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The Hertzsprung-Russell Diagram of the Nearest Stars

The nearest star to the Sun is Proxima Centauri, a very dim main-sequence star 1.30 parsecs away.  With an apparent visual magnitude of 11, it is invisible to the unaided eye; the limiting magnitude for the unaided eye under the best of circumstances is 6.  The absolute visual magnitude of the star is 15.5.

The next closes star, at a distance of 1.34 parsecs, is Rigil Kentaurus (α Centauri), which in fact is a binary star.  This is the second brightest star in the night sky, visible to those in the Southern Hemisphere.  The brighter star of the binary, the A star, has an apparent visual magnitude of 0.0.  The companion B star has an apparent visual magnitude of 1.3.  These stars have absolute visual magnitudes of 4.4 and 5.7, respectively.  In comparison, the Sun has a absolute visual magnitude of 4.8.

Which of these nearby stars is the more typical of the stars in the Galactic disk in the power they generate?  The dimmer star is more typical.  Most stars in the Galactic disk are dark, red, and invisible to the unaided eye, unlike the rarities, the luminous blue stars that we see so easily in the night sky.  The typical star has an absolute visual magnitude in the range of 8 to 15, so most stars are more luminous than Proxima Centauri, which lies near the dark boundary of stellar luminosity.

The prevalence of small stars in the Galactic disk is obvious in the surveys of local stars, and is clearly visible in the Hertzsprung-Russell diagram of the nearest stars, which is displayed below. This diagram is based on data given in the Preliminary Version of the Third Catalogue of Nearby Stars of Gliese and Jahreiss (1991).[1]  Astronomers know of 326 stars within 10 parsecs of the Sun. Of these, color indexes have been measured for 284 stars.  This last group of stars are plotted on the HR diagram. This diagram is very different from the HR diagram of bright stars. While the main sequence on the bright-star diagram wanes with absolute visual magnitudes greater than 5, the main sequence of nearby stars extends beyond 15, with the largest number of stars having values between 10 and 15.  The red end of the main sequence, with the color index B−V greater than 1.3, contains 201 stars, or 71% of the stars on the diagram.

Through a distinct lack of imagination, the Sun and the main-sequence stars less luminous than the Sun are called dwarf stars.  These stars are quite different from the other type of dwarf star—the degenerate (white) dwarf—that appears on the HR diagram.  The main-sequence dwarfs are power by core hydrogen fusion, but the degenerate dwarfs are unpowered remnant stars.

The Hertzsprung-Russell Diagram for the stars nearest the Sun. The plot shows the 284 stars with measured B and V out of the 326 known stars within 10 parsecs of the Sun. The upper group of stars are the main-sequence stars, while the lower group of stars are the degenerate (white) dwarfs.   The Sun, if it were on this diagram, would fall just below Rigil Kentaurus A (α Centauri A).  This data is take from the catalog of Gliese et al. (1991), and is available through the VizierR service as catalog V/70A/catalog.

The four stars that dominate the high-luminosity end of the main-sequence are all A stars, which typically have masses around 2 solar masses.  The two brightest, Vega and Sirius A (the brighter star in the Sirius binary), are labeled in the diagram.  The remaining two A stars are equally well known;  from blue to red, they are Fomalhaut and Altair.  These stars stand out because they are all very luminous and nearby.  The nearest of these is Sirius A at 2.63 parsecs, while the most distant is Vega at 7.72 parsecs.  Next in luminosity on the main-sequence in this diagram is Procyon A, the brighter star in the Procyon binary system;  this F star is only 3.50 parsecs away.  Most of the nearby bright stars we see in the night sky are in the luminous end of the main-sequence.

