21.1.
The Milky way
• Diameter: 100-120 l years (31-37 kpc) • Thickness: 1k lyears (0.31 kpc)
• Sun is about 8kpc from center
• Thin disk: 6. 1010 Msun, young (8 Gy) stars 25x.35kpc
• Thick disk: 3.109 Msun, older (10-11Gy) stars, 25x1kpc
• Central Buldge: 1010 Msun, stars of all ages, 5x2kpc
• Halo: 3.109 Msun, oldest (11-13 Gy) stars
21.2.
Tracking matter
The matter we can see depends on the band frequency:
21.3.
The Milky way disk structure
21.4.
The Milky Buldge and Core
• Dense molecular cloud, but no ongoing star formation
• The motion of material around the center indicates that Sagittarius A* harbors a massive, compact object. This concentration of mass is best explained as a supermassive black hole with an estimated mass ~ 4 million times the mass of the Sun. Observations indicate that there are supermassive black holes located near the center of most normal galaxies.
21.5.
The Milky Halo
• The Galactic disk is surrounded by a spheroidal halo of old stars and globular clusters, of which 90% lie within 100,000 light-years (30 kpc) of the Galactic Center
• The temperature of this halo was said to be between 1 million and 2.5 million kelvin or a few hundred times hotter than the surface of the sun, stated by scientists
• On September 24, 2012, a team of five astronomers working with the Chandra X-ray Observatory, along with data gathered by the XMM-Newton, and Suzaku (satellite) missions, announced that the halo had a mass nearly equivalent to the galaxy itself
• On January 9, 2006, Mario Jurić and others of Princeton University announced that the Sloan Digital Sky Survey of the northern sky found a huge and diffuse structure (spread out across an area around 5,000 times the size of a full moon) within the Milky Way that does not seem to fit within current models. The collection of stars rises close to perpendicular to the plane of the spiral arms of the Galaxy. The proposed likely interpretation is that a dwarf galaxy is merging with the Milky Way.
21.6.
Weighting the Milky way
• Sun orbits the Milky way at 220 km/s at 8kpc, with a period of 230 My (so the Sun has orbited 20-25 times in its life so far)
• Using the Sun’s orbiting period and its distance from the center of the galaxy, we can estimate the total mass of the galaxy:
• Or knowing the Sun’s speed we can also use: where M(R) is the mass within the R radius
21.7.
Dark matter
• After a short increase (until we
englobe all the known mass), the speed should decrease, which is not the case! This means that mass keeps adding. Is it coming from dark matter?
• 95% of the mass is neither luminous nor absorbing. That’s 20 times the weight of the Milky way.
• Dark matter is a type of matter hypothesized to account for a large part of the total mass in the universe. Dark matter is in spherical halo with
radius 200-300 kpc and mass of 2.1012 Msun with no optical activity.
• We think dark matter is present as MACHOS: Massive Compact Halo Objects, i.e. Brown/Red/White Dwarfs or other dim compact objects
• Search for HALOS is done using gravitational microlensing, but Machos explain only 10% of this missing mass.
• WIMPS: Weakly Interacting Massive ParticleS: a new kind of particle that interacts only very weekly to form dark matter.
The center of galaxies are made of a huge black hole (stars in the center of galaxies orbit much faster), and the external part of galaxies are made of dark matter.
21.8.
Spiral galaxies
• Spirals cannot be made of stars, because differential rotation would destroy them quickly rotation would throw away the stars
• Density Wave model: Spirals are quasistatic density waves where density increases by 10%-20%. As gas enters a density wave, it gets squeezed and makes new stars. Stars then exit through the end of the spiral
• Stochastic self-propagating star formation model: this model proposes that star formation propagates via the action of shock waves produced by stellar winds and supernovae that compose the interstellar medium. Star
formation begins randomly, then OB supernovae shock wave trigger star formation further out. Differential rotation pulls new stars into trailing arms.
21.9.
Galactic evolution
• Most galaxies are in clusters. Interactions are important.
