VLBI measurements of plasma turbulence associated with the Cygnus OB1 Association

We have made dual-frequency (1.67 and 5.00 GHz) VLBI observations of five compact, presumably extragalactic radio sources in the Galactic plane in the constellation of Cygnus. The lines of sight to these sources pass through a part of the interstellar medium that is modified by the Cygnus OB1 association. The VLBI observations were processed to yield measurements of the scattering measure due to interstellar plasma turbulence. The dual-frequency VLBI observations allowed estimates of the possible intrinsic structure contamination of the scattering measurements. Such an error is estimated to be less than 5% of the scattering measure for our two best-observed cases, and 15% to as high as 30% for a more weakly scattered source. Modeling the spatial power spectrum of the turbulence by P-delta n(q) = C(N)(2)q(-alpha), where a is the spatial wavenumber of the turbulent fluctuations, our observations provide a measurement of integral(o)(L)C(N)(2)dz, where L is the thickness of the scattering medium and z is a coordinate along the line of sight. When combined with our earlier observations of the radio source 2013+370, we have a total of six lines of sight through the Cygnus OB1 association. Our observations show that the scattering through the Cygnus OB1 association is heavy and that the scattering measures vary from 0.14 to 2.21 m(-20/3) kpc on Lines of sight separated by as little as 1 degrees-2 degrees. When combined with measurements of the emission measure in the same directions, our scattering-measure results constrain properties of the turbulence in the Cygnus OB1 association. Specifically, if epsilon is the normalized amplitude of the density fluctuations, and l(o) is the outer scale to the Kolmogorov spectrum, then our combined scattering measure emission measure data set constrains the quantity epsilon(2)/(1+epsilon(2))l(o)(2/3). The mean Value is similar to 4.3 x 10(-13) cm(-2/3), with a range of about 0.5 in the logarithm. We do-not have sufficient information to determine epsilon and l(o) separately, but plausible ranges are epsilon<1 and l(o)<3 pc. For the most heavily scattered lines of sight, the outer scale must be considerably less than a parsec. In the case of two of our sources, 2005+372 and 2020+351, the observations are of sufficient quality to determine the spectral index cc of the density spectrum. In both cases our measurements are consistent within the errors with the Kolmogorov value of 3.67. These new measurements are in accord with a previous, similar measurement for 2013+370 and thus suggest that the mechanism responsible for generating turbulence in the vicinity of stellar OB associations is similar to that operative in the diffuse ionized gas (DIG) of the interstellar medium. Our observations also show anisotropy of the scattering for 2005+-372 and 2020+351, with axial ratios of 1.83+/-0.10 and 1.05-1.50, respectively. These observations are quantitatively consistent with a handful of other such observations, and suggest that the irregularities responsible for interstellar scintillations are extended along the interstellar magnetic field. We briefly and qualitatively discuss mechanisms by which the plasma shell surrounding Cygnus OB1 has become turbulent.