3 Units of Chapter The Solar Neighborhood 17.2 Luminosity and Apparent Brightness 17.3 Stellar Temperatures More Precisely 17-1 More on the Magnitude Scale 17.4 Stellar Sizes More Precisely 17-2 Estimating Stellar Radii 17.5 The Hertzsprung Russell Diagram
4 Units of Chapter 17 (cont.) 17.6 Extending the Cosmic Distance Scale 17.7 Stellar Masses More Precisely 17-3 Measuring Stellar Masses in Binary Stars 17.8 Mass and Other Stellar Properties
5 17.1 The Solar Neighborhood Remember that stellar distances can be measured using parallax
6 17.1 The Solar Neighborhood Nearest star to the Sun: Proxima Centauri, which is a member of the three-star system Alpha Centauri complex Model of distances: Sun is a marble, Earth is a grain of sand orbiting 1 m away Nearest star is another marble 270 km away Solar system extends about 50 m from Sun; rest of distance to nearest star is basically empty
7 17.1 The Solar Neighborhood The 30 closest stars to the Sun
8 17.1 The Solar Neighborhood Next nearest neighbor: Barnard s star Barnard s star has the largest proper motion of any star proper motion is the actual shift of the star in the sky, after correcting for parallax These pictures were taken 22 years apart
9 17.1 The Solar Neighborhood Actual motion of the Alpha Centauri complex
10 17.2 Luminosity and Apparent Brightness Luminosity, or absolute brightness, is a measure of the total power radiated by a star. Apparent brightness is how bright a star appears when viewed from Earth; it depends on the absolute brightness but also on the distance of the star. apparent brightness (energy flux) luminosity 2 distance.
11 17.2 Luminosity and Apparent Brightness Therefore, two stars that appear equally bright might be a closer, dimmer star and a farther, brighter one
12 17.2 Luminosity and Apparent Brightness Apparent luminosity is measured using a magnitude scale, which is related to our perception. It is a logarithmic scale; a change of 5 in magnitude corresponds to a change of a factor of 100 in apparent brightness. It is also inverted larger magnitudes are dimmer.
13 17.2 Luminosity and Apparent Brightness If we know a star s apparent magnitude and its distance from us, we can calculate its absolute luminosity.
14 17.3 Stellar Temperatures The color of a star is indicative of its temperature. Red stars are relatively cool, whereas blue ones are hotter.
15 17.3 Stellar Temperatures The radiation from stars is blackbody radiation; as the blackbody curve is not symmetric, observations at two wavelengths are enough to define the temperature.
16 17.3 Stellar Temperatures Stellar spectra are much more informative than the blackbody curves. There are seven general categories of stellar spectra, corresponding to different temperatures. From highest to lowest, those categories are O B A F G K M
17 17.3 Stellar Temperatures Here are their spectra
18 17.3 Stellar Temperatures Characteristics of the spectral classifications
19 More Precisely 17-1: More on the Magnitude Scale Converting from magnitude to luminosity in solar units: This graph allows us to perform this conversion simply by reading horizontally. A reduction of 5 in magnitude corresponds to an increase in a factor of 100 in luminosity, as it should.
20 17.4 Stellar Sizes A few very large, very close stars can be imaged directly using speckle interferometry. This is Betelgeuse.
21 17.4 Stellar Sizes For the vast majority of stars that cannot be imaged directly, size must be calculated knowing the luminosity and temperature 2 4 luminosity radius temperature. Giant stars have radii between 10 and 100 times the Sun s Dwarf stars have radii equal to, or less than, the Sun s Supergiant stars have radii more than 100 times the Sun s
22 17.4 Stellar Sizes Stellar radii vary widely
23 More Precisely 17-2: Estimating Stellar Radii Combining the Stefan-Boltzman law for the power per unit area emitted by a blackbody as a function of temperature with the formula for the area of a sphere gives the total luminosity L = 4 R 2 T 4 If we measure luminosity, radius, and temperature in solar units, we can write L = R 2 T 4
24 17.5 The Hertzsprung Russell Diagram The H R diagram plots stellar luminosity against surface temperature. This is an H R diagram of a few prominent stars.
