Folding Search - Period Folding

   

The command MAKE/FOLDING is available for the period search via folding of the data. This command takes the input PET and folds it to the specified periods and period derivatives. The curve corresponding to the period which has the smallest probability for beeing generated by a fluctuation is selected by means of a statistical test against constancy. Three different test are available: a  test, a ``pure'' Z  (Rayleigh) test,   and a ``fast'' Z  (Rayleigh) test. Being the ``pure'' version   of the Rayleigh test quite slow (especially with a high number of harmonics requested), for strong sources it is advisable to use the ``fast'' version, which is less accurate, but considerably faster.

Note:WARNING! The ``pure'' Rayleigh test presents a crucial difference from the  test: the data is not binned into phase bins. This means that the effect of uneven coverage of the phase is not taken into account. In the  case the statistical test is performed after dividing each phase bin by its accumulated exposure. If the data presents gaps which tend to be concentrated around some specific range of phases, the ``pure'' Rayleigh test will pick up spurious periods. It is advisable to run a  test anyway to check for these effects.

All the parameters for the analysis (filenames included) are passed via a parameter file. The output of the program is a MIDAS table containing the folded light curve corresponding to the best found period (in counts/s for the ``fast'' Rayleigh test and the  test, in counts for the ``pure'' Rayleigh test), and a MIDAS image containing the values of the test (chi-square or Rayleigh) as a function of period and period derivative. You can obtain the probability associated to the value of the  or Z  found by using the INTEGRATE/CHI2 command.   Remember that the Z follow a chi-square distribution with 2  degrees of freedom. The syntax of the command is:

MAKE/FOLDING parfil

where parfil is the name of the parameter file. The parameter file can be generated by calling CREATE/PARFIL with the option FOLD. The parameter file entries are shown in Table 7.10.

  
Table 7.10: Parameter file entries for MAKE/FOLDING

The meaning of the parameters is as follows:

• N_OF_PHASE_BINS is the number of bins to fold the data into. The maximum number accepted is 100. Default is 20.
• VARIABILITY_TEST is the variability test selected. The available options are:
  1. Chi-square ( ) test,
  2. Rayleigh (Z ) test (``pure'' version),
  3. Rayleigh (Z ) test (``fast'' version).
• INPUT_FILENAME is the input PET table name. Default extension is TBL. There is no default.
• WINDOW_FILENAME is the name of the ASCII file containing the start-end times of the periods accepted for the analysis. The default filename for the window file is dummy.win. If the window file is not found, all times will be accepted. The default extension for window files is WIN.
• CENTERAL_PERIOD is the center value for the period range to be covered. There is no default value.
• PERIOD_STEP is the step on period. There is no default.
• CENTERAL_PDOT is the center value for the period derivative range to be covered. There is no default value.
• PDOT_STEP is the step on period derivative. There is no default.
• OUTPUT_FILENAME is the filename of the output table containing the folded light curve corresponding to the best period and period derivative, and of the  map image. The default extensions are TBL and BDF respectively.
• N_OF_PERIODS is the number of periods to test. If this parameter is set to 1, only one period (corresponding to the start period), is analyzed. Maximum value is 200. Default value is 20.
• N_OF_PDOTS is the number of period derivatives to test. If this parameter is set to 1, only one period derivative (corresponding to the start period derivative), is analyzed. Maximum value is 20. Default value is 20.
• EPOCH is the epoch in SCC (or UTC for barycentric corrected tables) of the start bin of the folded light curve. It can be used for phase relating purposes. Default value is 0.0, but a value closer to the actual SCC arrival times should be used.
• N_OF_HARMONICS is the number of harmonics to take into account for the Rayleigh test (both in the ``pure'' and in the ``fast'' versions). The maximum value is 10. Default value is 1.
• Format of the input: the files input to this command are:
  • PARAMETER FILE: standard ASCII file. Its general format is described in section 7.2.3.
  • DATA TABLE: it is a PET as produced by the EXSAS projection package. Its format is described in section 7.2.2.
  • WINDOW FILE: it is a standard ASCII file. Each line of the file contains the start and end time of an accepted time interval. No comment lines are allowed.
• Format of the output: the files in output from this command are:
  • FOLDED LIGHT CURVE: it corresponds to the best period. It is in the format of a MIDAS table with 3 columns: the first column always contains the phase (from 0.0 to 2.0); the second and third column contain the count rate and error on count rate in the case of chi-square and ``fast'' Rayleigh test, and the counts and error on counts in the case of the ``pure'' Rayleigh test (this difference is because of the non-binned nature of the Rayleigh test). The descriptors of the main EXSAS header are copied from the input table to the output light curve. Some new descriptors are present in this table. The descriptor CHI_SQUARE or Z_SQUARE (R*4) contain the best  or Z  respectively. The descriptor PERIOD (R*8) contains the best period, and the descriptor PDOT (R*8) contains the best period derivative.
  • statistical test image: it is in the format of a MIDAS bulk data frame. It contains the values of the selected statistical test as a function of the scanned periods (X coordinate) and period derivatives (Y coordinate). It can be displayed by means of the standard MIDAS commands PLOT/PERSPECTIVE and PLOT/CONTOUR. The descriptors of the main EXSAS header are copied from the input table to this image. No additional descriptors are introduced.
  • LOGFILE: it is an ASCII file containing a copy of the output to terminal. The useful parameters read in from the parameter file are reported. The status of the window file opening and reading is displayed. The total observation time and the total number of photons are listed. The best values for period and period derivative are reported, together with the best value of the statistical test selected. The logfile has the standard name fo_lon.log