On the first page of this Section, we stated that stars are a fundamental unit making up the visible Universe. We repeat the definition of a star given in the Overview on that page: A star is defined as a massive, spherical astronomical body that is undergoing (or has undergone) burning of nuclear fuels (initially Hydrogen; as it evolves elements of greater atomic number are both produced and consumed as well) so as to release energy in large amounts of both luminous and non-luminous radiation (over a wide range of the EM spectrum). The vast majority of stars are found within or close to collections of stars in vast assemblages called galaxies. Almost all stars used as illustrations on this and the next page lie within our own galaxy, the Milky Way, since those in other galaxies are too far away to be resolved (the majority of other images of features smaller than galaxies shown in this Section are also "local" in the sense that they are found within the Milky Way as well).
We concentrate on this page on the inception, evolution, and demise of individual stars. A helpful Web Site that supplements the content of this page has been put online by Prof. Nick Strobel of Bakersfield College (Note: his original online Astronomy Notes have disappeared off the Internet; this link is to a mirror site in Denmark) . Also recommended is the University of Oregon site cited in the Preface (especially relevant are Lectures 15-18, and 20). Another source of information is at the Wikepedia Star web site. Before reading the next two pages, it may be profitable for you to get an overview of Star Formation by reading relevant pages from the just-cited Oregon lectures.
Stars have fascinated humans since way back in prehistoric times. Stars are a favorite subject of artists. Here is a painting by Vincent Van Gogh, which is firmly embedded in the writer's (NMS) memory from childhood since my uncle had made a copy (art was his hobby) that hung in my grandmother's home.
Most stars, seen through telescopes, are rather bland and non-descript, appearing as uniform bright round objects. Some, when photographed, take on an added feature that make them appear more dramatic. These spokes or rays, seen in this image, are not real or part of the actual star; they are artifacts related to the mounting in reflection type telescopes produced by a diffraction process that is preserved in the photographic product:
The number of stars in the Universe must be incredibly huge - a good guess is 100 billion galaxies each containing on average 100-200 billion stars or (1011 times 1011, which calculates as 1022). More recently, an independent estimate using other means states the value as 7 x 1022 stars; that survey made by Simon Driver of the Australian National University is said by him to still be a conservative underestimate. To make this point, here are two views of stars near us that indicates the densities just within a small part of the Milky Way - our own galaxy, the host of our parent star, the Sun.
Yet on a very clear, moonless night in dry air (say, in the western Great Plains of the United States), one sees at any one location, without using a telescope or binoculars, only about 2500 "star" points within the Milky Way in the northern hemisphere and a similar number in the southern hemisphere (some of the points are nearby galaxies). Catalogs exist that list 9100 'naked eye visible' stars that have been located and inventoried as to position. Under normal (unaided eye) viewing conditions, outside the Milky Way band only a few individual stars can be seen by eye alone (less than 200 in a typical suburban [which cuts down detection because of city lights] setting with humid air; this number increases to more than a thousand in a rural area with an arid climate). (The best viewing experienced by the writer [NMS] was during a July night on the plains of South Dakota.) Most of the observed stars are close to Earth (first few hundred light years) in the halo of the Milky Way, but several are planets, and a small number are nearby galaxies (the unaided eye can discern a galaxy only as an apparent single light source). The brightest stars are generally those closest to the Sun (around 1 to 100 light years away). Only when powerful telescopes are used does the astronomer realize by estimate or extrapolation that billions of galaxies exist; by inference we deduce that these probably contain stars in numbers similar to those that can be roughly counted in the Milky Way (in many tens of billions). The picture below recreates a typical view of part of the sky on a clear night:
Wherever you happen to be on the Earth's globe, as you look up into the sky you will see a myriad of hundreds to a few thousand stars (depending on atmospheric conditions) that extend from directly above to the horizon in any, and all, directions. Some groupings of stars form distinct patterns that the ancients imagined were signs from the gods telling humans how to live their lives. These were given names and were called constellations (discussed later on this page). Here is a "star map" with some common constellations (left unnamed):
Let us talk a bit more about constellations. That in itself is not truly a scientific topic but which remains useful to astronomers as a convenient way to locate stars by reference to "Sky Maps". Such maps contain the Constellations - patterns of certain visible stars (a few were actually galaxies but this was not known at the time) that the ancients imaginatively discerned in looking at individual stars within narrow patches of the celestial hemisphere which seemed to be distinctive and readily recognized. These arrangements were given fanciful names, of gods, animals, and other descriptors from their everyday experiences. This began with the Babylonians in Mesopotamia, and the system was expanded to 88 named constellations by the Greeks and Romans some 2000 years ago. (Astrologers, Psychics and Fortune Tellers have used constellations as "signs" and for horoscopes for several millenia.) This next pair of illustrations shows some of the major constellations in the Northern hemisphere, plotted in two half circle fields, one for summertime, the other for winter; the look direction is towards the north:
The constellations visible from the Southern hemisphere are different:
In each Hemisphere the stars and constellations shift positions with the seasons. To illustrate this, we repeat here an illustration first included on page 19-2:
To the ancients, the stars were all equidistant on the Celestial Sphere and varied only in brightness. Modern astronomers now know that individual stars/galaxies in the light points that make up the constellation pattern are actually located at various distances from Earth, which together with diifferences in size account for their different brightnesses. Most of the defining stars in a constellation are located in our galaxy, the Milky Way.