25 17.5 The Hertzsprung Russell Once many stars are plotted on an H R diagram, a pattern begins to form. These are the 80 closest stars to us; note the dashed lines of constant radius. The darkened curve is called the main sequence, as this is where most stars are. Also indicated is the white dwarf region; these stars are hot but not very luminous, as they are quite small. Diagram
26 17.5 The Hertzsprung Russell An H R diagram of the 100 brightest stars looks quite different. These stars are all more luminous than the Sun. Two new categories appear here the red giants and the blue giants. Clearly, the brightest stars in the sky appear bright because of their enormous luminosities, not their proximity. Diagram
27 17.5 The Hertzsprung Russell Diagram This is an H R plot of about 20,000 stars. The main sequence is clear, as is the red giant region. About 90% of stars lie on the main sequence; 9% are red giants and 1% are white dwarfs.
28 17.6 Extending the Cosmic Distance Scale Spectroscopic parallax: Has nothing to do with parallax, but does use spectroscopy in finding the distance to a star. 1. Measure the star s apparent magnitude and spectral class 2. Use spectral class to estimate luminosity 3. Apply inverse-square law to find distance
29 17.6 Extending the Cosmic Distance Scale Spectroscopic parallax can extend the cosmic distance scale to several thousand parsecs
30 17.6 Extending the Cosmic Distance Scale The spectroscopic parallax calculation can be misleading if the star is not on the main sequence. The width of spectral lines can be used to define luminosity classes.
31 17.6 Extending the Cosmic Distance Scale In this way, giants and supergiants can be distinguished from main-sequence stars
32 17.7 Stellar Masses Determination of stellar masses: Many stars are in binary pairs; measurement of their orbital motion allows determination of the masses of the stars. Visual binaries can be measured directly. This is Kruger 60.
33 17.7 Stellar Masses Spectroscopic binaries can be measured using their Doppler shifts
34 17.7 Stellar Masses Finally, eclipsing binaries can be measured using the changes in luminosity
35 17.7 Stellar Masses Mass is the main determinant of where a star will be on the main sequence
36 More Precisely 17-3: Measuring Stellar Masses in Binary Stars In order to measure stellar masses in a binary star, the period and semimajor axis of the orbit must be measured. Once this is done, Kepler s third law gives the sum of the masses of the two stars. Then the relative speeds of the two stars can be measured using the Doppler effect; the speed will be inversely proportional to the mass. This allows us to calculate the mass of each star.
37 17.8 Mass and Other Stellar Properties This pie chart shows the distribution of stellar masses. The more massive stars are much rarer than the least massive.
38 17.8 Mass and Other Stellar Properties Mass is correlated with radius and is very strongly correlated with luminosity
39 17.8 Mass and Other Stellar Properties Mass is also related to stellar lifetime stellar lifetime stellar mass. stellar luminosity Using the mass luminosity relationship stellar lifetime 1 (stellar mass) 3.
40 17.8 Mass and Other Stellar Properties So the most massive stars have the shortest lifetimes they have a lot of fuel but burn it at a very rapid pace. On the other hand, small red dwarfs burn their fuel extremely slowly and can have lifetimes of a trillion years or more.
41 Summary of Chapter 17 Can measure distances to nearby stars using parallax Apparent magnitude is related to apparent brightness Absolute magnitude is a measure of the power output of the star Spectral analysis has led to the defining of seven spectral classes of stars Stellar radii can be calculated if distance and luminosity are known
42 Summary of Chapter 17 (cont.) In addition to normal stars, there are also red giants, red supergiants, blue giants, blue supergiants, red dwarfs, and white dwarfs Luminosity class can distinguish giant star from mainsequence one in the same spectral class If spectrum is measured, can find luminosity; combining this with apparent brightness allows distance to be calculated
43 Summary of Chapter 17 (cont.) Measurements of binary-star systems allow stellar masses to be measured directly Mass is well correlated with radius and luminosity Stellar lifetimes depend on mass; the more the mass, the shorter the lifetime
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