Stars II Stellar Characteristics: Mass, Temperature, & Size Attendance Quiz

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• Jason Anaya • Andres Gomez • Scott Carmack • Chris Kuoh • Frankie Combs, Jr. • Kevin McCondichie • Jessie Garcia • Bianca Pescina • Danyel Gil Today’s Topics

• Stellar luminosities • Stellar masses • Stellar temperatures and sizes • Laws of Thermal Radiation • Stefan-Boltzmann Law • Luminosity, Temperature and Size • Hertzsprung-Russell Diagram (intro) • Wein’s Law • Stellar Temperatures Any questions on Parallax LT? Stellar Luminosities

• Stellar luminosities vary from 0.0001 L¤–1,000,000 L¤, ten orders of magnitude • Note that most of the stars in this image are at the same distance, so their relative apparent brightness is the same as their relative luminosities

• Note that there are many more faint stars than bright stars, suggesting that less luminous stars are far more common Stellar Masses • Stellar masses are quite difficult to measure • However, about 2/3 of stars are part of a binary system • In those cases, we can use Kepler’s 3rd law to find masses p2 ∝ a3 where the proportionality constant depends on the masses of the system • In general, for two objects orbiting their center-of-mass 4π 2 a3 M1 + M2 = × 2 G p

• For the Solar System M1+M2 ≈ M¤ Stellar Masses

• For binary stars, M1 and M2 are more similar than in the solar system • However, if we can measure the relative speeds of the two stars as they orbit, these allow us to determine the ratio of the two masses, which together with Kepler’s 3rd Law, allows us to find the masses individually • There are three observable types of binary star systems • Visual binaries • Spectrocopic binaries • Eclipsing binaries Binary Star Systems • In visual binaries, it is possible to measure a and p directly, and get v from the orbit • In spectroscopic binaries, the absorption lines shift back and forth as the stars orbit each other, due to the Doppler shift (Interactive Figure 15.8) • From the Doppler shifts, we can find the speeds (along the line of sight) of the orbits • Eclipsing binaries are the most important of the binary systems: the orbit is almost edge-on, and the stars move in front of each other, causing dips in their brightness (Interactive Figure 15.7) • We can find p from the time between eclipses; v from the Doppler shifts (which we know is LOS), and find a from p and v Stellar Masses • To summarize: 1. For a binary system, if we can find the period p, and the semi-major axis, a, of the orbit, then we can find the sum of the stellar masses using Kepler’s 3rd Law 4π 2 a3 M1 + M2 = × 2 G p 2. If we can find the relative speeds of the two stars in their orbits (using either our knowledge of orbital mechanics or the Doppler shift), we can use this information to find the relative masses 3. Together, this information allow us to find the masses of the two stars

• Stellar masses vary from 0.08M¤ to 150M¤ • Less massive stars are more common than more massive stars Stellar Temperatures and Sizes

• As we have seen, stars emit an absorption spectrum • The hot inner core emits thermal (continuous) radiation • The cooler atoms in the outer atmosphere of the star absorb light at the specific wavelengths corresponding to the transitions within those atoms • The continuous part of this spectrum can be used to find stellar temperatures • We can also use a combination of luminosity and temperature to determine stellar sizes (radii) Laws of Thermal Radiation • A plot of intensity v. wavelength of a continuous spectrum looks like the curves below • There are two rules that govern curves of thermal radiation 1. Stefan-Boltzmann Law - each square meter of a hotter object emits more light at all wavelengths than a cooler object (L/m2 ∝ T4) 2. Wein’s (“veen’s”) Law - hotter objects emit photons with a higher average energy (shorter wavelength) (λmax ∝ 1/T)

(Active Figure 5.19) Stefan-Boltzmann Law • The Stefan-Boltzmann Law means that objects can be more luminous for two possible reasons 1. If an object is hotter, it will give off more total energy (L ∝ T4) 2. Since the energy per square meter of surface is the same for all objects at the same temperature, an object which has a bigger surface area will give off more total energy, for a given temperature 3. For a sphere, surface area = 4πR2, so L ∝ T4R2 Luminosity Quiz I

A lump of lead is heated to a high temperature. A lump of gold of the same size as the lump of lead is also heated to the same high temperature. Which lump of material is brighter? a) The lump of lead is brighter. b) The lump of gold is brighter. c) Both lumps are equally bright. d) You cannot tell which lump is brighter without knowing more about the chemistry of lead and gold. Hertzsprung-Russell (HR) Diagram

