21 ast4 lecppt_ch13_sample
TRANSCRIPT
![Page 1: 21 ast4 lecppt_ch13_sample](https://reader038.vdocuments.mx/reader038/viewer/2022110118/554eab1bb4c905fb7c8b4d19/html5/thumbnails/1.jpg)
Chapter 13
Taking the Measure
of Stars
©2013 W.W. Norton & Company, Inc.
21st CENTURY ASTRONOMY
FOURTH EDITIONKay | Palen | Smith | Blumenthal
![Page 2: 21 ast4 lecppt_ch13_sample](https://reader038.vdocuments.mx/reader038/viewer/2022110118/554eab1bb4c905fb7c8b4d19/html5/thumbnails/2.jpg)
, Inc.©2013 W.W. Norton & Company, Inc.© 2013 W. W. Norton & Company
We study stars by observing light and using physics and mathematics.
There are different types and colors of stars.
They are at varying distances.
![Page 3: 21 ast4 lecppt_ch13_sample](https://reader038.vdocuments.mx/reader038/viewer/2022110118/554eab1bb4c905fb7c8b4d19/html5/thumbnails/3.jpg)
, Inc.©2013 W.W. Norton & Company, Inc.© 2013 W. W. Norton & Company
Our brains compare views of the left and right eyes to get nearby distances.
Depth perception comes from stereoscopic vision (resulting from having two eyes).
![Page 4: 21 ast4 lecppt_ch13_sample](https://reader038.vdocuments.mx/reader038/viewer/2022110118/554eab1bb4c905fb7c8b4d19/html5/thumbnails/4.jpg)
, Inc.©2013 W.W. Norton & Company, Inc.© 2013 W. W. Norton & Company
As Earth orbits the Sun, nearby stars change their positions slightly against the background.
Comparing the position six months apart yields the distance.
![Page 5: 21 ast4 lecppt_ch13_sample](https://reader038.vdocuments.mx/reader038/viewer/2022110118/554eab1bb4c905fb7c8b4d19/html5/thumbnails/5.jpg)
, Inc.©2013 W.W. Norton & Company, Inc.© 2013 W. W. Norton & Company
Parallax: a change in apparent position due to a change in the position of the observer.
The only direct way to measure the distance to a star is from the parallax.
![Page 6: 21 ast4 lecppt_ch13_sample](https://reader038.vdocuments.mx/reader038/viewer/2022110118/554eab1bb4c905fb7c8b4d19/html5/thumbnails/6.jpg)
, Inc.©2013 W.W. Norton & Company, Inc.© 2013 W. W. Norton & Company
The greater the parallax (or parallactic angle), the smaller the distance.
By definition, a star with a parallax of 1 arcsecond (arcsec) is at a distance of 1 parsec (pc). 1 arcsec = 1/3,600 degree.
![Page 7: 21 ast4 lecppt_ch13_sample](https://reader038.vdocuments.mx/reader038/viewer/2022110118/554eab1bb4c905fb7c8b4d19/html5/thumbnails/7.jpg)
, Inc.©2013 W.W. Norton & Company, Inc.© 2013 W. W. Norton & Company
Not many stars are near the Sun. Obtaining distances is essential. Luminosity: total energy radiated by a star
each second. Brightness: rate at which we receive that
energy (depends on observer’s perspective).
![Page 8: 21 ast4 lecppt_ch13_sample](https://reader038.vdocuments.mx/reader038/viewer/2022110118/554eab1bb4c905fb7c8b4d19/html5/thumbnails/8.jpg)
, Inc.©2013 W.W. Norton & Company, Inc.© 2013 W. W. Norton & Company
Brightness depends on both luminosity and distance.
A dim star could have a low luminosity or be far away.
A bright star could be close or have a high luminosity.
