USERID -32000.0 32000.0 User ID - ignored INNAME Image name INCLASS Image class INSEQ 0.0 9999.0 Image seq. # INDISK 0.0 9.0 Disk drive # IN2NAME Weight image name IN2CLASS Weight image class IN2SEQ 0.0 9999.0 Weight image seq. # IN2DISK 0.0 9.0 Weight image disk drive # OUTNAME Output image name (name) OUTCLASS Output image name (class) OUTSEQ 0.0 9999.0 Output image name (seq. #) OUTDISK 0.0 9.0 Output disk drive # BLC 0.0 4096.0 Bottom left corner of image 0=>entire image TRC 0.0 4096.0 Top right corner of image 0=>entire image SOLCON 0.0 1.0 Convergence criterion. 0=> 0.001 FUNCTYPE Type of rotation curve: 'BR': Brandt, 'EX' : exponential, 'CC' : constant, 'SB' : solid body. APARM $ First guesses to parameters: $ (1,2) (x,y) center in pixels $ (3) position angle major ax $ (4) inclination (deg) $ (5) systemic velocity (km/s) $ (6) maximum velocity (km/s) $ (7) radius max velocity (") $ (8) exponent (0=>1). CPARM (1) >0 residual map written (see help for choices) (2) > 0 => make plot (3) Code for fixed params (see help for choices) (4) > 0 use IN2C map for weighting (5) > 0 copy old history (6) 0: write one line to OUTTEXT; -1/1 write position to OUTTEXT (7) > 0 just plot using inputs, else fit too DPARM (1,2) lower/upper limit to radius ("); (3,4) range of cos (position angle in galaxy); (5,6) idem for sine; (7) max. plotted radius; (8) max. plotted velocity; (9) min plotted velocity . (10) width of annuli (pixels) INTEXT Text file containing rotation curve information. OUTTEXT Text file to which one line of output results is written. ' ' means don't write one PIXSTD Estimated rms uncertainty in the observed radial velocity (km/s) at one pixel. 0=>10 SYMBOL 0.0 24.0 Plot symbol number: 1 - 24 FACTOR 0.0 Scale plot symbol by FACTOR DOTV -1.0 1.0 > 0 Do plot on the TV, else make a plot file GRCHAN 0.0 8.0 Graphics channel 0 => 1.

GAL Type: Task Use: GAL calculates eight parameters specifying the orientation (# 1 to 5) and the rotation curve (# 6 to 8) of a galaxy, using its velocity field as input. If this velocity field consists of M data points, the parameters are determined by a nonlinear least squares fitting of eight parameters to M data points. If CPARM(1)> 0, a residual velocity field (observed minus model) is produced. If CPARM(2)> 0, the observed rotation curve is plotted together with the fitted model curve. Adverbs: USERID......User ID of owner of image. Ignored. INNAME......Image name(name). blank=>any INCLASS.....Image name(class). blank=>any INSEQ.......Image name(seq. #). 0=>any INDISK......Disk drive # of image. 0=>any IN2NAME.....Weight image name(name). blank=>any IN2CLASS....Weight image name(class). blank=>any IN2SEQ......Weight image name(seq. #). 0=>any IN2DISK.....Disk drive # of weight image. 0=>any OUTNAME.....Output image name(name). blank=>INNAME OUTCLASS....Output image name(class). blank=>'GAL' OUTSEQ......Output image name(seq). 0=>next unique OUTDISK.....Output image disk drive #. 0=>any BLC.........The Bottom Left-hand pixel of the subarray of the image to be analysed. The value (0,0) means (1,1). TRC.........The Top Right-hand pixel of the subarray of the image to be analysed. (0,0) => (1,1). the top right hand corner of the entire image. SOLCON......Criterion to stop least squares fitting. FUNCTYPE....Type of rotation curve to be fitted. 'BR' : Brandt curve, given by : R / Rmax V / Vmax = ---------------------- n 3/2n (1/3 + 2/3 * (R / Rmax) ) 'EX' : Exponential flat curve : - ln(100.0) * (R / Rmax) V / Vmax = 1 - e 'CC' : Constant curve : V / Vmax = 1 'SB' : Solid Body curve : V / Vmax = R / 60 APARM.......The eight parameters to be fitted: (1) x pixel central position (2) y pixel central position (3) position angle receding major axis (4) inclination orbital plane (5) systemic velocity (6) Vmax, maximum rotation velocity (7) Rmax, radius(") of maximum rot. velocity (8) n, measure of extent of 'flat' part of curve, 0=>1. (8) is only used if FUNCTYPE='BR', and (7) only if FUNCTYPE='BR' or 'EX'. On input, these parameters are the initial guesses; on output they are the fit values. CPARM (1) > 0 => a residual output map is made if 1, using the whole field; if 2, using a specified part of the field only; if 3, using INTEXT rather than fitting (2) if >0, the observed and the model rotation curves are plotted. (3) parameters to be held fixed in the order given in APARM. e.g. if parameters i, j, and k are to be held fixed, CPARM(3) = 2**(i-1) + 2**(j-1) + 2**(k-1). 