Stars Evolution PDF

 Contents   Stellar Evolution  Introduction  The birth of Stars  Stellar Maturity and old age.  The deaths of stars.  Neutron stars and black holes Introduction  Introduction   Since star emit huge a...

 Contents   Stellar Evolution  Introduction  The birth of Stars  Stellar Maturity and old age.  The deaths of stars.  Neutron stars and black holes Introduction  Introduction   Since star emit huge amount of energy they should evolve.  They look unchanged for humans because their time scales are between millions to billions of years.  The different populated regions in the H-R diagram correspond to different stellar phases.  Astrophysicists have developed a theory of stellar evolution by combining observations and theoretical models.  The theory explains how the stars are born in huge clouds of interstellar gas, they mature, grow old, and die while enriching the space with new material for future star generations The birth of stars  The birth of stars   Interstellar space is not empty but filled with tenuous matter (gas and dust)  Photographies, spectroscopy, and interstellar extinction provide evidences about the existence of this matter.  Stars are formed from cold and dark clouds of interestellar medium named dark nebulae.  Typical dark nebulae contains few thousand solar masses of gas and dust spread over a volume of 103pc3 and temperature 10K.  The temperature (and the pressure) is Horsehead Nebulae so low that the cloud contracts under its own gravity.  Star formation can be triggered by nearby supernova explosions, collision of galaxies,…  The Jeans Instability  Problem first proposed by Newton: “Imagine a gas with tiny density fluctuation. Under what condition the fluctuations grows to produce a permanent object ?” Regions where density is slightly higher a) will gravitationally attract nearby material and gain mass (contraction) b) The pressure will be higher and the regions will expand and disperse James H. Jeans (1877-1946) c) ¿Under which conditions (a) > (b) ?  The Jeans Instability  Large scale Problem first proposed by Newton: fluctuations “Imagine a gas with tiny density Density fluctuation. Under what condition the fluctuations grows to produce a permanent object ?” Small scale fluctuations Regions where density is slightly higher Distance a) will gravitationally attract nearby material and gain mass (contraction) Density b) The pressure will be higher and the regions will expand and disperse c) ¿Under which conditions (a) > (b) ? Distance  The Jeans Instability   Consider a spherically symmetric distribution of mass with average density 𝜌 and radius L.  There are two important characteristic times:  free-fall time: characteristic time that would take a system to collapse under the action of its own gravity 1 𝑇𝑓𝑓 ~ 𝐺𝜌  Time that a sound wave need to cross the cloud 𝐿 𝑇𝑠 ~ 𝐶𝑠  When 𝑇𝑠 < 𝑇𝑓𝑓 , density perturbations are damped out because pressure can balance gravity.  When 𝑇𝑠 > 𝑇𝑓𝑓 , pressure force cannot counterbalance gravity and density perturbations grow.  The Jeans Instability   The cloud will collapse if the fluctuation extends a distance greater than the Jeans length 𝜋𝑘𝐵 𝑇 𝐿𝐽 = 𝑚𝐺𝜌 10−23 𝐽  Where 𝑘𝐵 = 1.38 × T is the temperature (K), m is , 𝐾 the mass of a single particle in the cloud (kg), 𝐺 = 6.67 10−11 𝑁𝑚2 × , and 𝜌 is the mean density of the gas (kg/m3) 𝑘𝑔2  The birth of stars  During the  contraction, the gravitational energy is converted into thermal energy and the gases heat up.  In few thousands of years of contraction, the surface temperature reaches 2000-3000K and it produces substantial luminosity.  Protostar contration follows until the core reaches few millions of degrees, when hydrogen burning begins.  The thermonuclear process release enormous amount of energy, that increases the pressure and stops the Pre-main sequence tracks contraction.  If M> 60 𝑀⊙, the protostar is too hot and radiation pressure too high.  