MINBAR X-ray burst light curves / method
Generating and preparing light curves
All light curves were extracted for the full bandpass and with a
resolution of 1 s. The basis for the extraction was a pre-determined
list of burst onset times. Standard, a time frame of 50 s before till
300 s after the onset time was extracted. For incidental long bursts
(from particularly GX 17+2), these time frames were chosen on a
burst-by-burst case.
RXTE
For RXTE, the light curves were extracted from the 'standard-1' data
(0.125 s resolution, no energy resolution, PCUs resolved). For
incidental cases, data in this mode were lacking and event-mode data
were employed instead. The light curves were normalized to the number
of active PCUs and the collimator response. The collimator response
was calculated as one minus the off-axis angle of the source in
degrees. A background level was subtracted that is the average of the
flux between -22 and -7 s with respect to the burst onset time. No
deadtime correction was applied. Note that these light curves are
subtracted for background emission as well as source persistent
emission.
WFC
For WFC, the light curves were generated from PSF fitting 1-s images
between -50 and +300 s from burst onset. The source position and PSF
shape is fixed in these fits, only the flux is left free. The source
position was determined in an iterative manner: 1) the burst time and
duration is identified in a light curve of the complete detector; 2)
an image is reconstructed for this time frame; 3) the burst source is
identified in this image; 4) an imaged light curve is generated for
this source using the initial position; 5) this light curve is
employed to determine the optimum time frame for the best
signal-to-noise ratio; 6) a new image is determined for this optimum
time frame; 7) the most accurate source position is determined from
this image. Note that these light curves are not subtracted for source
persistent emission.
JEM-X
The light curves were obtained from Duncan. I am unaware of the manner
in which they were generated, but they seem to be generated in two
different manners, since they seem to have two different units: one in
c/s/collimator-response and the other in c/s/cm2. There are 268 bursts
for which both JEM-X1 and JEM-X2 were active. The signals from both units
were combined and divided by 2 to keep the same normalization.
Fitting light curves
First, the light curves needed to be normalized to the same flux
unit. For the PCA data, the light curves were re-normalized from
c/s/PCU to c/s/cm2 by division through 1300. For JEM-X, some light
curves needed to be re-normalized from c/s to c/s/cm2 by division by
100. Times were redefined to be measured with respect to input burst
onset time.
The following tasks were carried out
- Determine in the 350-s data peak flux and time. These are calculated for 3
time scales:
1, 3 and 5 s. The 1-s time scale is the standard, but if the peak flux
significance is smaller than 2 and the difference between the 5-s and 1-s
peak time is more than 6 seconds and the 5-s peak flux is at least
half the 1-s peak flux, the peak flux and time are re-determined from
within the 5-s time frame of the 5-s peak.
- The background as determined between -50 and -15 s was determined
and subtracted. If there was no data in that time frame, no background
was subtracted and the burst flagged 'p'.
- The burst onset time is re-determined, different for the PCA and the other
instruments: for the PCA the burst onset time is set by the time bin where
the flux gradient is largest positive, within the time frame between the
peak time and 20 s earlier. For the other instruments, the burst onset time
is defined to be the time of the 2nd time bin from the peak down that has
a negative flux. If the new start time is more than 20 s earlier than the
previously determined start time, the latter remains in place.
- Determination of two kinds of burst rise times. The first is the
number of 1-s bins with fluxes 5sigma above the background till the
peak. The second is the number of 1-s bins with fluxes above a
certain threshold. This threshold is defined to be 5% of the peak
flux. The latter is provided in the output table.
- Determination of start data point for the model fit of the decay phase.
This is empirically determined to be the data point where the flux is
larger than 75% of the peak flux when moving from the end of the burst to
peak. It sometimes happens that lower data points occur closer to the peak.
- Three model fits to the decay phase beyond the start point defined in 5.
- Exponential decay, with free parameters flux at t=0, exponential decay
time and background level
- Power law decay, with fixed parameter pownorm which is the difference
between the time of burst onset and fit start, and free parameters the
flux at t=fit start, power law index and background level. Note that
the power law index is a strong function of pownorm. Ergo, if pownorm
is badly determined (in all WFC and JEM-X data), then the index is
bad representative of the true index
- Power law decay plus a Gauss 'hump'. Many bursts have a hump, probably
due to residual rp-burning, which is modeled by a 1-sided Gauss function
with the fixed centroid at the burst onset. The two addition free
parameters are the Gaussian standard deviation and normalization.
