• The magnitude scale just discussed measures the apparent brightness of stars---i.e. how they appear from the Earth. It does not refer to their intrinsic brightnesses. The apparent brightness depends on the intrinsic brightness but also on the distance to the star.

• In the 19th century, astronomers obtained the first accurate measures of stellar distances (using the geometrical parallax method). This enabled us to determined the intrinsic luminosity of stars---i.e. their total energy output per second, measured in units like watts (energy output per unit time).

• Even the nearest stars turn out to be very distant, at least by the expectations of early astronomers (and certainly by everyday standards!).
  • Alpha Centauri (in the southern hemisphere) is the nearest star. It is at a distance of 1.3 parsecs.

  • A parsec is a unit of distance which is defined in terms of the size of the Earth's orbit. It is 3.1 x 10¹³ km(!), 206,000 times the distance to the Sun, or about 3.25 light years (one light year is the distance light travels in a year).

  • Here is a perspective plot of the stars within 50 light years (15.4 parsecs) of the Sun.

  • Here is a list of the 50 nearest stars to the Sun. Most of the names will be unfamiliar, because these objects are mostly quite faint (despite their proximity).

• Because of uncertainties in the flux scales which weren't resolved until late in the 20th century, astronomers established a convenient, but arbitrary, version of the magnitude system to measure luminosities. This is the absolute magnitude, which is defined to be the apparent magnitude that a star would have if it were at a distance of 10 parsecs.

• Since most stars lie at distances far greater than 10 parsecs, their absolute magnitudes are much brighter than their apparent magnitudes.

• It turns out that the easily visible stars, which have an apparent brightness range of only about 100:1, have a luminosity range of over 10,000:1.

• Although the Sun dominates our sky, this is only a proximity effect. Intrinsically, the Sun is a relatively faint star. If placed at 10 parsecs distance, the Sun would appear only as a star of 4.8 magnitude (barely visible under typical viewing conditions), whereas Antares (Alpha Sco) would be at -5.2 magnitudes, brighter than Venus.

• Here is magnitude and distance information for some familiar stars. Barnard's Star is typical of the very faint "red dwarf" stars which predominate numerically.
  Magnitudes and Distances For Some Well-Known Stars^*
  

  Star	App.Mag.	Distance (pc)	Abs.Mag.	Luminosity/Sun
  Sun	-26.7	4.84813×10-6	4.8	1
  Sirius	-1.4	2.64	1.5	22.5
  Arcturus	-0.05	11.25	-0.31	114
  Vega	0.03	7.76	0.58	50.1
  Spica	0.98	80.5	-3.6	2250
  Deneb	1.3	3230	-8.7	250,000
  Barnard's Star	9.5	1.82	13.2	1/2310

  ^*Magnitudes in the ``V'' filter. Original table by Nick Strobel.

• We have learned to measure the surface temperatures of stars using their electromagnetic spectra, following experiments first done by the physicist Kirchhoff in the 19th century.
  Bad Philosophy Footnote: Click here for a description of one of the worst, but not one of the last, faulty prognostications about science by a philosopher, in this case the claim that we could never know the temperatures of the stars.

• The EM spectrum of any star depends on its temperature. Hotter objects emit more energy at shorter wavelengths; cooler objects emit more energy at longer wavelengths. Hence, hot stars will look blue-white to the eye while cool stars look yellow-red.
  
  
• The diagram above shows the gross EM spectra of 3 stars with different temperatures. It illustrates how temperature affects the wavelength at which the energy output of a star peaks. (500 nm on this wavelength scale corresponds to 5000 Å.) The higher the temperature, the shorter the wavelength of the peak. The visible band is shown in color in the diagram.

• The Sun, with a surface temperature of 6000^o Kelvin, has a spectrum which peaks at about 5000 Å---i.e. in yellow-green light.
  
  (Does this fact, combined with the principle of natural biological selection, suggest a reason why our eyes are most sensitive to yellow-green light?).

• Vega, Sirius, and Rigel, with temperatures near 10000^o K, look blue-white. Arcturus or Pollux, with temperatures near 4500^o K, are yellowish. Cooler stars, like Aldebaran, Antares, and Betelgeuse are orange-red. The image at right shows Orion in color, contrasting Betelgeuse (upper left) with the other bright blue-white stars in the constellation, including Rigel (lower right). Click here for an image of the Southern Cross in dispersed color. Only unusual objects, like carbon stars, look "stoplight red."

• Colors are more apparent in telescopes or binoculars, because your eye requires more flux to distinguish color than simply brightness.

• For a Java demo of the effects of temperature on EM radiation, see this Davidson Webphysics applet..

• [Note: the colors of stars reflect only their surface temperatures. The deep interiors of stars have much higher temperatures, 15 million degrees in the case of the Sun.]