![Page 9: 21 ast4 lecppt_ch13_sample](https://reader038.vdocuments.mx/reader038/viewer/2022110118/554eab1bb4c905fb7c8b4d19/html5/thumbnails/9.jpg)
, Inc.©2013 W.W. Norton & Company, Inc.© 2013 W. W. Norton & Company
From distance and brightness, we know a star’s luminosity.
Idea: How much light must the star emit to be as bright as it is at its distance?
Luminosity = 4d2 brightness.
![Page 10: 21 ast4 lecppt_ch13_sample](https://reader038.vdocuments.mx/reader038/viewer/2022110118/554eab1bb4c905fb7c8b4d19/html5/thumbnails/10.jpg)
, Inc.©2013 W.W. Norton & Company, Inc.© 2013 W. W. Norton & Company
Usually the luminosity is expressed as the solar luminosity = 1 L.
The most luminous stars are 106 L. The least luminous are 104 L. More low-luminosity stars than high.
![Page 11: 21 ast4 lecppt_ch13_sample](https://reader038.vdocuments.mx/reader038/viewer/2022110118/554eab1bb4c905fb7c8b4d19/html5/thumbnails/11.jpg)
, Inc.©2013 W.W. Norton & Company, Inc.© 2013 W. W. Norton & Company
Measuring the color of a star tells us the surface temperature.
We can measure stellar surface temperatures from Wien’s law.
![Page 12: 21 ast4 lecppt_ch13_sample](https://reader038.vdocuments.mx/reader038/viewer/2022110118/554eab1bb4c905fb7c8b4d19/html5/thumbnails/12.jpg)
, Inc.©2013 W.W. Norton & Company, Inc.© 2013 W. W. Norton & Company
peak is the wavelength at which a star is brightest.
“Hotter means bluer” (the spectrum shifts to shorter wavelengths at higher temperatures).
peak
Knm000,900,2
T
![Page 13: 21 ast4 lecppt_ch13_sample](https://reader038.vdocuments.mx/reader038/viewer/2022110118/554eab1bb4c905fb7c8b4d19/html5/thumbnails/13.jpg)
, Inc.©2013 W.W. Norton & Company, Inc.© 2013 W. W. Norton & Company
Spectrum: the amount of light emitted as a function of wavelength.
Some light leaving the staris absorbed by atoms or molecules in the star’s atmosphere.
![Page 14: 21 ast4 lecppt_ch13_sample](https://reader038.vdocuments.mx/reader038/viewer/2022110118/554eab1bb4c905fb7c8b4d19/html5/thumbnails/14.jpg)
, Inc.©2013 W.W. Norton & Company, Inc.© 2013 W. W. Norton & Company
Absorption lines in the spectrum result.
Sometimes emission lines are also seen.
Both are superimposed on a Planck (or continuous) spectrum.
![Page 15: 21 ast4 lecppt_ch13_sample](https://reader038.vdocuments.mx/reader038/viewer/2022110118/554eab1bb4c905fb7c8b4d19/html5/thumbnails/15.jpg)
, Inc.©2013 W.W. Norton & Company, Inc.© 2013 W. W. Norton & Company
Stars are classified into spectral types according to the appearance of their spectra.
Absorption lines depend mainly on the temperature.
Full sequence: O B A F G K M. Sun = G2.
![Page 16: 21 ast4 lecppt_ch13_sample](https://reader038.vdocuments.mx/reader038/viewer/2022110118/554eab1bb4c905fb7c8b4d19/html5/thumbnails/16.jpg)
, Inc.©2013 W.W. Norton & Company, Inc.© 2013 W. W. Norton & Company
Hottest stars: weak absorption by hydrogen and helium (type O).
Medium: strong hydrogen absorption (type A). Coolest: absorption by heavy elements or
molecules (type M).
![Page 17: 21 ast4 lecppt_ch13_sample](https://reader038.vdocuments.mx/reader038/viewer/2022110118/554eab1bb4c905fb7c8b4d19/html5/thumbnails/17.jpg)
, Inc.©2013 W.W. Norton & Company, Inc.© 2013 W. W. Norton & Company
Spectral lines are used to find the composition of stars.