0 defaults to NO fixed parameters. CPARM(3)=3 holds the center positions fixed (4) >0 use IN2C map for weights, else don't use a weighting image. Zeroth moment often used. (5) >0 copy old history file; else don't copy it. (6) 0: write one line with fitted parameters to OUTTEXT; NOT 0: write position of ends of major major axis (receding then approaching) to OUTTEXT and write the full set of plot data - radius, velocity, and rms of velocity as well. Used only if OUTTEXT not blank. (7) : no fit, residual field only; DPARM (1) and (2): lower and upper limit to radius ("); No default except when CPARM(1)=3 where the range of radii in the input text file is used. (3) and (4): limits to cos(azimuth angle); (5) and (6): limits to sin(azimuth angle); (7) max. radius to be plotted; (8) and (9) max and min velocity to be plotted (10) : width annuli in plotting observed rotation curve. INTEXT......Text file containing rotation curve information. This is used to determine the residual field when CPARM(1)=3 and must be specified then. OUTTEXT.....Not blank => Text file to which one line of output results is written. When OUTTEXT exists, GAL will append. Meant to be used in loop when using concentric rings; OUTTEXT can then become INTEXT of next run. If CPARM(6) is not zero, the file instead contains the measured rotation curve and the positions of the two ends of the major axis. PIXSTD......Estimated rms uncertainty in observed radial velocity at one pixel (km/s) SYMBOL.....1: Plus sign 12: Five pointed star 2: Cross (X) 13: Star of David 3: Circle (default) 14: Seven-pointed star 4: Box 15: Eight-pointed star 5: Triangle 16: Nine-pointed star 6: Diamond 17: Ten-pointed star 7: Pentagon 18: 11-pointed star 8: Hexagon 19: 12-pointed star 9: Septagon 20: 13-pointed star 10: Octagon 21: 14-pointed star 11: Nine-gon 22: Plus with gap 24: Cross with gap Type 23 (vertical line) is not allowed since a vertical line is drawn for an error bar. 0 -> 3. FACTOR......Scale the plot symbol by FACTOR; 0 -> 1. DOTV........> 0 => plot directly on the TV device, otherwise make a plot file for later display on one or more devices (including the TV if desired). GRCHAN......Graphics channel (1 - 7) to use for line drawing. 0 => multiple.

GAL : Task which analyses a velocity field. In the present implementation it is assumed that the object is a rotating disk. The user has to specify initial guesses to the parameters to be fitted to the velocity field, using the adverb APARM. GAL will then determine the best least squares' fit to the input velocity field, and give the final best fit values of the parameters. Of course a good initial guess will speed up the procedure, whereas a very bad one will cause divergence and failure. Some remarks on specific adverbs : IN2NAME, etc. Specifies a map of which the pixel values are weights to be applied to the velocities in the velocity field map INNAME. It is up to the user to supply such a map. Several possibilities are open: one can use the total HI map, or the square of the total HI map (using COMB). The latter choice is the correct one if the noise in the velocity maps can be assumed Gaussian with respect to the intensity map which normally is a reasonable assumption. Other possibilities are the width of the profile, the skewness of the profile, or - if the velocity field was determined using XGAUS - the goodness of fit. BLC , TRC The velocity field is read in as a whole, which imposes an upper limit to the area that may be used. A 1024*1024 velocity should be handled easily. When your image is too big, make sure you are not oversampling too much; more than two points per beam is unnecessary. SOLCON The value of SOLCON determines when to stop the iteration, the default 0.001 should be adequate for most purposes. FUNCTYPE Four schematic rotation curves are available now. The Brandt curve (FUNCTYPE = 'BR') attains a maximum value Vmax at R = Rmax, and declines Keplerian thereafter. The exponential curve (FUNCTYPE = 'EX') is flat throughout after an initially linear increasing part. The factor ln(100) in the exponent was chosen to give analogous meanings to Rmax for the two representations, in fact Rmax is the radius where Vmax attains 99 percent of its maximum value. Still, the fitted value of Rmax may well differ depending on the value of FUNCTYPE. FUNCTYPE='CC' fits a one parameter rotation curve, V = constant. This is