Galaxies (AS 7007) Galactic dynamics, cont.
Transcript of Galaxies (AS 7007) Galactic dynamics, cont.
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Galaxies (AS 7007)Autumn 2007
Teacher: Göran ÖstlinAssistant: Jens Melinder
Lecture 2, contents:- Galaxy dynamics- Cosmology cathup- Stellar physics basics- Properties of local galaxies
Galactic dynamics, cont.
Our Galaxy, and other spirals, are supported by rotation
Equate inward force and centripetal acceleration
!
mMG
r2
=mv
rot
2
r" M(< r) =
rvrot
2
G
2
3
Equatorial vs
Galactic coordinates
DifferentialRotation:
Stars at smaller R move fasterStars at larger R lag behind
!
" = v /r
Constant velocity v means decreasing angular velocity Ω
Tangent methodto determine rotationcurve of our Galaxy
Only works for R<R0
vR: radial velocityvT: tangential velocity
vR has maximum at T,the tangent point
Hence, we need onlyto determine the max ofvR to know v at T
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Here we canapply the tangentmethod for eachGalactic longitude(l = 0 ± 90°) to findthe rotation curve
Galactic rotation curve (by the way: Galaxy = MW, galaxy = any galaxy)
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Epicyclic motion Epicyclic motion
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Asymetric drift COSMOLOGY
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Critical densityAssume matter with p=0 and Λ=0
Use:
That is, if: Then k=0
About 5 protons/m3
Properties of the Universe set by3 parameters: Ωm, ΩΛ, Ωk of Which only 2 areIndependent: Ωm + ΩΛ + Ωk = 1
Matter-domination ends and darkenergy-domination begins
Density
MatterRadiation
Darkenergy
tDE~10 Gyr
? ?
? ?
Dark energy dominates
Time
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The early universe
Gamov criterium: A reaction may be important as long as itsinteraction time scale is shorter than the expansion time scaleof the universe
Pair production. e.g. γ + γ e- + e+
reaction balance set by temperature, e.g: νe + n e- + p
As long as mAc2 < kT a particle ’A’ may be kept in equilibrium,then ”freeze out”
The early universe…Baryogenesis: matter-antimatter equality broken, Possibly by the decay of a so called X-boson⇒Net amount of matter⇒Photon to baryon ratio η = 109
Neutrino freeze out (decoupling) at t=0.7s Electron-positron pair production ceased and theAnnihilation of existing pairs heated up radiation and Matter but not the neutrinos that had already decoupled
Primordial nucleosynthesisAll fusion of hydrogen to heavier elements go throughthe stage of deuterium. p + n → D + γ
However, D can be dissociated by photons more energetic than 2.2 Mev
Since there are many more photons than baryonsThis will occur frequently enough also at much lowerTemperatures than kT=2.2 Mev ~1010 K
⇒Nucleosynthesis inhibited until the D productionrate was higher than the distruction rate (109K, t=200s)
DEUTERIUM BOTTLENECK
Primordialnucleo-
synthesis…
Only a smallFraction of allMatter may beBaryonic
Still larger than The luminous Matter density
Galaxies could be baryonic?
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(re)combinationSimilarly to above, the vast amount of photons canKeep hydrogen ionised to temperatures well below13.6 eV. But when T<4500 K the number of energetic Enough photons is to small and protons and electronscan combine to form neutral hydrogen
Matter and radiation decouples
Last scattering surface at z = 1100 (T=3000K)
Leads to dramatic drop in pressure for the matter
Observable as 3000/1100=3K CMBR, no lines sinceη>>1 and Δz >>1
CMBR according to COBE
Penzias & Wilson
Cosmic microwaveBackground
Early universeHot & Dense
Stellar evolutionAny star spend most of its life on the so called main sequence fusing hydrogen to helium. 0.7% goes to E=mc2
L ∝ Mα , α = 2.2 to 5 on main sequence
⇒ Massive stars run out of fuel faster ! (metallicity effect)
After hydrogen is exhausted the core of the star contractsand its outer parts expand => red luminous giant
If the temperature gets high enough in the core, then HeCan be fused into Oxygen, etc. This depends on the massOf the star, but there is a limit…
AGB stars (pulsating) give WD, massive stars give SN
L=4 R2SBT4
Luminosity of black body
Stellar spectra are black bodies modified by absorptionin stellar atmospheres
Defines effective temperature: Teff
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Herzsprung-Russel / Colour-Magnitude DiagramHR diagram / CMD
Luminosity ↑
← Temperatureblue red
Iso-chrones / Stellar populations
Positions of stars of given age
RGB more sensitive to metallicitythan age
Metal-rich
Metal-poor
Stellar evolutiontime scale is setby Mass
Z = metallicity(mass fractionof elementsheavier than He)
Not to be confusedwith redshift: z