Chapter 10 Measuring the Stars

Chapter 10 Measuring the Stars

Units of Chapter 10

The Solar NeighborhoodLuminosity and Apparent BrightnessStellar TemperaturesStellar SizesThe Hertzsprung–Russell DiagramExtending the Cosmic Distance ScaleStellar MassesSummary of Chapter 10

10.1 The Solar Neighborhood

Parallax: Look at apparent motion of object against distant background from two vantage points; knowing baseline allows calculation of distance:

distance (in parsecs) = 1/parallax (in arc seconds)

10.1 The Solar Neighborhood

Nearest star to the Sun: Proxima Centauri, which is a member of a 3-star system: Alpha Centauri complexModel of distances: • Sun is a marble, Earth is a grain of sand orbiting 1 m away.• Nearest star is another marble 270 km away.• Solar system extends about 50 m from the Sun; rest of distance to nearest star is basically empty.

The 30 closest stars to the Sun

Barnard’s Star (top) has the largest proper motion of any – proper motion is the actual shift of the star in the sky, after correcting for parallax.The pictures (a) were taken 22 years apart. (b) shows the actual motion of the Alpha Centauri complex.

Luminosity, or absolute brightness, is a measure of the total power radiated by a star.Apparent brightness is how bright a star appears when viewed from Earth; it depends on the absolute brightness but also on the distance of the star:

apparent brightness luminosity/distance2

10.2 Luminosity and Apparent Brightness

This is an example of an inverse square law.

Therefore, two stars that appear equally bright might be a closer, dimmer star and a farther, brighter one.

Apparent luminosity is measured using a magnitude scale, which is related to our perception.It is a logarithmic scale; a change of 5 in magnitude corresponds to a change of a factor of 100 in apparent brightness. It is also inverted – larger magnitudes are dimmer.

10.3 Stellar TemperaturesThe color of a star is indicative of its temperature. Red stars are relatively cool, whereas blue ones are hotter.

The radiation from stars is blackbody radiation; as the blackbody curve is not symmetric, observations at two wavelengths are enough to define the temperature.

Stellar spectra are much more informative than the blackbody curves.There are seven general categories of stellar spectra, corresponding to different temperatures. From highest to lowest, those categories are:

O B A F G K M

The seven spectral types

The different spectral classes have distinctive absorption lines.

10.4 Stellar SizesA few very large, very close stars can be imaged directly; this is Betelgeuse.

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

luminosity radius2 temperature4

Giant stars have radii between 10 and 100 times the Sun’s.Dwarf stars have radii equal to, or less than, the Sun’s.Supergiant stars have radii more than 100 times the Sun’s.

Stellar radii vary widely.

10.5 The Hertzsprung–Russell Diagram

The H–R diagram plots stellar luminosity versus surface temperature.

This is an H–R diagram of a few prominent stars.

Once many stars are plotted on an H–R diagram, a pattern begins to form:

These are the 80 closest stars to us; note the dashed lines of constant radius.The darkened curve is called the main sequence, as this is where most stars are.Also indicated is the white dwarf region; these stars are hot but not very luminous, as they are quite small.

An H–R diagram of the 100 brightest stars looks quite different.

These stars are all more luminous than the Sun. Two new categories appear here – the red giants and the blue giants.Clearly, the brightest stars in the sky appear bright because of their enormous luminosities, not their proximity.

10.5 The Hertzsprung–Russell Diagram

This is an H–R plot of about 20,000 stars. The main sequence is clear, as is the red giant region.

About 90 percent of stars lie on the main sequence; 9 percent are red giants and 1 percent are white dwarfs.

10.6 Extending the Cosmic Distance Scale

Spectroscopic parallax: Has nothing to do with parallax, but does use spectroscopy in finding the distance to a star.1. Measure the star’s apparent magnitude and spectral class.2. Use spectral class to estimate luminosity.3. Apply inverse-square law to find distance.

Spectroscopic parallax can extend the cosmic distance scale to several thousand parsecs.

The spectroscopic parallax calculation can be misleading if the star is not on the main sequence. The width of spectral lines can be used to define luminosity classes.

In this way, giants and supergiants can be distinguished from main-sequence stars.

10.7 Stellar MassesMany stars are in binary pairs; measurement of their orbital motion allows determination of the masses of the stars. Orbits of visual binaries can be observed directly; Doppler shifts in spectroscopic binaries allow measurement of motion; and the period of eclipsing binaries can be measured using intensity variations.

Mass is the main determinant of where a star will be on the main sequence.

Stellar mass distributions – there are many more small stars than large ones!

Assuming that stars radiate like black bodies, you must know which of the following properties in order to infer the radius of a star?

A. Luminosity and surface temperature.

B. Luminosity and distance.C. Luminosity and flux.D. Luminosity and mass.

The apparent brightness of an object such as a star does not depend on

A. how fast the star is moving across our line of sight.

B. the strength of the light emanating from the star.

C. the distance from us to the star.D. the amount and kind of obstacles

between us and the star.

The luminosity of a star is a unique measure of its

A. velocity of recession away from us.

B. temperature.C. total energy output.D. physical size.

If the sun were twice as far away as it is now, we would receive

A. twice as much flux.B. the same amount of flux.C. half as much flux.D. one-fourth as much flux.

What is the relation between the apparent magnitude of a star and its color?

A. the apparent magnitude of a star is a direct indicator of its color.

B. the apparent magnitude of a star is not an indicator of its color.

C. the answer depends on what time of night the star is observed.

D. the relationship is not fully known.

The difference between a star's actual brightness and apparent brightness is a measure of its

A. distance.B. brightness.C. temperature.D. luminosity.

The most fundamental property of a star is its

A. temperature.B. luminosity.C. mass.D. diameter.

Which of the following observed quantities depends upon the distance to the object

A. Doppler shiftB. ColorC. actual brightnessD. apparent brightness

If two stars in the sky have the same apparent brightness and are not hidden by gas or dust clouds, then

A. they have the same temperature.B. they must be at the same

distance away from us.C. the furthest one has the greatest

luminosity.D. they have the same angular size.

Which of the following spectra originates from the reddest star?

A. aB. bC. gD. m

Summary of Chapter 10

• Distance to nearest stars can be measured by parallax.• Apparent brightness is as observed from Earth; depends on distance and absolute luminosity.• Spectral classes correspond to different surface temperatures.• Stellar size is related to luminosity and temperature.

Summary of Chapter 10, cont.

• H–R diagram is plot of luminosity vs. temperature; most stars lie on main sequence.• Distance ladder can be extended using spectroscopic parallax.• Masses of stars in binary systems can be measured.• Mass determines where star lies on main sequence.