Our Place Our Place in in the the Cosmos Cosmos following - PDF document

Understanding Stars • We saw in the last lecture that by measuring the brightness, distance (via parallax) and spectrum of a star, we can determine the Our Place Our Place in in the the Cosmos Cosmos following physical properties • Surface temperature • Radius Lecture 11 • Luminosity Understanding Stars - • Mass (for binary stars) • Just knowing these properties does not mean the H-R Diagram that we understand stars The H-R diagram plots H-R Diagram luminosity against surface temperature or colour • The Hertzsprung-Russell diagram (H-R diagram for short) enables one to see patterns in the Hot, blue stars lie to properties of stars the left, luminous • It is named after Einar Hertzsprung and stars lie to the top Henry Norris Russell, the first astronomers to independently make plots of the luminosity of Both axes are plotted stars against their temperature or colour, logarithmically so around 1906-1913 that stars of fixed size lie along diagonal • The H-R diagram allows one to track the lines as shown birth, life and death of stars Captions H-R Diagram and Size The Main Sequence • A star near the top-right corner of the H-R • When one plots the locations of many stars on diagram is cool but luminous the H-R diagram, they are not spread all over the plot • Stefan’s law L = � A T 4 tells us that such a star must have a very large surface area A • Most stars lie along a well-defined sequence and hence radius r running from lower-right to upper-left • Conversely, a star near the lower-left is hot • This is called the main sequence but dim, so it must be very small • On the left of it are the hottest, most • The H-R diagram thus also allows one to luminous stars known as O stars gauge sizes of stars, increasing from lower- • On the right lie the coolest, dimmest stars, left to upper-right known as M stars

Distance Estimates • The Main Sequence is of great practical use in estimating distances to stars too far away to measure a trigonometric parallax • We can determine a star’s colour or surface temperature independent of distance via photometry or spectroscopy respectively • If it lies on the main sequence than we can read its approximate luminosity off the H-R diagram • Comparing apparent brightness with luminosity then yields an estimate of distance • This distance estimate is known as photometric parallax or spectroscopic parallax Hipparcos sample of 16,600 stars Brightest Closest Selection Effects Stellar Mass • The distribution of stars on the H-R diagram depends • Stellar mass increases from lower-right to strongly on how they are selected upper-left along main sequence • The stars very close to the Sun are mostly dimmer • Stars less massive than the Sun are cooler, and cooler than the Sun redder, smaller and dimmer • The (apparently) brightest stars in the sky are mostly • Stars more massive than the Sun are hotter, more luminous and hotter than the Sun bluer, larger and more luminous • There are more cool, dim stars in the Galaxy than hot luminous stars, and these dominate the small volume • The mass of a star determines its position on of space near the Sun the main sequence and its ultimate fate • By selecting stars by apparent brightness rather than • Mass is the primary determining characteristic distance, we preferentially select the most luminous of any main sequence star stars Mass determines location of a star More massive main sequence stars are … on the main sequence High-mass stars are hot and luminous Low mass stars more luminous… …larger… …and hotter are cool and dim (Note logarithmic axes)

Non-Main Sequence Stars The Structure of the Sun • Although the majority of stars lie on the main • Being so close, we can study the Sun - a sequence (MS), some do not prototypical MS star - in much greater detail than any other star • Some stars lie above and to the right of the MS - these are bloated, luminous, cool giants • Our understanding of the Sun comes from with radii 100s-1000s times larger than the many decades of careful observation, theory Sun and computer modelling • In the lower-left of the H-R diagram lie tiny • The Sun is a huge ball of hot gas, held in (and hence dim) but very hot stars balance by hydrostatic equilibrium • Before studying these non-MS stars, we will • Gravity, which unopposed would cause the Sun first study a prototypical MS star - the Sun to collapse, is balanced by pressure • The Sun’s surface is thus in equilibrium Hydrostatic Equilibrium Hydrostatic Equilibrium • Towards the centre of the Sun, the weight of At each point within the Sun the the material above becomes greater and so outward force of the pressure must increase pressure is balanced • Gases at higher pressure become denser and by the inward force hotter of gravity • Thus density and temperature also increase towards the centre of the Sun The energy radiated • Energy must also balance to maintain Sun’s from the Sun’s luminosity - just enough energy must be surface balances the energy produced produced in the interior to provide the energy in its interior radiated away at the surface Sun’s Energy Source • The only source of energy efficient enough to provide Sun’s luminosity is nuclear fusion • Hydrogen nuclei (single protons) are fused together to make helium nuclei (two protons plus two neutrons) - a process known as hydrogen burning or hydrogen fusion • All main sequence stars get their energy from hydrogen fusion NB same data plotted twice… logarithmic linear

