Chapter 10 Measuring the Stars

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

10.1 The Solar Neighborhood Nearest star to the Sun is Proxima Centauri, which is a member of a 3-star system: Alpha Centauri complex

10.1 The Solar Neighborhood Nearest star to the Sun is Proxima Centauri, which is a member of a 3-star system: Alpha Centauri complex The “auditorium scale model”:

10.1 The Solar Neighborhood Nearest star to the Sun is Proxima Centauri, which is a member of a 3-star system: Alpha Centauri complex The “auditorium scale model”: Sun is a BB, Earth is a biological cell orbiting 21.5 cm away

10.1 The Solar Neighborhood Nearest star to the Sun is Proxima Centauri, which is a member of a 3-star system: Alpha Centauri complex The “auditorium scale model”: Sun is a BB, Earth is a biological cell orbiting 21.5 cm away Nearest star (Proxima Centauri) is another BB 57 km away (in St Augustine)

10.1 The Solar Neighborhood Nearest star to the Sun is Proxima Centauri, which is a member of a 3-star system: Alpha Centauri complex The “auditorium scale model”: Sun is a BB, Earth is a biological cell orbiting 21.5 cm away Nearest star (Proxima Centauri) is another BB 57 km away (in St Augustine) Solar system extends to near the top of the steps about 10 m from Sun; rest of distance to nearest star is basically empty

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

End of 2 April 2007 Lecture

10.1 The Solar Neighborhood Barnard’s Star (top) has the largest proper motion of any star –

10.1 The Solar Neighborhood Barnard’s Star (top) has the largest proper motion of any star – proper motion is the actual shift of the star in the sky, after correcting for parallax.

10.1 The Solar Neighborhood Barnard’s Star (top) has the largest proper motion of any star – proper motion is the actual shift of the star in the sky, after correcting for parallax. 88 km/s

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

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

10.2 Luminosity and Apparent Brightness 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:

10.2 Luminosity and Apparent Brightness This is an example of an inverse square law

10.2 Luminosity and Apparent Brightness As an exact equality instead of a proportionality:

10.2 Luminosity and Apparent Brightness So two stars that appear equally bright

10.2 Luminosity and Apparent Brightness So two stars that appear equally bright

10.2 Luminosity and Apparent Brightness So two stars that appear equally bright might be identical stars the same distance from us…

10.2 Luminosity and Apparent Brightness Or they might be a closer, dimmer star and a farther, brighter one:

10.2 Luminosity and Apparent Brightness Apparent brightness can also be measured using a magnitude scale, which is related to our perception.

10.2 Luminosity and Apparent Brightness Apparent brightness can also be 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.

10.2 Luminosity and Apparent Brightness Apparent brightness can also be 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 (more positive) magnitudes are dimmer.

10.2 Luminosity and Apparent Brightness The magnitudes listed here are apparent magnitudes

10.2 Luminosity and Apparent Brightness The magnitudes listed here are apparent magnitudes Apparent magnitude is related to apparent brightness

10.2 Luminosity and Apparent Brightness The magnitudes listed here are apparent magnitudes Apparent magnitude is related to apparent brightness But luminosity is related to absolute magnitude

10.2 Luminosity and Apparent Brightness The magnitudes listed here are apparent magnitudes Apparent magnitude is related to apparent brightness But luminosity is related to absolute magnitude Absolute magnitude = apparent magnitude at 10 parsecs

10.2 Luminosity and Apparent Brightness An equation relating apparent and absolute magnitudes to distance is

10.2 Luminosity and Apparent Brightness This is equivalent to the previous equation relating distance, apparent brightness, and luminosity

10.2 Luminosity and Apparent Brightness So there are two equations relating distance to apparent brightness and luminosity:

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

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

10.3 Stellar Temperatures 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 – called spectral classes or spectral types – are: O B A F G K M

10.3 Stellar Temperatures The seven spectral types:

10.3 Stellar Temperatures The different spectral classes have distinctive absorption lines.

10.4 Stellar Sizes A few very large, very close stars can be imaged directly using speckle interferometry; this is Betelgeuse:

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

10.4 Stellar Sizes Stellar radii vary widely:

10.5 The Hertzsprung-Russell Diagram The H-R diagram plots stellar luminosity against surface temperature. This is an H-R diagram of a few prominent stars

10.5 The Hertzsprung-Russell Diagram The H-R diagram plots stellar luminosity against surface temperature. This is an H-R diagram of a few prominent stars There is not very much of a pattern

10.5 The Hertzsprung-Russell Diagram Once many stars are plotted on an H-R diagram, a pattern begins to form:

10.5 The Hertzsprung-Russell Diagram Once many stars are plotted on an H-R diagram, a pattern begins to form: These are the 80 closest stars to us (within ~5 pc); note lines of constant radius.

