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On-demand light curves — Online Documentation

Contents

Summary

When you build a light curve via the online product generator, the result will be available through a web page. From this page you can view the curves, download the plots or the data files, modify the plots, either by changing the axis scales or by showing/hiding systematic errors and potentially unreliable data. Here, we explain these controls and describe the different products presented on the web page.

The process of light curve creation is described in full in two refereed papers: Evans et al. (2007, A&A, 469, 379) and Evans et al. (2009, MNRAS, 397, 1177). Most of the questions we are commonly asked about the light curves can be answered by looking at these papers. An overview of the algorithm is also given online.

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Plots and downloads

There are up to three light curves available to view and download, followed by a list of up to 16 files. The images are:

Basic light curve
A light curve showing the source count rate, after the background has been subtracted and corrections for pileup, bad columns, and the size of the source-data extraction region have been applied.
Detailed light curve
As above, but with the background level shown on the same plot (note that at low count rates, the net source count rate can lie below the background rate but still be a 3-σ detection). The fractional exposure is also shown, in the bottom panel.
Hardness ratio
Similar to the basic light curve, but in two bands. The bottom panel is the ratio: hard/soft. The default bands are 1.5—10 keV and 0.3—1.5 keV, but these can be changed.

The links at the foot of the page include postscript versions of all of the plots, the ASCII versions (which can also be reached by clicking on the images), and various other files which are described under File formats and contents below.

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Modifying the plots

There are up to three ways in which you can manipulate the plots shown, which are described below. If the light curve includes WT mode data then you can toggle whether the systematic errors are shown, and if there are ‘unreliable’ data points then you can select whether or not to show them. These controls affect all plots on the page simultaneously, and also the ASCII file linked to by the plots. You can also rescale the plots, that is, change the axis limits and regenerate the graphical image of the light curve.

WT-mode systematic errors

WT-mode data are subject to extra uncertainties in addition to the statistical errors, when the source is near to the bad columns on the CCD or the edge of the field of view, or the data are piled up. This uncertainty is understood and calibrated, and we add an error to each WT-mode data point which reflects this. For simplicity, we refer to this as a systematic error, that is, it reflects an uncertainty in the absolute flux level of the object (a DC offset). This error will be different each time the spacecraft slews to the object, so the systematic error should be considered when comparing the flux level of an object in one snapshot with that in another (of course, since we have calibrated this as a 1-σ error, it is expected that for a constant source, 1 in 3 snapshots will not be consistent with the rest). In reality, the error is not always systematic in nature but can vary in magnitude between bins in the same snapshot, therefore whether this error should be taken into account should be decided on a case by case basis, as we now explain.

The systematic error is caused by inaccurate knowledge of the source position on the XRT CCD, and is a calibrated quantification of the uncertainty caused by this inaccurate knowedge (full details are at the end of this section). So if the source maintains a constant position on the CCD, this error is purely systematic: all datapoints in a snapshot are affected in exactly the same way. Therefore in this case, the systematic error should not be considered when evaluating point-to-point variation within a snapshot, otherwise the significance of such variation will be underestimated. On the other hand, if the object is moving on the CCD, the ‘systematic’ error may be variable within a snapshot. For example, if our measurement of the source position on the CCD is incorrect by one pixel, but the source is 5 pixels from the bad columns, then the systematic error caused by the poor position is small; but if the spacecraft moves such that the source drifts onto the bad columns, then the systematic error will get larger as the source moves towards and onto the columns. In this case, the variation between the bins within that snapshot is being exaggerated by the poor positional information, and therefore the ‘systematic’ error should be used when considering the significance of those variations.

The practical impact of this is that, in order to evaluate the significance of intra-snapshot variability, one must check whether the source position within the CCD is stable. Since in WT mode only 1-dimensional position information is available, only DETX position variations need considering. On the light curve pages a link is provided above each light curve, entitled, ‘View systematics and position variation’. This opens up a plot showing the DETX position of the object and the fractional systematic error, as a function of time. This can be used to decide whether or not the source remains in a stable position during the time interval in question (this plot can also be rescaled to zoom in on a specific time range. An example is given in Fig. 1. During times where the DETX position is varying (within a snapshot) the systematic error should be taken into account when assessing source variability; during times where DETX is constant, the systematic can be safely disregarded, for the evaluation of source variability within the snapshot. At all times, when determining the absolute flux level, the systematic should be included.

The systematic and position plot for one snapshot of Mkn 421 observations The light curve corresponding to the previous plot

Fig. 1. Left: An example of position variation and the resulting systematic error factors. This shows one snapshot in which the object moves significantly on the CCD which, due to the proximity to the bad columns, causes significant uncertainty at early times. Thus the variation seen in the light curve (right) at the start of the snapshot should only be interpreted when the systematic errors are included.

As Fig 1 shows, the systematic error plotted is actually a factor, since (see below) it is really an uncertainty in the PSF correction factor that is applied to the light curve.