As we shall see next, the groups of constellations also shift with the seasons and with the place on Earth where the stargazer is positioned (also, different constellations are seen by those in the Southern Hemisphere of the Earth than those in the Northern Hemisphere [lookers at the Equator will see some of the constellations visible in each Hemisphere]). More about the constellations can be found at the Star Map Internet site.
How do astronomers - or anyone - locate a particular star among the plethora that can be seen? You can imagine that the pinpoints of light, which can be stars, galaxies, planets, asteroids, comets, and large spacecraft, are located over a hemisphere of infinite depth that extends from your local horizon to the zenith point directly vertical to your location (latitude). Although you cannot see it, there is a complimentary hemisphere either to your south (if you are in the northern terrestrial hemisphere) or to your north (for southern hemisphere dwellers). These two hemispheres constitute the Celestial Sphere. On any given night, the various heavenly bodies will seem to travel across the sky in arcuate paths, owing to the rotation of the Earth. The Moon follows a definite path on any given night and the Sun goes from horizon to horizon on a path a few degrees displaced from the Moon; these too shift with seasons and location. Some insight into this sphere as it relates to a person on Earth is given by this Celestial Sphere plastic globe:
How does one locate any point of light on the Celestial Sphere? By consensus, the Earth's North and South Pole (through which pass its rotational axis) are made to coincide with the North and South Poles of the Celestial Sphere. In the northern hemisphere a star called Polaris - the North Star - coincides almost exactly with the extension of the Earth's rotational pole onto the Sphere.) Here is one way to determine the location of any light point (e.g., star) on this sphere:
In this figure, the Celestial Sphere is held fixed (does not rotate). Here, the frame of coordinate reference is a great circle plane (equatorial) passing through the horizon as defined by true N(orth), S, E, and W. A second great circle contains the N & S directions and two points directly above the observer at any location on Earth - the zenith - and below - the nadir. At some given moment, the star's position on the Sphere can be specified by fixing its azimuth in degrees with respect to North or South and its altitude in degrees from 0 to 90°. (These are equivalent to longitude and latitude in the geographic coordinate system.)
If one were looking straight up overhead while standing on the North Pole, the relative locations of the constellation at that moment would constitute a reference Celestial (Hemi-)Sphere (same for South Pole but with different star patterns). Locating a given star would be done using the above azimuth-altitude spherical geometry. But globally the location is complicated by the three major types of motion involved in the real world: 1) on any given night the stars will move in arcs across the sky (centered on the Celestial Pole) in arcuate patterns; thus each star shifts position such that at different times it will lie at different points along its arc; 2) as the Earth revolves around the Sun (giving the different seasons), the positions of the stars will shift; 3) at any specific point on the Earth's sphere away from a Pole, the particular portion of the Celestial Sphere that is visible will differ (different hemispherical segments will be visible at different localities);
The effect of the Earth's rotation on the stars can be illustrated by a simple experiment: point a wide-angle lens camera up towards the hemisphere and keep its shutter open for hours. This would be the result:
Various constellations seemingly occupy different positions in the sky as the months and seasons pass during an earth year. Actually, the Earth's rotational axis retains its direction in space relative to the fixed stars (around the celestial poles) as it makes its annual revolution around the stars. There is an apparent shift of the constellations owing to the position of the Earth at each season:
As the seasons progress, the Sun has different locations within the constellations on each seaons' starting date at the time of its daily zenith when crossing the ecliptic, as follows: Vernal Equinox(Spring) = Aries; Summer Solstice = Cancer; Autumnal Equinox = Libra; Winter Solstice = Capricorn.
