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Appendix A: Quality screening of the 2XMM light-curves

We list here the main features found in the data products that were likely to compromise the quality of the light-curves with respect to validity of the detection of “variability” and its characterisation. These features were identified mainly from visual inspection of the graphical products. Identification of any of these features in a dataset led to rejection of the light-curve for the present work.

Type of feature and number of 2XMM-Tycho variable detections rejected:

• Optical loading (see 2XMM Appendix A): 11.

• Confusion and contamination of source flux by another (usually brighter) nearby source: 8.

• Problems in the background determination (e.g. poor background subtraction, background contamination from a nearby source): 7.

• Exposure correction or GTI problem (leading to zeros or NULL-values in some of the source light-curve bins): 2.

• Spurious detection (due to a nearby bright source): 1.

Thus in total, 29 out of the 157 2XMM-Tycho variable detections were rejected.

Of these 29, 11 had 2XMM SUM_FLAG ≥ 3, and none had SUM_FLAG=2 (see 2XMM Appendix D, Sect. D.5 for description of the SUM_FLAG values).

Appendix B: Calculation of the “completeness correction factor” C

Here we outline the calculation of the correction factor, C, used in Sect. 7.4.2 to account for variations in the minimum detectable flare strength. These arose mainly from the source quiescent flux upon which the flare was superimposed. C is the fraction of the survey time in which the flare could have been detected. We note that our primary aim was to demonstrate that our flare rates and related estimates were insensitive to incompleteness at the levels of accuracy needed for our analysis and warranted by the limited numbers in our samples, i.e. to estimate C to better than a factor ~2 and to utilise it at relatively modest correction values, i.e. 1 /C ≲ 2. We wished to generate an estimate of C in a simple and rapid manner, and based on quantities directly available from the 2XMM catalogue, rather than, for example, engaging in extensive simulations.

The minimum flare peak flux detectable above a signal-to-noise threshold of SN_min is: (B.1)where σ_f,cat is the EPIC total-band flux error in the 2XMM catalogue (i.e. column ep_8_flux_err), τ_on is the observation duration (“on-time”), τ_dur is the flare duration, and S:N is evaluated over the time interval τ_dur (Sect. 3.1).

The assumption here is that σ_f,cat provides a reasonable representation of the error on the source time-series. Comparison of the EPIC total-band count-rate error with the count-rate error derived directly from the individual camera (pn, MOS1, MOS2) light-curves indicates that the latter can be a up to a factor ~2 greater than the former (especially for MOS1, MOS2)²⁰. As discussed in Sect. 7.4.2, we have examined the effects of such errors in C on the resulting flare rates and distributions. We have also verified that using σ_f,cat, rather than an error estimate based on the quiescent count rate from the light-curve, results in ≲20% change in the error value.

Strictly, the value of τ_on is not precisely determined, since it varies between cameras (pn, MOS1, MOS2), and a flare (or other variability) could be flagged in any of the active cameras. Our solution for the present purpose was to use MOS1 on-time if available, else MOS2, else pn. This introduces an acceptably small “uncertainty” in τ_on, e.g. ≲30% variation in derived τ_on in ~80% of cases.

C is given by the normalised, cumulative distribution of observation on-times, i.e.: (B.2)where n is the total number of observations in the sample being considered (and will, in general, include observations where no flares were detected), and the set of [f_{X,peak,SNmin,i},i = 1,n] is ordered by increasing value.

C can also be expressed in terms of flare peak luminosity or emitted energy, via:

where d is the source distance.

Alternatively, C can be expressed in terms of maximum observable distance: Example curves are shown in Fig. 24.

Appendix C: Additional tables and figures

Appendix C.1: The stars in the 2XMM-Tycho flare survey

Table C.1. The stars in the 2XMM-Tycho flare survey (1 row per XMM observation).

Appendix C.2: The flares in the 2XMM-Tycho flare survey

Table C.2. The flares and other time-variability events in the 2XMM-Tycho flare survey (1 row per event).

Appendix C.3: X-ray and ultraviolet light-curves

Appendix C.4: X-ray count-rate and hardness-ratio light-curves

© ESO, 2015