galaxies (as 7007) galactic dynamics, cont

10
1 Galaxies (AS 7007) Autumn 2007 Teacher: Göran Östlin Assistant: 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 r 2 = mv rot 2 r " M (< r) = rv rot 2 G

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Page 1: Galaxies (AS 7007) Galactic dynamics, cont

1

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

Page 2: Galaxies (AS 7007) Galactic dynamics, cont

2

Page 3: Galaxies (AS 7007) Galactic dynamics, cont

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

Page 4: Galaxies (AS 7007) Galactic dynamics, cont

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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)

Page 5: Galaxies (AS 7007) Galactic dynamics, cont

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Epicyclic motion Epicyclic motion

Page 6: Galaxies (AS 7007) Galactic dynamics, cont

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Asymetric drift COSMOLOGY

Page 7: Galaxies (AS 7007) Galactic dynamics, cont

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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

Page 8: Galaxies (AS 7007) Galactic dynamics, cont

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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