1. Improved Model of Spinning Dust Emission and Implications Thiem Hoang (UW-Madison) in collaboration with Alex Lazarian (UW-Madison), Bruce T. Draine (Princeton)

2. 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

3. Motivation: Precision Cosmology K band (23 GHz) Understanding Galactic Foregrounds cleaning LAMBDA Spergel et al. 2003

4. 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)

5. What are small dust grains? PAHs Disk-like shape (DL98 model) Irregular shape!

6. Step 1: Grain Precession PAH modeling DL98 model μ 1D rotation Grain wobbling our new model μ Grain precession a2a2 a1a1 Ĵ θ a3a3 μ HDL10

7. Spinning Dust: Power Spectrum Ĵ  Torque-free motion: Euler angles ϕ, ψ, θ, and rates  Electric dipole moment:  Fourier Transform:  Power Spectrum: a2a2 a1a1 Ĵ θ a3a3 μ a3a3

8. Power Spectrum  Precessing grain radiates at frequency modes:  Dominant modes: What makes dust grain rotating? DL98 ω/(J/I 1 )1

9. Rotational Damping and Excitation ion H (R~ 10 -7 /s) H PAH IR emission (~10 2 s after UV absorption) UV photon (R~10 -8 /s)

10. 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 f J  Emissivity per H atom: 

11. Emission Spectrum  Peak emissivity increases by a factor ~2.  Peak frequency increases by factors ~1.4 to 1.8. DL98 our result DL98 HDL10

12. Step 2: Irregular Shape What is the effect of irregular shape? Disk-like shape, (DL98) Irregular shape!

13. Power Spectrum  Multiple frequency modes: where denotes time averaging. a1a1 μ J DL98 HLD11

14. Emission Spectrum  Working model: Simple irregular shape  Irregularity: η=b 3 /b 2 case 1 (μ 1 =μ/3 1/2 ) η=b 3 /b 2

15. ★ Emissivity increases with η ★ Emissivity increases with T vib

16. Dobler, Draine & Finkbeiner 2009 CMB5 Constraining Physical Parameters: Fitting to WMAP data

17. Fitting to Hα-correlated spectrum  Model:  Minimizing  Fitting parameters: F 0 : e temperature Sd 0 : variation of PAH abundance C 0 : CMB bias  Spinning dust parameters: n H, dipole moment β 0

18. 20 40 100 ★ F 0 =0.09  T e ~ 2500K (Dong & Draine 2011 explain low T e ) ★ Sd 0 =0.06  PAH depleted in WIM ★ Dipole β 0 ~ 0.65 D, n H ~0.11 cm -3

19. 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 a1a1 μ Thank you! J

20. Thermal Dust-Correlated Spectrum ★ T 0 =0.8 ★ Sd 0 ~ 0.9 ★ β 0 =0.95 D,n H ~10 cm -3