# Stars and their properties: (Chapters 11 and 12)

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1 Stars and their properties: (Chapters 11 and 12) To classify stars we determine the following properties for stars: 1. Distance : Needed to determine how much energy stars produce and radiate away by using the inverse square law and determining reddening due to dust. 2. Luminosity L: This is the amount of energy generated in the star and released as EM radiation. 3. Temperature T: Found by using colors to determine the surface temperature. 4. Radius: By using the relation: 5. Chemical composition : L= (surface area A = 4 R 2 ) T 4 Determined from absorption line spectra. The Milky Way Galaxy has stars and its disc has a diameter of 10 5 Ly The solar neighbourhood is about 100 Ly in diameter and contains about 1000 stars. See closer look 11.5 : How we measure basic stellar parameters

2 Note that apparent brightness is determined by star's distance and obscuration by intervening dust. The relationship between Luminosity and color or equivalently temperature is the H R (Hertzsprung Russell) diagram shown here: Luminosity L on log scale: Sun =1 Blue line is the Main Sequence on this plot. Compare with Fig in text

3 Stellar Masses: Determined by analysis of motion of binary star systems. Eclipsing binaries, optical binaries or spectroscopic binaries. From such measurements we can obtain relation between stellar masses and their luminosities, shown below: See: Figure it Out 11.6 for Luminosity Mass relation. The one shown here is L M 3

4 For each position on HR diagram main sequence there is a corresponding stellar mass:

5 Stars are shine and energy is provided by nuclear fusion. ( see section 12.2 to 12.4 ) Stars have masses greater than M_sun. For Brown dwarfs see12.6 (Jupiter which is a planet has a mass which is M_sun, which is 100 times less than the mass of the lightest star!) Lifetime of a star depends on its mass. M = 1010 years 2 M M sun Large mass stars live a short life! For M = 10 M_sun, Lifetime is only 100 million years! A star with 0.2 M_sun, will live for 250 billion years! section 11.8b in text

6 Usually nuclear fusion takes place towards the center of the star where temperatures are high enough for fusion to occur. Energy created is transported to the outside of the star by two main mechanisms: Convective and Radiative transfer. Convective transfer thoroughly mixes the nuclei which are fusing throughout the convective region, while radiative transfer limits the fusion region towards the central core. Evolution of stars and stellar deaths : Chapter 13 (1) Smallest stars: M 0.3 M sun have convection They operate on the p p fusion cycle in their cores until 10% of H is used up (2) Intermediate stars: 0.3 M sun M 1.5 M sun have radiative core and convective envelope They also use the p p fusion cycle until 10% of hydrogen is used up. After that they become red giants and move up the RGB(Red Giant Branch)

7 (3) Stars with mass M 1.5 M sun have a radiative envelope but a convective core. They fuse hydrogen to helium, but by the CNO cycle. They have higher temperatures in the core. They also fuse H to He until 10 % of H is used up In the next two figures I show the evolution of different mass stars on the HR diagram (1) Those leading the formation of planetary nebula and white dwarfs See figure 13 8 in the text and section 13.1 d and (2) Those leading to the big bang of a Supernova. See section 13.2 in text

8 0: MS star with < 1.5 M_sun fusion: p p chain 1: Exhaustion of core hydrogen 2: Rapid contraction, envelop expansion 3: Shell H burning Red Giant 4. Core helium ignition helium flash for < 1.5 sun very fast HRB 5. Core He exhaustion 6. Shell helium burning 7: Super wind removes H 8: M < 8 sun planetary nebula phase with a nucleus of C star 9: White dwarf remains Structure of star from 5 to 7 is shown in the next slide Asymptotic Red Giant Branch Structure of Planetary nebula stage in region 8 is shown slide after that.

9 Asymptotic Red Giant branch Later the red giant becomes a Horizontal branch star, when temperature is high enough and helium fusion can take place in the core, with hydrogen burning in the outer shell. The star moves horizontally to the luminosity being approximately constant but temperature increasing on the way to becoming a white dwarf! This hot central core and a shell of hot gas which appears like a ring is the planetary nebula stage.

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11 Evolution of a massive star: Mass > 8 solar masses 10 For stars with Mass > 8 solar masses Here sequential fusion of C, Ne, O, Si Short time scale. Lot of neutrino emission 10: Core collapse after Fe is formed in seconds. Supernova Type II. What remains is a neutron star and a supernova remnant. Sometimes for even more massive stars a black hole is produced instead of a neutron star! Evolution of a binary with a compact object and a companion star: Supernova Type I In Binary stars, the two stars affect each other's evolution and exchange mass. This can lead to instability of the massive star (white dwarf ) leading to the formation of Supernova Type I.

