Download Estimation of Magnetic Field Strength in the Turbulent Warm

Estimation of Magnetic Field Strength in
the Turbulent Warm Ionized Medium
Qing-wen Wu
吳慶文
Korean Astronomy and Space Science Institute
Collaborators:
Jongsoo Kim (KASI), Dongsu Ryu (CNU) Jungyeon Cho (CNU)
Wu et al. 2009, ApJ Letter, under review
Outline (15 pages)
• Self-introduction (1 pages)
• Introduction (5 pages)
Observations on ne and B in WIM, questions from observations, and aim of our work from simulation
• Numerical Method (1 pages)
• Results and Discussions (7 pages)
Relation between ne and B in WIM, bias problems in B estimation, new methods for B estimation
.
• Conclusion and Future-work (1 pages)
0. Self-introduction
Turbulence
1. 2002.9-2007.6: Ph.D - Shanghai Astronomical Observatory, Chinese Academy of
Science
XRBsin black hole systems
Major: Accretion-Ejection
AGNs
2. 2007.7-present: Postdoc - Korea Astronomy and Space Science Institute
Research activities:
(I) MHD simulation on WIM and magnetic field
GRBs
Wu, Kim, Ryu,
Jet-ISM interaction
on & Cho, ApJL, submitted, and In-preparation
kpc scale?
(II) Observational phenomena in high energy objects (e.g., AGNs, XRBs, ULXs, or
FRII
even GRBs. Unification of BH systems?)
Wu & Gu, ApJ, 2008;
Wu & Cao, ApJ, 2008;
Xu, Cao &Wu, ApJL, 2009 FRI
(III) Accretion-Ejection and feedback (kpc-scale narrow line kinematics, star formation,
and… next may be also galaxy evolution)
Wu, MNRAS, 2009; Wu, ApJL, 2009; Wu, Gu, & Humphrey, Sci. in China-G, 2009
I.
Introduction
• Interstellar Medium in galaxies: complex and multi-phases
Cold neutral medium (80K/40cm-3), warm neutral medium
(8000K/0.4cm-3),warm ionized medium (8000K/0.1cm-3), hot ionized
medium (106K/0.003cm-3).
dust grains, cosmic ray, magnetic field, etc.
• Warm Ionized Medium (WIM) or Diffuse Ionized Gas:
WIM is the major component in our galaxy with temperature ~
8000K, density~0.08 cm-3 , and occupy~20-40% of the volume of a
scale height of ~1 kpc layer about the galactic plane.
1.1 Observational tracers of density in WIM
• Emission Measure:
Hα Map=37, 565 Hα Spectra
Haffner et al. 2003
• Dispersion Measure:
Due to travel through ionized ISM, the pulse signals(emitted by a pulsar) will
suffer dispersion. The time delay at two different frequencies is proportion to
DM.
• Therefore, we can know
(1) Characteristic density: < ne >=EM/DM
(2) Characteristic size: L~DM 2/EM
(2) Fluctuations of EM and/or DM (e.g., power spectra, structure
function)
1.2 Observational tracers of magnetic field in WIM
• Magnetic field: complicated structure ~regular(uniform)+irregular (random)
• Magnetic field measurement techniques:
1) Zeeman splitting--------dense gas(e.g., molecular cloud)
2) polarization of starlight
3) polarized thermal emission from the dusts in cloud
4) synchrotron radiation (intensity &polarization )
WIM
5) Faraday rotation of polarized radiation(B//)
Open: RM<0
Filled: RM>0
NGC 4631
Han et al.97
•
Magnetic field from Rotation Measure (
B//
WIM
) and DM
M51 Beck2 009
NGC 891
1.3 Density and Magnetic field estimates in our galaxy-MilkWay
• Typical volume-averaged density: n0~(20-40%)*0.08~0.02-0.03 cm -3
Han et al. 2002
• Magnetic field in WM: structure & strength
Syn emission imply Btot~6+_2 uG
Breg~4uG
Syn polarization imply Breg/Btot~0.6
(local field)
However, Faraday rotation of local field imply Breg ~ 1.4-1.7 uG,
which is smaller than that derived from other method!!
Where is the problem?????
•
Two possible reasons:
(1) Bias in the estimation of the Breg from the RM.
ANTI-correlation of ne-B???  underestimate the B (Beck et al. 2003)
This is possible if the pressure is constant in WIM ( B*B + ne = constant).
POSITIVE correlation of ne-B  overestimate the B
Wielebinski et al.
2005
Han et al. 2006
(2) Observational bias:
RM is proportional to B, while Syn. Intensity is proportional to B2,
so, Syn. may biased to dense region (stronger B) , while RMs can detected even in thin region
with weaker B).
1.4 Aim of our work
• Observation gives estimates of density, magnetic field (random +
regular), and also the RM, EM, DM fluctuations (e.g., power spectra
and/or structure function).
Can we give constraints on the physical models in WIM from
observations? Or else, can we use the MHD simulations to help us
understanding the observations?
