INFILE Q/U spectrum input to TARS OUTFILE RM spectrum output by TARS NITER 0.0 4000.0 Max # fit iterations 0 -> 100. NGAUSS 1.0 4.0 Max number components DOSPIX -1.0 4.0 1 => fit spectral index 2,3,4 => fit thickness else keep both at zero RMSLIMIT RMS level above which a solution is "bad"

FTARS Task: Fits a single polarization spectrum for one or more components of total polarization, polarization angle at 0 wavelength, and rotation measure. FTARS will be used on the Q and U text file spectrum input to TARS and the rotation measure spectrum output by TARS. The task fits up to 4 polarization components the spectrum. It is based on task RMFIT, but does only a single spectrum rather than whole data cubes. Just as TARS is used to test isolated real or model cases for FARS, FTARS is used to carry the test through the RM fitting stage. Color differentiates what is plotted. Graphics channel 1 (usually yellow) is used for axis labels and the data. The FARS output is plotted in amplitude/phase initially. The initial guess is shown as a large X in graphics channel 2 (usually green). This screen may be used to reset the initial guess. Then the Q and U data are plotted. Since the Q and U data may be on a FQID axis and so may not actually be in frequency order, the Q and U data are plotted as small X's. The initial guess is shown as a smooth curve in graphics channel 2 (usually green). The fit is then shown as somewhat large X's in graphics channel 4 (usually cyan). Details of the interactive operation and options are described in the EXPLAIN file. See also AIPS Memo 118, "Modeling spectral cubes in AIPS", May 2020 for a more detailed description of the use of RMFIT. The model fit is: Q(i) = SUM_j [ P_j cos ( 2 theta_j + 2 RM_j lambda(i)^2) F (beta_j, lambda(i)^2) ] U(i) = SUM_j [ P_j sin ( 2 theta_j + 2 RM_j lambda(i)^2) F (beta_j, lambda(i)^2) ] where P_j is the polarized flux at 1 GHz, theta_j is the intrinsic polarization angle, and RM_j is the rotation measure in radians/m/m. F(beta_j, lambda(i)^2) is an amplitude function that solves for a spectral index or one of several possible thickness parameters. The spectral index function is (lambda_1^2 / lambda(i)^2)^(beta_j/2) while the thickness functions are ('SLAB' in MODIM) and ('GAUS' in MODIM) and ('EXP ' in MODIM) sin (beta_j lambda(i)^2) / (beta_j lambda(i)^2) exp (-ln(2) * (beta_j lambda(i)^2 / 1.8954)^2) exp (-ln(2) * beta_j lambda(i)^2 / 1.8954) where lambda_1 is the wavelength at 1 GHz and beta_j is the spectral index or the thickness parameter, the latter in rad/m/m. Set DOSPIX(j) to 1 for spectral index or 2,3,4 for SLAB, GAUS, or EXP. respectively, or set it to 0 to omit fitting a thickness to component j. The 1.8954 was chosen to make all functions have the same half-power point. Output images are written of the P_j, theta_j, RM_j, beta_j, Q0_j, and U0_j and their uncertainties, where Q0_j = P_j cos ( 2 theta_j ) U0_j = P_j sin ( 2 theta_j ) are Q and U at 1 GHz with no rotation measure. The beta_j images are only written when they have been fit. Adverbs: INFILE.....The input file to TARS with three columns: frequency in Hz, then Q in Jy/beam, then U in Jy/beam. A semi-colon in column 1 means the line is a comment. OUTFILE....The output file from TARS containing the rotation measure spectrum. The 3 columns are RM, Real part, Imaginary part or RM, amplitude, phase. A semi-colon in column 1 means the line is a comment. NOTE: TARS can write many RM spectra to a single file. Only the first of these is used by FTARS. NITER......Maximum function evaluations during the fit of each row. (< 10 -> 100 for NGAUSS > 1, < 100 -> 150 for 1 Component) NGAUSS.....Number of Components to fit (between 1 and 4). DOSPIX.....If 0.5 < DOSPIX < 1.5, solve for spectral index in the corresponding component, otherwise take the spectral index to be zero. If 1.5 < DOSPIX < 2.5, solve for the thickness parameter in the corresponding component with sin(x)/x form, or, if 2.5 < DOSPIX < 3.5, solve for the thickness parameter in the corresponding component with Gaussian form, or, if 3.5 < DOSPIX < 4.5, solve for the thickness parameter in the corresponding component with Exponential form. Otherwise take the thickness parameter to be zero. NOTE: all values of DOSPIX must be either 0 or indicate the same functional form. RMSLIMIT...If the RMS exceeds this, the solution is reported as "bad". 0 -> 1000.0

