## A DESCRIPTION OF THE EXOSAT TIMING ANALYSIS
INTERACTIVE SYSTEM

A short description is given of the facilities supported by the EXOSAT Timing
Analysis Interactive System and of the improvements which will be implemented in
the near future.

1. __Rate Buffers and Light Curves__

The EXOSAT Timing Analysis Interactive System consists of a set of programs
scheduled from a control program (TINTE), which can be executed directly from the
File Manager or from the LE, ME or GS interactive system. The Timing Analysis
system uses as input files X-ray light curve points stored in the so-called rate
buffers by the interactive analysis system of the various instruments. Rate
buffers consist of a header containing the basic information concerning the
instrument, the PHA channel, the integration time etc., and of a binned light
curve whose points are described by: start time of the bin, exposure fraction (to
correct for instrumental dead times), count rate and count rate error.

The Timing Analysis Interactive System is designed to operate on one or two rate
buffers which partially overlap in time and refer to two different energy bands
(or instruments). The latter is to permit the determination of hardness ratio,
cross-correlations etc. which can require the use of two (simultaneous) time
series.

2. __Interaction__

The interaction between the system and the user can be handled in 3 different
ways which correspond, more or less, to various levels of expertise of the user.
In particular:

- After issuing a command, all the following parameters are input by replying to
the relevant questions.

- The command and all the following parameters are input to the system as a
single string.

- The string(s) as in b. can be written into a macro file and run
automatically via a special command.

At the current state of development the following commands
are available:

`--- Set up commands -------------------`

SF set input files

SR set no. of recs

EL set min expos limits

EB set error bar option

BG set manual bkgd subtraction

GA set gap filling options

BU set params for burst search

SI set selection on intensity

SC set params for correlat. anal.

RD reset defaults

PU purge file(s) one by one

PA purge files automatically

MD map good data intervals

HA hardcopy alphanumeric screen

HG hardcopy graphic screen

ED edit a file

RB rebin the data

WI time window(s) handling

IN infos on set up

EX exit

`- Execution commands -----------`

ST run statistical analysis

VA run detailed RMS variab analysis

HD run hdns ratio vs intensity

PL write data in Pablo-like file

PC prepare correlation input files

PF run phase fitting

LH list rate buffer header

LR list rate buffer points

CC run correlation analysis

FC final correlation analysis

PD plot results or data

FG execute a FMGR command

VE write energy in RMS variab file

PT plot (or fold) rate buffer data

FT FFT power spectrum analysis

F2 FFT with trend rem. & selection

FD folding period search run macro MA

@@,MA run macro MA

??,XX infos on command XX

??,?? general infos

3. __Objectives__

The purposes of the Timing Analysis Interactive System are as
follows:

a. __'Clean' the Data.__ A series of set-up commands is designed to remove
all bad-quality light-curve points from the time series to be analysed. This
data, which only marginally affecting the average count rate, can strongly affect
the determination of the higher statistical moments. 'Cleaning' is carried out
through a set of qualification criteria (such as time windows, intensity windows,
exposure fraction windows etc.) which can be enabled and disabled.

b. __Remove Long-Term Trends. __Trend removal techniques are often needed to
exclude the effects of long-term variability in the evaluation of the Correlation
Functions and the Power Spectrum (PS). A facility is provided to remove trends by
means of a polynomial fit to the data.

c . __ Bridge Data Gaps. __ Several timing analysis techniques (e.g. Correlation
Functions, PS) require the use of uninterrupted time series. Bad data gaps and/or
telemetry dropouts can be filled with simulated data obtained by the use of
several different techniques.

d. __ Test the Hypothesis of Source Constancy. __ This is done by
the use of the 2 and the RMS variability tests and by the determination of the source
statistical moments.

e. __ Search for Flares/Bursts. __ A search for flares and/or bursts can be
performed interactively by specifying the significance level above which an event
is revealed. It is also possible to carry out a millisecond burst search by using
the local average technique discussed by Rothschild et al. 1974 (Ap.J.Lett., 189,
L13) in connection with the very short-term activity of Cyg X-1.

f. __ Compute Correlation Functions. __ Partially unbiasd Auto Correlation (ACF)
and Time Skewness (TSF) Functions can be calculated for a time series of any
length shorter than 5000 bins. When analysing two simultaneous time series
from different instruments and/or energy bands, a partially unbiased Cross
Correlation Function (CCF) can also be calculated (for details see Stella et al.
1984, Ap.J., 282, 713). The results from different time intervals (5000 bins)
can be averaged to produce an average ACF, CCF and TSF. To allow for maximum
flexibility the programs which compute the correlation functions do not use Fast
Fourier Transform algorithms. Correlation Functions are widely used to
characterise the aperiodic source flickering and to investigate the amount of
correlation and any possible time lag between the source variations in two
different energy hands.

g. __ Search for Coherent Pulsations. __ This can be done using 3 different
approaches: (1) the Power Spectrum Technique (which uses an FFT algorithm on data
intervals long up to 4096 bins), (2) The Folding Analysis Technique (which can
use an unlimited number of data bins to search for coherent pulsations over up to
75 trial periods), (3) the Phase Fitting Technique (which is normally used to
determine the pulsation period as accurately as possible). The Power Spectrum
Technique is rapid and straightforward to search for pulsations over a wide range
of frequencies and is the most commonly used technique. The Folding analysis
allows a more sensitive search for coherent pulsations when dealing with
non-continuous or unevenly spaced data (cf. Leahy et al. 1983, Ap.J., 266, 160),
but is highly CPU consuming and is usually applied over a limited number of trial
periods.

h. __ Characterise the RMS Variability as a Function of
Energy. __ This technique is often used to establish whether the source is
more variable at high or low energies.

j. __ Investigate the Hardness Ratio as a Function of Time
and/or Source Intensity. __ This simple investigation of the
source spectral changes has proven to be very powerful in
establishing the presence of absorption dips, intensity
correlated spectral changes etc.

4. __Recent Developments__

Following the interest in the recent discovery of fast (1-50 Hz) Quasi- Periodic
Oscillations (QPO) in the flux of several bright galactic X-ray sources, a
dedicated software package has been developed as part of the EXOSAT Timing
Interactive System to search for QPO and investigate their properties. A new type
of compact rate buffer, the so-called Millisecond-Type Rate Buffers, has been
defined and implemented in order to store onto disk a very high number of light
curve bins (currently up to 2-4 X 10^{7}, depending on disk, space availability). These rate buffers are accessed by a
dedicated Power Spectrum Program which uses an FFT algorithm and allows storage
of <256 colour-coded power spectra together with the source light curve into
an 'PS image'. This type of display has proven to be a very powerful means of
investigating QPO. The 'PS images' can be analysed and the power spectra fitted
to various models using a dedicated program which allows a fully interactive
selection of the power spectra in order to investigate the possible dependence of
the QPO parameters on source intensity, activity state etc.

5. __Future Developments__

A major rewrite of the EXOSAT Timing Analysis Interactive System will be made
during 1986 in order to:

- make the software more complete and flexible (in
particular the limitations on the maximum number of points which can be analysed
at once, will be made less stringent).

- adapt the package to Vax machines.

- make the system more user-friendly, by standardising the interaction with
the various programs.

__L. Stella__