Because the altitude and azimuth of a star are constantly changing in response to Earth's motion and to one' position on the terrestrial sphere, it is not always useful to rely on the above horizontal coordinate system to catalog the positions of stars. A more convenient coordinate system for cataloging purposes is one based on the celestial equator and the celestial poles and defined in a similar manner to latitude and longitude on the surface of the Earth. This location system takes the hours of observation into account. This means that one must consider both the specific time (usually relative to Greenwich Mean Time) when the observation is to be made (say, through a telescope in an Observatory) and the geographic location of the Observatory. Examine this diagram, in which the Celestial Pole is tilted 23° to accommodate the tilt of the Earth's rotational pole:
In this system, known as the Equatorial Coordinate system, the analog of latitude is the declination, δ. The declination of a star is its angular distance in degrees measured from the celestial equator along the meridian through the star. It is measured north (as +) and south (-) of the celestial equator and ranges from 0° at the celestial equator to 90° at the celestial poles, being taken to be + when north of the celestial equator and - when south. The zero point chosen on the celestial sphere is the first point of the constellation Aries, γ, and the angle between it and the intersection of the meridian through a celestial object such as a star and the celestial equator is called the Right Ascension (RA) of the star. RA is sometimes denoted by the Greek letter α and is measured from 0h to 24h along the celestial equator eastwards from the first point of Aries, i.e., in the opposite direction to that in which hour angle is measured.
Because of the rotation of the Earth, a reference called the hour angle (HA) increases uniformly with time, going from 0° to 360° in 24 hours. Defining the observer's meridian as the arc of the great circle which passes from the north celestial pole through the zenith to the south celestial pole, the hour angle of a star - which changes with time of day - is measured from the observer's meridian westwards (for both northern and southern hemisphere observers) to the meridian through the star (from 0° to 360°). The hour angle of a particular object is therefore a measure of the time since it crossed the observer's meridian - hence the name. For this reason it is often measured in hours, minutes and seconds of time rather than in angular measure (just like longitude). The hour angle is referenced to the hour angle of the Constellation Aries at Vernal Equinox.
In practice, if one wishes to locate a particular star, galaxy, or planet at some moment, the main steps are to look up declination δ and RA in a star catalog or Ephemeris, read the time using a sidereal clock, and adjust the telescope settings to the hour angle τ and the δ value, taking into account location and time. (This time is usually sidereal time, exactly 24 hrs earth time. The so-called 24-hr solar day is not really precisely 24 hours because the Earth has moved along its orbital path a specific distance during a full rotation, so that it is 3 minutes and 56 seconds longer that the sidereal day,)
The relationship between the stars and Earth's time and space location proved a means of marine navigation even for the ancients. But precise determination of latitude and longitude requires two important capabilities: 1) fixing the location as declination of a star, and 2) establishing accurately the time relative to some place of reference (Greenwich). The development of the sextant (shown below) and of a Chronometer made this possible.
The above is only a part of the story about the celestial sphere and ways to find individual planets, stars, and galaxies. Additional treatment of how to navigate the sky at night is found on the aforementioned University of Oregon website. Perusal of this review is highly recommended.
Interesting, but back to Astronomical Science. The standard model for a star is, of course, our Sun. The Sun is typical of most stars; as we shall note shortly, these stellar bodies vary from about 0.1 to 100 times the mass contained in the Sun. Without a telescope, under exceptional viewing conditions (using binoculars), about 9000 individual stars can be seen in the wide celestial band that is the central disc of the Milky Way (M.W.) galaxy. Others elsewhere in the celestial hemisphere make up about 2000 points of stellar light that can be seen (in clear air, away from urban light contamination) by the naked eye. Some are nearby within our galaxy and are not particularly large, while others are mostly stars of the Giant/Supergiant types in the halo (see below) around the Milky Way. Still others (a minority) are galaxies that lie in intergalactic space beyond the Milky Way but mostly within a billion light years from Earth. The solar planets are interspersed with these cosmic bodies. Telescopes can resolve countless more stars in the M.W., can recognize millions of galaxies, and can pick out some individual stars in nearby galaxies.
