Chapter 17 Measuring the Stars - University of Texas at Austin · 17.1 The Solar Neighborhood...

Chapter 17Measuring the Stars

17.1 The Solar Neighborhood XXNaming the Stars

17.2 Luminosity and Apparent Brightness

17.3 Stellar Temperatures XXMore on the Magnitude Scale

17.4 Stellar Sizes Estimating Stellar Radii

17.5 The Hertzsprung-Russell Diagram

Units of Chapter 17

17.6 Extending the Cosmic Distance Scale

17.7 Stellar Masses XXMeasuring Stellar Masses in Binary Stars

17.8 Mass and Other Stellar Properties

Units of Chapter 17 (cont.)

Remember that stellardistances can bemeasured usingparallax:

17.1 The Solar Neighborhood

Nearest star to the Sun: Proxima Centauri,which is a member of the three-star systemAlpha Centauri complex

Model of distances:

Sun is a marble, Earth is a grain of sandorbiting 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 basicallyempty


The 30 closest stars to the Sun:17.1 The Solar Neighborhood

Next nearest neighbor: Barnard’s Star

Barnard’s Star has the largest propermotion of any star—proper motion is theactual shift of the star in the sky, aftercorrecting for parallax

These pictures were taken 22 years apart:


Actual motion of the Alpha Centauri complex:17.1 The Solar Neighborhood

Luminosity, or absolute brightness, is ameasure of the total power radiated by a star.

Apparent brightness is how bright a starappears when viewed from Earth; it depends onthe absolute brightness but also on the distanceof the star:

17.2 Luminosity and ApparentBrightness

Therefore, two stars that appear equallybright might be a closer, dimmer star and afarther, brighter one:


Apparent luminosity ismeasured using a magnitudescale, which is related to ourperception.

It is a logarithmic scale; achange of 5 in magnitudecorresponds to a change ofa factor of 100 in apparentbrightness.

It is also inverted—largermagnitudes are dimmer.


If we know a star’s apparent brightness and itsdistance from us, we can calculate its absoluteluminosity.


Recall Wein’s Lawfor blackbodies:

The color of a staris indicative of itstemperature. Redstars are relativelycool, while blueones are hotter.

17.3 Stellar Temperatures

The radiation from stars is approximately blackbodyradiation; as the blackbody curve is not symmetric,observations at two wavelengths are enough to definethe temperature. The relative amount of light in twowavelength bands is an object’s color.


Stellar spectra are much more informative thanthe blackbody curves (continuous part of thespectrum).

There are seven general categories of stellarspectra, corresponding to differenttemperatures.

From highest to lowest, those categories are:

O B A F G K M


Here are theirspectra:


Characteristics of the spectral classifications:17.3 Stellar Temperatures

A few very large, veryclose stars can beimaged directly usingspeckle interferometry.This is Betelgeuse.

17.4 Stellar Sizes

For the vast majority of stars that cannot beimaged directly, size must be calculated knowingthe luminosity and temperature:

• Giant stars have radii between 10 and 100times the Sun’s

• Dwarf stars have radii equal to, or lessthan, the Sun’s

• Supergiant stars have radii more than 100times the Sun’s

17.4 Stellar Sizes

Stellar radii vary widely:

17.4 Stellar Sizes

More Precisely 17-2:Estimating Stellar Radii

Combining the Stefan-Boltzmann law forthe power per unit area emitted by ablackbody as a function of temperaturewith the formula for the area of a spheregives the total luminosity:

If we measure luminosity, radius, andtemperature in solar units, we can write

L = R2T4

The H-R diagram plots stellar luminosityagainst surface temperature.

This is an H-Rdiagram of a fewprominent stars:


Once many stars are plotted on an H-Rdiagram, a pattern begins to form:

These are the 80 closest starsto us; note the dashed lines ofconstant radius.

The darkened curve is calledthe main sequence, as this iswhere most stars are.

Also indicated is the whitedwarf region; these stars arehot but not very luminous, asthey are quite small.


An H-R diagram of the 100 brightest stars looksquite different:

These stars are all moreluminous than the Sun.Two new categoriesappear here—the redgiants and the blue giants.

Clearly, the brightest starsin the sky appear brightbecause of their enormousluminosities, not theirproximity.


This is an H-R plot ofabout 20,000 stars. Themain sequence is clear,as is the red giantregion.

About 90% of stars lieon the main sequence;9% are red giants and1% are white dwarfs.


Spectroscopic parallax: Has nothing to do withparallax, but does use spectroscopy infinding the distance to a star.

1. Measure the star’s apparent magnitude andspectral class

2. Use spectral class to estimate luminosity

3. Apply inverse-square law to find distance

17.6 Extending the Cosmic DistanceScale

Spectroscopic parallax can extend the cosmicdistance scale to several thousand parsecs:


The spectroscopic parallax calculation can bemisleading if the star is not on the mainsequence. The width of spectral lines can beused to define luminosity classes:


In this way, giants and supergiants can bedistinguished from main-sequence stars


Determination of stellar masses:

Many stars are in binary pairs; measurement oftheir orbital motion allows determination of themasses of the stars.

Visual binaries canbe measureddirectly. This isKruger 60:

17.7 Stellar Masses

Spectroscopic binaries can be measured usingtheir Doppler shifts:

17.7 Stellar Masses

Finally, eclipsing binaries can be measuredusing the changes in luminosity.

17.7 Stellar Masses

Mass is the maindeterminant of where astar will be on the MainSequence. Masscontrols a star’slifetime, and the way inwhich it will die.

(We cover stellarevolution in ch.19-20,but we will get tolifetimes here.)

17.7 Stellar Masses

More Precisely 17-3:Measuring Stellar Masses in Binary Stars

In order to measure stellar masses in a binarystar, the period and semimajor axis of the orbitmust be measured. Once this is done, Kepler’sthird law gives the sum of the masses of thetwo stars. Then the relative speeds of the twostars can be measured using the Dopplereffect; the speed will be inversely proportionalto the mass. This allows us to calculate themass of each star.

17.8 Mass and Other StellarProperties

This pie chartshows thedistribution ofstellar masses. Themore massive starsare much rarer thanthe least massive.

Mass is correlated with radius and is verystrongly correlated with luminosity:


Mass is also related to stellar lifetime:

Using the mass–luminosity relationship:


So the most massive stars have theshortest lifetimes—they have a lot offuel but burn it at a very rapid pace.

On the other hand, small red dwarfsburn their fuel extremely slowly and canhave lifetimes of a trillion years or more.


• Can measure distances to nearby stars using parallax

• Apparent brightness is easy to measure, but tells usnothing about a star’s intrinsic properties, only how bright itappears.

• Absolute luminosity L is a measure of the power output ofthe star. We can obtain L from the apparent brightness anddistance.

• Spectral analysis has led to the defining of seven spectralclasses of stars, which correspond to differences intemperature.

• Stellar radii can be calculated if distance and luminosityare known. (See if you can explain how.)

Summary of Chapter 17

• In addition to “normal” stars, there are also red giants, redsupergiants, blue giants, blue supergiants, red dwarfs, andwhite dwarfs

• Luminosity class can distinguish giant star from main-sequence one in the same spectral class

• If spectrum is measured, can find luminosity; combiningthis with apparent brightness allows distance to becalculated

Summary of Chapter 17 (cont.)

• Measurements of binary-star systems allow stellarmasses to be measured directly

• Mass is well correlated with radius and luminosity

• Stellar lifetimes depend on mass; the more the mass, theshorter the lifetime

Chapter 17 Measuring the Stars - University of Texas at Austin · 17.1 The Solar Neighborhood...

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