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Chapter 6: Stellar Evolution (Part 1)

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Chapter 6: Stellar Evolution (Part 1) The CD-ROM that came with the text book (HKT) contains some nice and informative description and movies from stellar evolution modeling (e.g., CD-ROM/StellarEvolnDemo/index.html). They cover the Main Sequence (MS) and evolved stages (although some of the movies are missing). The same programs may also be obtained from http://astro.if.ufrgs.br/evol/evolve/hansen/index.htm. Chapter 6: Stellar Evolution (part 1) With the understanding of the basic physical processes in stars, we now proceed to study their evolution. In particular, we will focus on discussing how such processes are related to key characteristics seen in the HRD. Chapter 6: Stellar Evolution (part 1) With the understanding of the basic physical processes in stars, we now proceed to study their evolution. In particular, we will focus on discussing how such processes are related to key characteristics seen in the HRD. The CD-ROM that came with the text book (HKT) contains some nice and informative description and movies from stellar evolution modeling (e.g., CD-ROM/StellarEvolnDemo/index.html). They cover the Main Sequence (MS) and evolved stages (although some of the movies are missing). The same programs may also be obtained from http://astro.if.ufrgs.br/evol/evolve/hansen/index.htm. Outline Star Formation Young Stellar Objects The Main Sequence Dependence on stellar mass Dependence on chemical composition Post-Main Sequence Evolution Leaving the MS The red giant branch The helium burning phase The asymptotic giant branch Final evolution stages of high-mass stars Consider a medium of uniform density and temperature, ρ and T . From the virial theorem, 2E = −Ω, we have Z M 1=3 3kTM GMr 3 2 3 4πρ 5=3 = dMr = (GM =R) = GM (1) µmA 0 r 5 5 3 for the hydrostatic equilibrium of a sphere with a total mass M. If the left side is instead smaller than the right side, the cloud would collapse. For the given chemical composition, this criterion gives the minimum mass (called Jeans mass) of the cloud to undergo a gravitational collapse: 3 1=2 5kT 3=2 M > MJ ≡ : 4πρ GµmA For a typical temperature and density of a large molecular cloud, 5 −1=2 MJ ∼ 10 M with a collapse time scale of tff ≈ (Gρ) . Star Formation Here we briefly discuss the gravitational instability, Jeans mass, fragmentation of gas clouds, as well as the resultant initial mass function (IMF) of stars. −1=2 tff ≈ (Gρ) . Star Formation Here we briefly discuss the gravitational instability, Jeans mass, fragmentation of gas clouds, as well as the resultant initial mass function (IMF) of stars. Consider a medium of uniform density and temperature, ρ and T . From the virial theorem, 2E = −Ω, we have Z M 1=3 3kTM GMr 3 2 3 4πρ 5=3 = dMr = (GM =R) = GM (1) µmA 0 r 5 5 3 for the hydrostatic equilibrium of a sphere with a total mass M. If the left side is instead smaller than the right side, the cloud would collapse. For the given chemical composition, this criterion gives the minimum mass (called Jeans mass) of the cloud to undergo a gravitational collapse: 3 1=2 5kT 3=2 M > MJ ≡ : 4πρ GµmA For a typical temperature and density of a large molecular cloud, 5 MJ ∼ 10 M with a collapse time scale of Star Formation Here we briefly discuss the gravitational instability, Jeans mass, fragmentation of gas clouds, as well as the resultant initial mass function (IMF) of stars. Consider a medium of uniform density and temperature, ρ and T . From the virial theorem, 2E = −Ω, we have Z M 1=3 3kTM GMr 3 2 3 4πρ 5=3 = dMr = (GM =R) = GM (1) µmA 0 r 5 5 3 for the hydrostatic equilibrium of a sphere with a total mass M. If the left side is instead smaller than the right side, the cloud would collapse. For the given chemical composition, this criterion gives the minimum mass (called Jeans mass) of the cloud to undergo a gravitational collapse: 3 1=2 5kT 3=2 M > MJ ≡ : 4πρ GµmA For a typical temperature and density of a large molecular cloud, 5 −1=2 MJ ∼ 10 M with a collapse time scale of tff ≈ (Gρ) . What exactly happens during the collapse depends very much on the temperature evolution of the cloud. I Initially, the cooling processes (due to molecular and dust radiation) are very efficient. If the cooling time scale tcool is much shorter than tff , the collapse is approximately isothermal. −1=2 I As MJ / ρ decreases, inhomogeneities with mass larger than the actual MJ will collapse by themselves with their local tff . This fragmentation process will continue as long as the local tcol is shorter than the local tff , producing increasingly smaller collapsing subunits. I Eventually the density of subunits becomes so large that they become optically thick and the evolution becomes adiabatic (i.e., 2=3 1=2 T / ρ for an ideal