By default, the systematic errors is included in the light curves on the repository, however by deselecting the check box above the light curve, these can be turned off. Note that the checkboxes are linked, so clicking on any of them toggles the inclusion of systematic errors for all of the plots on the page. If the GRB is not piled up or near the bad columns or field-of-view edge, then the systematic errors are negligible, and toggling this box will make no difference to the light curves.

More detail: The need for, and determination of, the systematic error

The systematic errors arise in cases where some of the events from the source are lost, either because they lie over the bad columns or outside the field of view, or because the core of the PSF had to be excluded because of pile up. In each of these cases, when the light curve is constructed the instrumental PSF is used to calculate the fraction of events that were lost, and the count-rate is multiplied by the corresponding correction factor. However, in order to do this calculation correctly, the position of the source on the XRT CCD must be known accurately. For example, if it is believed that the wings of the PSF are over the bad columns such that only 2% of the flux is lost, whereas in reality the source is much closer to those columns and 30% of the flux is lost, then the correction factor will be far too small and consequently the light curve bins at those time will report a spuriously low count-rate. Or, in the case of pile up, if we believe we are excluding the central 4 pixels of the PSF, but actually the annulus is not correctly centred on the source, then the correction factor will clearly be wrong.

To solve this problem, we use PSF centroiding once per snapshot to determine the position of the source in the XRT's RA/Dec coordinate frame. This may not be the same as the ICRS RA/Dec system, due to uncertainties in the spacecraft attitude, hence the need to centroid repeatedly. Although it is the CCD position we are interested in, we need to centroid in RA & Dec, because Swift does not remain stationary while on target, but moves slightly, thus the PSF in the raw CCD images becomes smeared. The spacecraft attitude information corrects for these movements, making the PSF well defined and stable in the RA & Dec frame (although there is a 3.5″ systematic uncertainty associated with Swift's absolute attitude, the relative attitude information appears to be stable within an orbit. That is, the size and direction of the small movements Swift makes while pointing are well described in the attitude files.). Note that this per-snapshot centroiding in WT mode is performed even if you chose not to centroid on the main product generator form: the WT mode data are not reliable without this centroiding.

Once the source position in the XRT coordinate frame has been determined, we use the attitude information from the spacecraft to convert the RA & Dec of the source into a CCD-coordinate position as a function of time. The uncertainty in the PSF centroiding is well constrained as a Gaussian with σ=0.64 pixels. Similarly the WT mode PSF is known, as is the location of the bad columns, and the box or box annulus within which source events are collated. Therefore, for a given measured CCD position, we can work out the probability of the source really being at any true CCD position, and how wrong the measured count-rate would be given that combination of measured and true positions. Integrating this over the Gaussian uncertainty in the centroiding output allows us to produce a systematic error in the correction factor as a function of the measured CCD position of the source, this is shown in Fig. 2. If this error in the correction factor is Ecf, then the error in the count-rate caused by the centroiding inaccuracy is Ecf(R-1), where R is the measured (uncorrected) count-rate. This can then be added in quadrature to the statistical error on the count-rate. The plot below shows the fractional error as a function of measured position on the CCD. As can be seen, this is slightly asymmetric, so the errors on the final light curve are also asymmetric.

The systematic error as a function of CCD position

Fig. 2 The 1-σ fractional systematic error as a function of the measured position of the source on the CCD. The upper and lower curves show the positive and negative errors respectively.

Unreliable data points

If the position of the object within the XRT CCD is not known, the count-rate may be unreliable. In part, this is due to the issues described above, but also of course, even in the absence of bad columns and pile up, the source extraction region needs to be centred on the source.

This is why we recommend allowing the software to try to centroid if possible. In that case a “default position” is determined from that centroid; if you do not allow centroiding then your input position will be used as the default position. As the XRT astrometry has a nominal accuracy of 3.5″ (90% confidence), the light curve software attempts to recentroid on the object for each snapshot (in PC mode this does not happen if you selected not to centroid). In any case that a centroid cannot be found, or is more than 12″ in WT mode / 20″ in PC mode from the default position, the default position is used, but the data from that snapshot are considered unreliable.

If unreliable data are found, a warning appears at the top of the results page to warn of this fact, give some information about the affected times, and a control is provided to toggle whether those data are included in the light curve. Note that “unreliable” does not mean “wrong” and in many cases the data will be reliable, it is only if the spacecraft astrometry is particularly bad that a problem is expected: the toggle switch is to draw your attention to the questionable data so that outlying values caused by bad centroids can be spotted.

Rescaling light curves

Before each of the light curve images is a link inviting you to "rescale" the light curve. This opens a new panel from which you can choose the axis limits, and whether they are linear or logarithmic, and then replot the data. Note that, unlike rebinning this does not change the data, only the visualisation.

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File formats and contents

The light curve images all serve as links to the data file from which they were produced, the formats of these files are discussed below. After the images there is a series of links to different files which are not plotted, but contain more information. The formats of these files are also given below. Note that whether or not the light curve data includes systematic errors and the bad WT points depends on the settings of the controls, described above.

