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The Dark, Missing Matter Chapter 69

The Dark, Missing Matter Chapter 69. What a snake sees, so little of the world, so different!. or “the realization that the luminous galaxies themselves are mere whitecaps immersed within a hidden cosmic sea of dark matter”. gravity centripetal force (i.e., tether). Fritz Zwicky.

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The Dark, Missing Matter Chapter 69

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  1. The Dark, Missing MatterChapter 69 What a snake sees, so little of the world, so different! or “the realization that the luminous galaxies themselves are mere whitecaps immersed within a hidden cosmic sea of dark matter”

  2. gravity centripetal force (i.e., tether) Fritz Zwicky 1898-1974, Brilliant, Eccentric In 1933 Zwicky analyzed the motions of galaxies in the Coma cluster. If galaxies are orbiting the center of mass, M Then: GMm/R2=mV2/R so M ~ V2R/G So the speeds of galaxies, V, and their locations, R, effectively weigh the whole cluster, M (just like in the solar system). He also tried a different way to measure the mass, M. He counted the mass of all the stars (in galaxies) whose light he could see. He found Mgravity>>Mlight ! About 90% of the matter was missing!

  3. R=2x106 ly 700 km/sec M ~ V2R/G Zwicky: R=2x106 ly=2x1022 m, V=7x105 m/s, M=5x1011(m/s)2x2x1022 m/(6.67x10-11 m3/kg s2) =1.3x1044 kg = 1014 Msun Big disagreement! Average galaxy 1010 Lsun, ~1000 galaxies so 1013 Lsun or 1013 Msun Method A: Add Up Light Method B: Measure Motions Zwicky Uses Two Methods to Weigh Coma Cluster

  4. Missing Matter Problem 1) If the mass came from the stars in galaxies, then the cluster did not appear to have enough mass to keep the whizzing galaxies together. So what held them together? 2) If the cluster had a lot more matter than you could see, what form did it take? Where was its light? Maybe an ocean of “dark matter” in or between galaxies--galaxies just the “whitecaps” whose stars we can see. Maybe dark matter in a form too faint to be seen… (remember Neptune?--but remember Vulcan?) (Zwicky said there must lots of cold stars, gas, dust-- ”dark matter” that forms the gravitational glue of clusters)

  5. Imagine flying over the ocean at night and considering only the water you see.

  6. Weighing Galaxies from Rotation Curves • About three decades passed with most doubting the existence of missing matter • 1970’s astronomers began to weigh individual galaxies by measuring their Rotation Curves—plots of rotation speeds of stars around galaxy centers versus stars’ radii • What would you expect of speed of stars farther from center? It depends…

  7. Mass=Sun Case 1: Keplerian Rotation Curve, if all the mass is at the center, v falls with r. Example: Solar System Mass in center (Sun), So v ~ 1/r1/2 v/vE=(1au / r )1/2

  8. Case 2: Rigid Body Rotation Curve, when bodies are nailed to a solid structure(like a merry-go-round) 45 rpm V 33 rpm R Constant RPM (revolution per minute) so [cycles/time] =constant, =v/(2R) , so v ~ R Are stars “nailed” to a giant, solid wheel or orbiting bright, heavy center? Rotation curves can show us!

  9. Question: If you feel sick on a Merry-go-round, where should you go? a) jump-off b) sit on edge c) go to center c), velocity drops to zero there

  10. We are stuck in the disk and can’t see rotation well in visible light due to dust. But radio waves from hydrogen gas (21 cm spin flip) provided measurement (~1978) of the speed of rotation around the center. Rotation of Milky Way (0.5,250) Keplerian Sun (2.0,125) Since most of light is near the center (and thus presumably the mass) why isn’t this curve dropping at large radius? Some weird MW effect?

  11. What about Other Galaxies? The vast majority of the light is contained within R~5 kpc, Surely most of the mass is too. Thus at R>5 kpc, rotation curve should start to drop as v~1/R1/2

  12. Vera Rubin

  13. If most of mass in center like light “The major result of this work is the observation that rotation Curves of spiral galaxies are flat at distances as great as R=50 kpc” Flat Rotation Curves of Other Galaxies • Rubin, Ford, Thonnard (1978), measured rotation speeds of external galaxies (see also Roberts 1969) Edge-on r redshift r blueshift

