Dark Energy Equation of State from Baryonic Acoustic Oscillations: An Interpretive Dance Approach

1. Dark Energy Equation of State from Baryonic Acoustic Oscillations:An Interpretive Dance Approach Peter Mendygral Steven Warren Cosmology December 4th, 2006 Astronomy 5022

2. Dark Energy Equation of State from Baryonic Acoustic Oscillations Peter Mendygral Steven Warren Cosmology December 4th, 2006 Astronomy 5022

3. Dark EnergyThe Story Begins… • Mid-1990’s • Brian Schmidt Astronomy 5022

4. How? • Type-Ia Supernova • Figured out Relationship between absolute magnitude and light curve decline time • Plot Redshift vs. Distance Astronomy 5022

5. Dark Energy Astronomy 5022

6. Astronomy 5022

7. Astronomy 5022

8. Dark Energy Dark Energy First hypothesized after the discovery of the accelerating universe. Reiss et al. 1998 Negative pressure P = wρ but w < -1/3 for an accelerating Universe Astronomy 5022

9. Dark Energy Astronomy 5022

10. What is Dark Energy? • Short answer: Nobody knows. • Baryonic Acoustic Oscillations Astronomy 5022

11. Baryonic Acoustic Oscillations (BAOs) • Story of oscillations begins in same environment as CMB temperature fluctuations • Baryons and photons are coupled through EM interactions => baryon-photon fluid • Baryon-photon fluid resides in cold dark matter potential wells • Fluid oscillates in these potential wells Astronomy 5022

12. Baryonic Acoustic OscillationsThe Oscillations • Attractive force is gravity • Restoring force is photon pressure • Thompson scattering • Compton scattering http://background.uchicago.edu/~whu/beginners/introduction.html Astronomy 5022

13. Baryonic Acoustic OscillationsIt’s frick’n freez’n • Photon pressure information is propagated through fluid at the sound speed, cs • As the fluid cools and expands the density goes down • Optical depth increases and photons and baryons start decouple • Decrease in density also decreases cs Astronomy 5022

14. Baryonic Acoustic OscillationsIt’s frick’n freez’n • As the baryon-photon fluid begins to decouple, some oscillations are won out by gravity and begin to collapse • Oscillations that maintained sound speeds sufficient to allow pressure waves to propagate quickly enough to counteract gravity survive • These guys are “frozen out” Astronomy 5022

15. Baryonic Acoustic OscillationsIt’s frick’n freez’n • Surviving oscillations, at later times, produce additional oscillatory patterns • Oscillations driven by velocity overshooting • Damping driven by • Silk damping • Prior to last scattering, photons diffuse from high to low density regions • Photons drag (via Compton scattering) matter with them • Gravitational drag • Expansion drag Astronomy 5022

16. Baryonic Acoustic OscillationsIt’s frick’n freez’n • The amplitude of these oscillations are determined by the ratio of baryonic matter to overall matter • Combination of oscillations produces a pattern of oscillating substructures superposed with a larger fluctuating density field Astronomy 5022

17. Baryonic Acoustic Oscillations • Amplitude of oscillations reduced by the drag affects, but phase of oscillations unaffected • Matter power spectrum through varying values of Ωb http://background.uchicago.edu/~whu/transfer/baryon.html Astronomy 5022

18. BAOs to Dark Energy • How can we use BAOs to arrive at the dark energy equation of state? • By analyzing matter power spectrum we can deduce the wavelength of the “wiggles” in k-space • We’ll call this wavelength kA Need wavelength of these oscillations Astronomy 5022

19. BAOs to Dark Energy • kA can be obtained through theory by the following steps: • kA can be related to sound horizon at last scattering through • At high redshift, affects of dark energy can be neglected, and s is given by • ar and aeq are scale factors at recombination and matter radiation equality • cs is sound speed (~c/√3) Astronomy 5022

20. BAOs to Dark Energy • A physical distance, x, at a given redshift, z, can be obtained by the following • w, the dark energy equation of state parameter, shows up • A physical distance, therefore depends on the geometry • The value of s, however, depends only on redshift and the known quantities, Ho and Ωm Astronomy 5022