The Basic Light Curve

The Basic Light Curve shows the count-rate as a function of time. The related ASCII file is ready for use in QDP, thus begins with a READ TERR line (to tell qdp which columns contain errors) There are 6 columns in this file, which are:

  1. Time
  2. Time -- positive error
  3. Time -- negative error
  4. Source count rate
  5. Positive error in count rate (1-σ)
  6. Negative error in count rate (1-σ)

There are up to five datasets in the file, separated by a line of NO NO NO NO NO, (again, for compatibility with QDP). The datasets appear in the following order: Windowed Timing (WT) settling mode data, WT data; WT upper limits; Photon Counting (PC) data; PC upper limits. Depending on the object, some of these may be missing, however each dataset begins with a comment (denoted by a leading !) identifying it.

The Detailed Light Curve

The Detailed Light Curve contains the information from the Basic Light Curve and also the background level in the top panel. The lower panel shows the fractional exposure in each bin. Note that the background level is the expected background rate in the source region, however as the source region is dynamic (it is smaller when the source is fainter) some correlation between source and background count-rates is expected.

The columns in the ASCII file are the same as for the basic light curve, however there are more datasets (again separated by lines of NO entries): the count-rate, upper limits (if applicable), background level and fractional exposure; first for WT mode then PC mode.

The Hardness Ratio Light Curve

The hardness ratio plot contains 3 panels, showing the hard-band data in the top panel, the soft-band data in the middle, and the hardness ratio in the bottom panel. The hardness ratio is defined as Hard/Soft. By default the hard and soft bands are 1.5—10 keV and 0.3—1.5 keV respectively, although these can be changed in the Light curve details forms before building the curve.

The hardness ratio ASCII file again contains the same basic 5 columns as in the basic light curve, with three datasets: hard band data, soft band data and hardness ratio, per instrument mode (WT settling mode, WT mode, PC mode).

Detailed data downloads

The files below the images comprise postscript versions of each light curve, per-mode light curves (referred to as the basic data), a detailed dataset per mode and event lists. The basic data are the same format as the basic light curve, whereas the detailed data contain many more fields, giving all available information about each bin. The columns in the detailed files are:

  1. Time
  2. Time -- positive error
  3. Time -- negative error
  4. Net source count rate
  5. Positive error in the above (1-σ)
  6. Negative error in the above (1-σ)
  7. Fractional exposure
  8. Background rate
  9. Error in background
  10. Total correction factor
  11. Total counts measured in the source region
  12. Expected number of background counts in the source region
  13. Exposure time in the bin (i.e. bin width * fractional exposure)
  14. Detection significance in this bin
  15. Signal-to-noise ratio in this bin
  16. The fractional systematic error in the negative direction (WT only)
  17. The fractional systematic error in the positive direction (WT only)

The "total correction factor" is the ratio of the corrected count rate to observed count rate in this bin. The corrected count rate has been amended to account for: bad pixels/columns, field of view effects, pile-up and source counts landing outside the extraction region.

Sigma is the detection significance of the source in this bin (=net counts/error in bg counts for a frequentist bin. For a Bayesian bin it is the confidence level at which the source count rate is above 0). For an upper limit, the value written is the detection significance of the data which were replaced with the limit. The limit is calculated using the Bayesian method (see Kraft, Burrows & Nousek, 1991, ApJ, 374, 344) and by default is at the 3-σ level.

The signal-to-noise ratio is simply the count-rate divided by its negative error.

The fractional systematic error is the multiplicative component of the error which reflects the systematic errors related to position uncertainty. For example, in the positive direction, if Eup is the extra error component, and Rmax is the 1-σ upper bound on the count-rate value including this component:
Eup = Rmax - R
     = R*S -R
     = R (S-1)
where R is the count-rate in the bin, and S is the fractional systematic error in the positive direction, and E is the resultant systematic error which has to be added in quadrature to the statistical error on the count rate to give the final error. If the ‘Include systematic errors?’ check-box is selected, the count-rate error already includes this component.

Event lists

The event lists (source and background for each mode), contain all source or background events selected during the light curve creation. As well as the standard columns (TIME, position information, energy etc), the following information has been added:

  1. SRCRAD - Source extraction region radius (pixels).
  2. PUPRAD - Radius excluded due to pileup (arcseconds) - source event lists only.
  3. SRCAREA - Area of the source extraction region (square pixels) - background event lists only.
  4. BGAREA - Area of the background extraction region (square pixels) - background event lists only.

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How to rebin the data

If, after creating a light curve, you decide that you would like to change the binning used, you can do this without rebuilding the light curve. Your original binning will not be lost. The “Rebin this light curve” link will take you to a page with a form similar to the light curve options from the page you used to build the light curve. You can select the new binning options here and submit the form. Your light curve will be rebinned: this usually takes a few seconds (unless there is a large number of Bayesian bins), and is much quicker than the original light curve creation. The new light curve will appear on a new page, which contains a link back to your original products.

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