The Sun and Other Stars Colours and luminosities Hydrostatic equilibrium Luminosity generation and transport stellar lifetimes

Review Properties of blackbody radiation Spectroscopy tells us:  Chemical composition (elements and molecules absorb/emit light at specific wavelengths)  Radial velocity, via the Doppler shift

Doppler shifts Doppler shifts of the spectral lines yield the radial (i.e. toward the observer) velocity of the star

1.Typical stars in the solar neighbourhood have velocities ~25 km/s. What is the size of their doppler shift? Doppler shifts: examples

2.Extragalactic objects (mostly galaxies and quasars) are strongly redshifted due to the expansion of the Universe. The most distant object currently known is quasar SDSS , with z=6.42. Since z is not small, we have to use the full expression:

The physics of stars A star begins simply as a roughly spherical ball of (mostly) hydrogen gas, responding only to gravity and it’s own pressure. To understand how this simple system behaves, however, requires an understanding of: 1.Fluid mechanics 2.Electromagnetism 3.Thermodynamics 4.Special relativity 5.Chemistry 6.Nuclear physics 7.Quantum mechanics X-ray ultraviolet infrared radio

The Sun The Solar luminosity is 3.8x10 26 J/s The surface temperature is about 5700 K From Wein’s Law: Most of the luminosity comes out at about 509 nm (green light)

The nature of stars Stars have a variety of brightnesses and colours Betelgeuse is a red giant, and one of the largest stars known Rigel is one of the brightest stars in the sky; blue-white in colour Betelgeuse Rigel

The Hertzsprung-Russell diagram The colours and luminosities of stars are strongly correlated The Hertzsprung-Russel (1914) diagram proved to be the key that unlocked the secrets of stellar evolution Principle feature is the main sequence The brighter stars are known as giants BLUE Colour RED Luminosity

Types of Stars Assuming stars are approximately blackbodies: Means bluer stars are hotter Means brighter stars are larger Betelgeuse is cool and very, very large White Dwarfs are hot and tiny

Types of stars Intrinsically faint stars are more common than luminous stars

Hydrostatic equilibrium The force of gravity is always directed toward the centre of the star. Why does it not collapse?  The opposing force is the gas pressure. As the star collapses, the pressure increases, pushing the gas back out. How must pressure vary with depth to remain in equilibrium?

Hydrostatic equilibrium Consider a small cylinder at distance r from the centre of a spherical star. Pressure acts on both the top and bottom of the cylinder.  By symmetry the pressure on the sides cancels out dr A dm F P,b F P,t It is the pressure gradient that supports the star against gravity The derivative is always negative. Pressure must get stronger toward the centre M r is the mass within radius r.  is the density at radius r

Stellar Structure Equations Hydrostatic equilibrium: Mass conservation: Equation of state: These equations can be combined to determine the pressure or density as a function of radius, if the temperature gradient is known  This depends on how energy is generated and transported through the star.

Stellar structure Making the very unrealistic assumption of a constant density star, solve the stellar structure equations.

The solar interior Observationally, one way to get a good “look” into the interior is using helioseismology  Vibrations on the surface result from sound waves propagating through the interior  We can observe these vibrations as Doppler shifts in the light

The solar interior Another way to test our models of the solar interior are to look at the Solar neutrinos  Neutrinos have a very small cross-section: a neutrino can travel through a slab of lead 1 light year thick before it scatters off another particle. The Sudbury Neutrino Observatory uses heavy water, and was able to directly detect the flux of all types of neutrinos from the Sun. The flux of all neutrino types is in agreement with the predicted electron neutrino production from nuclear reactions This confirms that electron neutrinos from the Sun are oscillating and the results are now completely consistent with the standard solar model.

Break

Stellar luminosity Where does this energy come from? Possibilities: Gravitational potential energy (energy is released as star contracts) Chemical energy (energy released when atoms combine) Nuclear energy (energy released when atoms form)

Gravitational potential So: how much energy can we get out of gravity? Assume the Sun was originally much larger than it is today, and contracted. This releases gravitational potential energy on the Kelvin- Helmholtz timescale.

