PHYSICAL PROPERTIES OF A STAR

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  1. To plot the H-R diagram for stars and use it to estimate the temperature and
    luminosity of a star, given its spectral class.
  2. To calculate the mass, radius, and lifetime of a star, using the appropriate equations
    and graphs.
    Equipment
    Calculator and semi-logarithmic graph paper (supplied at the end of this lab).
    Introduction
    There are five physical quantities, which are used to define a star:
  3. Temperature
  4. Luminosity
  5. Mass
  6. Radius
  7. Lifetime and chemical composition
    Let us examine how each of these quantities can be deduced.
    Temperature
    The temperature (T) of the photosphere is measured in degrees K. This can be
    calculated by direct observation from Earth. The photosphere of a star emits a
    continuous spectrum observable from the Earth. By dispersing the spectrum and
    graphing its Planck curve, the maximum wavelength can be determined by using Wien’s
    Law, T Wien = 2,900,000 nm K/  max where  max is the maximum wavelength measured
    in nanometers.
    Another method used to determine the temperature of a star is by interpreting its
    spectral signature. Astronomers have correlated the spectral lines seen with the degree
    of ionization present in the star’s photosphere. Since temperature determines the degree
    of ionization, once the spectral class of a star is identified, it is possible to use a table
    like the one below to determine a star’s temperature. Remember the spectral sequence
    is O, B, A, F, G, K, M, with the O stars being the hottest. Each letter category is in turn
    divided into 10 sub-categories, ranging from zero to nine. A star with the classification
    B9 is therefore slightly cooler than B8, but hotter than A0.
    2
    Spectral type Temperature
    O5 30,000 K
    B0 25,000 K
    A0 10,000 K
    F0 8,000 K
    G0 6,000 K
    K0 5,000 K
    M0 4,000 K
    M7 2,000 K
    Luminosity
    The luminosity is the energy emitted by the star’s photosphere each second and over all
    wavelengths of the electromagnetic spectrum. If the distance to the star is known, the
    luminosity can be calculated either by using the equations for apparent brightness or
    absolute magnitude. The former is
    Apparent Brightness = Luminosity/4 π r2 where r = distance
    To use absolute magnitude the steps are listed below:
  8. The parallax angle of the star is measured.
  9. The distance (d) is calculated.
  10. The apparent visual magnitude (m) is measured.
  11. The apparent visual magnitude (m) and distance modulus (m – M) are used to
    calculate the absolute visual magnitude (M), since m – M = 5 log d – 5.
  12. The luminosity (L) is calculated from the absolute visual magnitude (M), using the
    equation, L = 85.51 x 10-0.4M where L is measured in solar units. This means that
    if the value of L works out to be 5, the star is 5 times more luminous than the
    Sun.
    Unfortunately stars that are further than 200 pc are too far away for their parallax to be
    measured. The luminosity for these stars has to be estimated using other techniques.
    The luminosity of a hydrogen-burning, main sequence star can be estimated using the
    H-R Diagram (i.e., luminosity-temperature plot) which does not require knowing the
    distance. As a matter of fact once the luminosity is estimated from the H-R Diagram, the
    distance can then be estimated using the five steps above, but in reverse order.
    Estimating the distance of a star in this manner is called the spectroscopic parallax
    method.
    3
    Mass
    The mass of a star is a measure of how many and what types of atoms it contains.
    Astronomers first measured the mass of stars in binary systems (i.e., systems that
    contain two stars gravitationally bound to each other). Approximately 50% of the stars
    are members of binary systems.
    For nearby systems with a measured parallax and known distance, Newton’s Law of
    Gravity and Kepler’s Third Law of Planetary Motion can be used to calculate the total
    mass of the stars in these systems. Further observations of the two stars as they orbit
    about each other can be used to calculate each of the two masses.
    Of course, not all stars are in binary systems, and not all binary systems have a
    measurable parallax. When astronomers compared the masses and luminosities of
    hydrogen-burning, main sequence stars, they discovered that the luminosity could be
    used to estimate the mass accurately. Today, astronomers call this the Mass-Luminosity
    Relationship, which is only valid for main sequence stars. A graph between the mass
    and luminosity is shown on the next page. Thus if a star’s luminosity is calculated to be
    1,000 from the graph, it can be seen that its mass will be 7 solar masses, or 7 times the
    mass of the Sun.

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