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PH507 Astrophysics MDS 1 Stars and Stellar Evolution For instance, the UBV system has about 100 standard stars measured to about ± 0.01 magnitude. Then if we can calibrate the flux of just one of these stars, we have calibrated the system. The calibration is usually given for zero magnitude at each filter; all fluxes are then derived from this base level. The star usually chosen as the calibration star is Vega. PH507 Astrophysics MDS 2 Colour index in the BV system. Blackbody curves for 20,000 K and 3000 K, along with their intensities at B and V wavelengths. Note that B - V is negative for the hotter star, positive for the cooler one. The Hertzsprung-Russell Diagram In 1911, Ejnar Hertzsprung plotted the first such two-dimensional diagram (absolute magnitude versus spectral type) for observed stars, followed (independently) in 1913 by Henry Norris Russell. The simple HR diagram represents one of the great observational syntheses in astrophysics. Note that any two of luminosity, magnitude, temperature, and radius could be used, but visual magnitude and temperature are universally obtained quantities. An original idea was that a star was born hot (early type) and cooled (late type). It’s a particular colour-magnitude diagram. PH507 Astrophysics MDS 3 Important stars: no obvious pattern…Sirius B, Betelgeuse in opposite corners: PH507 Astrophysics MDS 4 Nearby stars: main-sequence appears. Most stars are less luminous and cooler than the Sun (alpha Centauri, nearest to us and a triple system, is similar). Note the hot small stars: the white dwarfs. PH507 Astrophysics MDS 5 Most stars have properties within the shaded region known as the main sequence. The points plotted here are for stars lying within about 5 pc of the Sun. The diagonal lines correspond to constant stellar radius, so that stellar size can be represented on the same diagram as luminosity and temperature. The first H-R diagrams considered stars in the solar neighbourhood and plotted absolute visual magnitude, M, versus spectral type, which is equivalent to luminosity versus spectral type or luminosity versus temperature. Note (a) the well-defined main sequence (class V) with everincreasing numbers of stars toward later spectral types and an absence of spectral classes earlier than A1 (Sirius), (b) the absence of giants and supergiants (class III and I), and (c) the few white dwarfs at the lower left. The brightest stars: PH507 Astrophysics MDS 6 An H-R diagram for the 100 brightest stars in the sky. Such a plot is biased in favour of the most luminous stars--which appear toward the upper right- PH507 Astrophysics MDS 7 because we can see them more easily than we can the faintest stars. These are the GIANTS and SUPERGIANTS In contrast, the H-R diagram for the brightest stars includes a significant number of giants and supergiants as well as several early-type mainsequence stars. Here we have made a selection that emphasises very luminous stars at distances far from the Sun. Note that the H-R diagram of the nearest stars is most representative of those throughout the Galaxy: the most common stars are low-luminosity spectral type M. The most prominent feature of the H-R diagram is the Main Sequence: Strong correlation between Luminosity and Temperature. Hotter stars are Brighter than cooler stars along the M-S. About 85% of nearby stars, including the Sun, are on the M-S. All other stars differ in size: Giants & Supergiants: Very large radius, but same masses as M-S stars White Dwarfs: Very compact stars: ~Rearth but with ~0.6 Msun! Example: Betelgeuse: • An M2 Iab Supergiant star - Red star in constellation of Orion. • Very luminous: L ~ 100000 LSUN. • Cooler than the Sun: T ~ 3300 K (Sun is G2 V MS star, T ~ 5800 K.) From Stefan-Boltzmann Law, (R/RSUN) ~ (TSUN/T)2(L/LSUN)0.5, so R/RSUN = (5800/3300)2(100000/1)0.5 • R ~ 977 RSUN This is about 4.5 AU – Betelgeuse would swallow everything out until almost the orbit of Jupiter if it was where the Sun is – it is big! PH507 Astrophysics MDS 8 Stellar luminosity classes: Ia : Brightest Supergiants Ib : Less luminous supergiants II : Bright giants III : Giants IV : Subgiants V : Main-sequence stars Luminosity Classes Stellar luminosity classes in the H-R diagram. Note that a star's location could be specified by its spectral type and luminosity class instead of by its temperature and luminosity. Giants possess cool low-density photospheres, hence absorption lines identify them (e.g. narrower lines). After spectral