21. Dark Energy EoS Measurement Process • Observations • Make observations of matter distribution at a high enough redshift where dark energy was negligible (e.g. recombination) • Deconstruct matter distribution in Fourier space • Measure k-space wavelength of BAO “wiggles” Astronomy 5022

22. Dark Energy EoS Measurement Process • Theory • Create concordance model simulation of evolving Universe • Make “observations” of redshift and angular size of matter density fluctuations by converting co-moving coordinate size into physical size • Extract “wiggles” in Fourier space • Process is titled FITEX Astronomy 5022

23. Dark Energy EoS Measurement Process • Comparison • Compare kA measured from real observations to kA measured from synthetic observations • Variations off of real kA represent incorrect assumption of w in models • Iterate models to best fit, χ2, to real observations • Process should have accuracies ~68% in the measurement of w Astronomy 5022

24. Complications (as always) P(k) • Power spectrum evolves through several different epochs, all of which transform power spectrum in their own way • The overall transfer function is the sum of each epoch’s separate transfer function k P(k) k P(k) k P(k) k P(k) time k P(k) Williams, L k Astronomy 5022

25. Complications (as always) • Total transfer function is given by sum of non-oscillatory and oscillatory parts • Non-oscillatory (Tc) • Baryons falling into CDM potential wells • Oscillatory (Tb) • (large-scale oscillations) • , the “wiggle function” (small-scale oscillations) Astronomy 5022

26. Complications (as always) • We want to isolate to extract kA • All other components of transfer function must be removed from observation • Other components dependent only on s, Ωc, Ωm and Ωb • Every component is based on known and understood physics Non-oscillatory total non-oscillatory oscillatory Astronomy 5022

27. Theory to Observation • What we need now is a real data set to run through this framework • The data set should be • Survey of galaxies at redshift z = 1 and z = 3 • Multiple redshifts allow us to test for a possibility of a w(z) • Several thousand galaxies over a wide field of view • Reduce statistical errors Astronomy 5022

28. Observational Methods • Many Proposed Dark Energy Experiments • LSST, SNAP, KAOS, DES, VIRUS • Basic Idea: • Measure spatial geometry of the Universe Astronomy 5022

29. VIRUS(Visible IFU Replicable Ultra-cheap Spectrograph ) • Atop the Hobby-Eberly 9.2-m telescope • 132 fiber-fed spectrographs • (132 CCD cameras) • ~29 arcsec^2 FOV • Only ~100 nights • ~$10 mil Astronomy 5022

30. VIRUS • Take Spectra of Lyman-α Galaxies at 2 < z < 4 • Need ~ 500,000 galaxies • Will get ~ 10^6 • Measure z • Find Power Spectrum • BAO…etc Astronomy 5022

31. Cosmological Importance • Dark energy is an essential source of job opportunities for aspiring cosmologists Astronomy 5022

32. References • Blake, C., & Glazebrook, K. 2003, ApJ, 594, 665 • Koehler, R., Schuecker, P., & Gebhardt, K. 2006, Astro-ph, 09/2006 • Hill, G. J., MacQueen, P. J., Tejada, C., and Cobos, F., “VIRUS: a massively replicated IFU spectrograph for HET,” in Ground-based Instrumentation for Astronomy. Edited by Moorwood, A.F.M and Iye, M. Proceedings of the SPIE, Volume 5492,, 2004, p. 251. • Hill, G. J., Gebhardt, K., Komatsu, E., and McQueen, P. J., “The Hobby-Eberly Telescope Dark Energy Experiment,” presented at the Mitchell Symposium • http://www.as.utexas.edu/hetdex/ • http://outreach.atnf.csiro.au/education/senior/astrophysics/images/spectra/spectrographschematic.gif • http://www.sciencenews.org/articles/20010407/bob14.asp • http://www.salt.ac.za/content/downloads/stobieworkshops/one/hill/Hill_VIRUS_SALToct03.pdf • http://het.as.utexas.edu/HET/PR/het-cutaway.gif • http://arxiv.org/PS_cache/hep-ph/pdf/0507/0507235.pdf • http://corelli.sdsu.edu/courses/astro301_spring2006/ Astronomy 5022