Scholars Online Astronomy - Chapter 17: The Nature of Stars

Homework

Reading Preparation
- Study Guide/Reading Notes
Key Formulae to Know
WebLecture
Study Activity
Chat Preparation Activities
Chapter Quiz
Lab Work

Reading Preparation

Reading: Astronomy, Chapter 17: The Nature of the Stars

Study Guide

Section 1: Because the Earth's position in space changes by 2 AU during a six-month period (the diameter of its orbit around the sun), we can observe the changing position of nearby stars against the background sky. Parallax can only be used for stars out to about 100 parsecs.
Section 2: A star's apparent brightness is a function of its absolute brightness or actual energy output and the distance of the star from Earth. If we know the distance to the star from other sources such as parallax, we can use the apparent magnitude of the star to determine its absolute brightness and luminosity, or energy flow.
Section 3: The logarithmic magnitude scale is used to measure brightness of stars based on Hipparchus' original scale in which a magnitude difference of five corresponds to a brightness difference of 100. Two adjacent magnitudes differ by ⁵√100, or 2.512 times in brightness. Apparent magnitude is the magnitude of a star as seen from Earth. Absolute magnitude is the apparent magnitude of a star seen a specific distance, normally 10 parsecs. In order to compare the luminosities of two stars, we need to compare their absolute magnitudes, avoiding apparent differences introduced by differences in distance.
Section 4: A star's color is the result of the dominant wavelength emitted by gases with a particular surface temperature. UVB photometry measures brightness in the ultraviolet, blue, and visual wavelengths. If the ratio of visual light to blue light and the ratio of blue light to ultraviolet light are less than one (more light is coming from the blue and UV spectrum than from the visible spectrum), then the star's surface is hot.
Section 5: The spectra of stars can be used to determine their chemical composition by matching spectra patterns against the patterns given by elements and molecules at similar temperatures in the la-. The width of the spectrum line indicates the abundance of the substance emitting the line. The combination of spectral lines from a given star can be used to determine its general composition and stellar type in the OBAFGKMTL scale.
Section 6: The Stefan Boltzmann law allows us to determine the radius of a star based on its observed luminosity and the temperatures calculated from spectroscopic and brightness studies. A cool red giant can actually have a greater luminosity and total energy output than a much brighter, but much smaller star such as a neutron star.
Section 7: The Hertzsprung-Russell diagram is used to summarize the relationship between surface temperature, absolute magnitude, luminosity, and spectral type for a large number of stars. When several hundred stars are plotted in the HR diagram, they form easily identifiable groups of super giants, giants, sub-giants, main sequence stars, and dwarf stars.
Section 8: Using the star's spectral class, we can determine its luminosity, and using reverse logic, calculate its distance from its calculated absolute magnitude.
Section 9: Binary stars follow Kepler's laws when orbiting their common center of mass. We can use observations of these orbital periods to determine the masses of the stars in the system. Analysis of a large number of stars reveals a mass-luminosity relationship, Which we can now use to determine the masses of stars which are not in binary systems.
Section 10: In some binary systems, the stars are too close together to allow us to form separate point images. However, we can use the spectroscopic signature of the light from each star to isolate information and identify which star it belongs to.
Section 11: If a binary system is oriented so that one star passes in front of the other during their revolutions around the common center of mass, we can plot the changes in light over time as one star eclipses the other, and uses information to determine the size and shape of the stars.