classification, their distance can be estimated according to their luminosity class. This is their spectroscopic parallax. PH507 Astrophysics MDS 9 Magnitude versus Colour Because stellar colours and spectral types are roughly correlated, we may construct a plot of absolute magnitude versus colour - called a colour- PH507 Astrophysics MDS 10 magnitude diagram. The relative ease and convenience with which colour indices (such as B - V) may be determined for vast numbers of stars dictates the popularity of colour-magnitude plots. The resulting diagrams are very similar to the magnitude-spectral type H-R diagrams considered above. The Mass-Luminosity Relationship Mass is the most important physical characteristic of stars - it determines luminosity, temperature, lifetime etc. How do we obtain the mass of stars? – use binary star systems and Kepler’s 3rd Law (for visible binaries – for spectroscopic binaries the orbital inclination needs to be known). Eclipsing binaries are even better! The method is the same as used to calculate the properties of extrasolar planets. As we need to know the distance (covered earlier in the course) to the binary system in order to work out the masses of the stars, we just have to measure the magnitudes of the stars and then calculate the luminosity. This was done for lots of binary star systems, and the resulting data plotted (Luminosity as a function of Mass). The resulting correlation is only really valid for Main Sequence stars! When the observed masses and luminosities for stars in binary systems are plotted, we obtain the correlation called the mass-luminosity relationship. PH507 Astrophysics MDS 11 In 1924, Arthur S. Eddington calculated that the mass and luminosity of normal stars like the Sun are related by L æ M ö ÷÷ = çç LQ è M Q ø a His first crude theoretical models indicated that α ≈ 3. On a log-log plot, this gives a straight line with a slope of 3. Main sequence stars do seem to conform to this relationship, although the exponent varies from α ≈ 3 for for dim red stars of low mass. From a sample of 126 well-studied binary systems, we find that the break in slope below this value is 2.26; above it, 3.99. Or : • The lifetime of a star depends on how quickly it uses up its fuel and how much fuel there is. • The rate of burning depends on the central temperature of the star. • The central temperature of the star depends on its mass. PH507 Astrophysics MDS 12 • The luminosity is proportional to the rate of fuel burning, hence central temperature, hence mass. For L proportional to Mn , α Mass range (in Msun) 2.3 M < 0.4 3.9 – 4 0.4 < M < 7 3 7 < M < 25 2.7 25 < M < ~80 Lifetime Mass/Luminosity Mass-3 -- S Suunn ccaann bbee ppoow weerreedd ffoorr 55 bbiillliioonn yyeeaarrss bbyy ccoonnvveerrttiinngg 55% % hhyyddrrooggeenn ttoo hheelliiuum . m. -- A s t a r 1 0 t i m e A star 10 timess aass m maassssiivvee aass tthhee S Suunn hhaass 1100 ttiim meess hhyyddrrooggeenn ttoo ppoow weerr nnuucclleeaarr ffuussiioonn -- B Buutt iitt iiss 1100000000 ttiim meess aass bbrriigghhtt -- TThheerreeffoorree iitt sshhoouulldd uussee uupp iittss ffuueell 11000000 ttiim meess m moorree qquuiicckkllyy ooff iittss m moorree Massive stars are very short-lived! If we use the mass-luminosity relation for stars of 0.4MSun and greater, PH507 Astrophysics MDS 13 or so a star with 10 x the mass of the Sun will have a main sequence lifetime of only 10 million yrs! So we know that O stars, the most massive stars, have main sequence lifetimes of only a million years so the fact that we see some O stars now means that star formation is still occurring in the Milky Way. The more massive stars burn their fuel very rapidly, leading to short lifetimes……….. Stellar (Main Sequence) Properties With Mass Mass 40 MSun 17 7 2 1 0.2 Temp Radius Luminosity tMS habitable zone 35,000 K 18 RSun 320,000 LSun 106 yrs 350-600 AU 21,000 13,500 8,100 5,800 2,600 8 4 2 1 0.32 13,000 630 20 1 0.0079 107 8x107 2x109 1010 5x1011 1-2 0.1-0.2 PH507 Astrophysics MDS 14 In order of spectral type….