a good approximation in many cases, but a minimum radius DPARM(1) should be specified since the approximation breaks down at low radii. It is particularly useful in applying GAL in concentric annuli. GAL then should be used in a loop with varying DPARM(1) and DPARM(2) fitting a constant velocity in each ring. FUNCTYPE='SB' fits a solid body rotation curve. In this case the theoretical velocity field has an infinite number of axes of symmetry, and the central position becomes undefined. Furthermore, the steepness and the inclination are directly related, so one of both (the inclination) is held fixed at its initial value. Vmax is defined as the circular velocity at a 60" radius. GAL keeps x,y, and i fixed, although of course you may add other fixed parameters by means of CPARM(3). APARM(1),APARM(2) The guess to the central position has to be given in pixels; the resulting fitted value is also displayed in RA and Dec. APARM(3) The position angle is defined measured form north eastward, to the receding part of the major axis (having the largest velocities). An initial guess which is 180 degrees off is bound to cause divergence. APARM(4) The inclination angle can have values from 0 (face on) to 90 (edge on). Don't use values close to 0 or 90 as initial guesses. APARM(5) A fair initial guess is the mean of the velocities on opposite ends of the major axis, or values around the minor axis. Specify velocities in km/s. Note that the units in the map should be in m/s. APARM(6) The height of the rotation curve can be guessed by halving the difference of two points on opposite ends of the major axis, and applying an cosec(i) correction. APARM(7) The extent of the rising part may be hard to guess, but usually the program converges if the initial guess is less off than a factor 2 or so. APARM(8) This is a measure of the flatness of the curve, if FUNCTYPE = 'BR'. Very flat curves have APARM(8) well below unity, while curves with a clear decline in the outer parts have APARM(8) values like 1.5, 2.0, or even 3.0. If uncertain, start with APARM(8) = 1. Avoid APARM(8) < 0.1 or > 4. A successful convergence in the 'BR' case depends critically on reasonable choices for both APARM(7) and APARM(8). CPARM(1) controls the residual field. If CPARM(1) = 1, 2, or 3, a residual output map is made. Such a map can be extremely useful to assess the quality of the fit, and to detect the presence of asymmetries. In the case CPARM(1)=1, the whole velocity field is used to generate the residual map, irrespective of the values in DPARM(1) through DPARM(6). When CPARM(1)=2, only the part of the velocity field specified in DPARM(1) => DPARM(6) is used. When CPARM(1)=3, no fitting is done, and the residual field is determined using a user supplied rotation curve in the textfile INTEXT. CPARM(2) If > 0, the observed rotation curve is plotted (by integrating the circular velocities in annuli), as well as the fitted model curve. CPARM(3) is a bit map of the parameters to be held fixed. If one wants to fix the position ( both x and y), and Rmax, specify CPARM(3) = 2**0 + 2**1 + 2**6 = 67. CPARM(3)=0 means NO fixed parameters. Note that some parameters may be fixed by the program anyway (x,y, and i if FUNCTYPE='SB'). CPARM(4) If <=0, don't use the image in IN2C as weighting image; if >0, use the IN2C image (if specified). CPARM(5) If <=0, don't copy the old history file; if >0: copy it. The reason for this is that in the case of very large history files a substantial fraction of the execution time of GAL is spent in copying the file. CPARM(6) Only important when OUTTEXT is specified. A one liner of information about the fit obtained is appended to OUTTEXT. If CPARM(6)=0, this one line contains the values of all fitted parameters. If CPARM(6) = 1/-1, the one line of output contains the position (RA, Dec) of the major axis of the ring under consideration. When +1, GAL will write the position of the receding major axis, and when -1, of the approaching major axis. When using GAL many times in rings, the output file contains a range of positions which trace the major axis of the galaxy. This file can than be turned in a ST extension file, and the major axis can be plotted on top of other maps. Use only these 3 values - the exact value of CPARM(6) is used. CPARM(7) If CPARM(7) > 0, no fitting is done, only a plot is generated, based on the input values in APARM. DPARM The parameters DPARM(1) through DPARM(6) allow