Lecture 5: The H-R diagram, standard Luminosity vs temperature of stars - the candles and cosmic distances Hertzsprung-Russell diagram

• The Hertzsprung-Russell diagram Vertical axis: • Classes of stars: main sequence, giants and luminosity of star dwarfs – could be measured as power, e.g., watts • Spectroscopic parallax – or absolute magnitude – or in units of Sun's • Stellar masses, and the mass-luminosity luminosity: L /L relation star  • Standard candles and the astronomical distance ladder Horizontal axis: surface temperature – T traditionally increases to the LEFT – Or use spectral type: OBAFGKM – Or colour (e.g. B-V), with blue to left

Hertzsprung-Russell (H-R) diagrams reveal Hertzsprung-Russell (H-R) diagrams reveal different classes of stars different classes of stars

Stars are not scattered at • Remember that for a spherical blackbody emitter, luminosity, random on the H-R diagram: temperature and radius are related by: • Most stars lie on the main L=4πR2 σT4 sequence, which runs from • Hence stars of a fixed size would hot, luminous stars (top left) to populate a line from top left to bottom right - the main sequence is almost cool faint ones (bottom right) such a line • Most of the other stars are • However, it is steeper - hotter stars on grouped into three other the MS are also larger regions • The two populated regions above the • What can we deduce about MS are much larger stars: the giants and supergiants their properties from their location on the H-R diagram? • The region below the MS consists of very small stars - these are the white dwarfs

1 Determining luminosity class from Spectroscopic parallaxes stellar spectra

By carefully examining a star’s spectral lines, astronomers can • If the approximate luminosity of star determine the luminosity class of a star - i.e. whether it is a main- can be determined from its spectral sequence star, giant, supergiant, or white dwarf. lines, coupled with position on the HR diagram, then comparing this with its apparent magnitude allows its distance to be estimated (see notes from Lecture 3). • This method of distance estimation is (unfortunately) referred to as spectroscopic parallax - it is not a parallax method at all! It does give very useful distances, though, since it can be used out to d~10 kpc, where standard parallaxes cannot currently be measured.

Spectroscopy makes it possible to study binary Stellar masses systems in which the two stars are close together

• We would also like to know the • Some binaries can be masses of stars detected and analysed, even • Information about stellar though the two star images masses can be deduced from cannot be resolved the motion of stars in binary • A spectrum binary appears systems to be a single star but has a spectrum with the absorption • Binary stars move along lines for two distinctly interlocking orbits, such that the different spectral types centre of mass of the system • A spectroscopic binary has remains stationary spectral lines that shift back • If the orbital size and binary and forth in wavelength due period can be measured, then to the Doppler effect, as the orbits of the stars carry them the total mass of the binary pair first toward then away from follows from the equation the Earth 3 2 M1+M2 = a /P • Analysis of these spectral where a is the semi-major axis shifts allows velocity and of the separation vector (in AU) period to be derived, and and P the orbital period in years hence M1+M2

2 Mass-luminosity relation for main sequence stars Standard candles • Once spectral masses are known we can study the way in which mass Suppose that all stars had exactly the same luminosity…. changes along the main sequence – Then, the brightness of the stars would only depend on their distance. • Main sequence stars are stars like the Sun but with a range of masses – By measuring the apparent brightness, we could calculate the distance to the star using the inverse square law of light. • The greater the mass of a MS star, the – Of course, stars have a large range of luminosities, and their greater its luminosity (and also the apparent brightness depends on distance, temperature, size greater its radius and surface (surface area), extinction, etc. temperature) • The mass-luminosity relation • However, there are certain classes of astronomical expresses a direct correlation between mass and luminosity for main- objects which have a small range of luminosities sequence stars. It is found that L • These objects are called standard candles scales strongly with mass, approximately as L∝M3.5 • The measured apparent brightness of a standard candle • Since luminosity rises faster than the can be used to determine its distance using the known amount of fuel available, massive hot luminosity and the inverse square law MS stars have much shorter lifetimes

Period-Luminosity relation Pulsating variables and Cepheids For example, if one Period=5.4 days • Pulsating variable stars are giant evolved Cepheid has a period of 3 stars that grow and shrink in size days and another has a period of 30 days, the star • Cepheid variables (named after δ Cephei, with the longer period is 2 the first one known) are large yellow stars magnitudes or about 6 – They have luminosities 1,000-10,000 times times brighter. greater than the Sun. – They have periods of 3-50 days. • Since all the stars are in the – They vary in luminosity from a few percent to a same stellar system (the factor of 10. LMC), they are all the same – Polaris is a well known Cepheid (period 4 distance from Earth. days). • Henrietta Leavitt at Harvard studied Henrietta Leavitt • Therefore, the brightness (1868–1921) differences indicate that the Cepheids in the Large Magellanic Cloud total luminosity of a Cepheid and found that their pulsation period was is related to its period of related to their magnitude variation.

3 The distance ladder The distance ladder

• Cepheids are especially useful as distance indicators • To extend the distance ladder because they are luminous enough (up to 104 L ) to be to more distant galaxies,  other indicators have to be studied in other fairly nearby galaxies used, for example… • Although Leavitt found that the apparent brightness of • Type Ia supernovae provide the Cepheids was related to the period, no one knew the brightest standard what the true luminosity of the Cepheid variables in the candles known, and can be LMC, because its distance was unknown detected to high redshifts • Approximate relations have • A variety of other techniques, such as spectroscopic also been discovered parallax were used to calibrate the Cepheid P-L relation between the luminosity of • Much confusion resulted from the fact that there turn out galaxies and their dynamical properties - an example is the to be two different classes of Cepheids, with different P- Tully-Fisher relation, which L relations relates the luminosity of a • Hipparchos eventually provided true parallaxes for a spiral galaxy to its rotation useful sample of Galactic Cepheids velocity

The distance ladder

A selection of distance determination methods: • Trigonometric parallax • Spectroscopic parallax • Cluster main sequence fitting • Cepheid variable stars • Type-Ia supernovae • Tully-Fisher relation Read more about this in “Universe”

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