……….. Spectral Mass Luminosity Temperature Type (MSUN) (LSUN) (K) Radius (RSUN) Mean Density (kg m-3) O5 40 400000 40000 13 25 B0 15 13000 28000 4.9 200 A0 3.5 80 10000 3 200 F0 1.7 6.4 7500 1.5 700 G0 1.1 1.4 6000 1.1 1200 K0 0.8 0.46 5000 0.9 1600 M0 0.5 0.08 3500 0.8 1400 Some stars have still not left the main sequence……… M*/Msun 60 30 10 3 1.5 1 0.1 time (years) 3 million 11 million 32 million 370 million 3 billion 10 billion 1000's billions Spectral type O3 O7 B4 A5 F5 G2 (Sun) M7 tthhee lliiffeettiim meess ooff ssttaarrss w wiitthh m maassss << 00..8855 M Mssuunn aarree lloonnggeerr tthhaann 1155 bbiilllliioonn yyeeaarrss ((>> tthhee aaggee ooff tthhee uunniivveerrssee)) Note the M-L law does not apply to highly evolved stars, such as red giants (with extended atmospheres) and white dwarfs (with degenerate matter. The ranges. While most stellar masses lie in the narrow range from 0.085Msun to 100Msun , PH507 Astrophysics MDS 15 stellar luminosities cover the vast span 10-4 ≤ L/LSun ≤ 106. A useful relationship to give a rule of thumb estimate of a stars surface temperature is: æMö T @ 5870 ç ÷ è M* ø 0.5 Stellar Density Mean Stellar Density: Mean Density = Mass / Volume Main Sequence: quite small range of mean densities: Sun (G2v): ~1.6 g/cc O5v Star: ~0.005 g/cc M0v Star: ~5 g/cc Giants: Low-density stars: ~10-7 g/cc (e.g., K5III) Supergiants: Very low-density: ~10-9 g/cc (e.g., M2I) White Dwarfs: High-density stars: ~105 g/cc For reference, at sea level on Earth, water has a density of 1 g/cc, and air has a density of ~0.001 g/cc. Stellar Evolution: In this section, we explain the HR tracks qualitatively in terms of: 1. The energy source…..chemical, gravitational and nuclear reactions. We exclude chemical energy (e.g. forest fires) for stars. Gravity (if contracting) can operate for short periods. 2. Transport from the source to the surface…..conduction, convection or radiation. We exclude conduction as ineffective. 3. Radiative transfer through the photosphere, as discussed above. Hydrogen ions can provide the opacity in stars like the Sun. PH507 Astrophysics MDS 16 The end of Hydrogen burning: During main sequence lifetime hydrogen burning is confined to the core. Hydrogen burning converts hydrogen into helium in the core. Eventually the core hydrogen is exhausted. Energy is then derived from a hydrogen shell With no energy production in the core, it contracts to maintain thermal hydrostatic equilibrium. The collapse of the core will cause it to heat up. The hydrogen burning shell dumps further helium onto the core. Hydrogen burning moves outward. The core collapses, releasing energy and the star’s envelope expands and cools – a subgiant branch phase Over a million years, the core of a Sun sized star decreases to about 1/10 original size. The core temperature rises from 15 to about 100 million K. PH507 Astrophysics MDS 17 The core is composed of helium ‘ash’. The outer layers of the star become heated by their proximity to the energy source. The inert hydrogen outside the shell hinders the movement of the photons. The energy is then transported by convection. (low temperature, high opacity, high temperature gradient, just what you need for convection) Processed material from the core mixes for the first time with the envelope - and photosphere. We call this the first dredge-up which should be visible as an increase in N at the expense of C and O. The outer layers are not so tightly bound by gravity and will expand enormously forming a red giant Why Helium won’t burn yet Hydrogen, a single proton, has a single electrostatic charge Helium has two. Helium nuclei must have a much higher kinetic energy (speed) to get close enough to bind Helium burning begins When the central temperature reaches 100 million K, helium burning starts. Two helium nuclei fuse to form an isotope of beryllium. Beryllium is very unstable. If it is hit by another helium they fuse into a stable isotope of carbon. This is known as the triple alpha process. A high energy gamma ray is released by each reaction A Star’s Safety-valve Gravity tries to compress a star When a perfect gas is compressed its density and temperature increase. If a gas heats up its pressure increases. PH507 Astrophysics MDS 18 The pressure tries to expand the star. If a reaction starts to run away, the temperature rises and the star expands. This drops the temperature and the reaction is slowed. Perfect and degenerate In a low-mass red giant (<3 Msol), the core must undergo considerable compression to drive the temperature high enough to start helium burning. No two identical particles may occupy the same quantum state. The electrons obey the Pauli exclusion principle (Wolfgang Pauli, 1925) and will not be compressed any further. The gas is said to be degenerate and is supported by degenerateelectron pressure. In the highly compressed core, free electrons are so crowded together that quantum effects must be considered. Helium flash: When the temperature in the core reaches that required for helium fusion, energy begins