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Physical properties. Brightness and distance. The apparent brightness of a star falls as the square of its distance from you. Discussion.
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Brightness and distance The apparent brightness of a star falls as the square of its distance from you.
Discussion I have two light bulbs, one is 25 watts and the other is 100 watts. If the 25-watt light bulb is 1 mile away, how far would I need to place the 100-watt light bulb to have the same apparent brightness?
Absolute magnitude Luminosity is the same as apparent brightness, without considering the distance. Absolute magnitude is magnitude a star would have if it were 10 parsecs away.
Apparent and absolute magnitudes Apparent magnitude measures brightness in the sky. Absolute magnitude measures luminosity.
Luminosity Distance If we know the luminosity of a star or galaxy, we can figure out how far away it is by comparing it to its apparent brightness.
Discussion But, what if there is a lot of dust between us and the object we are observing. That would make the object appear fainter and we would be misled into thinking the object was much farther away than it really is. How can astronomers determine if dust is making things fainter?
Determining Luminosity The intensity of the emitted light from a blackbody depends on the temperature. Intensity is energy emitted per unit surface area. To get the luminosity of a star, we need to know the star’s size, i.e. its radius. The larger the star, the more luminous it will be.
More distances The key to determining the luminosity of a blackbody is knowing its temperature and surface area. The sizes of stars can vary from 0.01 R to 1000 R, where R is the radius of the Sun.
Discussion How do you think astronomers can estimate the sizes of stars?
We can find the temperature of a star from its color, use the temperature to calculate the intensity, and if the star just happens to be an eclipsing binary, use its radius to calculate its luminosity. Comparing its luminosity to its apparent brightness we can finally arrive at its distance.
Discussion If two stars have the same mass, determined by each being a binary star and using Kepler’s 3rd law, but one has a radius that is 10 times bigger than the other, what is the difference in their surface gravities?
Discussion In which star do you think the atoms suffer more collisions, one with low surface gravity, or one with high surface gravity? Explain.
Discussion What do you think is the difference between the spectral lines produced by atoms that rarely collide and those that suffer thousands of collisions per second?
Discussion The picture show spectra of two B8 type stars, which star is hotter?
Discussion Which B8 star has the larger surface gravity? If these stars are the same mass, which is bigger?
Luminosity class With temperature (from spectral type) and size (from width of spectral lines) we can calculate the luminosity of stars. The bigger the star the higher its luminosity. The width of the spectral lines is divided into luminosity classes; I being the narrowest, II being less narrow, and V being the broadest.
The Sun The Sun is a G2 V, or sometimes referred to as a G2 dwarf star.
Summing up The spectrum of a star gives that star’s surface temperature by the relative strength of the absorption lines of different elements. The broadness of the lines gives the star’s surface gravity. If we know the mass, we can calculate the radius and thus the luminosity of the star.
Summing up Knowing the star’s luminosity (its intrinsic brightness) and comparing it with the star’s apparent brightness, we can use the inverse square law to calculate its distance. Spectroscopic parallax
H-R diagrams A plot of stars’ spectral class, or temperature, or color ratio, vs. the luminosity.
Discussion In the H-R diagram, 90% of stars lie along a band running from the upper left to the lower right which we call the main sequence. The most luminous stars are the bluest. Why is that?
The Main Sequence Main sequence stars are fusing hydrogen in their cores. 1% of stars are giant or supergiants in which core H fusion has ceased. 9% are white dwarf stars.
Discussion Most of the bright stars in the sky are giant or supergiant stars. How can this be if only 1% of the stars are giants and supergiants?
Discussion Why do you think higher mass stars are more luminous?
Main sequence is also a mass sequence, hotter, more luminous stars on the main sequence are more massive.
Discussion How do we get the distance to a star with 1 kpc of the Sun? What can we do if it is farther away?
Distance If the star is within 1 kpc, we can use geometric parallax. If not, we can get a spectrum, determine its spectral class and compare it with its apparent brightness to determine the distance. This method is often referred to as spectroscopic parallax.
Discussion What are the three ways we have of determining a star’s surface temperature?
Temperature Measure the star’s color index using UBVIR photometry and use Wien’s law for blackbodies. Or get the stars spectrum and use the relative strength of its absorption lines for different elements. That is, determine the star’s spectral classification or fit the continuum
Discussion How do we determine a star’s mass if it is in a binary system? What if it is not a binary, but is a main sequence star?
Mass If the star is in a binary system, can use Kepler’s 3rd law to calculate the mass. If the star is a main sequence star you could use the mass-luminosity relation. If not, you need the star’s radius and the width of the spectral lines to find the surface gravity.
Radius If it is the right type of eclipsing binary, measure the length of the eclipses. If not, the radius of a star can be roughly determined from its luminosity class (width of spectral lines), apparent brightness and distance.
Composition Can be determined from the strength of the absorption lines in its spectrum, after the effects of temperature have been removed.
Discussion How do we get the radial velocity of a star?
Radial Velocity Radial velocity can be determined using the Doppler effect or shifts in the absorption lines in the spectra.
Proper motions To measure a star’s motion perpendicular to the line of sight, i.e. in the plane of the sky, we must know its distance and wait to see it move. Typically, proper motion is measured in milliarcsec/year.
Barnard’s Star Has the highest proper motion of about 10 arcsec/year
