Lecture 13

Review: Static Stellar structure equations Hydrostatic equilibrium: Mass conservation: Equation of state: Energy generation: Radiation Convection Polytrope or

The Solar model In this way we can build up a model of the interior structure of the Sun In general the differential equations are solved numerically Instead of assuming a polytrope, choose the temperature gradient depending on the mode of energy transport Boundary conditions:  in the simplest case, , P and T =0 at r=R  M,L=0 at r=0

Convection zones in the Sun For the solar model we can plot dlnP/dlnT as a function of radius. Where this is >2.5, radiation is the most effective form of energy transport.

The Solar interior The interior can be divided into three regions: 1.Core: site of nuclear reactions 2.The radiative zone 3.The convective zone

Abundance distribution H is depleted in the core, where He is produced is an intermediate species in the pp chain. It is most abundant at the top of the H-burning region, where the temperature is lower. Abundances are homogeneous within the convective zone, since the plasma is effectively mixed

The solar model: evolution As the abundances in the core change, the nuclear reaction rates change accordingly, and the luminosity, temperature and radius of the star are affected.

Energy production Although nuclear reaction rates are higher where the temperature is higher, most of the energy is not produced at the centre of the Sun, because:  The amount of mass in a shell at radius r is  i.e. there is more mass per unit volume at large radius (assuming constant density)  The mass fraction of hydrogen (X) at the centre has been depleted due to fusion, and the rate equations depend on X 2.

Recall: Proton-proton chain The net reactions are: PPI PPII PPIII

Direct observations of the core: neutrinos One type of neutrino detector on Earth uses an isotope of chlorine, which will (rarely) interact with a neutrino to produce a radioactive isotope of argon. This reaction requires the neutrino to have an energy of MeV or more, and can only detect neutrinos from the “side-reactions” in the PP chain: PPIIPPIII The Homestake detector contains ~400,000 L of cleaning fluid 2x10 30 atoms of Cl isotope Detect one Argon atom every 2-3 days.

Direct observations of the core: neutrinos More recently, the GALLEX (also SAGE) experiments uses 30 tons of natural gallium in a 100 ton aqueous gallium chloride solution to detect neutrinos via: This is sensitive to lower neutrino energies (0.233 MeV) and can detect neutrinos from the main branch of the PP chain

The Solar neutrino problem Both the Homestake and GALLEX experiments detected fewer neutrinos (by a factor 2-3) than were expected from the PP-chain reactions. This problem existed for about 30 years. The solution to the problem was suggested by results from the Super-Kamiokande detector in Japan  Results showed that electron neutrinos produced in the upper atmosphere can change into tau- or muon-neutrinos  This means neutrinos must have some mass and can therefore oscillate between flavours.

The Solar neutrino problem… solved The Sudbury Neutrino Observatory uses heavy water, and was able to directly detect the flux of all types of neutrinos from the Sun. The results are now completely consistent with the standard solar model.

Break

The main sequence The atmospheres of most stars are mostly hydrogen, X=0.7. The fraction of metals varies from Z~0 to Z~0.03 Because of the relative slow burning of hydrogen, the structure of the star changes only slowly with time. In general, the central temperature is higher for more massive stars  Thus, low mass stars will be dominated by the pp-chain  Higher mass stars undergo the CNO cycle Central density is actually lower for more massive stars. Increasing mass age

The main sequence Assuming hydrogen-burning reactions in the core, we can construct a theoretical relation between L, T and M Stars undergoing hydrogen burning lie along the main sequence For low-mass stars, <0.08M Sun, central temperatures are not high enough to allow nuclear fusion At very high masses, M>90 M Sun, the stars become unstable: thermal oscillations in the core coupled with extreme temperature sensitivity of the nuclear reactions means an equilibrium is never attained.

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? 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 extended solar spectrum While the solar radiation is similar to a blackbody prediction at optical wavelengths, there is excess radiation at very short wavelengths.  This light is also highly variable.

The radio sun Radio waves penetrate through the chromosphere and corona. The image here shows the "transition region" between the chromosphere and the corona.

The infrared sun Infrared images show some features of the Sun's chromosphere, and some features in the corona. Dark markings are caused by absorption of the infrared light by regions of high density

The chromosphere UV (30.4 nm) images reveal the chromosphere Can sometimes see large prominences rising high above the surface of the Sun. At the north and south poles of the Sun, less EUV light is emitted - these regions often end up looking dark in the pictures, giving rise to the term coronal holes.  These are low density regions extending above the surface where the solar magnetic field opens up HeI emission

The X-ray sun The X-rays we see all come from the corona. The corona is a very stormy place, constantly changing and erupting. Movie from

Sunspots Dark (cool) regions of the photosphere Number of spots changes on a 11 year cycle Concentrations of magnetic field lines

The Sun’s magnetic field By studying sunspots we can learn about the nature of the Sun’s magnetic field Switches polarity every 11 years