ASTR 498N              Lecture 3       The Stellar Menagerie Part 1

 

(online at www.astro.umd.edu/~drabin/)

 

The truth is out there.

 

Approach

 

You’ve all been exposed to magnitudes, distance moduli, spectral types, and Hertzsprung-Russell (HR) diagrams.   You may not have considered luminosity functions, which work hand-in-glove with HR diagrams.

 

We’ll approach the HR diagram primarily from a “consumer” viewpointas a tool for summarizing the range of intrinsic stellar properties that we should aspire to explain with a theory of stellar structure and evolution.  If we were approaching the subject primarily as observers, or as practicing model builders, we would need to look much more closely “under the hood” at the complex web of methods employed to construct HR diagrams and the uncertainties and selection effects associated with each method.  As in any physical theory, the depth of the theoretical treatment is driven by the precision of the data:  even apparently minute discrepancies can be worth pursuing if they are observationally significant (an example we’ll discuss later:  the discrepancies between observed and theoretical frequencies of the global oscillation modes of the Sun).

 

The Hertzsprung-Russell Diagram

(O&C §8.2)

 

The HR diagram was introduced by E. Hertzsprung in 1905 and H. N. Russell in 1913.  Russell’s original diagram plots absolute visual magnitude against spectral type.  

                  

                    It’s not a scatterplot!

Since absolute magnitude is a measure of intrinsic luminosity, and spectral type is primarily determined by temperature,

 

·       Conclusion:  many (but not all) stars follow a fairly well-defined relationship between luminosity and temperature.

 

The HR diagram is so important that we’ll take a leisurely gallery tour of the many guises in which the diagram can appear.  First, we’ll review some of the ingredients.

 

 

Magnitudes and photometric Systems

(O&C §3.2)

 

Magnitude scale                                    

 

where F is flux.   Just a logarithmic scale for measuring flux with the historical factor -2.5 included to make ()five magnitudes correspond exactly to a flux ratio of 100.  Smaller magnitudes correspond to brighter objects.

 

Absolute bolometric magnitude           

 

where the absolute bolometric magnitude of theSun, M_bol=4.74, anchors the scale (the zero point is, ultimately, arbitrary).  Note that bolometric magnitude (or luminosity) includes energy at all wavelengths.

 

Apparent magnitude m                          

 

Where m  M is called the distance modulus.          By definition, then, the apparent and absolute magnitudes coincide for an object at a distance of 10 pc (and with no interstellar absorption).  Apparent and absolute magnitude scales both involve an arbitrary constant, but those constants must be linked by this relationship.

 

Bolometric luminosity is not easily measured, since it includes all wavelengths.  More commonly, the wavelength range is restricted by the sensitivity of the detector or intentionally (with filters, for example) to provide crude spectral resolution.  A calibrated restriction of this kind is called a photometric system.  The sensitivity function R(λ) gives the fraction of flux F(λ) incident on the detector system (which may include the telescope) that is ultimately measured.  A general photometric system will be defined by

Apparent photometric magnitude m_S               

where C_S is an arbitrary constant.  Early photometric systems were visual (response of the human eye) or photographic (tied to a photographic emulsionthe absolute magnitudes in Russell’s HR diagram would be of this type).  Today, all commonly used photometric systems are specified by precisely defined filter pass bands and constants C_S .  An extension of the classical UBV (Ultraviolet/Blue/Visual) to Red and Infrared is shown below.  Other infrared filters (JHKLMN, out to 10 μm) are increasingly used; they are better matched to cool objects and are less affected by interstellar aborption.

 

P  A star of what T_e peaks (B_λ)  at the peak wavelength of the L filter, 3.55 μm?

 

 

Astronomers convert between photometric and bolometric magnitudes with a bolometric correction,

 

 

Note that the correction BC_s is specific to a given band S (even though you will often see “the” bolometric correction used as if it were universal).

 

Color index                                        

 

Where .  Any other photometric pass bands may be substituted for B or V.  The constants C_B and C_V in the definitions of m_B  and m_V were chosen historically to make   for an A0 dwarf star (in fact,  for spectral type A0 V).

 

 

Spectral classification

(O&C §8.2)

 

 

Spectral class (class and type are used interchangeably) is primarily determined by temperature (Saha and Boltzmann equations).  A single basic type (say, G) can be reliably divided into several subtypes (e.g., G0, G2, G5, G8) on the basis of the observed spectrum.  Not all possible subtypes are used in practice.  There are also more exotic types used for cool stars (e.g., C for “carbon” stars showing strong molecular bands of C₂, CN and CH).

 

Smaller differencesin absorption line widths and line-strength ratiosamong stars of the same basic spectral type can distinguish luminosity classes.

 

The standard system for two-dimensional (temperature-luminosity) spectral classification is called MK after two of its originators.  Note that the MK system is based on spectral characteristics in the “classical” wavelength region, roughly 380700 nm.  For very hot or very cool stars, the ultraviolet or infrared spectrum often provides stronger discriminators than the visible/near-IR spectrum.

 

 

Luminosity classes

 

                              Ia       most luminous supergiants

                              Ib       less luminous supergiants

                              II       luminous giants

                              III      normal giants

                              IV      subgiants

                              V       dwarfs (main sequence)

P  Is the spectrum actually sensitive to the luminosity (radiative output) of the star?  If not, what is the physical effect behind luminosity classes?  How much does that effect vary among stars?