Improved Model of Spinning Dust Emission and Implications

Thiem Hoang (UW-Madison)

in collaboration with

Alex Lazarian (UW-Madison), Bruce T. Draine (Princeton)

Outline

• Motivation• Galactic Foregrounds to CMB and Anomalous

Microwave Emission (Clive’s talk)• Draine & Lazarian Model (DL98, Alex’s talk)• Improved Model of Spinning Dust • Constraining Physical Parameters using WMAP data• Summary and Future Works

Motivation: Precision Cosmology

K band (23 GHz)

Understanding

Galactic Foregrounds

cleaning

LAMBDA

Spergel et al. 2003

Improved Model of Spinning Dust

Step 1: Improve grain rotational dynamics

-Grain precession, internal relaxation

(Hoang, Draine & Lazarian 2010, ApJ 465, 1602)

Silsbee, Ali-Haimoud & Hirata 2011: Grain precession, no internal relaxation

Step 2: Deal with realistic grain shape

- Triaxial ellipsoid (irregular shape)

- Grain wobbling

(Hoang, Lazarian, & Draine 2011, submitted, ArXiv 1105.2302)

What are small dust grains? PAHs

Disk-like shape

(DL98 model)

Irregular shape!

Step 1: Grain Precession PAH

modeling

DL98 model

μ

1D rotation

Grain wobbling

our new model

μ

Grain precession

a2

a1

Ĵ

θ

a3

μ

HDL10

Spinning Dust: Power Spectrum

Ĵ

Torque-free motion: Euler angles ϕ, ψ, θ, and rates

Electric dipole moment:

Fourier Transform:

Power Spectrum:

€

˙ θ = 0, ˙ ψ =J cosθ (1− h)

I1

, ˙ φ =JI2

€

rμ(J,θ , t) = μ1

r a 1 +μ 2

r a 2

€

˙ μ i,k = ˙ μ i (t)exp(−i2πν kt)dt0

∞

∫ , i = x, y, z

€

Ped,k (J,θ ) =2

3c3 ( ˙ μ i,k )2

i∑

€

r μ (J,θ , t) = μ1

r ˙ a 1 +μ 2

r ˙ a 2

a2

a1

Ĵ

θ

a3

μ

€

h =I1

I2

a3

Power Spectrum

Precessing grain radiates at frequency modes:

Dominant modes:

What makes dust grain rotating?€

ωk = ˙ φ , ˙ φ ± ˙ ψ , ˙ ψ

€

ωk = ˙ φ ± ˙ ψ

DL98

ω/(J/I1) 1

Rotational Damping and Excitation

ion

H (R~ 10-7 /s)

H

PAH

IR emission (~102 s after UV absorption)

UV photon (R~10-8 /s)

Numerical Method: Langevin Equations

Angular momentum J in the lab system is described by Langevin equations (LEs):

Integrate LEs to get J(t) and find momentum distribution fJ

Emissivity per H atom:€

dJi = Aidt + Biidqi ,

Ai =ΔJi

Δt∑ , Bii =

(ΔJi )2

Δt, dq2∑ = dt

€

jνa = probmod ω | J( )

mod∑ Ped (J )2πfJ∫ dJ

€

jν

nH

=1

4π1nH

dadnda

∫ jνa

Emission Spectrum

Peak emissivity increases by a factor ~2 .

Peak frequency increases by factors ~1.4 to 1.8.

DL98

our result

our result

DL98

HDL10

Step 2: Irregular Shape

What is the effect of irregular shape?

Disk-like shape,

(DL98)

Irregular shape!

Power Spectrum

Multiple frequency modes:

where <…> denotes time averaging.

€

ωm = ˙ φ + m ˙ ψ , m = 0,±1,±2...,

ωn = n ˙ ψ ,n = 0,1,2

€

q =2I1Erot

J2

€

q =2I1Erot

J2

€

I1 : I2 : I3 =1:0.6 :0.5a1

μ

J

DL98

HLD11

Emission Spectrum

Working model: Simple irregular shape

Irregularity: η=b3/b2

case 1 (μ1=μ/31/2)

η=b3/b2

Emissivity increases with η

★ Emissivity increases with Tvib

Dobler, Draine & Finkbeiner 2009

CMB5

Constraining Physical Parameters:Fitting to WMAP data

Fitting to Hα-correlated spectrum

€

Iνmod = F0

ν23GHz

⎛ ⎝ ⎜

⎞ ⎠ ⎟−0.12

+ Sd0

Iνsd

IHα

⎡

⎣ ⎢

⎤

⎦ ⎥

WIM

+C0

ν23GHz

⎛ ⎝ ⎜

⎞ ⎠ ⎟2

€

χ 2 = Iνmod − Iν

obs( )

ν∑

2/σ ν

2

Model:

Minimizing

Fitting parameters:

F0: e temperature

Sd0: variation of PAH abundance

C0: CMB bias

Spinning dust parameters: nH, dipole moment β0

20 40 100

★ F0=0.09 Te~ 2500K (Dong & Draine 2011 explain low Te)

★ Sd0=0.06 PAH depleted in WIM

★ Dipole β0~ 0.65 D, nH ~0.11 cm-3

1. Improved model accounts for wobbling grain, irregular shape

internal relaxation, transient events.

2. Improved model can reproduce high peak frequency in Hα-correlated spectrum from WMAP data.

3. Improved model can be used to diagnose dust physical parameters.

4. Future works will address polarization from spinning dust and implications to B-mode of CMB polarization experiments.

Summary and Future Works

DL98

J

μ

a1

μ

Than

k yo

u!

J

Thermal Dust-Correlated Spectrum

€

Iνmod

T94GHz

= Sd0

Iνsd (CNM)T94GHz

+C0

ν23GHz

⎛ ⎝ ⎜

⎞ ⎠ ⎟2

+T0

ν94GHz

⎛ ⎝ ⎜

⎞ ⎠ ⎟3.8

★ T0=0.8

★ Sd0 ~ 0.9

★ β0=0.95 D,nH ~10 cm-

3