to be released. Because the star is supported by electron degenerate pressure, it does not expand. (Remember degeneracy is a quantum effect and not influenced by temperature in the same way.) Without its safety valve the temperature soars and the fusion process runs away. This runaway takes only a few seconds and is called a Helium Flash It releases a vast quantity of energy which drives the temperature so high that the gas behaves in an ideal way again: the degeneracy is ‘lifted’. The Helium Flash is not observable, since the photons produced in the explosion are trapped in the Hydrogen layers. PH507 Astrophysics MDS 19 Low mass stars: After the helium flash, substantial carbon and oxygen ‘ash’ is dumped at the core. The core contracts until electron degeneracy again supports the star. The temperature reached is enough to start shell helium burning around the core Helium shell burning, like the hydrogen shell before it, heats the outer layers of the star and it expands again to form a red supergiant. Low mass planetary nebulae The helium shell is much thinner than the hydrogen one and is unable to swell the star to relieve the temperature build up. PH507 Astrophysics MDS 20 The process runs away until the helium layer is thick enough to expand the star thus cooling it. These helium flashes raise the luminosity from 100 to 100,000 times that of the Sun. The flashes can also re-start the hydrogen burning. Can be so energetic that the outer layers of the star are blown clean off. The escape velocity from the surface of a star is v esc = (2GM/R)1/2 . The expanding shell of ejected gasses is ionized by ultraviolet light from the hot core left behind. The White Dwarf core has a surface temperature over 100,000 K. Wein's law for a hot body with this temperature gives a peak wavelength of 2.9 x 10 -8m, corresponding to ultraviolet light. When the electrons recombine with the surrounding ions, they often enter an excited state and then jump down to the ground state emitting visible photons. This process is known as fluorescence. HST images of Planetary Nebulae Henize 1357 The Helix NGC 6543 MyCn18 PH507 Astrophysics MDS 21 Planetary nebulae Last for around 50,000 years after which it has dispersed and faded from view. Accounts for 15% of matter returned to the Inter-Stellar Medium (ISM) by stars. The planetary nebula takes ~ 60% of the star with it leaving only the core. White dwarfs < 4 Msol, never produce temperature high enough to ignite carbon and oxygen. During this phase, the star moves to the left on the H-R diagram. The track will sometimes loop corresponding to thermal pulses. As the ejected nebula fades and the core cools, the stars track turns sharply downward. The core becomes more and more compressed as the temperature drops. Most of the matter becomes degenerate again and the contraction halts. The star is now called a white dwarf - about the same size as the Earth. Its density is typically 109 kg/m3. One teaspoon weighs as much as an elephant (5.5 tons) Remember that electron degeneracy is a quantum effect. This means that the more massive a white dwarf, the smaller it becomes. The end of the road The Chandrasekhar mass (1.4 Msun) is the largest mass that a white dwarf can possibly have. Highly ionized atoms floating in a sea of degenerate electrons. PH507 Astrophysics MDS 22 As the star cools, the random motions of the particles slow and the electric forces between ions line them up in a crystalline lattice. From this point on the star is ‘solid’ the electrons, though degenerate, may move around the lattice. The core is similar to copper or silver. As it cools further it evolves into a cold dark diamond sphere of carbon and oxygen, about the size of the Earth. Higher Mass Stars: How far can it go? For an element to serve as fuel energy must be given off when its nuclei collide and fuse. This energy comes from packing together more tightly the neutrons and protons in the ash nuclei than in the fuel nuclei. Once iron is reached with 56 protons and neutrons, no further energy can be extracted by the addition of more. Iron does not burn. The fuel layers burn outward dumping more and more iron onto the core which is supported by degeneracy pressure alone. Eventually this fails, catastrophically and violently. **Mass Dictates the Life of a Star** (Russell-Vogt Theorem) The early stages of evolution for the medium and high mass stars are very similar to the low mass stars, but they occur faster. The life of stars of all masses during the main sequence phase is very