These luminous stars are rare compared to the dwarf stars.  A big part of the reason is that dwarf stars are born at a greater frequency than A stars.  The other part of the reason is that the A stars have a short lifetime.  They are more massive than the dwarf stars, so they generate and radiate way power at a dramatically higher rate that the dwarf stars.  Their greater power generation far outpaces their greater fuel supply, so they consume their energy in a much  shorter time than do the dwarf stars.  As a consequence, most of the A stars born during the lifetime of the universe have burned through their fuel and are now degenerate dwarfs, but most of the dwarf stars born over this time remain main-sequence stars.

With so many A stars now deceased, we should see many remnant stars, and we do, but not with the unaided eye.  Many of the dim nearby stars are degenerate dwarfs.  Like the darkest main-sequence dwarfs, the degenerate dwarfs have absolute visual magnitudes greater than 10, but while the main-sequence dwarfs are red at this magnitude, the degenerate dwarfs are blue. These remnant stars lie in a band that stretches diagonally across the HR diagram below the main sequence.  They are at their most-luminous blue when young, but they become dimmer and redder as they cool.  Degenerate dwarfs are supported by degeneracy pressure, so their size does not change.  This means that the luminosity of a degenerate dwarf changes only with photospheric temperature, and because the color goes from blue to red as the temperature drops, the color of the star goes from blue to red as the luminosity drops.  This is the reason the degenerate dwarfs form a diagonal band on the HR diagram: the stars move on this diagonal as they age.  The stars at the blue end of the degenerate dwarf region of the diagram are young and hot, and the stars at the red end are old and cold.  Among the young and hot degenerate dwarfs is Sirius B, the companion of Sirius A.

The lone red giant on this diagram is the star Pollux of the Gemini constellation, and, at a distance of 9.97 parsecs, it is narrowly in the sample.  At this distance, we see Pollux with an apparent magnitude that nearly equals its absolute magnitude.  Red giants are rare because they are the short-lived helium burning stage of stars of about 1 solar mass or more.  Only stars with these high masses have had time to evolve away from the main-sequence to the red giant region.  A star is on the red giant branch for only about 25% of the time that it spends on the man sequence, so the number of red giants should be about about 25% of the stars more luminous than the Sun or Rigil Kentaurus A.  We expect 2 or 3 red giants within 10 parsecs, and we see 1, so what we see is about right for what we expect.

The HR diagram for nearby stars shows clearly the prevalence of various types of stars in the Galactic plane.  Most prevalent are the main-sequence dwarf stars. Next are the stars similar to the Sun in mass.  Following these are the degenerate dwarfs, the remnants of stars of 1 or more solar masses.  More rare are the luminous A stars, followed by the red giants.  Rarest of all are the O and B stars, which are very massive main-sequence stars, such as the B supergiant Rigel in the constellation Orion.  No local star is in this league, and those O and B stars that we see in the night sky are hundreds of parsecs away.

The ordering of the local stars gives the order in which each type of star contributes to the mass of the Galactic plane.  Despite varying dramatically in luminosity, these stars do not vary greatly in mass, with the smallest of the main sequence stars expected to carry 0.07 solar masses, and the most massive stars on this diagram, Sirius A and Vega, which are respectively 2.14 solar masses (from the binary orbit [Gatewood and Gatewood, 1978]) and 2.5 solar masses (from stellar evolution calculations [Allende Prieto and Lambert, 1999]) .[2, 3]  The mass of the Galactic disk that is in stars is therefore hidden in the small main-sequence dwarf stars.

[1]Gliese, W., and Jahreiss, H.  Preliminary Version of the Third Catalogue of Nearby Stars.  Astronomisches Rechen-Institut (ARI), Heidelberg (1991).  The catalog is available through the home page of ARI or through the VizieR service as catalog V/70A.

[2]Gatewood, G.D., and Gatewood, C.V.  “A Study of Sirius.”  The Astrophysical Journal 225 (1978): 191–197.

[3]Allende Prieto, C., and Lambert, D.L.  “Fundamental Parameters of Nearby Stars from the Comparison with Evolutionary Calculations: Masses, Radii and Effective Temperatures.”  Astronomy and Astrophysics 352 (1999): 555–562.

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