If M< 0.08 𝑀⊙ temperature is not high enough to burn hydrogen (brown dwarfs) The main sequence  The main-sequence   Stars spend most of their life in the main sequence, burning hydrogen into helium 4H → He + energy  There is a mass loss 4H = 6.693 × 10-27kg 1He = 6.645 × 10-27kg -------------------------------------- From NASA Mass loss = 0.048 × 10-27kg According to Einstein’s formula E= mc2 = 4.3 × 10-12J  The main-sequence   It can be shown that, for star of mass M, the luminosity and its lifetime are 𝐿 ∝ 𝑀3.5 1 T ∝ 2.5 𝑀  Therefore, star with a large mass has a high luminosity but a short lifetime ! From NASA’s Cosmos Stellar Maturity  Stellar Maturity  From Main-Sequence to Red Giant  As hydrogen decreases, core has troubles to support the weight of the outer region.  The core contracts, the temperature Red Supergiant increases, and the region of hydrogen burning expands outward from the core → ↑ Luminosity  At some point there is no more hydrogen in the core, and hydrogen burning just Red Giant happens in a spherical shell around the core.  The core contracts, and the graviational energy comming from this contraction increases the temperature to 100 million of K.  Hydrogen burning in the shell is stimulated → ↑ Luminosity.  The outer layers of the star expand and cool.  The star size increases and its temperature decreases (Red Giant)  Stellar Maturity Red Giant Evolution   As the hydrogen-burning shell moves outwards in the Red Giant, it adds mass to the Helium core. Red Supergiant  The Helium core contract and its temperature reaches 100 Million K, enough to ignite the thermonuclear reactions Red Giant 4He+ 4 He →8Be 8Be+ 4 He → 12C + γ 12C+ 4 He → 16O + γ  These reactions liberate energy that stops the core contraction.  The amount of time burning He is 20% of the one in the main-sequence.  Stellar Maturity Asymptotic Giant Branch   In the AGB, the main source of energy is helium and hydrogen fusions in shells around a core of Carbon and Oxygen. Red Supergiant  Helium produced in the hydrogen shell drops toward the center of the star. This produces that the energy of the helium shell varies periodicall (thermal pulse) Red Giant  “Mira Variables” are a class of pulsating variable AGB stars (periods longer that 100 days and amplitude greater than one magnitude).  They pulsate because the entire star expands and contract, changing the temperature (shifting energy output between infra-red and visual wavelengths)  Stellar Maturity  Chi Cygni: example of Mira Variable stars  Brightest magnitude 3.3  Dimmest magnitude 14.2  Period: 408 days  Distance 180 pc Light Curve of Chi-Cygni  Other Pulsating stars  Type of pulsating stars  Cepheids: very luminous and massive. T=1-70 days. 2 types: classical and Virginis. Pulsating stars in the HR diagram  Other Pulsating stars  Type of pulsating stars  Cepheids: very luminous and massive. T=1-70 days. 2 types: classical and Virginis.  Other Pulsating stars  Type of pulsating stars  Cepheids: very luminous and massive. T=1-70 days. 2 types: classical and Virginis.  RR Lyrae: old population of giant star in globular clusters. T = 1.5 hours-days  RV Tauri: yellow supergiant. T: 20-100 days  Mira-Type Pulsating stars in the HR diagram Stellar Death  Stellar Death 0.4 𝑀⊙ < M < 8 𝑀⊙   Temperature is not enough to ignite the carbon.  During a thermal oscillation, the outer layers of the star separate from the Carbon-Oxygen core.  The core has approximately the size of the Earth and the mass of the Sun (M 8 𝑀⊙   Gravitational compression increases the star temperature up to 600 Million Kelvin, enough to burn the Carbon (and produce Ne, Mg)  Ne can also burn to produce more O and Mg.  If the mass is large enough to reach 1.5billion K, then Oxygen burning starts to produce S, Si, P, Mg.  Silicon burning produces 56Fe. From Wikipedia  The proton and neutron in 56Fe are so tightly bound together that no further energy can be extracted by fusing more nuclei with iron.  The sequence of burning stage finishes with Fe.  Stellar Death M> 8 𝑀⊙   The electrons in the star core should support the pressure but the continuous deposition of Fe make the mass exceed the Chandrasekhar limit  The core collapses, the temperature raises to 5 billion K and the gamma- ray photons associated with this intense heat break down the Fe nuclei into He (photodisintegration).  As the density climbs, electrons and protons combined to produce neutrons and neutrinos Crab Nebula. From Wikipedia (neutronization).  A stellar explosion named supernova happens.  Stellar Death  For M< 25 𝑀⊙ , the final product is a neutron star:  Made mostly by neutrons (but not only).  Radius about 10km.  1.4 𝑀⊙