All stars are mostly hydrogen and helium.
Sun: 74.5% H, 23.7% He by mass (92.5% H, 7.4% He by number), and the rest are heavy elements.
![Page 18: 21 ast4 lecppt_ch13_sample](https://reader038.vdocuments.mx/reader038/viewer/2022110118/554eab1bb4c905fb7c8b4d19/html5/thumbnails/18.jpg)
, Inc.©2013 W.W. Norton & Company, Inc.© 2013 W. W. Norton & Company
With luminosity and temperature, we can calculate the size of the star.
Size: radius (half the diameter), R.
The radius comes from the Stefan-Boltzmann law.
There are many more small stars than large ones.
![Page 19: 21 ast4 lecppt_ch13_sample](https://reader038.vdocuments.mx/reader038/viewer/2022110118/554eab1bb4c905fb7c8b4d19/html5/thumbnails/19.jpg)
, Inc.©2013 W.W. Norton & Company, Inc.© 2013 W. W. Norton & Company
To measure mass, we must look for the effects of gravity.
Many stars are binary stars orbiting a common center of mass.
A less massive star moves faster on a larger orbit.
![Page 20: 21 ast4 lecppt_ch13_sample](https://reader038.vdocuments.mx/reader038/viewer/2022110118/554eab1bb4c905fb7c8b4d19/html5/thumbnails/20.jpg)
, Inc.©2013 W.W. Norton & Company, Inc.© 2013 W. W. Norton & Company
Measure velocities of the stars as they orbit.
Calculate total mass of both stars from Kepler’s law and a ratio of one star’s mass to the other.
Lowest-mass stars have M = 0.08 M.
Highest-mass are likely a little bigger than 150 M.
![Page 21: 21 ast4 lecppt_ch13_sample](https://reader038.vdocuments.mx/reader038/viewer/2022110118/554eab1bb4c905fb7c8b4d19/html5/thumbnails/21.jpg)
, Inc.©2013 W.W. Norton & Company, Inc.© 2013 W. W. Norton & Company
Visual binary: can distinguish both stars visually.
Spectroscopic binary: stars are too far away to distinguish; pairs of Doppler-shifted lines trade places.
![Page 22: 21 ast4 lecppt_ch13_sample](https://reader038.vdocuments.mx/reader038/viewer/2022110118/554eab1bb4c905fb7c8b4d19/html5/thumbnails/22.jpg)
, Inc.©2013 W.W. Norton & Company, Inc.© 2013 W. W. Norton & Company
Eclipsing binary: The total light coming from the star system decreases when one star passes in front of the other.
Could also potentially measure the radii of the stars in these systems.
![Page 23: 21 ast4 lecppt_ch13_sample](https://reader038.vdocuments.mx/reader038/viewer/2022110118/554eab1bb4c905fb7c8b4d19/html5/thumbnails/23.jpg)
, Inc.©2013 W.W. Norton & Company, Inc.© 2013 W. W. Norton & Company
H-R diagram (named for Hertzsprung and Russell) is a plot of luminosity vs. temperature.
Key to unraveling stellar evolution: how stars change with time.
![Page 24: 21 ast4 lecppt_ch13_sample](https://reader038.vdocuments.mx/reader038/viewer/2022110118/554eab1bb4c905fb7c8b4d19/html5/thumbnails/24.jpg)
, Inc.©2013 W.W. Norton & Company, Inc.© 2013 W. W. Norton & Company
Most stars exist on the main sequence.
Runs from luminous/hot to low-luminosity/cool.
Massive main sequence stars are large, luminous, and hot.
The Sun is on the main sequence.