Chemical energy Chemical reactions are based on the interactions of orbital electrons in atoms. Typical energy differences between atomic orbitals are ~10 eV. e.g. assume the Sun is pure hydrogen. The total number of atoms is therefore If each atom releases 10 eV of energy due to chemical reactions, this means the total amount of chemical energy available is This is ~100 times less than the gravitational potential energy available, and would be radiated in only 100,000 years at the present solar luminosity

Binding energy There is also a binding energy associated with the nucleons themselves. Making a larger nucleus out of smaller ones is a process known as fusion. For example: The mass of 4 H atoms is u. The mass of He is u. The mass difference is u, equivalent to MeV!  ~0.7% of the H mass is converted into energy : E=mc 2

Nuclear energy: fusion In contrast with chemical reactions, nuclear reactions (which change one type of nucleus into another) typically release energies in the MeV range, 1 million times larger. E.g. Assume the Sun was originally 100% hydrogen, and converted the central 10% of H into helium. This would release an energy: Assuming the Sun’s luminosity has been constant at 3.8x10 26 J/s, it would take ~10 billion years to radiate all this energy.  Nuclear energy can sustain the solar luminosity over its likely lifetime

Energy transport How is energy transported from the core to the surface?  Radiation: the photons carry the energy as they move through the star, and are absorbed at a rate that depends on the opacity.  Transfers energy, but not matter  Convection: buoyant, hot mass will rise  This mixes matter as well as energy  Conduction: collisions between particles transfer kinetic energy of particles. This is usually not important because gas densities are too low.

Convection Convection is a very complex process for which we don’t yet have a good theoretical model  The Navier-Stokes equations are a complex set of 3-D differential equations that must be solved numerically. Solving 3-D systems of stars requires enormous computing power  Convective flow is turbulent and therefore requires a detailed understanding of viscosity and heat dissipation  The typical convective length scale is comparable to the size of the star (so you can’t just simulate a small region reliably)  The timescale for convection is comparable to the timescale for significant changes in stellar structure to occur.

Convection Observations of granulation on solar surface each “cell” is typically 1000 km across Movie is sped up: typical lifetime of a granule is a few minutes

The Solar interior The interior can be divided into three regions: 1.Core: In the very centre, the temperature is high enough to sustain nuclear reactions 2.The radiative zone: energy is transported via radiation 3.The convective zone: the temperature here is lower, and the opacity is higher due to recombination. Thus convection takes over as the main mechanism for energy transport.

Main sequence lifetimes At the lower end of the main sequence, Such low-mass stars are entirely convective, so all the hydrogen (70% by mass) is available for fusion. What is the lifetime of such a star?

Main sequence lifetimes At the upper end of the main sequence, Only the central ~10% of the mass is available for hydrogen fusion, because the star is not fully convective. What is the lifetime of such a star?

Stellar lifetimes From observations of the cosmic microwave background, we know the Big Bang occurred about 13.7 billion years ago Galaxies have been observed at a time when the Universe was less than 1 billion years old. Thus stars have been forming for at least ~13 billion years

Main sequence lifetimes Bluer (hotter) stars must be very young, formed within the last 0.01% of the age of the Universe On the other hand, some of the reddest (coolest) stars may have been formed shortly after the Big Bang, and would still be around. The stars lying off the main sequence are not explained by the hydrogen-burning model: something else must be going on…

The Solar Atmosphere T~10 6 K T~25000 K T~5770 K The solar atmosphere extends thousands of km above the photosphere (from which the optical radiation is emitted) It is of much lower density and higher temperature than the photosphere T~10 7 K Core

The X-ray sun The X-rays we see all come from the corona, the outermost and hottest visible layer of the Sun's atmosphere. Not all the corona emits the same amount of X-rays. We often see structures called "loops" and "arches" and "streamers". Movies made from X-ray pictures show that the corona is a very stormy place, constantly changing and erupting. Movie from

The ultraviolet sun Both images reveal the chromosphere: the 19.5-nm picture (right) comes from higher up in the chromosphere. Most of the 19.5-nm light comes from "active regions", where we can sometimes see loops. In the 30.4-nm image we can sometimes see large prominences rising high above the surface of the Sun. These images come from the Extreme ultraviolet Imaging Telescope (EIT), an instrument on the SOlar and Heliospheric Observatory (SOHO). Left: 19.5 nm; Right: 30.4 nm

The infrared sun The picture shows some features of the Sun's chromosphere, and some features in the corona. Infrared pictures often show dark markings on the Sun that are caused by absorption of the infrared light.  darker features in an infrared picture show where the gas is more dense.

The radio sun Radio waves penetrate through the chromosphere and corona. The image here is constructed from microwaves with wavelength 1.7 centimeters. It shows us the structure of the Sun's atmosphere near the "transition region" between the chromosphere and the corona, about km above the photosphere. You can sometimes see prominences - great strands of gas that extend above the edge of the Sun. This radio image comes from the Nobeyama Radio Observatory, in Japan.

Next lecture Meteors  How to estimate their sizes, orbits  Their fate: break-up or impact?  Classification