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21.MS_evolution

ms evolution<br>

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21.MS_evolution

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  1. Stellar Evolution Section II Prof. F. R. Ferraro

  2. ZAMS – Zero Age Main Sequence Pre-MS evolutionary tracks 2

  3. ZAMS Zero Age Main Sequence In the HR diagram the ZAMS is a sort of reference locus where stars with DIFFERENT MASS locate when they start the H- burning process It is NOT an evolutionary track, is a sort of “starting line” from which stars with different masses start they evolution PAY ATTENTION: this is the sole place in the HR diagram where we can easily and firmly link MASS AND LUMINOSITY Also: any star along the ZAMS is essentially chemically homogeneous due to the deep – complete- mixing operated by the convection during the pre-MS stage Evoluzione Stellare - parte II 3

  4. Two cut-off masses 90 M¤ 0.08M¤ Evoluzione Stellare - parte I 4

  5. There is a lower limit (low cut-off) mass for the H ignition 0.08 M¤ Mcrit=0.08M0≈0.1Mo Stars with M<Mcritdo not reach the temperature needed by the core to activate the H-burning: they are NOT stars (brown dwarfs == failed stars) 5

  6. For M>Mupthe stellar structure becomes unstable This is not a rigorous cut-off (it dendends on metallicity) but the message is that it is difficult to form stable stars as massive as 100 M¤ Mup~ 90Mo € For M< Mlowthe central temperature is not sufficient to ignite the ENTIRE PP chain Mlow~ 0.08Mo € Evoluzione Stellare - parte I 6

  7. Eddington Luminosity As we have seen there is a portion of Log r-Log T diagram where the RADIATION PRESSURE dominates over the GAS PRESSURE Essentially the conditions of the external portion of high-mass stars High temperature very low density In this case the GRADIENT PRESSURE is driven by the RADIATION FLUX : dP dr=−κρ L FradFrad= 4πr2 c On the other hand the hydrostatic equilibrium requires: dP = −GMρ dr r2 Evoluzione Stellare - parte I 7 €

  8. By combining the relations: GMρ r2 L =κρ 4πr2 c GMρ r2 L =κρ 4πr2 c Once fixed the opacity, the relation sets the maximum Luminosity that a star of Mass M can reach in order to mantain the Hydrostatic equilibrium Led=GM4πc κ For L > Ledthe RADIATION PRESSURE makes the Hydrostatic Equilibrium in the outer regions unstable Evoluzione Stellare - parte I 8

  9. A convenient expression for Led Led=GM4πc κ Let’s express M in M¤ : Led= 6.7⋅10−8⋅4π⋅3⋅10101 M Mo 2⋅1033 κ = 50⋅10−8⋅1044 M Mo κ = 5⋅1037 M Mo κ 9

  10. In hot stars the opacity is essentially due to scatter: κ = 0.2(1+ X) and by assuming X=0.7, we get Led~5⋅1037 M M0 0.34 Led~ 1.5 ⋅ 1038 M ergsec−1 Mo € Next step: let’s express it in L¤=4x1033erg/sec € Evoluzione Stellare - parte I 10

  11. ~1.5 ×1038 4 ×1033 Led Lo M Mo Led Lo = 3.8 ⋅ 104 M Mo € for 90Mo Led~ 3.5⋅106Lo € The LUMINOSITY turns out to be of the same order of magnitude (it is only 3 times larger) than the value expected for a star 90 M¤ star along the ZAMS This is the reason why (at the current metallicity) it is difficult to form stable star larger than 90M¤ Evoluzione Stellare - parte I 11

  12. Log T =3.4 (2500K) Log T =4.7 (50000k) 12

  13. Teff~ 2700°K 0.08 M¤ 90 M¤ Teff~ 53000 °K T varies a factor 20 Mass varies a factor 1000! 13

  14. ALL stars along the ZAMS are core H-burning stars Remember that there are two main chains for the H-burning (which have sligthly different activation temperatures: TC=1.4 107K for the pp-chain and Tc=1.8 107K for the CNO-cycle) + The core temperature (Tc) increases as a function of the stellar mass Thus we can naturally expect that high-mass stars will activate the CNO burning process. The transition is expected at a surprising low-value of the mass ~ 1.2M¤ TC=1.4⋅107°K 1Mo⇒ H→He via pp chain TC=3.4⋅107°K 15Mo⇒ H→He via CNO-cycle 14

  15. In the SUN core : e epp/e eCNO~100 15

  16. ALL stars along the ZAMS are core H-burning stars H-burning via CNO chain H-burning via pp chain 16

  17. Stellar structure along the ZAMS Log L/Lo The structure of a star along the ZAMS depends on its mass. In particular what is different is the location and the extension of the convective portion inside the star 1.2 M¤ 0.3 M¤ Log Te Evoluzione Stellare - parte II 17