• The mass of a star turns out to be the key to determining its life cycle.
  Masses of stars are measured mainly by applying Newton's laws of motion and gravitation to stars which are in orbit around one another, i.e. binary or "double" stars.
  Newton showed that the time taken to complete one orbit (the "period") by any object in a gravitational orbit around another is related to the combined mass of the two objects. By measuring the orbital sizes and periods of binary stars (and also their distances from us), we can therefore determine their masses. During the 19th and early 20th centuries, small telescopes were often used for this kind of study.
  Norton's Star Atlas contains good lists of the brighter binary star systems with information on their motions.

• The masses of normal stars have a smaller range than do their intrinsic brightnesses. The lowest mass, self-sustaining stars are about 0.1 solar mass, while the most massive are in the range 20-50 solar masses.

C. STELLAR EVOLUTION

• The basic observational insight to understanding the structure & evolution of stars is the correlation between the luminosities and temperatures of stars found in the Hertzsprung-Russell (HR) diagram, which was discovered independently by two astronomers ca. 1910. Their work depended on the painstaking accumulation of measures of accurate distances to stars. A modern version for stars in the vicinity of the Sun is shown below:
  
  
• In the HRD, stellar luminosity increases upwards while temperature increases to the left (an artifact of tradition). The important point is that stars are not randomly scattered in the diagram but instead confined to well-defined sequences.

• Most stars fall on the main sequence (MS), which runs diagonally across the HRD. Brighter MS stars are also hotter. The Sun is an MS star (lying at T = 6000 and AbsMag = 4.8).

• A second concentration of the so-called red giants and supergiants falls in the upper right hand quadrant of the HRD (luminous but cool). These are "giants" both in luminosity and in diameter (can be over 100 times the size of the Sun). Finally, the white dwarfs are very faint stars lying beneath the MS.

• A key discovery was that the masses of stars on the main sequence are systematically higher at brighter magnitudes (higher luminosities) and higher temperatures.

• The structure present in the HRD and the mass-luminosity relation are basic clues to stellar physics. This was enough information to allow astrophysicists like Eddington and Bethe to analyze the basic structure of stars and then, in the late 1930's, to discover the prodigious energy source that maintains them: nuclear fusion reactions.
  
• If its interior is not kept hot, a star like the Sun would collapse under its own gravity in only 15 minutes. But nuclear reactions in the core of a star release enough energy to keep its interior hot enough (15 million degrees) to produce pressure sufficient to resist collapse.
  • The nuclear reactions which sustain a star involve the fusion of light elements like hydrogen (H) and helium (He) to make heavier elements, with the release of energy. The most important reactions during the MS phase fuse four H nuclei (protons) to form one He nucleus. Click on the thumbnail at right for a more detailed illustration of the proton-proton reaction.

• There is obviously a tremendous amount of nuclear fuel in a star like the Sun. Hence, it can stay in the MS phase burning hydrogen for a very long period of time. The MS lifetime for a star like the Sun is 10 billion years. The Sun is now 5 billion years old---therefore halfway through its MS phase.

• More massive stars have more fuel but also burn it more quickly, so that the MS lifetime for a star which is 15 times the mass of the sun is "only" 10 million years.
  
• As efficient as are nuclear reactions, however, stars have only a finite supply of fuel. They can remain on the MS burning hydrogen for a long time, but the accumulation of nuclear "ashes" in their centers means that eventually nuclear burning will cease there. Stars must readjust to avoid collapse. This is the reason that stars must evolve and consequently change their locations in the HRD.

• The late stages of evolution involve a complex series of switches to other fuel sources (e.g. He and carbon) and gross changes in the structure of the stars. The most important of these is an enormous inflation of their outer envelopes, which produces the red giants. Red giants are therefore not a different species of stars; instead, they are normal stars in the late stages of evolution.

• The diagram at the right shows evolutionary tracks in the HRD for stars of different initial masses. Ages are marked on the tracks. Note that stars like the Sun become much more luminous as evolution proceeds. More massive stars undergo the whole process much more rapidly than lower mass stars.

D. STELLAR EVOLUTION IN THE SKY

Apart from individual stars and binaries, the brighter objects relevant to stellar evolution are mostly listed in the Messier Catalog: This catalog was compiled by the 18^th century astronomer Charles Messier. It contains star clusters, nebulae, and galaxies. Messier compiled it not because of an interest in these kinds of objects but so he would not mistake them for comets, which were his passion. The web site listed below and Norton's contain lists and descriptions of the Messier objects. Here is a mosaic of images of the 110 Messier objects.

• Star formation occurs inside clouds of interstellar gas which are shielded and refrigerated by dust grains (tiny, solid particles like smoke) and have become dense and cold enough to form molecules.
  Because the dust absorbs and scatters light at optical wavelengths, dust clouds look like dark blotches when seen in projection against more distant nebulae or star fields.
  Starbirth begins when interstellar clouds begin to collapse under their own gravity. Most of this process is hidden from easy view at optical wavelengths by the dust and can only be observed with infrared telescopes.
  However, once stars form, they disrupt the surrounding clouds, blowing away the gas and dust and often causing it to glow by virtue of ionization from hot stars. (In an ionized gas, one or more electrons are stripped from its atoms.)
  A visible signature of an ionized nebula is a "pinkish" glow, produced by concentrated emission from hydrogen gas. Many spectacular examples of this nebular phase can be seen in the sky, including the Eagle, Triffid, and Lagoon nebulae. The Orion Nebula is the easiest example to observe.

  
  Starbirth region in the Eagle Nebula, a beautiful mixture of cold dust pillars (dark lanes) surrounded by hot gas. At left is a wide-field view of the whole Nebula. At right is the HST closeup of the central dust pillars. Click for enlarged view.
  
  The Orion Nebula surrounds the (multiple) central star of Orion's "sword." Stars are continuously forming in a dark molecular cloud (not visible) behind the Nebula; the Nebula is only a small part of the cloud where hot stars have begun to blow out and ionize the gas.

• Stars often form in clusters---compact groups of a few hundred up to hundreds of thousands of stars, all with the same age.
  The youngest, still-forming star clusters are usually enshrouded by dust. But clusters can stay together for long times, so we can see many mature clusters easily in small telescopes. Good descriptions of the brighter clusters are given in the SEDS Messier pages.
  Star clusters are essential diagnostics of stellar evolution, since their constituent stars differ only in mass, and one can use them to trace the rate of evolution with mass.
  Younger bright star clusters include the Pleiades, Hyades, and Praesepe. Their estimated ages are 100, 800, and 700 million years, respectively. These are of the "open" type---not highly concentrated and containing only a few hundred up to a few thousand stars.
  The most spectacular clusters are the "globular" type, such as Messier 13, Messier 4, and Messier 15. These are spherical, dense, and very massive (100,000 or more stars). They are also very old (10-13 billion years) and are keys to age-dating the universe. Below is a view of the globular cluster Messier 13.

  
  
  Imagine that the Sun were situated in the middle of a globular cluster like M13. There would be over 1000 stars brighter than Sirius!

• Many of the familiar bright stars are in the main sequence phase. This is the longest-lived phase of evolution, fueled by hydrogen burning, and relatively quiescent. The Sun, Vega, Sirius, and Spica are all MS stars; their intrinsic brightness and temperature depends only on their masses.

• Other bright stars are in the giant phase of evolution. They are evolving relatively rapidly, burning He in their cores and H in a shell surrounding the core. They have swollen to enormous volumes. Bright giants include Arcturus and Aldebaran. Betelgeuse and Antares are red supergiants. Deneb is a white supergiant.

• Especially in the giant phase, but also in other phases, stars can become variable. The most common cause of variability is pulsation of the stellar surface, which changes its luminosity and temperature. Cepheids (named after Delta Ceph) and RR Lyrae stars are two important types of pulsational variables. These types are widely used to estimate distances to star clusters and galaxies.
  
• Binary stars are widely observed by amateur astronomers. They can present nice color contrasts (Albireo is shown at the right). Observers like to test the quality of their equipment by trying to resolve very close binaries.
  The orbits of binary components around one another are often determined with small telescopes, though this, of course, may take years of observations.
  Some binaries, like Algol, can vary in brightness because of eclipses of one star by the other or gravitational interactions between the two companions. Amateur astronomers have made enormous contributions to the study of variable stars and binaries.

• The final phases of evolution depend on a star's mass. Lower mass stars like the Sun become very distended and eject their outer layers.
  The remaining core collapses and heats up, ionizing the expanding shell, on its way to becoming a white dwarf. The ejected material can produce a "planetary" nebula, so called because of their often round shapes. Planetaries are nice targets for small telescopes. The Ring Nebula (Messier 57) and the Dumbbell Nebula (Messier 27) are bright planetaries. HST images of two other examples are shown below:

  
  
  
• More massive stars undergo a tremendous supernova explosion, leaving behind a compact neutron star or black hole. The Crab Nebula (Messier 1) is a remnant of such an event (image below). Most of the heavy elements found on the Earth, including those in your body, were created during supernova explosions and recycled back to the interstellar medium through nebulae like these.
  
  NASA recently released some remarkable time-lapse X-ray and optical movies of the Crab Nebula which show waves of energy being injected into the nebula from the central spinning neutron star.

Download, print, and read the webnotes for this lecture.
Supplementary reading: The best resource for this material is a good ASTR 121/124 textbook. Texts are available for consultation in the Day Lab (268 Astronomy).
You should finish Lab 2 at the first opportunity and move on to Lab 3.

Nick Strobel's Astronomy Pages for background information on stellar and galactic astronomy
Tutorial on stellar evolution by John Lattanzio. Intended for advanced undergrads or grad students, but gives a good impression of how well the details of stellar evolution are now understood.
Anglo-Australian Observatory Images Page--best site for ground-based pictures of astronomical objects
The Messier Catalog--- information and links for the brightest nebulae, star clusters, and galaxies
American Association of Variable Star Observers---main site for information on variable stars