• Elliptical galaxies much more common in the center of the dense clusters • Half the mass is gas between galaxies
where C is a constant depending on how vM compares to the velocity dispersion of the surrounding matter.
• In close encounters, tidal forces break spreading it in stellar steam • When 2 galaxies meet, the combined galaxy could have 2 black holes
• The detailed process by which such early galaxy formation occurred is a major open question in astronomy. Theories could be divided into two categories: top-down and bottom-up. In top-down theories (such as the Eggen–Lynden-Bell–Sandage [ELS] model), protogalaxies form in a large-scale simultaneous collapse lasting about one hundred million years. In bottom-up theories (such as the Searle-Zinn [SZ] model), small structures such as globular clusters form first, and then a number of such bodies accrete to form a larger galaxy.
21.10. Measuring distance to galaxies: Redshift
• If galaxy is not too far (< 107pc), we can use Cepheids standard candles
• For further, spiral galaxies, Tully-Fisher relation relates rotation to luminosity & type • For further, elliptical galaxies, Fundamental plane relation relates luminosity to size &
velocity dispersion
• This allows galaxies to be used as standard candles for distance measurement
• Red shift indicates galaxy speed. What Hubble noticed, is that the farther the galaxy, the faster it goes away from us : v=H0.D Hubble law H0=100.h km/s/Mpc
h=0.71 hubble constant This law gives the speed of a galaxy (in km/s), 1 megaparsec away.
Redshift z:
From this is follows that we can deduce the galaxy speed straight from the Doppler shift:
for small Doppler shifts
21.11. Cosmic expansion
• In fact, Hubble constant varies with time: the rate of expansion is not constant in time. For unbound objects:
D(t) = D(t0). [1 + H0(t-t0)] where D(t) is the distance to a galaxy, measured at time t. t0 is now
• Earth, Sun etc are bounded, therefore they are not expanding vs. each other
• From this, we can deduce the age of the Universe: 1 + H0.(t-t0) = 0, which gives t = t0 - H0-1 → concerting everything to same units: H
0-1 = 13.8Gy ago
• This can be expressed also as: for z <<1 which means that the emitted wavelength expands with the universe. The Redshift is a cosmological shift, not a Doppler shift.
21.12. Recap on formulas
From a star orbiting a galaxy:
• From a star’s orbiting period, its mass and its distance from the center of the galaxy, we can estimate the total mass of the galaxy:
• From the Star’s speed we can estimate the total mass of the galaxy: where M(R) is the mass within the R radius
Using the galaxy’s redshift:
• From the distance to a galaxy, we can find its speed: V = H0.D (Hubble law) H0=100.h km/s/Mpc, h=0.71 • Based on shift of wavelength emitted by galaxy, we compute the redshift:
• We can compute galaxy’s speed: ≈ z for small Doppler shifts
• We can compute galaxy’s distance from us: or for z <<1, i.e. for speed low enough, e.g. D << c/H0.
• We can compute the time when the light that we observe from the galaxy has been emitted:
• From the time of light journey, we can also estimate the distance to the galaxy
We could also use which gives where
since λ0 is λ observed now.
The above relations ignore the relativist corrections needed at high speed, and the history of the universe: H0 is now, we need to integrate trough all previous H.
In deducting the age of the universe we assumed H constant, which is not the case: the gravity effect will bring back all galaxies together, therefore the expansion will slow and
21.13. Galaxy clusters
• Milky way is part of a cluster, or local group.
• Estimated mass of 4.1022 Msun , most of it is dark matter
• Virgo cluster has 250 large galaxies and over 2000 smaller ones. 68% spirals and 19% ellipticals.
• Intracluster medium of hot 106 gas contains 8 times more mass than galaxies • Intergalactic stars account for 10% mass
• Gravitational lensing by clusters can be used to find mass distribution of lens:
• Most of the dark matter is diffuse
• Dark matter interacts weakly so follows galaxies
• Clusters are organized in Superclusters. Our supercenter is centered on Virgo galaxy
• Superclusters are grouped into metastructures
• Correlation data shows after 100Mpcs universe is homogeneous: there is no larger structure