  18. Where do we expect a convective region inside the star? ∇RAD> ∇ad dT drrad 3xρLr 4acT34πr2 ∇ad = − It is essentially constant (0.4) inside the star but it can DECREASES (to 0.1) in PARTIALLY IONIZED regions It is affected by OPACITY and the radiative FLUX € γ =cP % ' ( * ∇ad= 1 −1 where cV γ & ) Both SPECIFIC HEATS ì and g à 1 Evoluzione Stellare - parte II 18 € €

  19. Stellar structure along the ZAMS Log L/Lo The structure of a star along the ZAMS depends on its mass. In particular what is different is the location and the extension of the convective portion inside the star Two “transition masses” are defined, which set three regimes 1.2 M¤ 0.3 M¤ Log Te Evoluzione Stellare - parte II 19

  20. Very LOW-MASS stars M<0.3 M¤ Log L/Lo 0.3 M¤ -HT 1.2 M¤ These stars are fully convective since their HT coincides with the ZAMS 0.3 M¤ Log Te Evoluzione Stellare - parte II 20

  21. Stars with M>1.2 M¤ Log L/Lo 1.2 M¤ corresponds to the “transition mass” between pp and CNO H-burning Is there any connection between the burning method and the stellar structure? 1.2 M¤ SURE !!! Indeed the different H combustion IS the REASON for the DIFFERENT STRUCTURE 0.3 M¤ Log Te Evoluzione Stellare - parte II 21

  22. The type of H-combustion DETERMINES the stellar structure along the ZAMS 5 εpp∝ ρX2T6 15 εCNO∝ ρXZCNOT6 Remember that the core temperature is NOT that different in the two cases: it is always a few 107 oK è (T6=14,15,18). But because of its impressive dependence on the temperature εCNO turns out to be tremendously larger than εpp € € dLr dr εCNO>>εpp = 4πr2ρε εì and Lì … thus Frì In fact, the CNO burning in general occurs in a smaller portion of the stellar core. In a 10 M¤ essentially 90% of the L is produced within the innermost 10% of the star, to be compared with only the 70% of L produced in the same region in a 1 M¤ star € € Evoluzione Stellare - parte II 22

  23. εì e Lì … Frì… This directly affects the RADIATIVE GRADIENT which activates the CONVECTION dT drrad 3xρ 4acT3 Lr = − 4πr2 Ñ>Ñad € H-buring via CNO CYCLE è è convective cores Evoluzione Stellare - parte II 23

  24. An example : the structure of a 5 M¤ ¤ RADIATIVE Envelope (70%) Convective region (20%) H-burning region (~10%) Evoluzione Stellare - parte II 24

  25. Stars with 0.3M¤<M<1.2 M¤ Log L/Lo In these stars the core is RADIATIVE Which is the origin of the external convective region? In this case is the low surface temperature that increases the opacity κ ∝T−3.5 1.2 M¤ and the radiative gradient 0.3 M¤ Log Te 25

  26. In addition in sufficiently low surface temperature stars, the partially ionized regions can help the onset of CONVECTION, because the reference gradient (the ADIABATIC GRADIENT) tends to decrease from 0.4 to 0.1, thus making easier the case Ñ>Ñad Partially ionized region Convective region The decrease of the ADIABATIC gradient (in red) in a partially ionized region. The behaviour of the RADIATIVE gradient is also plotted as a black solid line 26

  27. An example : the structure of a 1 M¤ ¤ Convective region (30%) RADIATIVE Envelope (50%) H-burning region (~20%) Evoluzione Stellare - parte II 27

  28. The transition p-p/CNO has an impact also in the characterization of a different relation between the mass and the central temperature Tc,6 pp Note that if also high-mass stars were supported by the pp chain, in order to mantain the same luminosity (to produce the same amount of energy) the required Tc should have been by far much larger 28 CNO 24 20 16 The CNO cycle allows to significantly limit the increase of Tc pp 12 1 2 3 4 5 M/M¤ ¤ 28

  29. Solar metallicity (Z=0.02, Y=0.27) stellar structures along the ZAMS The increase of the core temperature as a function of the star mass is modest To produce the same amount of energy, the CNO cycle REQUIRES much LOWER core temperatures with respect to the pp chain 29

  30. METALLICITY EFFECTS: In low metallicity regimes CNO is by far less efficient Hence the pp- burning dominates the energy production. Thus low metallicity stars are expected to have much HOTTER stellar cores Z=0.0001 Z=0.02 30

  31. METALLICITY EFFECTS: As global effect low metallicity star are expected to appear HOTTER than high metallicity stars Z=0.0001 Z=0.02 31

  32. Solar metallicity (Z=0.02, Y=0.27) stellar structures along the ZAMS Note: At increasing mass the central density decreases High-mass stars host cores SIGNICANTLY LESS DENSE than low-mass stars This suggests that high mass stars have less probability to develope ELECTRON DEGENERACY in the core 32

