# Harvard Astronomy 201b

## Magnetic Fields and Spiral arms in M51

In Uncategorized on March 24, 2011 at 9:54 pm

Paper Discussion by Gongjie Li

Read the Paper by Fletcher et al. (2011)

ABSTRACT

We use new multiwavelength radio observations, made with the VLA and Effelsberg telescopes, to study the magnetic field of the nearby galaxy M51 on scales from 200 pc to several kpc. Interferometric and single-dish data are combined to obtain new maps at λλ3, 6 cm in total and polarized emission, and earlier λ20 cm data are reduced. We compare the spatial distribution of the radio emission with observations of the neutral gas, derive radio spectral index and Faraday depolarization maps, and model the large-scale variation in Faraday rotation in order to deduce the structure of the regular magnetic field. We find that the λ20 cm emission from the disc is severely depolarized and that a dominating fraction of the observed polarized emission at λ6 cm must be due to anisotropic small-scale magnetic fields. Taking this into account, we derive two components for the regular magnetic field in this galaxy; the disc is dominated by a combination of azimuthal modes, m = 0, 2, but in the halo only an m = 1 mode is required to fit the observations. We discuss how the observed arm–interarm contrast in radio intensities can be reconciled with evidence for strong gas compression in the spiral shocks. In the inner spiral arms, the strong arm–interarm contrasts in total and polarized radio emission are roughly consistent with expectations from shock compression of the regular and turbulent components of the magnetic field. However, the average arm-interam contrast, representative of the radii r > 2 kpc where the spiral arms are broader, is not compatible with straightforward compression: lower arm–interarm contrasts than expected may be due to resolution effects and decompression of the magnetic field as it leaves the arms. We suggest a simple method to estimate the turbulent scale in the magneto-ionic medium from the dependence of the standard deviation of the observed Faraday rotation measure on resolution. We thus obtain an estimate of 50 pc for the size of the turbulent eddies.

1) Brief introduction on M51:

M51, the whirlpool galaxy is a spiral galaxy, which is 23+-4Mly away from us. It was the first external galaxy where polarized radio emission was detected and one of the few external galaxies where optical polarization has been studied.

2) Main points of the paper:

1. The authors mapped the polarized emission of M51
2. The authors used Faraday rotation and depolarization to introduce a new method to estimate the size of the turbulence cell
3. The authors fit the polarization angles using a superposition of azimuthal magnetic field modes. They noticed the difference in the dominate modes in the disk and the halo of M51.
4. The authors calculated the arm and interarm contrast in B field, and gave an explanation to the long standing arm and inter-arm contrast problem.

In detail…

1) The M51 maps

The authors compared the arm inter-arm contracts of gas with magnetic fields, and discussed for the first time the interaction of the magnetic fields with the shock fronts in detail. The polarization of the light is obtained using the stoke parameters (covered in Ay150).

As shown in fig 1, the emission at wavelength = 3cm and 6cm, correspond with the optical spiral arms, and as shown in fig 4, the polarized radio emission correspond with the CO line emission. Because shock compresses gas and magnetic fields (traced by polarized emission), then molecules are formed (traced by CO), and finally thermal emission is generated (traced by infrared). There are systematic shifts between the spiral ridges seen in polarized and total radio emission, integrated CO line emission and infrared. (For more details, see Patrikeev et al. 2006)

Magnetic field strength is calculated using the synchrotron radiation. Specifically, the authors assume equipartition between the energy densities of the magnetic field and cosmic rays, a proton-to-electron ratio of 100 and a path-length through the synchrotron-emitting regions of 1 kpc, estimates for the total field strength are shown in Fig. 8, applying the revised formulae by Beck & Krause (2005)

2) Faraday rotation and depolarization

Faraday depolarization is caused by Faraday dispersion due to turbulent magnetic fields. The authors introduce a new method to estimate the size of the turbulence cell using Faraday depolarization.

The Rotation measure dispersion within a beam of a linear diameter D is related to the dispersion within a cell by: $\sigma_{RM, D} \simeq N^{1/2} \sigma_{RM}=\sigma_{RM} \frac{d}{D}$, where d is the size of the cell and D is the diameter. Because the internal Faraday dispersion within a cell is determined by turbulence in the magneto-ionic interstellar medium, the dispersion within a cell can be determined as the following: $\sigma_{RM} = 0.81\langle n_e \rangle Br(Ld)^{1/2}$, where Br is the strength of the component of the random field along the line of sight, L is the total path-length through the ionized gas (see details in Burn 1966; Sokoloff et al. 1998).

Combining these two equations, the size of the turbulence cell can be determined:

$d\simeq[\frac{D \sigma_{RM, D}}{0.81\langle n_e \rangle Br(L)^{1/2}}]^{2/3}$

or $d \simeq 50pc(\frac{D}{600pc})^{2/3}(\frac{\sigma_{RM, D}}{15rad m^2})^{2/3}(\frac{\langle n_e \rangle}{0.1cm^3})^{-2/3}(\frac{Br}{20\mu G})^{-2/3}(\frac{L}{1kpc})^{-1/3}$.

The authors estimated the turbulent cell to be 50pc.

3) Regular magnetic field structure

Fit the polarization angles using a superposition of azimuthal magnetic field modes exp(imf) with integer m, where f is the azimuthal angle in the galaxy’s plane measured anticlockwise from the north end of the major axis. The authors found that in the disc, the field can be described as a combination of m=0, 2 and in the halo, the field can be described as m=1. The origin of the halo field is unclear.

4) Arm-interarm contrast

Arm-interarm contrast in the strength of B field is a long-standing problem.

1970: Roberts and Yuan suggested that magnetic field increase in proportion to the gas density at the spiral shock.

1988: Tilanus et al. noticed that from observation, synchrotron emitting interstellar medium is not compressed by shocks.

1974 and 2009: Mouschovias et al. (1974),  and Mouschovias et al. (2009) suggested that only a moderate increase in synchrotron emission is expected due to the Parker instability (instability caused by the magnetic fields and the cosmic ray), so the magnetic fields should be compressed in loops with a scale of 500-1000pc. However, no observations of the periodic pattern of loops are found.

In this paper, the arm-interarm contrast in gas density and radio emission was compared to a model where a regular and isotropic random magnetic field is compressed by shocks along the spiral arms. The inner arms region, where r<1.6kpc is consistent with the model, however, the region where r>2kpc is not consistent with the model. The authors argue that it is because the random field is isotropic in the arms, but the random field becomes anisotropic due to decompression as it enters the interarm in the outer regions, which produce an increase in polarized emission in the interarm region.

2. (From Drain)

Influence of magnetic fields:

The ratio of the magnetic energy density to the kinetic energy density is (va/sigv)2 where, va is the Alfven speed (B/sqrt(0) and sigv is the 3-dimensional velocity dispersion. If the magnetic energy density is comparable to the kinetic energy density, the magnetic field is contributing significantly to supporting the cloud against self-gravity. Then virial equilibrium equation underestimates the mass. However, the mass estimates only increase by a factor of square root of 2. No qualitative changes will be made

Detection of magnetic fields:

a) Zeeman effects

Measuring the splitting of a spectral line into several components in the presence of a static magnetic field

Examples: Crutcher et al. (2010)

b) Chandrasekhar-Fermi method

Measuring the dispersion in directions of polarization over the map (if magnetic field is strong enough to resist substantial distortion by the turbulence, dispersion is small)

Examples:

Disadvantage:

Local effects due to the magnetic field smeared along the line of sight, so that the net magnetic field is underestimated if the magnetic field were “tangled”.

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