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Interstellar matter. Galaxies

87

Magnetic eld strengths from polarimetric VLBI observations of water masers in W51 M
K. Leppanen1 , T. Liljestrom1, and P. Diamond2
1

Metsahovi Radio Observatory, Helsinki University of Technology, Finland 2 National Radio Astronomy Observatory, Socorro, USA

Introduction
The idea that interstellar magnetic elds are coupled to gas motions was rst discussed by Alfven 1943 and Fermi 1949. Magnetic elds reveal themselves by polarizing radiation. According to the classical maser polarization theory Goldreich et al., 1973a, 1973b, maser polarization is linear if the stimulated emission rate of a saturated maser is smaller than the Zeeman splitting rate, which on the other hand should be smaller than the linewidth of the ampli ed radiation. This is generally the case for water masers. Powerful 22 GHz water masers are commonly associated with energetic protostellar outows. Shocks with velocities exceeding some 20 km s,1 running into high-density magnetized material successfully explain the water maser emission associated with out ows from young stellar ob jects Hollenbach and McKee, 1989; Elitzur et al., 1989. Here we summarize the main results of Leppanen, Liljestrom, and Diamond 1998, who reported the rst 22 GHz linear-polarization VLBI images obtained with VLBA of low-velocity water masers in the star-forming region W51 M. The spatial and spectral resolution obtained were 0.3 milliarcseconds mas and 0.2 km s,1, respectively. The principal di erence of polarimetric VLBI from total intensity VLBI is the need to calibrate the instrumental polarization parameters, which have been solved by Leppanen 1995 with a feed self-calibration algoritm.

Kinematic and linear polarization structure of water masers in W51 M
Figure 1a shows the spatial distribution of the low-velocity 54 Vlsr 68 km s,1 water maser spots. Superimposed on the spots are the linear polarization vectors with their lengths proportional to the degrees of polarization. The inset of Figure 1a is an enlargement of the compact maser concentration near the reference position 0,0 of W51 M. The dotted line in the inset separates blueshifted west of the dotted line and redshifted east of the dotted line maser spots with respect to the velocity centroid, 61.5 km s,1 , of this maser concentration, hereafter called the protostellar cocoon. With a distance of 7.0 kpc to W51 M, the inner and outer radii of this maser cocoon are approximately 5 AU and 66 AU, respectively. Besides the maser cocoon, Figure 1a reveals a 1200 AU long linear maser structure at a position angle, P.A., of 200 . This structure, which is blueshifted some 5 km s,1 with respect to the protostar, is roughly aligned with the Galactic magnetic eld pro jection on the sky, P.A. = 205 Matthewson and Ford, 1970; Mufson and Liszt, 1979 and the polarization position angle of these masers median EVPA = 197 . The proper motion vectors, presented in Figure 1b, show that these masers move longitudinally along this


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direction with a median space velocity of25km s,1 relative to the centroid of the cocoon. The proper motions exclude the interpretation of this large-scale streamer as a low-velocity bipolar out ow from W51 M. Most likely the stream is produced by shocks caused by the nearby expanding HII region, W51 IRS 1, which interacts with the dense molecular core of W51 M on its western side. In contrast to the cocoon masers, which show a mean linear polarization of only 3 maximum 13, the masers in the streamer exhibit higher degrees of linear polarization mean 12; maximum 35. This is in good agreement with the classical maser polarization theory Goldreich et al., 1973a, 1973b, which predicts linear polarization degrees between 0 and 1 3. The cocoon masers show larger velocity dispersions and smaller ux densities than the streamer masers. While for cocoon masers the degree of linear polarization tends to decrease with increasing velocity dispersion of a spot, the polarization degree of the streamer masers is independent of the velocity dispersion inside a spot.