  33. ANOTHER NATURAL EFFECT OF THE CNO BURNING IS THE CHANGE OF THE MASS-LUMINOSITY RELATION L≈M3.6 L≈M4 33

  34. IMPACT OF THE STAR STRUCTURE ON THE MASS-LUMINOSITY RELATION L≈M3.6 L≈M4.5 L≈M2.6 34

  35. EFFECTS OF DIFFERENT H-BURNING 1. THE STELLAR STRUCTURE (CNO-BURNING SETS A CONVECTIVE CORE) 2. THE CORE TEMPERATURE (CNO-BURNING LIMITS THE INCREASE OF THE CORE TEMPERATURE) 3. MASS-LUMINOSITY RELATION (CNO-BURNING REDUCES THE DEPENDENCE OF THE LUMINOSITY ON THE MASS) 4. THE SHAPE of post-MS EVOLUTIONARY TRACKS (CNO-BURNING SHAPES THE H-PROFILE INSIDE THE STAR PRODUCING A CLEAR SIGNATURE IN THE EVOLUTIONARY TRACKS IMMEDIATELY AFTER THE H EXHAUSTION) 35

  36. ZAMS 36

  37. The H-burning phase == the so-called MAIN SEQUENCE The blue-dashed line ideally connects point 2 in all the evolutionary tracks ZAMS Point 1= ignition of the H-burning into the core Point 2= exhaustion of the H-burning into the core Segment 1-2è Evolution during the MS è 37

  38. The core H-burning phase is by far the LONGEST evolutionary stage in the star lifetime. This is because the H-burning process is the most efficient thermonuclear reaction M in M¤ 15.0 9 5 3 2.25 1.5 1.0 tMS[yr] 1×107 2.2×107 7×107 2×108 5×108 1.7×109 9×109 Again we find a very strong relation between the star mass and the phase duration tMS when M Evoluzione Stellare - parte II 38

  39. An approximate relation can be derived from the table tMS≅1010M−3yr For M~10M¤ tMS~107yr For M~1M¤ tMS~1010yr € This is an intriguing indication: the MS time scale for low mass stars (M=0.8M¤) is comparable to the Hubble time ! Then stars with masses lower than M<0.8M¤ (formed at the epoch of the Big-Bang) are still burning H in their cores. 39

  40. During the MS the macroscopic characteristics of stars change very little 40

  41. No energy is produced in the most external 75-80% portion of the SUN Evoluzione Stellare - parte II 41

  42. initial H-abundance Excess of He3 generated by the H2combustion H2+ H1→ He3+ γ but not transformed in He4because of the low temperature He3+ He3→ He4+ H1+ H1 € € Evoluzione Stellare - parte II 42

  43. initial H-abundance Small effect due to the DIFFUSIVE SETTLING of elements heavier than H the original chemical composition of the SUN adopted in the Carroll-Ostlie textbook is X=0.71 Y=0.27 Z=0.02 Evoluzione Stellare - parte II 43

  44. The morphology of the evolutionary tracks for stars with M>1.2 M¤ is very different from that of stars with M<1.2M¤ pp/CNO Transition mass OF COURSE ITS NOT A COINCIDENCE THAT THIS HAPPENS JUST AT M=1.2 M¤!! Even this phenomenon is due to the different H-burning process 44

  45. Segment 1 - 2 Point 1= ignition of the H-burning into the core Point 2= exhaustion of the H-burning into the core (X<0.05) Evoluzione Stellare - parte II 45

  46. What is going on in the core? The H-burning produces the systematic transformation of 4 nuclei of H into one nucleus of He ê The number of free particles DECREASES ê PRESSURE DECREASES At fixed temperature, pressure is directly proportional to the number of particles Is the num of particles for unit of volume ρ µH= P =kρT indeed µH 46 € €

  47. Let’s have a look in the Sun. This is the situation we expect now in the core: Initial chemical composition: X=0.71 Y=0.27 Z=0.02 Current chemical composition:X=0.35 Y=0.63 Z=0.02 Future chemical composition: X=0.0 Y=0.98 Z=0.02 47

  48. Let’s see the effect of µ variation on the core structure Initial chemical composition: X=0.71 Y=0.27 Z=0.02 Current chemical composition: X=0.35 Y=0.63 Z=0.02 Future chemical composition: X=0.0 Y=0.98 Z=0.02 µ=0.62 (original) 1 µ = µ=0.85 (current) 2X +3 Y +1 Z 4 2 µ=1.35 (future) P =kρT Since € µH µ ì then Pî The core CONTRACTS rì € The star is a VIRIALIZED STRUCTURE, thus the core contraction implies an increase of the core Temperature Tcì 48

  49. Let’s see the effect of such variation on the core structure µ ì then Pî The core CONTRACTS rì and Tì The contraction increases the efficiency of the H- burning eì e Lì Time-scale? Thermonuclear time-scale: very very very slow 49

  50. Segment 1 - 2 In fact in all the cases the Segment 1-2 is characterized by an increase of the Luminosity while the behaviour of the surface Temperature is different 50

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