10.5 The Hertzsprung-Russell Diagram Once many stars are plotted on an H-R diagram, a pattern begins to form: These are the 80 closest stars to us (within ~5 pc); note lines of constant radius. The darkened curve is called the Main Sequence, as this is where most stars are.

10.5 The Hertzsprung-Russell Diagram Once many stars are plotted on an H-R diagram, a pattern begins to form: These are the 80 closest stars to us (within ~5 pc); note 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.

10.5 The Hertzsprung-Russell Diagram Once many stars are plotted on an H-R diagram, a pattern begins to form: These are the 80 closest stars to us (within ~5 pc); note 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. Note that most of the closest stars are not very luminous

10.5 The Hertzsprung-Russell Diagram An H-R diagram of the 100 brightest stars looks quite different:

10.5 The Hertzsprung-Russell Diagram 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.

10.5 The Hertzsprung-Russell Diagram 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 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. Very few very luminous stars are nearby

End of 4 April 2007 Lecture

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

10.6 Extending the Cosmic Distance Scale The H-R diagram can be used to measure distances to stars

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.

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. Measure the star’s apparent magnitude and spectral class

The seven spectral types:

10.3 Stellar Temperatures The different spectral classes have distinctive absorption lines.

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. Measure the star’s apparent magnitude and spectral class Use spectral class to estimate luminosity

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. Measure the star’s apparent magnitude and spectral class Use spectral class to estimate luminosity Apply inverse-square law to find distance.

10.6 Extending the Cosmic Distance Scale

10.6 Extending the Cosmic Distance Scale Spectroscopic parallax can extend the cosmic distance scale to several thousand parsecs:

10.6 Extending the Cosmic Distance Scale Spectroscopic parallax can extend the cosmic distance scale to several thousand parsecs But there is a problem…

10.6 Extending the Cosmic Distance Scale Spectroscopic parallax can extend the cosmic distance scale to several thousand parsecs But there is a problem… Look at the steps again:

10.6 Extending the Cosmic Distance Scale Spectroscopic parallax can extend the cosmic distance scale to several thousand parsecs But there is a problem… Look at the steps again: Measure the star’s apparent magnitude and spectral class

10.6 Extending the Cosmic Distance Scale Spectroscopic parallax can extend the cosmic distance scale to several thousand parsecs But there is a problem… Look at the steps again: Measure the star’s apparent magnitude and spectral class Use spectral class to estimate luminosity

10.6 Extending the Cosmic Distance Scale Spectroscopic parallax can extend the cosmic distance scale to several thousand parsecs But there is a problem… Look at the steps again: Measure the star’s apparent magnitude and spectral class Use spectral class to estimate luminosity Apply inverse-square law to find distance.

10.6 Extending the Cosmic Distance Scale Spectroscopic parallax can extend the cosmic distance scale to several thousand parsecs But there is a problem… Look at the steps again: Measure the star’s apparent magnitude and spectral class Use spectral class to estimate luminosity Apply inverse-square law to find distance.

10.6 Extending the Cosmic Distance Scale The spectroscopic parallax calculation can be misleading if the star is not on the main sequence.

10.6 Extending the Cosmic Distance Scale 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:

10.6 Extending the Cosmic Distance Scale 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:

10.6 Extending the Cosmic Distance Scale In this way, giants and supergiants can be distinguished from main sequence stars.

10.6 Extending the Cosmic Distance Scale In this way, giants and supergiants can be distinguished from main sequence stars. And that makes a difference:

Stellar mass

One of the most important things about a star Stellar mass One of the most important things about a star

Stellar mass How do we find it?

10.7 Stellar Masses Many stars are in binary pairs; measurement of their orbital motion allows determination of the masses of the stars.

10.7 Stellar Masses Many stars are in binary pairs; measurement of their orbital motion allows determination of the masses of the stars.

10.7 Stellar Masses Many 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.

10.7 Stellar Masses Many 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.

10.7 Stellar Masses Many 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. The period of eclipsing binaries can be measured using intensity variations.

10.7 Stellar Masses

10.7 Stellar Masses

10.7 Stellar Masses Mass is the main determinant of where a star will be on the Main Sequence:

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

The central temperature goes up only slightly with mass

The central temperature goes up only slightly with mass But the luminosity goes up much faster

The central temperature goes up only slightly with mass But the luminosity goes up much faster This is because the rate of fusion increases nearly as the fourth power of temperature

The central temperature goes up only slightly with mass But the luminosity goes up much faster This is because the rate of fusion increases nearly as the fourth power of temperature So it increases much faster than the mass does

The central temperature goes up only slightly with mass But the luminosity goes up much faster This is because the rate of fusion increases nearly as the fourth power of temperature So it increases much faster than the mass does This allows us to estimate the lifetime of a star

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 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