Key Formulae to Know

Purpose	Formula	Variables
Calculate Parallax	$d = \frac{1}{p}$	d = distance in parsecs p = parallax angle in arcseconds
Absolute luminosity, distance, and apparent brightness	$L = 4 π d^{2} b$	L = Luminosity d = distance from star b = brightness
Relative luminosity, distance, and apparent brightness	$\frac{L}{L_{✩}} = {(\frac{d}{d_{✩}})}^{2} \frac{b}{b_{✩}}$	L = luminosity in watts d = distance in any units b = brightness * refers to the Sun Luminosity is often calculated relative to L_SUN for convenience.
Brightness and Magnitude	$\frac{b_{1}}{b_{2}} = {2.5}^{(m_{2} - m_{1})}$	b = apparent brightness m = apparent magnitude
Brightness to Magnitude	$m_{2} - m_{1} = 2.5 \log (\frac{b_{1}}{b_{2}})$	m = apparent magnitude b = apparent brightness
Distance Modulus	$m - M = 5 \log (d) - 5$	m = apparent magnitude M = absolute magnitude d = distance in parsecs
UBV Photometry	$\begin{matrix} \frac{b_{V}}{b_{B}} \\ and \\ \frac{b_{B}}{b_{U}} \end{matrix}$	Relative brightness indicates dominant wavelength location. b_V / b_B < 1, b_B/b_U > 1 Star is cool b_V / b_B < 1, b_B/b_U > 1 Star is hot
Stefan-Boltzmann Law	$L = 4 π R^{2} σ T^{4}$	L = Luminosity R = stellar radius in meters T = surface temperature in K in Watts σ = 5.67 * 10^-8 W/m²K⁴
Kepler's Third Law	$M_{1} + M_{2} = \frac{a^{3}}{P^{2}}$	M₁ and M₂: stellar masses in solar mass units a = semimajor axis of one star's orbit around the other in AU P = orbital period in years
Mass-Luminosity Relationship	$L = M^{3.5}$ $Use : \frac{L}{L_{⊙}} = \frac{M^{3.5}}{M_{⊙ 3.5}}$	L = Luminosity M = Stellar Mass Note that the logical connector is a proportion, not an equal sign. To use this relationship, we need a ratio with known values, such as those of the Sun(☉).

Web Lecture

Read the following weblecture before chat: Observing Stars: What we can learn from starlight

Study Activity

Planetarium Program: Use your planetarium program to explore the 10 brightest stars in Earth's night sky. If your program does not list these, check the list of 26 Brightest Stars seen from Earth.

Which of these stars are visible from your location?
Given the temperature of each star, what color do you expect each star to be?
If possible, use the planetarium program to investigate the Hertzsprung-Russell diagram.
If possible, use your planetarium program to view the sun and record its apparent magnitude from 1 AU (Earth distance), 2 AU, 3 AU, 4 AU, 8 AU, 16 AU.

UNL Tools Exercises

Interactives:
- Under Luminosity of Stars, do Luminosity interactive tasks 3, 4, and 5.
ClassAction:
- Under Stellar Properties, work through general concepts 1-18.
- Under activities, look at the Spectroscopic Parallax Simulator.
NAAP Labs:
- Under the Hertzprung-Russell Diagram, read about Spectral Classification, Luminosity, and the HR Diagram itself.
- Using the HR Diagram Explorer, examine the default settings for the Sun. Where is it on the HR diagram? Then check out at least three of the "brightest stars" from the list above, and compare the radius of the star and its position on the HR diagram with that of the sun. Bring up the "brightest and nearest stars" and look at the overlap.

Website of the Week: Read about the Gaia Mission, a follow-on mission to Hipparcos from the European Space Agency. Hipparcos ( the high precision parallax collecting satellite) operated between 1989 and 1993 into a geostationary transfer orbit. Because of a failure in a boost motor, it never reached its target orbit, but scientists were still able to gather data from it for over 3 1/2 years. The Gaia mission was scheduled to be launched in the summer of 2012 and placed into orbit at the Sun-Earth L2 Lagrangian point, but launch was delayed until 19 December 2013. Its mission is to create a precise three-dimensional map of stars throughout the Milky Way galaxy and determine their motions, luminosity, effect of temperature, gravity, and chemical composition.

Chapter Quiz

Required: Complete the Mastery exercise with a passing score of 85% or better.
Go to the Moodle and take the quiz for this chat session to see how much you already know about astronomy!

Lab Work

Read through the lab for this week; bring questions to chat on any aspect of the lab, whether you intend not perform it or not. If you decide to perform the lab, be sure to submit your report by the posted due date.

Lab instructions: Determining the distance to a star using parallax measurements

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Astronomy

Chapter 17 Homework