• In the early 20th century, two astronomers independently had the idea of plotting stars on a temperature-luminosity plot • This diagram is named in their honor a Hertsprung-Russell diagram (HR diagram for short) • Note that the x-axis has temperature increasing to the left (backwards) • This is because HR actually plotted the stars using a measure of color (spectral type) from blue to red • This diagram (which will discuss in a great deal of detail) is the key to unlocking the secrets of how stars differ both in their properties and their evolution Stefan-Boltzmann Law (summary) • The Stefan-Boltzmann Law means that objects can be more luminous for two possible reasons 1. If an object is hotter it will be more luminous 2. If an object has a bigger surface area it will give off more total energy, for a given temperature 3. A star can be luminous either because it is hot or because it is big Lecture Tutorial: Luminosity, Temperature and Size, pp. 55-58 • Work with one or more partners - not alone! • Get right to work - you have 15 minutes – For question 1, each of the four pairs of burners requires an answer to the question: which burner will cook the spaghetti more quickly? – For each pair, make sure to consider all the options: ü the left-hand burner cooks faster, ü the right-hand burner cooks faster, and ü there is not enough information to tell – If you find yourself unsure of how to answer for any of the pairs, just put a question mark and move on Luminosity Quiz II

In question 1D in the Luminosity, Temperature, and Size LT, which hot plate cooks the spaghetti faster? a) The smaller, hotter (left-hand) plate b) The larger, cooler (right-hand) plate c) There is not enough information to tell Luminosity Quiz III

The stars Antares and Mimosa each have the same luminosity. Antares is cooler than Mimosa. Which star is larger? a) Antares b) Mimosa c) They are the same size d) There is not enough information to tell Luminosity Quiz IV

You observe two stars with the same luminosity and determine that one is larger than the other. Which star has the greater temperature? a) the smaller star b) the larger star c) The temperatures are the same d) There is not enough information to tell Luminosity Quiz V

Imagine you are observing two stars. One star is hot and small and the other star is cooler and larger. Which star is more luminous? a) the hotter star b) the larger star c) They have the same luminosity d) There is not enough information to tell Luminosity Quiz VI

Rigel is much more luminous than Sirius B. Rigel and Sirius B have the same temperature. Which star has the greater surface area? a) Rigel b) Sirius B c) They have the same surface area d) There is not enough information to tell Stellar Temperatures (Colors) • As we have seen, a hot, dense object gives off a thermal spectrum • Wein’s Law states that the peak wavelength varies inversely with the temperature of the object (Interactive Figure 5.19) • Thus, bluer = hotter and redder = cooler • Distance does not affect color Stellar Temperatures (Colors) • We can see the effect of Wein’s Law with stars • Note that many of the stars are blue, but many more are red • This is because there are many more cool stars than hot stars (similar to what we have seen with mass and luminosity) • To determine T it is not necessary to measure the entire spectrum • Simply measuring the relative amount of blue and yellow (or blue and red) light, it is possible to get a fairly accurate surface temperature for a star Lecture Tutorial: Blackbody Radiation, pp. 59-62

• Work with one or more partners - not alone! • Get right to work - you have 15 minutes • Read the instructions and questions carefully. • Discuss the concepts and your answers with one another. Take time to understand it now!!!! • Come to a consensus answer you all agree on. • Write clear explanations for your answers. • If you get stuck or are not sure of your answer, ask another group. • If you get really stuck or don’t understand what the Lecture Tutorial is asking, ask me for help. Stellar Temperature Quiz I For Question 15 (based on Figure 2c) of the Blackbody Radiation Lecture Tutorial, which star is larger? a) Star E is larger b) Star D is larger c) They are the same size d) There is not enough information to tell Stellar Temperature Quiz II Use the graph at right to determine which of the following best describes how Star A would appear as compared with Star B a) Star A would appear more red than Star B b) Both stars would appear more red than blue c) Both stars would appear more blue than red d) Star A would appear more blue than Star B e) None of the above Stellar Temperature Quiz III Use the graph at right to determine which of the two stars (A or B) emits light with the longer wavelength peak a) Star A b) Star B c) Both stars’ peak emissions are at the same wavelength d) None of the above are possible Stellar Temperature Quiz IV

The graph at right shows the blackbody spectra for three different stars. Which of the stars is at the highest temperature? a) Star A b) Star B c) Star C