FTARS: One-dimensional polarization fitting of image cubes Documenter: E. W. Greisen NRAO Related Programs: IMFIT, JMFIT, SAD, SLFIT, ZEMAN, XGAUS Initial guesses for the fit are found from the TARS output data. When NGAUSS = 1 this can happen automatically from the row data. For the spectrum, the first step in the fitting process is to determine an initial guess non-interactively. the next steps are 1. The input FARS RM data are plotted on the TV as amplitude and phase. The task initially skips step 2 and goes to step 3 for an interactive initial guess. 2. If either NGAUSS > 1 or a fitting has been forced, FTARS asks in a TV menu for instructions. If your answer is RE-GUESS on the TV, FTARS will ask you to enter a new initial guess (step 3). If your answer is DO FIT, then DARS goes on to step 4. If the answer is QUIT, the task prints its best fit and exits. 3. To enter a new initial guess, you will be prompted to position the TV cursor at the rotation measure of each Component (note that only the X position matters). To mark each point, hit any button (A, B, C, or D). FTARS then returns to step 1 above to plot the new guess and ask again. 4. Once an acceptable initial guess has been found, FTARS proceeds to call a non-linear least squares fitting routine to determine the polarization parameters that appear to fit the data best. The answers are then checked to see if they are "reasonable" - negative and very large components and components with rotation measures outside the input data are unreasonable. 6. The final model is added to the plot. In the input terminal, you are then told if the answers are "unreasonable" and are shown the answers, reasonable or not. You are then offered a variety of choices. If your selected option is QUIT - FTARS exits cleanly RE-GUESS - FTARS returns to step 1 to try again with the current number of components (<= NGAUSS) 1, 2, 3, or 4 - FTARS returns to step 1 to try again with the specified number of Components (note that only numbers <= NGAUSS are respected) HAND - FTARS prompts you to enter the polarization parameters for each component (HAND on the TV). You enter in the input terminal window, the total polarization in input image units, the polarization position angle at zero wavelength in degrees (-90 to +90), the rotation measure in radians per meter squared and, if appropriate, the spectral index (unitless) or RM thickness (radians per meter squared). All 3 or 4 numbers must appear in one line. It will prompt for all NGAUSS components, but will change the prompt if the current number of Components is < NGAUSS. If you enter something besides 0 in that case, then the current number of Components is increased appropriately. FTARS then returns to the start of this step 6 to allow you to see if you made a good guess. DO FIT - After a HAND operation, a DO FIT option is available. It loops back using the hand-entered parameters as the initial guess to the fitting routine. PIXRANGE - FTARS prompts you for the Q and U display ranges to re-display the data Enter Qmin, Qmax, Umin, Umax in that order in one line. If you enter only two values, then Umin and Umax are taken to equal Qmin and Qmax. If you enter no values, then the plot reverts to self-scaling. The Q plot self-scales if Qmin >= Qmax; the U plot self-scales if Umin >= Umax. Note that on the re-plot, the smooth "initial guess" line is now actually the result of the fit. SHOW P&A - FTARS will switch the display between Q plus U SHOW Q&U and total polarization and polarization angle. The plotted "initial guess" becomes the actual fit results.