Table 3
Summary of the flare frequency statistics and distributions, for the CVS serendipitous-stars sample.
| Quantity | A | B | |||
| Raw, | Coverage | Raw, | Coverage | ||
| measured | corrected | measured | corrected | ||
|
|
|||||
| Min. selected signal:noise | 10.0 | ||||
|
|
|||||
| Min. selected peak flux, fX,peak,min | (erg cm-2 s-1) | 2.5 × 10-13 | 1.0 × 10-12 | ||
| Above fX,peak,min: | |||||
| No. of flares in survey | 15 | 16.3 | 10 | 10.2 | |
| No. of flares predicted, all-sky/year | 4.4 × 106 | 2.8 × 106 | |||
| No. of flares predicted per star/year | (a) | 4.3 × 10-2 | 2.7 × 10-2 | ||
| Power-law index, αf | (b, c) | 0.55 ± 0.14 | 0.58 ± 0.15 | 0.94 ± 0.30 | 0.94 ± 0.30 |
| Normalisation, Nref,f | (b) | 7.0 | 7.3 | 10.0 | 10.2 |
| with fX,ref = 1 × 10-12erg cm-2 s-1 | |||||
|
|
|||||
| Flare duty cycle (fraction) | (a) | 4.3 × 10-3 | 2.0 × 10-3 | ||
| (d) | 7.3 × 10-2 | 3.4 × 10-2 | |||
|
|
|||||
| Min. selected peak luminosity, LX,peak,min | (erg s-1) | 2.0 × 1029 | 1.0 × 1030 | ||
| Above LX,peak,min: | |||||
| No. of flares in survey | 14 | 16.5 | 11 | 13.3 | |
| No. of flares predicted per star/year | (a) | 4.3 × 10-2 | 3.5 × 10-2 | ||
| Power-law index, αL | (b, c) | 0.29 ± 0.08 | 0.28 ± 0.07 | 0.38 ± 0.12 | 0.37 ± 0.11 |
| Normalisation, Nref,L | (b) | 8.8 | 10.5 | 11.0 | 13.3 |
| with LX,ref = 1 × 1030erg s-1 | |||||
|
|
|||||
| Min. selected emitted energy, EX,min | (erg) | 1.0 × 1033 | 1.0 × 1034 | ||
| Above EX,min: | |||||
| No. of flares in survey | 13 | 15.4 | 9 | 11.3 | |
| No. of flares predicted per star/year | (a) | 4.03 × 10-2 | 2.9 × 10-2 | ||
| (d) | 11.6 | 8.5 | |||
| (a, e) | 4.9 × 10-4 | 4.4 × 10-5 | |||
| Power-law index, αE | (b, c) | 0.29 ± 0.08 | 0.28 ± 0.08 | 0.47 ± 0.16 | 0.47 ± 0.16 |
| (e) | 0.72 ± 0.20 | 0.56 ± 0.19 | |||
| Normalisation, Nref,E | (b) | 13.0 | 15.4 | 26.6 | 33.1 |
| with EX,ref = 1 × 1033 erg | |||||
Notes. Columns A: results for thresholds (fX,peak,min, LX,peak,min, EX,min) based on lowest value in the set, with minimum S:N ≥ 10.0. Cols. B: as A, but for substantially higher thresholds. (a) Considering all serendipitous-sample stars (504) with 2XMM light-curves, irrespective of detected variability; associated survey on-time ttotal ~ 2.4 × 107 s; (b) from ML fit; (c) no correction has been made to these values, e.g. the bias correction (N − 1) /N suggested by Crawford et al. (1970), which could reduce the values by up to ~10%; (d) considering only serendipitous-sample stars (30) observed to flare; associated survey on-time ttotal ~ 1.4 × 106 s; (e) applying scaling factor based on each star’s quiescent X-ray luminosity and normalised to a quiescent solar X-ray luminosity, see text Sect. 7.4.2 for details.
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