Download Shane Spivey University of Texas at Arlington

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)