similar. The main difference is that the higher the mass, the more luminous the star and the shorter the main sequence lifetime. What happens after the main sequence phase depends on the mass of the star. Define the following mass ranges: o Low Mass Stars: M < 4 MSun o Medium Mass Stars: 4 MSun < M < 8 MSun o High Mass Stars: M > 8 MSun PH507 Astrophysics MDS 23 Medium and High mass stars are not degenerate while red giants. Low mass stars end up as White Dwarfs composed of mainly Carbon and Oxygen. Medium mass stars have higher temperatures in their cores. The higher T allows fusion reactions creating Oxygen, Neon, Sodium and Magnesium. Medium mass stars end up as White Dwarfs composed of the higher mass elements. High Mass Stars: Mass > 8 MSun High mass stars can have many successive stages of fusion of higher mass element in a core and lighter elements in shells around the core The general trend is for the star's surface to become cooler and to become a blue giant and later a red supergiant. If the mass of the white dwarf in the core is larger than 1.4 M Sun (called the Chandrasekhar limit) the electrons would have to move faster than the speed of light in order to create enough degeneracy pressure to halt the gravitational collapse. Electrons can't move faster than light, so a white dwarf with M > 1.4 MSun collapses. Main sequence stars with mass larger than about 8 M Sun eventually form white dwarf stars with masses larger than the Chandrasekhar limit and collapse. This is the beginning of a Core Collapse Supernova also known as a Type II Supernova A Supernova in a star with 8 MSun < M < 20 MSun When the supernova begins the iron core collapses rapidly under free-fall and becomes denser. When the density is very high, protons and electrons can combine together to form neutrons and neutrinos: p + e -> n + This reaction is called inverse beta decay. The neutrinos escape easily since they don't interact well with matter and carry off energy. PH507 Astrophysics MDS 24 The resulting neutron gas collapses until the density is extremely high. The core of neutrons held stable by neutron degeneracy pressure is called a neutron star. The outer layers collapse and collide with the hard surface of the newly formed neutron star. This collision causes a violent rebound and a shock wave. This energy can provide the fuel which allows the endothermic fusion reactions to create very high mass elements such as Uranium. The supernovae are responsible for all the elements with masses larger than iron found on Earth. Core Collapse Supernovae probably occur about once every 50 years in our galaxy, but most of them are hidden by the dust of the galaxy. A Supernova in a star with M > 20 MSun The evolution of very massive stars is similar with the formation of a neutron star at the core in a supernova. However, neutron stars (like white dwarfs) have a maximum mass near 3 MSun, over which neutron degeneracy pressure can't balance gravity. In the very high mass stars, the neutron star goes over the critical mass, and the neutron star collapses. No other sources of pressure are available, and the collapsing material forms a black hole. A White Dwarf in a Semi-Detached Binary: Type Ia Supernovae Suppose that a white dwarf is receiving mass from a companion star. The White dwarf's mass will slowly increase. If it receives enough mass, the White Dwarf's mass will approach the Chandrasekhar limit and collapse. The collapse causes the degenerate Carbon gas in the White dwarf to begin fusing together explosively. PH507 Astrophysics MDS 25 This type of supernova is essentially a giant Carbon bomb. Summary of endpoints of stellar evolution Type White Dwarf Neutron star Core Mass Main Sequence Mass Msun Msun <1.4 <~6 1.4-~3 ~6-~12 Source of pressure electrons neutrons PH507 Black hole Astrophysics >~3 MDS >~12 26 ---- Protostar – Young Star evolution is not so well known: From Protostar to Young Star Protostars are cool when they begin to shine in the visible so start to the right of the diagram. Continued gravitational contraction of the protostar. Decreasing surface area means a reduction of luminosity PH507 Astrophysics MDS 27 Decreasing radius (higher pressure and therefore higher temperature) Different masses of star will follow different paths to their main destination on the main sequence. Protostars shine because they are hotter than their surroundings: Need an energy source to stay hot, but Central temperature is too cool for nuclear fusion to ignite Initial energy source is gravity: (1) accretion