![Page 25: 21 ast4 lecppt_ch13_sample](https://reader038.vdocuments.mx/reader038/viewer/2022110118/554eab1bb4c905fb7c8b4d19/html5/thumbnails/25.jpg)
, Inc.©2013 W.W. Norton & Company, Inc.© 2013 W. W. Norton & Company
Knowing a star’s spectral type and position on the H-R diagram allows you to know its luminosity and find its distance (spectroscopic parallax).
The mass of a star determines its fate.
![Page 26: 21 ast4 lecppt_ch13_sample](https://reader038.vdocuments.mx/reader038/viewer/2022110118/554eab1bb4c905fb7c8b4d19/html5/thumbnails/26.jpg)
, Inc.©2013 W.W. Norton & Company, Inc.© 2013 W. W. Norton & Company
Not all stars are on the main sequence.
Remember Stefan-Boltzmann.
Some stars are cool but very luminous: giants or supergiants.
Some have low luminosity but are very hot: white dwarfs.
Different luminosity classes.
![Page 27: 21 ast4 lecppt_ch13_sample](https://reader038.vdocuments.mx/reader038/viewer/2022110118/554eab1bb4c905fb7c8b4d19/html5/thumbnails/27.jpg)
, Inc.©2013 W.W. Norton & Company, Inc.© 2013 W. W. Norton & Company
Different temperature stars have different habitable zones: regions where life as we know it could be supported.
Water must be able to exist as liquid. So far, only a few planets have been found in
the habitable zones of their stars.
![Page 28: 21 ast4 lecppt_ch13_sample](https://reader038.vdocuments.mx/reader038/viewer/2022110118/554eab1bb4c905fb7c8b4d19/html5/thumbnails/28.jpg)
, Inc.©2013 W.W. Norton & Company, Inc.© 2013 W. W. Norton & Company
The parallax (p) of a star is inversely proportional to the distance (d) to a star.
Let p be the parallactic angle in arcseconds.• 1 arcsecond = 1/3,600 of a degree.
Let d be the distance in parsecs.• 1 parsec = 206,205 AU = 3.26 light-years.
Then:
Parsec: distance at which p = 1 arcsecond. Even the closest star to the Sun has a
parallax of only about ¾ arcsecond.
MATH TOOLS 13.1MATH TOOLS 13.1
pd
1
![Page 29: 21 ast4 lecppt_ch13_sample](https://reader038.vdocuments.mx/reader038/viewer/2022110118/554eab1bb4c905fb7c8b4d19/html5/thumbnails/29.jpg)
, Inc.©2013 W.W. Norton & Company, Inc.© 2013 W. W. Norton & Company
The magnitude system was developed by Hipparchus in ancient Greece.
Divides stars into categories of brightness (originally 1st through 6th).
The greater the magnitude, the dimmer the star.
Apparent magnitude: the brightness of a star as it appears in the sky from Earth.
Absolute magnitude: the brightness of a star if it were 10 pc from Earth.
CONNECTIONS 13.1CONNECTIONS 13.1
![Page 30: 21 ast4 lecppt_ch13_sample](https://reader038.vdocuments.mx/reader038/viewer/2022110118/554eab1bb4c905fb7c8b4d19/html5/thumbnails/30.jpg)
, Inc.©2013 W.W. Norton & Company, Inc.© 2013 W. W. Norton & Company
Understanding the meaning behind stellar data took decades, and the contributions of dozens of people, all working toward a common goal.
PROCESS OF SCIENCEPROCESS OF SCIENCE
![Page 31: 21 ast4 lecppt_ch13_sample](https://reader038.vdocuments.mx/reader038/viewer/2022110118/554eab1bb4c905fb7c8b4d19/html5/thumbnails/31.jpg)
, Inc.©2013 W.W. Norton & Company, Inc.© 2013 W. W. Norton & Company
The Stefan-Boltzmann law allows you to estimate the sizes of stars.
The luminosity (L) of a star is related to its temperature (T) and radius (R):
Rearranging, you get:
Called the luminosity-temperature-radius relationship for stars.