gas), then MJ / ρ . I As the density has to increase, the evolution will always reach a point when M = MJ , when a subunit reaches approximately hydrostatic equilibrium. We assume that a stellar object is born. Cloud fragmentation Such mass clouds may be formed in spiral density waves and other density perturbations (e.g., caused by the expansion of a supernova remnant or superbubble). Cloud fragmentation Such mass clouds may be formed in spiral density waves and other density perturbations (e.g., caused by the expansion of a supernova remnant or superbubble). What exactly happens during the collapse depends very much on the temperature evolution of the cloud. I Initially, the cooling processes (due to molecular and dust radiation) are very efficient. If the cooling time scale tcool is much shorter than tff , the collapse is approximately isothermal. −1=2 I As MJ / ρ decreases, inhomogeneities with mass larger than the actual MJ will collapse by themselves with their local tff . This fragmentation process will continue as long as the local tcol is shorter than the local tff , producing increasingly smaller collapsing subunits. I Eventually the density of subunits becomes so large that they become optically thick and the evolution becomes adiabatic (i.e., 2=3 1=2 T / ρ for an ideal gas), then MJ / ρ . I As the density has to increase, the evolution will always reach a point when M = MJ , when a subunit reaches approximately hydrostatic equilibrium. We assume that a stellar object is born. We cannot yet theoretically determine the initial mass function (IMF) of stars. The IMF may be determined empirically and may be expressed in forms such as −x dn=dm = φ(M) = C(M=0:5M ) where x = 2:35 (Salpeter’s law), valid for M=M ≥ 0:5, and x = 1:3 for 0:1 ≤ M=M < 0:5 in the solar neighborhood. The Initial Mass Function This way a giant molecular cloud can form a group of stars with their mass distribution being determined by the fragmentation process. The process depends on the physical and chemical properties of the cloud (ambient pressure, magnetic field, rotation, composition, dust fraction, stellar feedback, etc.). Much of the process is yet to be understood. The Initial Mass Function This way a giant molecular cloud can form a group of stars with their mass distribution being determined by the fragmentation process. The process depends on the physical and chemical properties of the cloud (ambient pressure, magnetic field, rotation, composition, dust fraction, stellar feedback, etc.). Much of the process is yet to be understood. We cannot yet theoretically determine the initial mass function (IMF) of stars. The IMF may be determined empirically and may be expressed in forms such as −x dn=dm = φ(M) = C(M=0:5M ) where x = 2:35 (Salpeter’s law), valid for M=M ≥ 0:5, and x = 1:3 for 0:1 ≤ M=M < 0:5 in the solar neighborhood. Probably the strongest evidence for a top heavy IMF comes from the Galactic center stellar clusters (Sunyaev & Churazov 1998, MNRAS, 297, 1279; Wang et al. 2006, MNRAS, 371, 38). Compared with the X-ray emission from young stars in the Orion nebula, the observed total diffuse X-ray luminosities from massive young stellar clusters suggest that the number of low-mass YSOs are a factor of ∼ 10 smaller than what would be expected from the standard IMF and the massive star populations observed in the clusters. If confirmed, this has strong implications for understanding the star formation at high z, the mass to light ratio, etc. Is the IMF universal? While the IMF in galactic disks of the MW and nearby galaxies seem to be quite consistent, there are good reasons and even lines of evidence suggesting different IMFs in more extreme environments (e.g., bottom-light in the Galactic center and top-cutoff in outer disks; Krumholz, M. R. & McKee, C. F. 2008, Nature, 451,1082). If confirmed, this has strong implications for understanding the star formation at high z, the mass to light ratio, etc. Is the IMF universal? While the IMF in galactic disks of the MW and nearby galaxies seem to be quite consistent, there are good reasons and even lines of evidence suggesting different IMFs in more extreme environments (e.g., bottom-light in the Galactic center and top-cutoff in outer disks; Krumholz, M. R. & McKee, C. F. 2008, Nature, 451,1082). Probably the strongest evidence for a top heavy IMF comes from the Galactic center stellar clusters (Sunyaev & Churazov 1998, MNRAS, 297, 1279; Wang et al. 2006, MNRAS, 371, 38). Compared with the X-ray emission from young stars in the Orion nebula, the observed total diffuse X-ray luminosities from massive young stellar clusters suggest that the number of low-mass YSOs are a factor of ∼ 10 smaller than what would be expected from the standard IMF and the massive star populations observed in the clusters.
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