21 ast4 lecppt_ch13_sample

Chapter 13

Taking the Measure

of Stars

©2013 W.W. Norton & Company, Inc.

21st CENTURY ASTRONOMY

FOURTH EDITIONKay | Palen | Smith | Blumenthal

, 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.


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).


As Earth orbits the Sun, nearby stars change their positions slightly against the background.

Comparing the position six months apart yields the distance.


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.


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.


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).


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.


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.


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.


Measuring the color of a star tells us the surface temperature.

We can measure stellar surface temperatures from Wien’s law.


peak is the wavelength at which a star is brightest.

“Hotter means bluer” (the spectrum shifts to shorter wavelengths at higher temperatures).

peak

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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.


Absorption lines in the spectrum result.

Sometimes emission lines are also seen.

Both are superimposed on a Planck (or continuous) spectrum.


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.


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).


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.


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.


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.


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.


Visual binary: can distinguish both stars visually.

Spectroscopic binary: stars are too far away to distinguish; pairs of Doppler-shifted lines trade places.


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.


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.


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.


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.


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.


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.


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


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


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


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.



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:



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.


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.


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.


AstroTour Stellar Spectrum

Click here to launch this AstroTour(Requires an active Internet connection.)


AstroTour H-R Diagram

Click here to launch this AstroTour(Requires an active Internet connection.)

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.

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Technology

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luminous stars

hottest stars

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composition of stars

total mass ofboth stars

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