|
Polarization:
-------------------------------
(reference book:
The Theory of Atomic Structure and Spectra
(Los Alamos Series in Basic and Applied Sciences, 3, 1984) (Hardcover)
by Robert D. Cowan (Author)
amazon book: new US$ 90.00, used US$54.80, link
to its amazon page.)
-------------------------------
 | Use Zeeman effect to measure interstellar
magnetic fields: (B// and B-|, from Kochukhov et al., 2004A&A...414..613K)
 | B//: A longitudinal
magnetic field splits spectral lines into oppositely-polarized
sigma components which results in a variation
of circular polarization across the line profile. This is
commonly referred to as a (Stokes V) Zeeman signature or magnetic
signature. The amplitude and morphology of the Zeeman signature
encode information about the strength and structure of the global
magnetic field. |
| B-|: A transverse
magnetic field splits spectral lines into oppositely-polarized
pi and sigma components which results in a variation
of linear polarization (characterized by Stokes
Q and U) across the line profile. |
|
| Use Hanle effect to measure magnetic fields:
...
| The critical magnetic field strength (in
unit of G) for Hanle effect to take effect is BH =
1.137x10^-7 / t_life / g, where t_life
is the radiative lifetime of the upper level of a spectral line, g is the Lande factor. |
| Although the g factor of molecular lines is usually much smaller than
that of atomic lines, the lifetime of molecular levels are usually much
longer, as a result, both molecular and atomic
lines have similar critical magnetic field strength for Hanle effect.
E.g., BH = 23 G for Sr I 4607 A line, while BH = 8 G for C25161.84 A
line. |
| To detect weak turbulent magnetic fields (like that in the quiet sun),
we need differential Hanle effect method:
obtaining field strength by observing polarization ratios in various
molecular lines. |
|
| Use pulsars to measure interstellar magnetic
fields: (B//, from Wikipedea pages: Pulsar, Dispersion, and Faraday effect)
| For interstellar medium where free electrons causes the Faraday rotation, the rotation angle (beta) is simply dependent upon the wavelength of
emission (lambda): beta
= RM * lambda^2, where RM is the rotation
measure that is related to the electron column density and
magnetical field strength as RM = e^3/(8pi^2 e0
m^2 c^3) * int_0^d{ne*B} = 2.62x10-13 int_0^d{ne*B}. Here RM is
in rad/m^2, B is in tesla (T), ne is electron density in m^-3. |
| Due to the dispersion property of the interstellar electron gas, the
pulsar timing delay (D) caused by the
electron gas is simply related to the radiation frequency (nu) as: D = 4.15ms *
(nu/GHz)^-2 * (DM/cm^-3pc), where DM is the dispersion
measure DM = int_0^d{ne}. |
| RM/DM gives a measure of the mean interstellar magnetical field between the pulsar and us. |
| RM is positive
when the rotation is anticlockwise (L-rotation), in which case the B field is parallel to the radiation propogation direction;
RM is negative when the rotation is clockwise (R-rotation),
in which case the B field is anti-parallel
to the radiation propogation direction. |
|
| Use Goldrech-Kylafis effect to measure
interstellar magnetic fields: ... (Goldreich & Kylafis, 1981ApJ...243L..75G,
1982ApJ...253..606G) |
| Use synchotron emission to measure interstellar
magnetic fields: (B|-) ... |
| Use dust polarization to measure interstellar
magenetic fields: (B|-) ... |
| Use star light polarization to measure
interstellar magenetic fields: (B|-) ... |
| They formulated the polarization of atomic
absorption lines caused by atomic alignment
in anisotropic incident radiation field and realignment
in magnetic field. They only confined their formulation to atoms (ions) with fine structure levels in the ground
electronic state. Simultaneous observation of several absorption lines allow
us to determine 3-D magnetic filed
distribution.They also gave a review of all
currently known methods to estimate magnetic field strength, and
gave a introductory summary
of many basic concepts related to atomic structure and spectrum
in their appendices. (from Yan & Lazarian, 2006ApJ...653.1292Y) |
| More atoms (ions) with hyperfine structure levels are
formulated to detecte magnetic field through their absorption and emission
lines. (from Yan & Lazarian, 2007ApJ...657..618Y) |
| They developed the atomic realignment technique into stronger
B field case where they consider the Hanel
effect modified by the atomic alignment in the ground state. It can
be applied to circumstellar and accretion disks.
(from Yan & Lazarian, 2008ApJ...677.1401Y) |
| Linear polarization simulation of accretion flow/wind of T Tauri stars:
Implication for spectropolarimetry observations. (from Lunch box talk by Dr.
Dinh-Van-Trung)
| Polarization was detected in T Tauri stars (e.g., RY Tau) and Herbig Ae stars (e.g., MWC 480). By assuming Rayleigh
scattering by electrons in the ionized regions in the environments
around a young star (accretion disk, accretion flow, accretion shock region,
X wind, circumstellar envelope, etc.), he explored the appearance of the
polarized emission region and its connection to the spectropolarimetry
observations. For Rayleigh scattering, when the
scattering angel is 90 degree, the scattered light is assumed to be
completely linearly polarized with the polarization direction perpendicular
to the source direction; when the scattering angle is zero, no polarization
happens. Discussed quantities are I, Q, U, the stokes parameters defined as
normal: I is the total line intensity, Q = Ip - Ih (with Ip
and Ih the vertically and horizontally polarized components), U = I45 - I-45 (with I45
and I-45 the components polarized along 45 degree and -45 degree
direction). |
|
|
(from ALMA example project) Polarization of a
molecular line can be either perpendicular or parallel to the
magnetic field line. But the polarization produced by
dust grain alignment in matinetic field is always perpendicular to
the B field line. |
|
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