phase, continually cooling into a compact dark object. Because of their small size and low temperature, they are extremely difficult to detect observationally. The term brown dwarf is reserved for objects more than 12 (but less than 80) Jupiter masses. Anything smaller than 12 times the size of Jupiter is considered a planet.

Because of the length of time that it takes for an interstellar cloud to become a star, it cannot be observed directly. Instead, different areas are studied at different stages of the process, and the data put together like pieces of a puzzle, to theorize the evolutionary cycle of a star.

A bright infrared source in which a surrounding cloud of gas and dust absorb ultraviolet radiation from a hot star and reemits it in the infrared is known as a cocoon nebula. Two considerations support the idea that the hot stars heating the dust have oly recently ignited. First, the dust cocoons are predicted to disperse quite rapidly once the central stars form, and second, they are invariably found in the dense cores of molecular clouds. The stars in the cocoon nebula are probably near stage 6.

As mentioned in stage 4, protostars often exhibit strong winds. The protostar may be embedded in an extensive protostellar disk of nebular material in which planets are forming. The strong heating within the turbulent disk and powerful protostellar winds combine to produce a bipolar flow, expelling two jets of matter in the directions perpendicular to the disk. That is, the jets come from the protostar’s north and south poles. As the protostellar wind destroys the disk, blowing it away into space, the outflow widens until (with the disk gone) the wind flows away from the star equally in all directions.

A shock wave is a wave of matter, which may be generated by a newborn star or supernova, that pushes material outward into the surrounding molecular cloud. The material tends to pile up, forming a rapidly moving shell of dense gas. Many astronomers regard the passage of a shock wave through interstellar matter as the triggering mechanism needed to initiate star formation in a galaxy. When a shock wave encounters an interstellar cloud, it surrounds the thinner exterior of the cloud more rapidly than it can penetrate the cloud’s thicker interior. Thus, the shock waves do not blast a cloud from only one direction, but effectively squeeze it from many directions (similar to the implosions of buildings during atomic bomb tests as the shock waves surrounded the buildings and made them fall in on themselves rather than be blown apart).

Emission nebulae are not the only generators of interstellar shock waves. At least four other forces are available: the relatively gentle deaths of old stars in the fomr of planetary nebulae, the much more violent ends of certain stars in supernova explosions, the spiral-arm waves that plow through the Milky Way, and interactions between galaxies.

The end result of the collapse of a cloud is a group of stars all formed from the same parent cloud and lying in the same region of space. This collection of stars is called a star cluster. The only factor distinguishing one star from another in the same cluster is mass. An open cluster is a loosely bound collection of tens to hundreds of stars, a few parsecs across, generally found in the plane of the Milky Way. Less massive, but more extended, clusters are known as associations. These clusters typically contain no more than a few hudred bright stars, but may span many tens of parsecs. They tend to be rich in very young stars. Those containing many pre-main sequence T Tauri stars are known as T associations. Those with prominent O and B type stars are known as OB associations.

Globular clusters are tightly bound, roughly spherical collections of hundreds of thousands, and sometimes millions, of stars spanning about 50 parsecs. They are distributed in the halos around the Milky Way and other galaxies. Most contain no main sequence stars with masses greater than about 0.8 times the mass of the Sun.

In general, the more massive the collapsing region, the more stars are likely to form there. Low-mass stars are much more common than high-mass stars. For every O and B type giant, hundreds or even thousands of G, K and M type dwarfs may form. The efficiency of star formation refers to the fraction of the total mass that actually finds its way into stars, which determines the amount of leftover material.

Eventually star clusters dissolve into individual stars. In some cases, ejection of unused gas reduces a cluster’s mass so much that it becomes gravitationally unbound and dissolves rapidly. For those that survive the early gas loss phase, stellar encounters tend to eject the lightest stars from the cluster. Occasional distant encounters, even a near miss, with giant molecular clouds tend to remove stars from a cluster.