It turns out that all WFC and JEM-X data can satisfactorily be modeled
with the exponential decay or power law, while the PCA data generally is
better modeled with either the pure power law or the power law plus Gauss.
- Burst parameters are determined:
- peak flux (see 1) and uncertainty
- burst duration and uncertainty. This is determined from the time
interval when the flux is above a threshold flux which is defined as 5%
of the peak flux. The interval end time is determined from the model fit
and the begin time as specified in 3. The 5% number is empirically
determined as a compromise between accuracy (lower values are more
uncertain since one reaches the noise level in WFC and JEM-X data) and
best representative of the burst duration.
- fluence (in c/cm2) and uncertainty. This is the sum of the integral
under the best fit model curve and the sum of all data points before
that until the burst onset time.
- For easy comparison with the literature, the fitted exponential decay time
is also provided in the results, even if the fit is bad (as in most PCA
data).
- 4-panel plots are generated of 1) the light curves with the
fitted exponential and power-law+gauss model running through the data
points (flux logarithmically plotted for the PCA curves and linearly
for the other curves) and 2-4) the deviations of the data points in
units of sigma with respect to the three models. Some fit parameters
are indicated, as well as the goodness-of-fit chi2-red.
- A visual inspection of all plots was carried out, to signal cases
where the fit was inappropriate and repair this. This includes cases where
- the start time is incorrect. This may presumably happen in
noisy data when the point with the gradient cannot easily be
identified (WFC and JEM-X data).
- the fit was inappropriate, usually because the data were so
noisy that the 75% cut off point ended up to late. This happens
quite often in WFC and JEM-X data In this case, the first data
point of the fit was forced closer to the peak to allow for
significant coverage of a decay phase.
- a confusing signal from another source was in the 350-s time
span. This may happen in PCA data, because those are not imaging,
particularly in galactic centre fields and Rapid+Slow Burster
fields. The burst may be cut short to mend this.
800 bursts (12%) had to be manually handled to obtain good fits. Therefore,
these bursts have different settings (either not 350-s data stretches or
start fit earlier or later in the burst than the 75% point).
- Additional fit parameters are saved in another file.
Calibration
The data need to be calibrated between the three instruments. This can
be done in two ways:
- Investigate bursts that were detected by multiple instruments. 15
bursts were detected by both PCA and WFC, 10 by both PCA and
JEM-X. None were detected by all three (INTEGRAL launched 2 years
after the termination of WFC). The comparison in peak flux is
reasonably fine with deviations ranging between - and + sigma. The
comparison in exponential decay time is fair between PCA and WFC, less
for PCA and JEM-X for which JEM-X decay times are generally lower. The
comparison in duration is similar as for exponential decay time, even
though for some PCA bursts this is based on a different model than the
WFC/JEM-X bursts. Lastly, the fluence comparison is most unfavorable
with JEM-X and WFC data generally showing less fluence by a factor of
1 to 2.
- Investigate histograms of all bursts of particular sources that are
known to exhibit reproducible burst parameters, most notably all
parameters of GS 1826-24 and the decay times of 4U 1728-34. These all
seem to be rather consistent.
Exceptions
The following bursts have been excluded from the analysis at a late stage:
RXTE-PCA
- 174804.8-244-PCA-4090-MJD55489.52815_lc.txt: this appears to be
the start of an observation
- 0918-549-PCA-2893-MJD52254.33611_lc.txt: accretion event in
2S-0918-549? (not the flux or time profile of an X-ray burst)
- 1744-300-PCA-3725-MJD54618.32132_lc.txt: this appears to be the
start of an observation
- 2123-058-PCA-8242-MJD55792.87627_lc.txt: this low and slow burst is only
apparent in PCU1 and not in the active PCU2
BeppoSAX-WFC
GX354-0_OP08769_W1_N12_200s.txt: this is actually a type II burst
from the Rapid Burster
Jean in 't Zand
(SRON,
30-Aug-16