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Appendix A: Measured and calculated physical parameters of the H₂O masers

	Fig. A.1 Total intensity spectra (I, upper panel) and circular polarization intensity spectra (V, lower panel) for the H2O masers VLA1.06, VLA1.12, VLA2.44, and VLA2.48 (see Tables A.1 and A.2). The thick red line is the best-fit models of I and V emission obtained using the full radiative transfer method code for 22 GHz H2O masers. The maser features were centered on zero velocity.
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In Tables A.1 and A.2 we list all the H₂O maser features detected towards the two YSOs, VLA 1 and VLA 2, respectively. The tables are organized as follows. The name of the feature is reported in Col. 1. The positions, Cols. 2 and 3, refer to the brightest H₂O maser feature VLA1.06 that was used to self-calibrate the data. We estimated the absolute position of VLA1.06 to be and δ₂₀₀₀ = 42°37′34′′.84 (see Sect. 2). The peak flux density (I), the LSR velocity (V_lsr), and the FWHM (Δv_L) of the total intensity spectra of the maser featuresare reported in Cols. 4–6, respectively; I, V_lsr, and Δv_L are obtained using a Gaussian fit. The mean linear polarization fraction (P_l) and the mean linear polarization angles (χ) are instead reported in Cols. 8 and 9, respectively. We determined P_l and χ of each H₂O maser feature by only considering the consecutive channels (more than two) across the total intensity spectrum for which the polarized intensity is ≥5σ.

In Cols. 9 and 10 are reported the values of the product of the brightness temperature T_b of the continuum radiation that is incident onto the masing region and the solid angle of the maser beam ΔΩ, which is known as the emerging brightness temperature T_bΔΩ, and the intrinsic thermal linewidth of the maser ΔV_i. Their values listed in the tables are the outputs of the FRTM code (Vlemmings et al. 2006) that is based on the model for 22 GHz H₂O maser of Nedoluha & Watson (1992), for which the shapes of the total intensity, linear polarization, and circular polarization spectra depend on T_bΔΩ and ΔV_i (Nedoluha & Watson 1991; 1992). We model the observed linear polarized and total intensity maser spectra by gridding ΔV_i between 0.4 km s^-1and 4.0 km s^-1, in steps of 0.025 km s^-1, using a least-squares fitting routine (χ²-model) with 10⁶ K sr <T_bΔΩ < 10¹¹ K sr. We also set in our fit (Γ + Γ_ν) = 1 s^-1, where Γ is the maser decay rate and Γ_ν is the cross-relaxation rate for the magnetic substated (see Vlemmings et al. 2006 and S11 for more details).

From the maser theory we know that P_l of the H₂O maser emission depends on the degree of its saturation and the angle between the maser propagation direction and the magnetic field (θ; e.g., Goldreich et al. 1973). Because T_bΔΩ determines the relation between P_l and θ, from the outputs of the FRTM code we are able to estimate the angles θ that are reported in Col. 13. The errors of T_bΔΩ, ΔV_i, and θ are determined by analyzing the full probability distribution function.

Finally, the best estimates of T_bΔΩ and ΔV_i are then included in the FRTM code to produce the I and V models that are used

for fitting the total intensity and circular polarized spectra of the H₂O masers (see Fig. A.1). The magnetic field strength along the line of sight, which is reported in Col. 12, is finally evaluated by using the equation (A.1)where Δv_L is the FWHM of the total intensity spectrum, P_V = (V_max − V_max) /I_max is the circular polarization fraction (Col. 11), and the A_{F − F′} coefficient, which depends on T_bΔΩ, describes the relation between the circular polarization and the magnetic field strength for a transition between a high (F) and low (F′) rotational energy level (Vlemmings et al. 2006).

In Table A.3 we compare the parameters of the 22 GHz H₂O masers detected around VLA 1 and VLA 2 in epochs 2005.89 and 2012.54. The first three rows are the observed parameters. In Rows 4 and 5 are reported the measured linear (P_l) and circular polarization fraction (P_V) in percentage. In the rest of the table we compare the intrinsic charateristics of the masers and the magnetic field properties that have all been estimated from the outputs of the FRTM code.

© ESO, 2014