Classifying and Measuring Stars

- A star can’t simply be measured by a thermometer (temperature) or a ruler (distance and radius) - The majority of the electromagnetic spectrum (other than radio and visible light) is absorbed and deflected by Earth’s atmosphere.  Therefore, in order to make observations, satellites need to be placed above Earth’s atmosphere. Visible Light lies in between infrared and ultraviolet   Importance of Spectroscopy Visible light from the stars can be passed through a prism to produce a spectrum.  Each star will produce a unique spectrum as seen from the three examples of stellar spectra shown to the right.  Astronomers use the spectra to determine the element’s motion, composition, temperature, and atmospheric density.     Properties of Stars 1. Composition of a Star Every element produces a unique pattern of bands: The absorption spectrum is a continuous spectrum with dark bands that are produced when light from a hot source passes through a cooler gas.  The elements in the gas absorb light at specific wavelengths. The examples in the diagram above are emission spectra. The emission spectrum is a series of unevenly spaced coloured lines (the opposite of the absorption spectra).  The bright lines indicate what elements are present (see below). A key point is that the absence of a spectral line does not necessarily mean that an element is not present.  It could be that the conditions in the star are not able to produce the emission or absorption lines for a particular element.   2. Motion of a Star (Doppler effect) The apparent shift in colour when a star is moving away or toward Earth can be detected with a shift in absorption or emission lines.  If the star is moving away from Earth then the spectral lines will shift to the longer wavelengths, a redshift.  If the star is moving toward Earth then the spectral lines will shift to the shorter wavelengths, a blueshift.   3. Atmosphere of a Star  (high or low pressure) When attempting to classify stars, astronomers found that some stars contained the same spectral lines; however, when comparing two of the stars it was found that some lines were “smeared” out and others were broader.  The explanation:   High atmospheric densities in the outer atmosphere layers of stars cause the lines to be smeared out. Low atmospheric density is generally found in giant stars, and these stars generally emit spectra with narrow lines   4. Temperature of a Star (Wien’s Law) Most stars behave like black-body radiators, indicating that they emit energy at different wavelengths, and that they have a peak maximum wavelength in which they emit most of their energy. In the 1890s Wilhem Wien found that the maximum wavelength emitted by a black body radiator was inversely proportional to the temperature.  If the maximum peak wavelength can be measured using a spectroscopy, and the temperature of the star can be determined using Wien’s Law:   The Sun emits energy over a wide range of wavelengths.  Calculate the surface temperature of the Sun when the maximum wavelength is 5 x10-7m (500nm). Solution: Therefore the temperature for the surface of the Sun is 5800K.  

Spectral Classification Spectra were obtained for many thousands of stars in the late 19th century. Astronomers were faced with the same problem the problem of how to classify the stars.  Annie Cannon and her team at Harvard University developed a system of classification.   Stars were classified based on the emission spectra lines.  The image to the left highlights the different spectral classes and the features of each.  Temperature of the star is important in understanding the spectral lines.  For example at high temperatures helium is ionized and the atoms of other elements are ripped apart and so the spectral lines for ionized helium appear, whereas at low temperatures the atoms in the outer atmosphere are not ripped apart and many more spectral lines are visible. Stars fit into one of the following classes: O B A F G K M. This classification can be easily remembered from the pneumonic: “Oh Be A Fine Girl/Guy Kiss Me”.     Long Description - Characteristics of Spectral Classes Spectral Class: O Colour: blue Temperature Range (K): 28 000 – 50 000 Prominent Absorption Lines: Lines of helium and weak hydrogen Spectral Class: B Colour: blue-white  Temperature Range (K): 10 000 – 28 000  Prominent Absorption Lines: Lines of helium are strong with weak lines for hydrogen and calcium Spectral Class: A  Colour: white  Temperature Range (K): 7 500 – 10 000  Prominent Absorption Lines: Lines of hydrogen are strong, some calcium strong Spectral Class: F  Colour: white-yellow  Temperature Range (K): 6 000 – 7 500  Prominent Absorption Lines: Dark lines for calcium and hydrogen Spectral Class: G  Colour: yellow  Temperature Range (K): 4 900 – 6 000  Prominent Absorption Lines: Calcium and other easily ionized elements are strong, neutral hydrogen lines weak Spectral Class: K  Colour: orange  Temperature Range (K): 3 500 – 4 900  Prominent Absorption Lines: Strong calcium lines, with neutral metal lines Spectral Class: M  Colour: red  Temperature Range (K): 2 000 – 3 500  Prominent Absorption Lines: Strong lines for neutral atoms, titanium oxide

Colour When iron is heated, it glows orange, yellow, white, and blue as it gets progressively hotter. Similarly, the colour of a star is directly related to its temperature.  “Cool” (they are still over a 1000º C) stars appear red and the hottest stars are blue.

The star on the left emits more energy with longer wavelengths (red end of the visible spectrum), therefore the star will be red in colour. The star in the middle appears yellow, and the star on the right emits more energy with shorter wavelengths (blue end of visible spectrum), therefore it appears to be blue. Image courtesy of NASA

Apparent Magnitude  This is how bright the stars appear from Earth.  The apparent magnitude scale ranges from -26 (really bright) to +25 (really dim stars visible with large telescopes). Note that the lower the magnitude, the brighter the star. However, apparent magnitude does not take into account the actual brightness of a star. Imagine how bright a 100 watt light bulb located 10 m away would be.  How bright would the light be if that same light was 1000 m away?  The apparent magnitude of a star does not take into account the distance a star is from the Sun. As a result, stars that are closer to Earth may appear brighter than stars much farther away even though there is less energy being emitted by the star.   Absolute Magnitude Is the apparent magnitude of a star if it was at a distance of 10 parsecs (32.6 light years).  Therefore, although the Sun has an apparent magnitude of -26 (because it is so close to Earth), it would have an absolute magnitude of 4.8, which means at 10 parsecs and it would be near the limit of being visible by the naked eye. Luminosity Is the energy output of a star measured in Watts.  It can be calculated if the distance and apparent magnitude are known.  Distance The distance to the stars can be determined by measuring its parallax, which will be discussed further later on in this unit.  Radius Most stars appear as a single point of light in the sky, and the radius, with a few exceptions, can’t be measured directly.  The radius can be determined from its temperature and luminosity using the Stefan-Boltzmann law.   An approximation of the star’s radius is determined using the formula:   

The Stefan-Boltzmann law proves that larger stars are brighter than smaller stars even though their temperatures are the same.      Ratios are used in the equation instead, and a value with “o” as a subscript indicates the Sun.  e.g., Mois the mass of the Sun. The significance of this equation is that you can now calculate the size of a distant star by observing its luminosity and using Wien’s law to calculate the temperature.