Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Shane Spivey University of Texas at Arlington PANIC11 Conference at MIT, July 26, 2011 Motivation for Quantum Cold Dark Matter Mass constraints using empirical data Self-Consistent QCDM Equation Addition of External Potentials Current and Future Work Newtonian Dynamics: Observed Galactic Dynamics: MaCHOs RAMBOs WIMPS Neutralinos Axions Merits: Can explain structure formation Can account for gravitational lensing Problems: CDM simulations produce cuspy cores CDM predicts more dwarf galaxies than are observed Solution: Quantum Cold Dark Matter? Also called ‘Fuzzy’ CDM or Extremely Light Bosonic Dark Matter (ELBDM) Extremely small mass, ~1e-25 eV Scalar particle Compton wavelength ~100 pc DM density @ Earth ~ 1e-25 g/cm^3* Interparticle distance ~ 10^-13 cm* Overlapping wavefunctions => Bose liquid* Described by Schrodinger equation * Sang-Jin Sin, Phys. Rev. D 50, 3650 (1994) Select density profiles for galactic halos and find the corresponding gravitational potentials. Solve the Schrödinger equation for each potential with the requirement that the resulting probability distribution has the same median. Assumptions: Particles are bosons in the ground state. Contributions of luminous matter are neglected. Schrodinger Equation: 𝑢′′ 𝑟 = 2𝑚 𝑉 𝑟 − 𝐸 𝑢(𝑟) ℎ2 Gravitational Potential: 1 𝑉 𝑟 = −4𝜋𝐺𝑚 𝑟 𝑟 ∞ ′2 𝑟 𝜌 𝑟 𝑑𝑟 + 0 𝑟 Median (half mass) Equation: 𝑟𝑒 2 𝑢 0 ∞ 2 𝑢 0 𝑟′𝜌 𝑟 𝑑𝑟 𝑟 𝑑𝑟 1 = 𝑟 𝑑𝑟 2 Navarro-Frenk-White (NFW) J. F. Navarro, C. S. Frenk, and S. D. White, Astrophysical Journal v.462 p.563 (1996) Modified Isothermal L. Bergstrom, P. Ullio, J.H. Buckley, Astropart. Phys. 9(1998) 137 Einasto Merritt, D., Navarro, J. F., Ludlow, A., and Jenkins, A. 2005, ApJ, 624, L85 Isothermal NFW Einasto ρ(x) V(x) NFW ISO Einasto Realistic limits from observations and simulations of spiral galaxies: M [0.5e12, 2e12] solar masses* R [200, 325] kpc* Particle mass ranges in 1e-25 eV: Einasto: [0.903, 3.61] NFW: [1.23, 1.92] Modified Isothermal: [3.49, 5.47] *A. Klypin et al, ApJ 573 597 (2002) Einasto: [0.903, 3.61] e-25 eV NFW: [1.23, 1.92] e-25 eV Overall mass range [9.03e-26 eV, 5.47e-25 eV ]. Hu et al.* predict a 1e-22eV particle using a method designed to eliminate the cuspy halo core. Sin** suggests a mass of 1e-24eV, with the caveat that the particle cannot be in the ground state. Both papers neglect the comparatively small contribution of luminous matter, as we have. Neither derive the mass of the particle. We have shown that a stable ground state solution is possible for a halo resembling one of several different commonly used density profiles, two of which do not present central cusps. *W. Hu, R. Barkana, and A. Gruzinov. Phys. Rev. Lett. 85, 11581161 (2000) ** Sang-Jin Sin, Phys. Rev. D 50, 3650 (1994) QCDM Axion Neutralino WIMPs ~ 10^-25 eV > 10^-6 eV > 10 GeV > 7-11 GeV Density Relation: 𝜌 𝑟 = 𝑀|(𝑟)|2 Poisson’s Equation: 𝛻 2 𝑉(𝑟) = 4𝜋𝐺𝑚𝜌(𝑟) Schrodinger Equation: 𝑢 ′′ 𝑟 = 2𝑚 ℎ2 𝑉 𝑟 − 𝐸 𝑢(𝑟) Density Relation: 𝜌 𝑟 = 𝑀|(𝑟)|2 Poisson’s Equation: 𝑟 𝑉 𝑟 = 4𝜋𝐺𝑚𝑀 0 1 𝑟′2 𝑟′ 𝑟 ′′ 2 𝑟 ′′ 𝑑𝑟′′ 𝑑𝑟′ 0 Schrodinger Equation: 𝑢 ′′ 𝑟 = 2𝑚 ℎ2 𝑉 𝑟 − 𝐸 𝑢(𝑟) Density Relation: 𝜌 𝑟 = 𝑀|(𝑟)|2 Poisson’s Equation: 𝑟 𝑉 𝑟 = 4𝜋𝐺𝑚𝑀 0 𝑟′ 1 𝑟′2 𝑟 ′′ 2 𝑟 ′′ 𝑑𝑟′′ 𝑑𝑟′ 0 Schrodinger Equation: 𝑑2𝑢 2𝑚 = 2 𝐺𝑚𝑀 2 𝑑𝑟 ℎ 𝑟 0 1 𝑟′2 𝑟′ 0 𝑢 𝑟 ′′ 2 𝑑𝑟 ′′ 𝑑𝑟 ′ − 𝐸 𝑢(𝑟) median: 157 kpc halo mass: 1012 solar masses particle mass: ~1.5 e-25 eV 𝜶 = 𝟏/𝟏𝟎𝟎𝟎 𝜶 = 𝟏/𝟏𝟎𝟎 𝜶 = 𝟏/𝟏𝟎 𝜶=𝟏 𝟏 𝟏 𝜶 = 𝟏, 𝒍 = 𝟐𝟓 𝟏 𝟏 𝜶 = 𝟏, 𝒍 = 𝟓 𝜶 = 𝟏𝟎 , 𝒍 = 𝟐𝟓 𝜶 = 𝟏𝟎 , 𝒍 = 𝟓 𝟏 𝟏 g=0 g=1 median: 157 kpc median: 166 kpc g = 0.1 g = 10 median: 158 kpc median: 223 kpc Examination of QCDM in excited states, including the addition of angular momentum Effects of halos on gravitational lensing Treatment of halo as a Bose-Einstein Condensate Halo Interactions Support for this work provided by the US Department of Education through the GAANN fellowship, and by the University of Texas at Arlington (UTA) Physics Department, the UTA College of Science, and the UTA Graduate School Special thanks to Dr. Zdzislaw Musielak and Dr. John Fry of UTA NASA Hubble image, November 11, 2010 C. G. Boehmer and T. Harko JCAP 0706, 025 (2007)