Magnetic eld strength of the large-scale streamer
The direction of the linear polarization of saturated masers is predicted Goldreich et al., 1973a to be parallel perpendicular to the magnetic eld pro jection on the sky if the angle between the eld and the line-of-sight is less than 55 over 55 . Since the line-ofsight toward the HII region W51 is roughly tangential to the Sagittarius spiral arm see Fig. 10 of Mufson and Liszt, 1979, linear polarization parallel to the eld is expected. The good alignment of the linear polarization vectors of the large-scale streamer suggests that the turbulent motions in the medium are more wavelike than eddylike. Since turbulent velocity elds produced by shocks induce turbulent magnetic elds, the level of magnetic uctuations is related to the associated uctuations in kinetic energy by the principle of equipartition Whitham, 1974. This enables us to estimate the preshock magnetic eld strength of the streamer indirectly from the relation, B =B = V VA, where VA = B 4 0:5 is the Alfven velocity is the mass density of the medium. The left-hand side of this relation B =B determines the angular deviation, , of the linear polarization vectors from the magnetic eld direction and can be replaced with it. If the velocity uctuation, V , is random, as in turbulence, then the above relation can be averaged over all data points yielding an Alfven velocity, VA = V rms rms, of 1.1 0:23 km s,1 . This corresponds to a magnetic eld parameter, b = VA 1.84 km s,1 Hollenbach and McKee, 1989, of 0.6. The relation Bo = bno0:5 G Hollenbach and McKee, 1989 yields thus a preshock eld strength of 1.2 0:25 mG. In the above relation, the preshock hydrogen nuclei density of W51 M, no = 3.8 106 cm,3,was adopted from Plume et al. 1997. Inside the masing regions of the streamer, the strength of the magnetic eld is relatively independent of the preshock eld strength, since the magnetic pressure which is determined by the ram pressure of the shock dominates in the masing region Hollenbach and McKee 1989. In addition, since the emission after a shock front occurs in the observer's frame in the range 3 4Vshock Vspace Vshock Hollenbach et al. 1989, the space velocities of masers should closely trace shock velocities. Thus, with the observed median space velocity of the streamer masers, 25 8:4 km s,1 , a characteristic magnetic eld strength of 38 15 mG results inside the masing regions of the streamer using eq. 4.6 of Elitzur et al., 1989, which depends on the shock velocity and preshock density.


Interstellar matter. Galaxies
100
10

89
80 60 40
Relative declination (mas)

-1 25 km s

80 60

5

0

Relative declination (mas)

40 20 0 -20 -40 -60

-5

20 0 -20 -40 -60 -80

-10 10

5

0

-80

-100
-100

Relative RA (mas) a b Figure 1: Left a: The rst VLBI linear polarization image of water masers in W51 M. The lines show the direction of the linear polarization; their lengths are proportional to the polarization degrees of the spots 1 mas = 1. The inset is an enlargement of the protostellar maser cocoon near the reference position 0,0 of W51 M polarization lines: 1 mas = 2. 1 mas corresponds to 7 AU. Right b: Proper motion vectors of the observed water masers in W51 M. The motions are relativetothe centroid of the cocoon masers

20 0 -20 -40 -60 Relative right ascension (mas)

20

0

-20

-40

-60

Conclusion
Sub-milliarcsecond linear polarization results of 22 GHz water masers in W51 M were presented. We showed that for the large-scale linear polarization structure found in W51 M the streamer both preshock and postshock magnetic eld strengths can be determined from VLBI linear polarization and proper motion measurements because the preshock hydrogen nuclei density of the medium is known. For the streamer of W51 M, a preshock eld strength perpendicular to the shock velocity of 1.2 0:25 mG resulted. Inside the masing regions of the streamer the typical total eld strength is 38 15 mG.

References
Alfven H., 1943, Ark. Mat. Astron. Fys., 29B, 2 Elitzur M., Hollenbach D., McKee C., 1989, Astrophys. J., 346, 983


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Fermi E., 1949, Phys. Rev., 75, 1169 GoldreichP., Keeley D., Kwan J., 1973a, Astrophys. J., 179, 111 GoldreichP., Keeley D., Kwan J., 1973b, Astrophys. J., 182, 55 Hollenbach D., McKee C., 1989, Astrophys. J., 342, 306 Hollenbach D., Cherno D., McKee C., 1989, in Infrared Spectroscopy in Astronomy, ed. B. Kaldeich Noordwijk: ESA, 245 Leppanen K., 1995, Ph.D. Thesis, Helsinki University of Technology Leppanen K., Liljestrom T., Diamond P., 1998, Astrophys. J., 507, 909 Matthewson D., Ford V., 1970, MmRAS, 74, 143 Mufson S., Liszt H., 1979, Astrophys. J., 232, 451 Plume R. et al., 1997, Astrophys. J., 476, 730 Whitham G., 1974, Linear and Nonlinear Waves New York: Wiley