MATH TOOLS 13.2MATH TOOLS 13.2
![Page 32: 21 ast4 lecppt_ch13_sample](https://reader038.vdocuments.mx/reader038/viewer/2022110118/554eab1bb4c905fb7c8b4d19/html5/thumbnails/32.jpg)
, Inc.©2013 W.W. Norton & Company, Inc.© 2013 W. W. Norton & Company
Masses of stars can directly be calculated if they are in an eclipsing binary system.
Using observations of the orbital periods and velocities with Newton’s formulation of Kepler’s Third law:
MATH TOOLS 13.3MATH TOOLS 13.3
![Page 33: 21 ast4 lecppt_ch13_sample](https://reader038.vdocuments.mx/reader038/viewer/2022110118/554eab1bb4c905fb7c8b4d19/html5/thumbnails/33.jpg)
, Inc.©2013 W.W. Norton & Company, Inc.© 2013 W. W. Norton & Company
Concept Quiz—Spectral Types
Stars such as the Sun (type G) have spectra with many absorption lines from heavy elements. Why?
A.The Sun is made mostly of heavy elements
B.The Sun is a red giant.
C.Heavy elements are efficient absorbers of light at the temperature of the Sun.
D.Hydrogen and helium never absorb light.
![Page 34: 21 ast4 lecppt_ch13_sample](https://reader038.vdocuments.mx/reader038/viewer/2022110118/554eab1bb4c905fb7c8b4d19/html5/thumbnails/34.jpg)
, Inc.©2013 W.W. Norton & Company, Inc.© 2013 W. W. Norton & Company
Concept Quiz—Getting Brighter
Suppose a star gets more luminous but does not change its
temperature. What is happening?
A. The star is expanding.
B. The star is contracting.
C. The star is getting more massive.
D. The star is changing its spectral type.
![Page 35: 21 ast4 lecppt_ch13_sample](https://reader038.vdocuments.mx/reader038/viewer/2022110118/554eab1bb4c905fb7c8b4d19/html5/thumbnails/35.jpg)
, Inc.©2013 W.W. Norton & Company, Inc.© 2013 W. W. Norton & Company
Concept Quiz—The Main Sequence
Which of the following statements about the main sequence is not true?
A.Hotter stars are more massive.
B.More massive stars are more luminous.
C.Hotter stars are more luminous.
D.Most main sequence stars are more luminous than the Sun.
![Page 36: 21 ast4 lecppt_ch13_sample](https://reader038.vdocuments.mx/reader038/viewer/2022110118/554eab1bb4c905fb7c8b4d19/html5/thumbnails/36.jpg)
, Inc.©2013 W.W. Norton & Company, Inc.© 2013 W. W. Norton & Company
AstroTour Stellar Spectrum
Click here to launch this AstroTour(Requires an active Internet connection.)
![Page 37: 21 ast4 lecppt_ch13_sample](https://reader038.vdocuments.mx/reader038/viewer/2022110118/554eab1bb4c905fb7c8b4d19/html5/thumbnails/37.jpg)
, Inc.©2013 W.W. Norton & Company, Inc.© 2013 W. W. Norton & Company
AstroTour H-R Diagram
Click here to launch this AstroTour(Requires an active Internet connection.)
![Page 38: 21 ast4 lecppt_ch13_sample](https://reader038.vdocuments.mx/reader038/viewer/2022110118/554eab1bb4c905fb7c8b4d19/html5/thumbnails/38.jpg)
This concludes the Lecture PowerPoint presentation for Chapter 13
Visit the StudySpace at:http://wwnorton.com/studyspaceFor more learning resources, please visit the StudySpace site for 21st Century Astronomy
21st CENTURY ASTRONOMY
FOURTH EDITIONKay | Palen | Smith | Blumenthal
©2013 W.W. Norton & Company, Inc.