Spectroscopy, Spectral Classes and the Doppler Effect

 

Two important laws were discovered during the 19th century relating to light and temperature:

 

  1. Wien’s Law (Weilheim  Wien 1893): The wavelength (or color) of maximum intensity of a radiating solid is inversely proportional to its temperature:

                                     

Here l is the wavelength in nanometers and T is the temperature in Kelvin (K).

 

  1. The Stefan-Boltzman Law:

 

 

Here L is total energy emitted by a glowing body per unit area.  T is the temperature and s is a constant.  For a star with a radius R, the total radiating surface is given by 4pR2, so

, 

where L is now the luminosity of the.  If L and T are known, then the radius of the star can be determined by:

 

                 

 

The website Online Journey Through Astronomy sponsored by Brooks/Cole Learning Center has a nice illustration of Wien’s Law and the Stefan-Boltzman. Law.  Click on:  Black Body Radiation Exercises

 

  1. Classification of stellar spectra:

 

Knowing that color means temperature, stars can be sorted into broad categories.  In 1866 father Peitro Angelo Secchi sorted stars into four broad categories and noted that the spectral lines correlated with color. His categories were:

 

·        White – absorption lines mostly hydrogen

·        Yellow (sun – like) – strong calcium lines, weaker hydrogen

·        Red (Betelgeuse) – many bunched bands , few hydrogen lines

·        Deep read (dim dwarf stars) – again, numerous bunched lines

 

In the late 1870s E.C. Pickering at Harvard began an all-out effort to obtain photographic spectra from thousands of stars.  For this project, he employed an objective prism, a large prism “filter” fitted on the front end of a refracting telescope.  With this device, all stars images projected onto the photographic plate are spread into spectra, and hundreds of stars can be cataloged and classified from one exposure.  Pickering further subdivided Secchi’s categories:

 

·        White – A,B,C,D

·        Yellow – E,F,G,H,I,J,K,L

·        Red – M

·        Deep Red – N

 

Pickering noted that with this classification, the spectra went from strong hydrogen lines (stars like Sirius) to very weak hydrogen lines (stars like Betelgeuse).  Although generally the weakening of H lines meant a steady march to the red (cool) end of the spectrum, there was a group of stars that showed virtually no lines at all but were blue-violet in color (therefore very hot).  These stars were assigned the classification “O”.

 

By the end of the 19th century thousands of photographic plates, each with hundreds of stellar spectrograms, had been produced at Harvard Observatory.  Most of the actual work of classifying these spectra was done by a group of women supervised by Annie Jump Cannon.  In all Cannon and her group classified over a quarter million stars! Cannon noted that when the stars were arranged strictly by temperature, the spectral lines showed an increasing complexity as you went from hot to cool stars.  In her view, hydrogen lines were not that important – it was the increase in the complexity that mattered.  The explanation for this particular relation between spectral lines and the temperature had to wait for further clarification provided by atomic theory in the twentieth century. 

However, with in a few years, it became the custom to arrange the spectral classes in the sequence suggested by Cannon – by temperature. 

 

One consequence of the new arrangement was that those O stars which were very hot, but showed very faint lines had to be moved to the top of the list, and the B stars which had hydrogen lines, but were hotter than A stars had to be next.  The sequence was further refined by combining some categories, effectively reducing the number of main classes to seven.   Thus we arrive at the spectral sequence as we know it today:

 

OBAFGKM

 

The sequence is immortalized by the mnemonic devised by Pickering himself to memorize it:

 

Oh Be A Fine Girl/Guy Kiss Me

 

Other mnemonics include:

Oh Boy, An F Grade Kills Me

Overseas Bulletin - A Flash: Godzilla Kills Mothra

 

In some systems certain red stars are subdivided into classes R, N and S. The sequence OBAFGKMRNS lends itself to even more creative flights of fancy:

 

 

Oh Be A Fine Girl/Guy Kiss Me - Right Now Smack!

Oh Bring A Full Grown Kangaroo, My Recipe Needs Some

Oh Brutal And Fierce Gorilla, Kill My Roommate Next Saturday

On Bad Afternoons, Fermented Grapes Keep Mrs. Richard Nixon Smiling

 

There is an excellent website sponsored by the Wilderness Center of Wilnot, Ohio illustrating the spectral classes. Click on: Spectral Classes

 

  1. Since for most stars all we can see directly is the brightness (apparent magnitude) and color (translates into temperature and spectral class), it would be helpful if there were a relationship between these quantities and luminosity.  This would be most helpful because knowledge of luminosity can be used to determine many other quantities such as distance, radius and mass.  In 1913 the American astronomer Henry Norris Russell published a diagram relating spectral class to luminosity.  Since this had been suggested earlier by the German astronomer Hertzsprung, the diagram is known today as the Hertzsprung-Russell or HR diagram. Basically, the HR diagram shows that for the great majority of stars, the hotter the star is the more luminous it is.  These stars fall along an s-shaped curve known as the main sequence. There are some stars, however, which are cool but luminous while others are hot with low luminosity.  The Stefen-Boltzman law above implies that the cool, bright stars must have very large diameters (hence the name, red giants), while the hot dim stars must have very small diameters and are therefore called white dwarfs.

 

  1. In 1842 Christian Doppler described the phenomenon that now bears his name.   This Doppler effect describes the change in wavelength experienced by a stationary observer when a sound or light source is approaching or receding.  When the source is moving toward the observer, the approaching wavelengths are shortened, while if the source is moving away from the observer, the receding wavelengths are lengthened.   For sound, shorter wavelengths = higher pitch while longer wavelengths = lower pitch.  For light, shorter wavelengths = shift towards the blue end of the spectrum, while longer wavelengths = shift toward the red end of the spectrum.  The acoustic Doppler effect is an everyday experience, usually obvious when a vehicle with a siren blaring races down the street, but the color shift experienced by light waves is too small to detect visually.  However, the shift is detectable in astronomical objects by precisely measuring the shift in their spectral lines.  Thus, the velocity v of a star is related to the shift in wavelength  by:

 

 

Where c is the speed of light.  William Huggins in 1868 showed that it was possible to measure the line-of-sight velocity of a star (the radial velocity) using the Doppler technique.