on to ‘core’ + (2) contraction of core. (1) Accretion: bolometric luminosity of protostar is ·. GM M L= R Where M*dot* is the mass accretion rate and GM/R is the energy released per unit mass onto the protostar of (accumulating) mass M and radius R. (2) Gravitational Contraction (aka, the Kelvin-Helmholz Mechanism): The Protostar shrinks slowly, releasing gravitational energy 50% goes into photons, and is radiated away as starlight other 50% goes into heating the Protostar interior How long does this last? Kelvin-Helmholz Timescale To understand how long a Protostar can shine by Gravitational Contraction, we need to compare two numbers The Energy Source: (GM2/R) The Energy Loss Rate: Luminosity (L) The ratio is the Kelvin-Helmholz Timescale: The Kelvin-Helmholz timescale is ~30 Myr for a 1 solar mass protostar. PH507 Astrophysics MDS 28 Consequences: Shorter K-H time for high-mass protostars Longer K-H time for low-mass protostars H-R Diagram of pre-Main Sequence evolution for stars of various masses: PH507 Astrophysics MDS 29 Note the vertical Hayashi tracks: as a low-mass protostar contracts, convection transports energy to surface. Opacity at surface determines the surface temperature. Luminosity falls but temperature is constant. Later, or for high-mass stars, radiative energy transport becomes effective – central temperature rises – luminosity increases slightly as surface temperature rises and contraction continues Heyney track PH507 Astrophysics MDS 30 PH507 Astrophysics Dr Dirk Froebrich 31 At an age of 1 million years the most massive stars have contracted to the Main sequence, lived out their hydrogen-burning lifetimes and are evolving off the Main Sequence. Lower mass stars like the sun are still in the PreMain Sequence phase. The youngest clusters observed in the Milky Way are estimated to have ages of a few million years. At 10 million years: stars of 1 solar mass are still above the Main Sequence, just beginning nuclear reactions. They will be observed as T-Tauri stars. Stars with M ~ 20M are just moving off the Main Sequence. Such clusters will still be associated with regions of gas & dust from which they formed. At 100 million years most stars are on or near the Main Sequence, but stars with M > 5M are now moving off the Main Sequence. The Pleiades cluster is estimated to have an age of about 100 million years. With an age of a billion years: Cluster stars with masses between 2--3 M are moving off the Main Sequence. The Main Sequence location at which stars are just PH507 Astrophysics Dr Dirk Froebrich 32 beginning to exhaust the hydrogen fuel in their cores and move toward the Red Giant region is called the Main Sequence Turnoff The oldest clusters in the Milky Way, the globular clusters, are estimated to have ages of the order of 10-15 billion years and show H-R Diagrams like that at the right. Because the globular cluster stars have very low abundances of the elements heavier than helium (C,N,O ...) some corrections need to be made to compare their H-R diagrams to younger clusters with higher abundances. PH507 Astrophysics Dr Dirk Froebrich 33 Observed clusters: After ten million years: The cooler stars are still collapsing and haven't yet reached their MS stage. H-R diagram of stars in the cluster NGC 2264 On this diagram the Main Sequence is marked with a red line. We don't see the hottest, most luminous (type O) MS stars since they have evolved out of the MS stage already. PH507 Astrophysics Dr Dirk Froebrich 34 After one hundred million years All the O and B MS stars have used up their Hydrogen. When we look at this cluster's H-R diagram, we shouldn't see O and B Main Sequence stars. All of the less massive stars should still be in their MS stage, since they burn their H slower than the O and B stars. In this H-R diagram for the Pleiades we don't see any of the hottest Main Sequence Stars. The "Turnoff Point" is the hottest temperature MS star which exist in the cluster. The temperature can be used to estimate the age of the cluster. The hotter the turnoff point temperature, the younger the cluster. The stars found above the red line correspond to the O and B stars which have left the Main Sequence. PH507 Astrophysics Dr Dirk Froebrich 35 After 3 billion years: After 3 x 109 years, all of the O, B, and A stars have used up their H. We won't see O, B, A Main Sequence stars when we plot an old cluster's H-R diagram. An HR diagram of the Open Cluster M67 is shown below. Here we see only the cooler main sequence stars. We also see lots of Red Giants.