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Dark Matter and the Equivalence Principle

Dark Matter and the Equivalence Principle. Marc Kamionkowski Caltech (work done with Michael Kesden, astro-ph/0606566 [PRL], 0608095) 20 September 2006. Aristotle (384-322 B.C.): Heavier things fall faster. Ioannes Phillipones (~600 AD): Observed objects fall ~same speed.

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Dark Matter and the Equivalence Principle

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  1. Dark Matter and the Equivalence Principle Marc Kamionkowski Caltech (work done with Michael Kesden, astro-ph/0606566 [PRL], 0608095) 20 September 2006

  2. Aristotle (384-322 B.C.): Heavier things fall faster

  3. Ioannes Phillipones (~600 AD): Observed objects fall ~samespeed

  4. Giambattista Benedetti(Venice, 1530-1590): Proposed equality of free-fallrates (1586)

  5. Simon Stevin (Flemish, 1548-1620): Demonstrated equality of free fallexperimentally (1586)

  6. Galileo Galilei (1564-1642): Leaning Tower story probably apocryphal,as arrived in Pisa ~1589, but didexperiments with rolling balls Vincenzo Viviani, b. 1622

  7. Isaac Newton (1642-1727): Principia (1687): 5 of 70 people found the following review helpful: I can't believe people still believe this stuff, September 20, 2005 Reviewer:Jeff "Jeff" (Lakeland, FL, USA) - See all my reviews

  8. Newton : pendulumcomposed of wood, gold, silver,lead, etc. Equivalence of inertialand gravitational mass ~10-3.Later experiments, ~10-5.

  9. Roland von Eotvos (1848-1919):used torsion balance (1889,1908) to demonstrate equivalence to ~10-9. Used rotation of Earthto provide non-gravitationalforce (as opposed to string inpendulum).

  10. Weak equivalence principle: All masses are accelerated the same wayin a gravitational field. Einstein: motion of freely-falling particles aresame in gravitational field and uniformlyaccelerated frame Einstein equivalence principle: laws of physicsare same in any freely falling frame Central underpinning of general relativity

  11. Further improvements (~1960-1970)(Dicke et al., Braginsky et al…..) Replaced Earth’s g by Sun’s g and Earth’s rotationby its orbit around Sun. Achieved ~10-12. Different elements have different (binding energy)/(mass), sohave tested equivalence of freefall for electromagnetic energyand for strong interactions

  12. Munich (1975): Free fall of freeneutrons to ~10-4.

  13. What about gravitational bindingenergy? Strong equivalence principle: Gravitationalbinding energy falls the same way in agravitational field……satisfied by GR,but not some alternatives (e.g., scalar-tensortheories)

  14. Nordtvedt effect (1968): If SEP violated, Moon and Earthfall differently in Sun’s gravitationalfield, affecting Moon-Earth orbit.Tested by lunar laser ranging.

  15. But what about dark matter? So far, all tests have been for g fields dueto baryons and test masses made of baryons Stubbs (1991): Eotvos-like data correlated with Milky Way---different terrestrialmaterials fall similarly in g field due partly(~50%) to dark matter. I.e., baryon-DM forceis still

  16. But does dark matter fall same wayin gravitational field? Does the force law, hold for dark matter as well? And if how would we know?

  17. Usual DM tracers (e.g., rotation curves,lensing) probe DM mass distribution only. If Gdm were different, could scale velocitydistribution, in accordance with virial theorem,to self-consistently obtain same massdistribution.

  18. Is Gdm=G? Why bother asking? • Curiosity….a fundamental prediction of GR • Cosmic acceleration suggests gravity may be more complicated than we thought and/or that there may be new long-range interaction associated with newscalar fields • E.g., new 1/r2 force law for DM introduced in stringtheories (Gubser, Peebles, Farrar) • Has been suggested to account for voids (Peebles,Gubser, Nusser), requiring new force law comparablein strength to gravity • May occur in “chameleon” DM theories (Khoury, Mota, Shaw…)

  19. E.g., if  is scalar field with coupling to(fermionic) DM particle  through Yukawainteraction, , leads to additionaldm-dm static potential, Leading to an effective with For distances

  20. How can we measure Gdm? Frieman-Gradwohl (1992): galactic halos in clusterswould appear “heavier” in dynamical measurements, but effect degenerate with mass Mainini-Bonometto (2006): discussed baryon lossfrom clusters, but is nasty We considered: galaxies and their DM halos wouldbe accelerated differently in cluster, giving rise to relative acceleration between galaxy and its halo. Ifstrong enough, galaxy would get stripped from halo.But is nasty theoretically/observationally.

  21. Instead, consider tidal streams of Sagittarius dwarf: • Sgr is DM dominated so acts as DM tracer of MilkyWay potential, while stripped stars act as baryonictracers. • Streams are long-lived and now well-observed with2MASS and SDSS • Detailed simulations compared with observationsalready provide remarkably precise constraints to Sgrmass, M/L, orbit, and Milky Way halo (e.g., Law,Johnston, Majewski 2005)

  22. Majewski et al. 2003

  23. Where do tidal streams come from?

  24. What we anticipated: Orbits of streams with EP-violation would differ from those without…. What we found, is different, more striking, and inretrospect, easily understandable: If Gdm > G, DM halo of Sgr accelerated toward MWmore strongly than stellar Sgr. Stars in Sgr are thusdisplaced to larger MW radii, and thus leak out of Sgrat apocenter only from the far side, and not the near side,leading to a trailing tail, but no leading tail.

  25. Simulations: • Modified GADGET-2 to include different Gdm • Include active disk, bulge, halo • Initial conditions from GALACTICS (Dubinski-Widrow) • Use same mass distn for Sgr DM and stars • 300,000 particles, 10K each for bulge and disk,80K for halo, and 200K for satellite • Runs for several orbits on CITA cluster

  26. Stellar Streams of Sgr Dwarf

  27. Leading-to-Trailing Stream Ratios • Attractive force suppresses leading-to-trailing ratio CurveColor Standard black Prograde red Retrograde green Planar orbit blue Heavy disk cyan Massive Sgr magenta

  28. Conclusions • Sgr tidal streams provide lab for testing 1/r2 force law for dark matter • Stronger force law for DM leads to depletion of leading tidal stream of Sgr dwarf • Such an effect difficult to mimic by changing Sgr, MW masses, orbital parameters, etc. • Conservative “by-eye” comparison with observation of roughly equal leading and trailing stream constrains DM force law to be within ~10% of that for baryons • Estimate ~1% sensitivity with more detailed comparisons of data with model

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