12 Main Sequence, Red Giant Branch, Horizontal branch and White dwarf trajectory

13 Again a recapitulation of star formation and stellar Evolution

14 Star Formation: Trajectory on HR diagram: Initially the contracting gas cloud has a very large area and is cool so it starts from top right hand corner of the HR diagram. As it contracts its area decreases and so does its luminosity and it gets hotter, so the track moves down and left on the HR diagram. When the temperature at the center of the star reaches sufficiently high nuclear fusion can start converting hydrogen into helium and the star comes to a halt on the main sequence.

15 Sun's path: After it arrives on the Main Sequence it continues to remain in hydrostatic equilibrium for 10 billion years, until it uses up enough hydrogen so as not to be able sustain hydrogen fusion in the core. Then its core contracts, gets hotter and its outer shell continues to fuse hydrogen. This causes the outer shells to expand and it becomes a red giant moving upwards and to the right on the HR diagram Red Giant Branch (RGB)

16 Key Concepts: 1. Ultimate fate of a star depends on its initial mass 2. Massive stars and accreting white dwarfs or neutron stars end their lives with violent explosions Supernova Two types: II and I respectively 3. Supernovae explosions distribute heavier elements into galaxies. Ashes from which we developed!

17 Stars are formed from gas and dust clouds. Mass of proto stars depend on density, temperature and nucleation in the gas and dust clouds. When a large numbers of stars are produced from the same initial gas or dust clouds we get star clusters: open clusters in the disk and globular clusters distributed more or less uniformly around the galactic center.

18 Elemental composition in order of abundance: H, He, C, O,... Fe Low Z elements : Deuterium, Lithium, Beryllium and Boron Traces of elements with atomic number Z>26 cooked in SN explosions. Light Elements, H and He produced in the big bang. Stars are consumers of hydrogen and cannot produce enough helium.

19 Some questions: 1. What supplies energy to the stars so that sun like stars shine for 10 billion years? Answer: Nuclear Fusion. 2.Why does nuclear fusion require high temperatures? Answer: One must overcome the electrical repulsion between nuclei of elements which undergo fusion. One needs more than 10 million degrees temperature for fusion to proceed. 3. How is this high temperature created? Initially, when stars form,this energy comes from Gravity causing high pressure as matter contracts and hence high temperature.

20 5. What keeps stars like the sun stable? Answer: Hydrostatic balance between gravitational pull and the push due to gas pressure 6. What keeps stars with very high density stable? Answer: Quantum pressure of anti social fundamental particles like electrons (white dwarfs) or neutrons (neutron stars). 7. What happens when gravity is greater than quantum pressure? Answer: Matter collapses into a singularity called a Black Hole.

21 Synthesis of Elements from H and He, occur in stars. The process is nuclear fusion: Heavier element fusion needs higher temperatures. Some fusion processes: Step 1: Temperature range: 10 7 degrees Kelvin Process : Conversion of 4 protons into 1 helium via the p p cycler Releases mass energy ~ 0.7 (mass of a proton) Step 2: Temperature range 2.4 to degrees Kelvin Process: Conversion of 4 protons in to 1 Helium via the CNO cycle Step 3: Temperature 10 8 degrees Kelvin. For some stars there occurs a Helium Flash Process fusing of 3 Helium nuclei into one Carbon nucleus! Step 4: Some stars which are more massive continue on without helium flash to make carbon and heavier and heavier until Iron (Fe) is reached

22 This last process is a runaway process which leads to formation of elements beyond iron through neutron and photon reactions. So much energy is released and the material falling in from the outer layers hits the Quantum pressure wall of the electrons (white dwarfs) or neutrons (neutron stars) in the core and causes the star to explode. It explodes, releasing energy close to the mass energy of our sun in a few seconds! This explosion is the Super nova. It can leave behind a neutron star or a black hole. Stars whose mass is in the mass range of the sun's mass do not end up in an explosion because their central temperatures cannot reach high enough to fuse beyond carbon. Their deaths leave behind a white dwarf objects with mass of the sun and radius of the earth!

23 Next two slides show the HR diagrams for star clusters. Stars in a cluster have two properties which are very important: 1. They are all at about the same distance so their relative luminosities can be determined well if the distance to the cluster can be estimated. 2. Their turnoff point in the HR diagram is a marker for their age. This is because the turnoff point occurs when hydrogen fusion ends. From the luminosity and the energy production rate from hydrogen fusion we can estimate when hydrogen fuel is depleted.

24 In hydrogen fusion some 25 MeV of energy is released when 4 protons combine to form 1 Helium nucleus. It continues until 10 % of the hydrogen is used up. Then there is not enough hydrogen in the core to sustain the p p chain. The outer layers are still burning hydrogen and they get hot and expand. Beginning of red giant phase. In the next figure: Which clusters are older and which are younger?

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27 Next slides show the life histories of 1. Stars which do not end up as supernovae. These develop through the planetary nebula phase and become white dwarfs. 2. Massive stars which end up as Supernovae Type II.

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