A degree of luminosity of an object in the sky (galaxy; star; glowing clouds; planet) can be represented by its apparent magnitude - a measure of how bright it actually appears as seen by the telescope or other measuring device. This magnitude is a function of 1) the intrinsic brightness which varies as a function of size, mass, and spectral type (related to star's surface temperature) and 2) its distance from Earth. (Magnitude as applied to a galaxy, which seldom shows many individual stars unless they are close [generally less than a billion years away], is an integrated value for the unresolved composite of glowing stars and gases within it.) The brightness of a star can be measured photometrically (at some arbitrary wavelength range) and assigned a luminosity L (radiant flux). For two stars (a and b) whose luminosities have been determined, this relationship holds:
from which can be derived:
To establish a numerical scale, some reference star(s) must be assigned an arbitrary value. Initially, the star chosen, Polaris, was rated at +2.0 but when it was later found to be a variable star, others were selected to be the 0 reference value for m. The magnitude scale ranges from -m (very bright) to +m (increasingly faint) values. The very brightest objects have larger negative numbers. The more positive the number, the fainter is the object (planet; star; galaxy); very distant galaxies, even though these may be extremely luminous, could have large positive apparent magnitudes because of the 1/r2 decrease in brightness with increasing distance. The Sun has the value - 26.5; the full Moon is -12.5; Venus is -4.4; the naked eye can see stars brighter than + 7; Pluto has a magnitude of +15; Earth-based telescopes can pick out stars visually with magnitudes down to ~+ 20 (faintest) and with CCD integrators to about +28, and the HST to about +30. Thus, the trend in these values is from decreasing negativity to increasing positivity as the objects get ever less luminous as observed through a telescope. Each change in magnitude by 1 unit represents an increase/decrease in apparent brightness of 2.512; a jump of 3 units towards decreasing luminosity, say from magnitude +4 to +7, results in a (2.512)3 = 15.87 decrease in brightness (the formula for this is derivable from the above equations, such that the ratio of luminosities is given by this expression: 10(0.4)(mb - ma). Below is a simple linear graph that shows various astronomical objects plotted on the apparent magnitude scale:
Absolute magnitude (M) is the apparent magnitude (m) a star would have if it were relocated to a standard distance from Earth. Apparent magnitude can be converted to absolute magnitude by calculating what the star's or galaxy's luminosity would appear to be if it were conceived as being moved to a reference distance of 10 parsecs (10 x 3.26 light years) from Earth. The formula for this is:
where r is the actual distance (in parsecs; 1 pc = 3.26 light years = 206,265 A.U. = 3.086 x 10 16 meters) of the star from Earth. Both positive and negative values for M are possible. The procedure envisions all stars of varying intrinsic brightnesses and at varying distances from Earth throughout the Cosmos as having been arbitrarily relocated at a single common distance away from Earth.
Both luminosity and magnitude are related to a star's mass (which is best determined by applying Newton's Laws of motion to binary stars [a pair; see below for a discussion of binaries]). The graph below, made from astrometric data in which mass is determined by gravitational effects, expresses this relationship; in the plot both mass and luminosity are referenced to the Sun (note that the numbers are plotted in logarithmic units on both axes):
There is a relationship between absolute magnitude (here given by L for luminosity) and mass (given by the conventional letter M; which accounts for replacing the absolute magnitude M with L). Here is one expression:
In the above, both L and M for a given star are ratioed to the values determined for the Sun. Note the two different power exponents. It seems that some stars obey a fourth power, others a 3, and a few are just the square of the mass. The most general expression in use is given as L = M3.5. There are relatively few stars with mass greater 50 times the Sun. Very rarely, we can find a star approaching 100s solar mass, but these are so short-lived that nearly all created before the last million years have exploded, with their mass being highly dispersed, and thus ceasing to send detectable radiation.
If the Sun were envisioned as displaced outward to a distance of 32.6 l.y., its apparent magnitude as seen from Earth would be -26.5; its absolute magnitude would be changed to +4.85. A quasar, which is commonly brighter than a galaxy, has an absolute brightness of - 27 (note that in the absolute scale increasingly negative values denote increasing intrinsic brightness).
Measurements of location in the celestial sphere, distance from Earth, and magnitudes of stars can be done through ground-based telescopes or from space observatories. One space telescope, Hipparcos, was dedicated exclusively to obtain precise measurements of these parameters. Launched in August, 1989 by ESA, it operated through March of 1993. High precision data were obtained for more than 118,000 stars and less precise results for another 1,000,000+.
One classification of stars is that of setting up categories of star types in a series of decreasing sizes and luminosities (see also the discussion below of the Hertzsprung-Russell [H-R] diagram). These are the Luminosity/Type Classes: Ia, Ib: Extreme Supergiants (Hypergiants); II: Supergiants (Betelgeuse); III: Giants (Antares); IV: Subgiants; V: Dwarfs (Sun): VI: Subdwarfs (metal poor); VII: White Dwarfs (burned out stars); VIII: Brown Dwarfs. Thus in this list luminosity decreases from left to right (the mass and size of a star, which determines its luminosity, also decreases left to right). The oddity in this classification is the omission of a category of "Normal"; a star is either a Giant or a Dwarf. The diagram below relates this hierarchy to star brightnesses (magnitudes) which decrease from top to bottom; the spectral types (indicated by letters) range from high luminosity/mass (left) to low luminosity/mass (right) but these letters do not relate to the Classes as plotted (the diagram is idiosyncratic in that the top Class - Hypergiant - is an O spectral type and the bottom Class - Brown Dwarf - is a T spectral type: