5. STELLAR ASTRONOMY

A. INTRODUCTION

B. INTRINSIC PROPERTIES OF THE STARS

• Astronomers measure brightnesses of stars using a refined version of the magnitude system introduced by the Greek astronomer Hipparchus about 130 BC. Hipparchus ranked the visible stars from first to sixth magnitude, with first being brightest. The system was elaborated and made quantitative after it became possible to measure accurate relative brightnesses of stars with telescopes and auxiliary instruments. The system is logarithmic because biological systems like the eye respond in proportion to the logarithm of the stimulus.

• The modern magnitude system is defined by the following expression:
  m = -2.5 log f + C

  where f is the flux of electromagnetic radiation received from a source. Flux is conventionally measured in units of energy received per second per unit area per unit wavelength. The constant C is adjusted, depending on the waveband being observed, in order to make the values of m conform to adopted values for a set of calibrator stars.

• As a result of this definition, a 1 magnitude difference in brightness corresponds to a factor of 2.51 in flux. For instance, a star with m = 4 produces 2.51 times less flux than a star with m = 3. A factor of 10 in flux corresponds to 2.5 magnitudes, and a factor of 100, to 5.0 magnitudes. The modern magnitude scale extends well past the sixth magnitude limit of Hipparchus and to negative values as well (for very bright objects).

• The chart below shows some familiar objects on the magnitude system. With your 8-in telescopes, you could see stars up to mag 12-13.
  
  

• 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 properties. 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.

• However, 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 intrinsic brightnesses. This is the absolute magnitude, which is defined to be the apparent magnitude which a star would have if it were at a distance of 10 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, or about 3.25 light years.

• In order to determine a star's absolute magnitude, we have to know its actual distance. Since most stars lie far beyond 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 an intrinsic brightness 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, 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	-26.74	4.84813×10-6	4.83	1
  Sirius	-1.44	2.6371	1.45	22.5
  Arcturus	-0.05	11.25	-0.31	114
  Vega	0.03	7.7561	0.58	50.1
  Spica	0.98	80.39	-3.55	2250
  Barnard's Star	9.54	1.8215	13.24	1/2310

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

• We have learned to measure the temperatures of stars using their electromagnetic spectra, following experiments first done by the physicist Kirchoff in the 19th century.
  Bad Philosophy Footnote: Click here for a related description of one of the worst, but not one of the last, faulty prognostications about science by a philosopher.

• 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 shows how temperature affects the wavelength at which the EM spectrum peaks. (500 nm on this wavelength scale corresponds to 5000 Å.)
  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.
  Vega, Sirius, or 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. 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..

• The mass of a star turns out to be the key to determining its life cycle. Masses of stars are determined mainly by applying Newton's laws of motion and graviation 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 by an 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. Binaries often present nice color constrasts in small telescopes as well.

• 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, intrinsic stellar brightness 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 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.

• The HRD is a basic clue to stellar physics. Another key discovery was that the masses of stars on the MS are systematically higher as you move upwards and to the left (i.e. to brighter, hotter stars). 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 which maintains them: nuclear reactions.
  
• If its interior is not kept hot, gravity would collapse a star like the Sun 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 as the nuclear "ashes" accumulate, they must readjust to avoid collapse. This is the reason that stars evolve and 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. 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

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.

• 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. 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. The 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. Click for enlarged view.
  
  The Orion Nebula. Stars are 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---groups of a few hundred up to hundreds of thousands of stars, all with the same age. 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. Bright star clusters include the Pleiades, Hyades, Praesepe, M13, M4, and M15. Below is a view of the old globular cluster M13:
  
  
• Many of the familiar stars are in the main sequence phase. This is the longest-lived phase of evolution, fueled by hydrogen burning, and relatively quiescent (so, boring in small telescopes). 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 inflated to enormous volumes. Bright giants include Arcturus and Aldebaran. Betelgeuse and Antares are red supergiants.

• 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 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 like Algol vary in brightness because of interactions between the two companions. Amateur astronomers have made enormous contributions to the study of variable stars.

• 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. Two examples, from HST, are shown below:
  
  
  
• More massive stars undergo a tremendous supernova explosion, leaving behind a compact neutron star. The Crab Nebula 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.
  
  

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 Astronomy Library and in the Day Lab (267 Astronomy).
You should be working on Labs 3 and 4.

Nick Strobel's Astronomy Pages for background information on stellar and galactic astronomy
Anglo-Australian Observatory Images Page--best site for ground-based pictures of astronomical objects
The Messier Catalog--- information and links for the brightest nebulae, stars clusters, and galaxies
American Association of Variable Star Observers---main site for information on variable stars