the user to spe- cify a wide variety of subsections of the plane of the galaxy. DPARM(1) and DPARM(2) specify the minimum and maximum radius to be used, e.g. to select an annulus, in which case FUNCTYPE='CC' or 'SB' would be advisable. DPARM(3) and DPARM(4) specify li- mits on the cosine of the azimuth angle in the galaxy (as pro- jected on the sky), e.g. 0,1 selects the receding half of the galaxy. DPARM(5) and DPARM(6) specify the sine of this angle, e.g. 0,1 selects the half plane traversed when the receding major axis is rotated in an anticlockwise direction to the ap- proaching major axis. DPARM(7) specifies the maximum radius in the plot (", 0=> auto scaling). DPARM(8) specifies the maximum rotation velocity to be plotted (km/s, 0=>auto scaling). DPARM(9) specifies the minimum rotation velocity to be plotted (km/s, 0=>auto scaling). DPARM(10) specifies the width of the annuli used in plotting the actual rotation curve, approximately in units of a pixel width (if DX=DY : exactly one pixel width, DX>>DY : DY * SQRT(2), DX<SQRT(2)). A value of 0 defaults to 3. INTEXT This is a text file containing rotation curve information from concentric rings. This file is used when CPARM(1) = 3. No fitting is done, but a residual map is produced based on the contents of INTEXT. Nine columns are used - inner and outer ring radius, X center pixel, Y center pixel, position angle of the major axis (CCW from N), inclination, systemic velocity, maximum velocity, radius of maximum velocity and Brandt index. You may have more than 10 columns with columns 11 and beyond ignored. A sample INTEXT: 0.0 60.0 308.5 333.4 -60.2 72.0 30.6 123.8 145.3 0.000 0.0 2.3 60.0 120.0 307.2 332.6 -59.6 72.6 24.9 114.4 153.2 0.000 0.0 2.2 120.0 180.0 309.0 333.5 -59.7 72.7 27.5 110.8 160.7 0.000 0.0 3.1 180.0 240.0 309.3 332.9 -60.4 73.2 27.8 112.0 157.3 0.000 0.0 2.6 240.0 300.0 308.7 332.8 -59.6 73.6 27.9 111.8 157.9 0.000 0.0 2.6 300.0 360.0 308.7 332.8 -59.6 73.6 27.9 111.8 158.3 0.000 -0.1 15.4 360.0 420.0 308.7 332.8 -59.6 73.6 27.9 111.8 150.2 0.000 0.2 19.4 420.0 480.0 308.7 332.8 -59.6 73.6 27.9 111.8 148.6 0.000 -0.8 18.8 480.0 540.0 308.7 332.8 -59.6 73.6 27.9 111.8 144.3 0.000 -0.9 53.0 540.0 600.0 308.7 332.8 -59.6 73.6 27.9 111.8 139.8 0.000 -1.4 65.5 If the radius of the maximum velocity is <= 0.0, 1/3 of the sum of the maximum and minimum radius in INTEXT will be used. Otherwise a zero divide occurs. This INTEXT defines 10 rings in intervals of 60". The parameter values are given in the next 6 columns: center pixel x and y, major axis position angle (CCW from N), inclination, systemic velocity, maximum velocity, and radius of maximum velocity with average residual and standard deviation in km/s ignored. Note that the fit is quite good for the first 5 rings and then deteriorates badly. Such a file typically is the result of several GAL runs on annuli. OUTTEXT Output results are written to this file, if specified. If CPARM(6)=0, output parameters are the radii of the ring used, plus the fitted parameters. To this are added the average difference between the fitted model and the velocity field (should be close to zero), and the standard deviation (should be close to the rms in the ring). If CPARM(6)=+/-1, the location of the major axis is written (see CPARM(6) explanation). PIXSTD PIXSTD is used to calculate the errors associated with the final results. The default is the velocity dispersion usually observed in unperturbed spirals, but the value may well be higher as a result of larger random motions and filter width. Hints ===== The curve types 'BR', and 'EX' should only be used on the whole field, and in the initial stage of determining the variables. Real-world rotation curves deviate from mathematical models. In the more advanced stages of velocity field analysis, it is suggested to use 'CC' only, on annuli determined by DPARM(1) and DPARM(2). The width of these annuli should be a trade-off between a minimum number of points in the ring to make a good fit, and a maximum width over which the rotation velocity may be assumed constant. The whole rotation curve can then be fitted by a command like: for i=1:10;dparm(1)=i*30;dparm(2)=(i+1)*30;go gal;wait gal;end A residual of this fit can be obtained by putting the fitted values in the textfile INTEXT, and running GAL once more with CPARM(1)=3. Note that in the above example the very central portion of the velocity field is not used.