Hydrogen Fusion Hydrogen Fusion • According to Einstein’s famous equation E = mc 2 , mass • Why is hydrogen fusion so hard to achieve on Earth? and energy are equivalent • The reason is that hydrogen nuclei (protons) have a • The mass of four hydrogen atoms is 1.007 times positive electric charge greater than the mass of a single helium atom • Two like charges experience a force known as • In hydrogen fusion, the excess mass is converted to electrostatic repulsion, this makes it extremely energy difficult to get two hydrogen nuclei close enough to bind (a separation of around 10 -15 metres) • Fusing 1 gramme of hydrogen into helium releases about 600 billion Joules of energy - enough to boil • Extremely high densities and temperatures are the water in about 10 swimming pools required to overcome electrostatic repulsion - conditions that are ordinarily only found in the cores • The Sun converts roughly 600 million tonnes of (central regions) of stars hydrogen into helium each second, releasing 3.85 x 10 26 Watts [Joules per second] • In the Sun’s core the density is about 150 times that of water and the temperature is about 15 million K Slow-moving protons are Why Hydrogen Fusion? repelled by electrostatic repulsion 1. Hydrogen is the most abundant element in the Universe 2. Hydrogen fusion is the most efficient nuclear fusion The faster they move, the process, converting a larger fraction of mass to closer together they can get energy than any other process 3. Hydrogen nuclei have a charge of +1 (in units of the electron’s charge) - there is a much greater At high enough temperatures electrostatic repulsion for other nuclei such as protons move fast enough carbon, which contains six protons and so has a nuclear charge of +6 that they may overcome Cannot directly fuse hydrogen into helium - reaction electrostatic repulsion • proceeds by a number of chains - the most common and fuse together of which is the proton-proton chain Proton-Proton Chain Testing the Model • Starting with just the mass of the Sun and its chemical composition, our Solar model correctly predicts all other observed properties - size, temperature and luminosity • For example, if the Sun were larger than it in fact is, it would radiate energy faster • However core density would be less and hydrogen fusion would slow down • Core would thus cool, pressure decrease and Sun would shrink back to its equilibrium size • If Sun were compressed, fusion rate would increase causing Sun to expand back to its equilibrium size Colliding protons first create deuterium ( 2 H), then helium-3 ( 3 He) and then helium-4 ( 4 He)

Solar Neutrinos • Hydrogen fusion as Sun’s energy supply is confirmed Captions by the observation of neutrinos produced as part of the proton-proton chain • Neutrinos are incredibly weakly-interacting and can escape from the core of the Sun much faster than photons of radiation • A small fraction can however be detected on Earth in underground labs • The rate at which neutrinos are detected agrees with the Solar model assuming that neutrinos have some mass , and are not massless as previously thought Summary • Most stars lie in a region of the H-R diagram known as the main sequence • Main sequence stars, of which the Sun is a proto-typical example, exist in a state of hydrostatic equilibrium • Energy is generated in the core of these stars by the fusion of hydrogen nuclei into helium, accompanied by the release of energy and solar neutrinos • Energy is transported to the star’s surface and is radiated away