• Evidence for WIM in a turbulent state
a) Density power spectra in local ISM
b) Log normal Distribution of H_alpha Emission
Composite power spectra from
RM, DM , etc.
Power law, with spectral index
similar to that of Kolmognov
Value
--- Armstrong et al. 1995 Nature
----Hill et al. 2008
• We research these problems through 3-D turbulent MHD simulations,
and try to investigate the possible relation between ne and B, and
distribution of ne, B, RM, EM, DM and their fluctuations.
II. Numerical Method
We performed 3D numerical simulations for the turbulent, magnetized
WIM. We solved the isothermal MHD equations using a code based on a total
variation diminishing methods, which is a second-order-accurate upwind
scheme (Kim et al. 1999).
The initial B is in X-direction in Cartesian coordinates, and grids number
N=5123. We add the velocity perturbations to generate a turbulent flow.
Two free parameters in simulations:
(1) Mach number: V(Halpha)~30km/s~thermal~20km/s+turbulent~13km/s.
Te~8000K, Cs~10km/s, then we Mach=Vt/Cs~1 for WIM.
Mach=0.5 and 2 (N=5123) are ongoing, low resolution N=2563
have been worked out.
(2) Magnetic beta value=Pg/Pm, we choose beta0=0.1, 1, 10, 100
for initial values, which are correspond to 4.1, 1.3, 0.41, 0.13 uG
if we using typical value ne~0.03cm-3 and Te~8000K.
III. Results and Discussions
3.1 The relation between B and density
• Contours of 2D histograms
• No strong positive correlations or
anti-correlations for both strong and
weak magnetic cases.
• Correlation coefficient
beta
0.1
1
Mach=0.5
-0.02
-0.12
Mach=1
0.004
Mach=2
0.08
-0.15
0.12
10
-0.07
-0.07
0.27
Mach=1
100
N=2563
0.16
N=2563
• Total pressure equilibrium in WIM?
---enable Beck (2003) to predict anti-correlation.
Mach=1
• Ptot is not a constant, the histogram become wider as magnetic field
increases (or beta decreases).
• Therefore, there is no simple complete anti-correlation or positive
correlation between magnetic field and density.
3.2 Magnetic field estimates based on simulations
Mach=1
Solid line: intrinsic
magnetic field strength
Dotted line: derived
from
• No strong bias. It should be the similar case for Mach=0.5 and 2.
•
The B// estimated from RM is less than that estimated from other methods
(e.g., Syn, or cosmic ray etc.), which may also caused by the other reasons,
for example--observational bias, since that Syn. emissivity (B2) are biased
toward dense regions.
3.2 Rotation Measure Image and Constraints on B
•
Rotation measure image—X-direction
Mach=1
Power spectra slope (1D)
beta
0.1
1
10
RM_x
-0.32
-1.19
- 1.35
- 0.76
RM_y
-1.38
-1.22
-1.09
-0.79
RM_z
-1.39
-1.29
-1.20
-0.69
Mach=0.5
beta_0=
0.1, 1, 10
•
•
100
Mach=2
beta_0=
0.1, 1, 10
The RM/RM0 dynamic range is increases as beta increases, and increases as Mach number
increases.
The morphology and statistics are affected by Mach number and the underlying magnetic fields.
• Probability distribution of RM histograms
Breg
Solid lines: Histogram
Dashed line: Gaussian fittings
•
The RM histogram can be well fitted by Gaussian profile, which is consistent
with the observations (Haverkorn et al. 2003).
•
The width of histogram is related to the underlying magnetic field (viewing angle
dependent).
• Relation bewteen B0// – WFWHM based on simulation and Applications
FWHM is full width of half maximum of the probability distribution.
Mach=1
This correlation provide us a convenient
method to estimate the Breg along
sightline.
B0//~-0.4uG
B0//~-0.08uG
n0 =0.16 is adopted
Auriga
Horologium
Assume n0 =0.03 , our methods gives
Horologium: B0//~-0.18uG
Auriga: B0//~-0.92uG
Consistent very well!
Primary results on B0// – WFWHM for cases of Mach=0.5 and 2
IV. Summary & Future work
•
In turbulent WIM, there is no strong correlation between B and ne with mach=0.5,
1, and 2. The magnetic field strength estimated from the rotation measure and
dispersion measure is roughly consistent with the intrinsic values, NO strong
BIAS.
•
The histogram of the RM can be well fitted by Gaussian function.
•
The width of the RM histogram is sensitive to the underlying magnetic fields
(B0// ), which provide a possible methods to estimate the magnetic field strength in
the WIM.
------• Calculate the power spectra of RM, DM,EM, etc. and compare with observations.
•
Calculate the random/regular magnetic field and compare with observations.
•
How about <Ne> distribution (or EM, DM) affected by Ms and magnetic field?
e.g., Hill et al. 2008
…
Rotation Measures in the Milky Way
Pulsars to be
detected with
the SKA
(Cordes 2001)