structures: existence stars

Transcription

1 structures: existence stars

2 Kelvin s paradox Some unknown source of energy laid down in the store house of creation

3 Kelvin s paradox The gravitational binding energy of the mass of the Sun after it falls from infinity to the radius of the Sun: U = 3 5 GM 2 R = erg Since the Sun produces: L = erg/s the gravitational energy released could have provided the energy radiated for U L = s = 10 7 yrs. 10 That is a lot of energy but our Sun has been glowing for almost 10 yrs.

4 free fall timescale Let!s take away the pressure of the sun! free fall velocity: v ff GM R t ff =(R/v ff ) R 3 GM 1 hour

5 nuclear energy what is possible in the Cavendish Laboratory cannot be too complicated for a star Arthur Eddington

6 structures: existence stars When the mass of the system is increased, the gravitational pressure increases and - to balance it - both the Fermi pressure and the thermal pressure will increase: ɛ = ɛ f (n) + k B T P nk B T + nɛ F This pressure can balance gravitational pressure if system we get k B T Gm 2 pn 2/3 n 1/3 (3π2 ) 2/3 2 (k B T + ɛ F ) ɛ g. For a classical 2 m e n 2/3. The maximum temperature of the system is reached when n = n c, with n c α ( ) G N 2/3 αg 2 ; k (3π 2 ) 2/3 B T 2(3π 2 ) (N 4/3 m 2/3 e c 2 ), λ e λ e = ( /m e c)

7 ( ) structures: existence stars ( An interesting phenomena arises when the maximum temperature is sufficiently high to trigger nuclear fusion ɛ nucl = ηα 2 m p c 2, with (η 0.1. The energy corresponding to the maximum temperature k B T will be larger than ɛ nucl when ( ) 3/4 ( ) 3/2 N > (2η) 3/4 (3π 2 ) 1/2 ( mp ) ( α ) m e for (η 0.1. The corresponding condition on mass is ( ( ) ) ( 3/4 ( M > M (2η) 3/4 (3π 2 ) 1/2 mp α m e α G α G ) 3/2 m p g which is comparable with the mass of ( the ) smallest ( stars observed in our Universe. The mass of the Sun, for example, is M = g

8 structures: existence stars The lowest-mass star that can fuse H into He in its core has a mass of about 0.07 solar masses

9 structures: existence stars The lowest-mass star that can fuse H into He in its core has a mass of about 0.07 solar masses

10 the sun s source of power

11 solar neutrinos

12 main-sequence lifetime Take the amount of H in the Sun!s core (7% of its total mass) and divide it by the amount of fuel consumed each second (360 million tons per second) to obtain an estimate of the sun!s main-sequence lifetime: t = kg kg/s = s = yr For the values given, we obtain a lifetime for the Sun of about 12 billion years on the main sequence. Other, more detailed stellar evolution models indicate that slightly less hydrogen will be fused in the core before the Sun leaves the main sequence phase, so the Sun!s main-sequence lifetime is rounded off to about 10 billion years.

13 stellar evolution

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15 massive stars

16 eddington limit

17 eddington limit If the luminosity of the source is L, we have by spherical symmetry that the inward force on an electron-positron pair is ( GMm p Lσ T 4πc ) 1 r 2. There is a limiting luminosity for which this expression vanishes, the Eddingron limit.

18 eddington limit The luminosity a body would have to have for the force generated by radiation pressure to exceed the gravitational force: ( ) ( ) M L Edd = 10 5 L M ( Since we know experimentally, ( ) ( ) 3 M L L form 10M M ( ) ( ) 2 M L form > 10M M a star will be unstable if M 180M

19 most massive stars List of the heaviest star Star name Solar Mass Eta Carinae 150 Pistol Star 150 LBV A1 in NGC S Doradus 100 Pismis Cyg OB WR 20a+b R 66 70

20 eta carinae

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