  14. Meaning of "Flat" rotation curves M~R V=constant 200 Total Mass speed of rotation (v) (km/s) Sun • The “flat rotation curve” implies that the total mass of a galaxy grows linearly with distance beyond the Sun’s orbit...yet we don’t see enough stars out there! • It must be mostly invisible, dark matter, ~10 times mass of luminous matter! • Just like Zwicky saw in clusters, but now in galaxies too! 100 R 0 3 6 9 12 15 distance from center (kpc) Recall for bodies orbiting mass, M ~ V2R/G so V (M/R)1/2, Where M is the mass interior to R Flat rotations curves mean V~constant, so M~R !! (instead of M=constant for solar system)

  15. Rising Mass, Dimming Light So sum of interior starlight (and thus the number of stars) increases slowly until it reaches a plateau*. But sum of interior mass just keeps growing as MR ! observed from star motions Dark matter seen in starlight * (for most galaxies surface brightness  e-r so interior light  C-re-r so interior goes to C as r goes to infinity)

  16. Disks in Halos Dark Matter Halo • Theorists have surmised that spiral galaxies must be embedded in spherical dark matter “halos”. In fact disks are not stable without halo (like this bug in amber)! • If the missing, dark matter was in a halo, how dense would it be?

  17. M(<r) Stars imbedded in Dark Matter “Halos” Empty halo: =3, M=constant Solid halo: =0, M  r3 Dark Matter Halo: =2, so M  r So Halo more centrally concentrated than solid body but still persisting to large radii (unlike empty) r Our best “model” today is that a galaxy is a disk (pancake) inside a halo (cloud) of dark matter.

  18. So what is Dark Matter? We now know there must be two flavors of dark matter, 20% baryonic (normal) and 80% non-baryonic (weird). The best data today says that the majority of baryonic is in hydrogen and helium gas and the non-baryonic must be “cold” dark matter in a form called WIMPS (Weakly Interacting Massive Particles). This is an active area of research! Answer not yet known… Gas

  19. More Evidencefor Dark Matter Since matter bends space which deflects path of light, we can also “weigh” matter by the deflection angle. So we test if there is really missing matter.

  20. Remember that matter bends space

  21. Bending of light by Sun • Sir Arthur Eddington measured in 1919, during a total solar eclipse.

  22. Further Evidence for Dark Matter: Extreme bending of space, known as gravitational lensing Dark Matter makes a cluster so heavy that it actually bends light around a cluster, distorting (focusing) the background like a lens would (chapter 70). Result: multiple false copies of real sources, Sources distorted, amplified. False copy lens real False copy

  23. "Einstein ring" • Light from an object is bent by the gravity of an intervening galaxy or cluster (warped space!). • If had a compact sphere lensed by a perfectly aligned, point-like lens, would get an “Einstein ring”: WOW!! An Einstein Ring!

  24. Announcements • HW #7 due Monday • Lab observing tonight!! (due 25th) • Wednesday Surprise…don’t miss class! • Final on May 14th, 9am

  25. Artist’s rendition of Einstein Ring

  26. Hubble Images of Einstein Rings

  27. Gravitational lensing of galaxies • When distant galaxies are lensed, tend to get arcs. These are seen around many rich clusters of galaxies: the clusters act as gravitational lenses. • The number and distribution of arcs depends on the mass of the cluster Þ measure total mass (luminous and dark). • Conclude that many clusters are dominated by dark matter (~90% of total mass)! Yet more evidence for dark matter.

  28. Artist’s rendition of arclets from lensing Einstein cross – grav lens.

  29. Real lensing ring and false images

  30. Example of lens: G2237+0305

  31. Observed Omega_M of Univ. • Omega_M = 0.2-0.3 has been favored for about a decade. • Clusters of galaxies, etc. • In past few years, consensus closer to 0.3 than to 0.2 for Omega_M.

  32. By varying model of location of Dark matter until it matches the observations we can pinpoint the dark matter in this cluster. It lives in galaxies and between galaxies. Looks like a sand castle! Pinpointing Dark Matter Model with dark matter also between galaxies Model if dark matter only in visible (orange) galaxies HST image of Abell 1689

  33. Gravitational Lenses: Nature’s Funhouse Mirror Light from a distant spiral galaxy (head of dragon) has been magnified and stretched into a long arc (dragon's body) by the gravity of an intervening galaxy cluster called Abell 370

  34. In Case You Are Still Not Convinced Two clusters of galaxies with galaxies (stars & hydrogen gas) in red and dark matter halo in blue collided (left). The cluster gases collide, shock, heat, linger, and emit X-rays (red on right) while clouds of dark matter pass on through which we can locate (blue on right) from their lensing (distortion) of background galaxies. Red on right is hot gas seen in x-rays. Bullet Cluster, 2006

  35. Cosmic Composition

  36. So the stars we see are just whitecaps on a sea of dark matter.

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