El riesgo en los colectivos sociales

Earlier in this chapter, I tested how well several candidate timescale metrics could reproduce the known timescales of synthetic lightcurves. While informative, this test has the limitation that it cannot be applied to real data, where the “true timescale” is necessarily unknown. A test thatdoes work for real data is desirable, if only for reassurance that the results ofChapter 4and this chapter

(a)Output Timescale for Sine (b)... for Squared Exponential GP

(c)... for Damped Random Walk

(d)Timescale Repeatability for Sine

(e)... for Squared Exponential GP

(f )... for Damped Random Walk

(g) Timescale Discrimination for Sine

(h)... for Squared Exponential GP

(i)... for Damped Random Walk

Figure 5.21: The timescale calculated from a squared exponential Gaussian process model, plotted as a function of the true underlying timescale. Only runs with an expected 5-95% amplitude of 0.5 mag are shown. Top panels show the average value of the output timescale. Middle panels show the ratio of the standard deviation to the mean output timescale. Bottom panels show the degree by which the input timescale has to change to significantly affect the output timescale. In all plots, blue represents a signal-to- noise ratio of 300, orange represents a signal-to-noise ratio of 20, green a signal-to- noise ratio of 10, and black a signal-to-noise ratio of 4.

163 do not apply only to mathematically tractable signals.

Another criterion a good timescale metric should satisfy is that its output looks plausible under visual inspection of the corresponding lightcurve. This is necessarily a subjective criterion, as con- firmation bias (Nickerson,1998, and references therein) ensures that there will be multiple, possibly very different, values for a timescale that all look “reasonable” when a lightcurve is compared to them a posteriori. Therefore, plausibility is a necessary but insufficient criterion, and should be treated only as a supplement to the more objective tests presented inChapter 4and earlier in this chapter.

For this test, I selected the 41 sources listed inTable 3.3as having bursting or fading behavior. I tested three timescale metrics on this set of lightcurves. The first was a ∆m-∆tplot with ∆tbins in steps of 0.15 dex from 10−1.97_{days to the maximum length of the lightcurve. The characteristic} timescale was defined to be the time bin in which the 90th percentile of the ∆mvalues first exceeds half the lightcurve’s amplitude, itself defined as the difference between 5th and 95th percentiles. The second metric was a peak-finding plot, with the characteristic timescale defined to be the separation between peaks differing by at least half the lightcurve amplitude. The third metric was a Gaussian process fit. The results are presented inTable 5.3.

Correlations between the computed and by-eye timescales are shown in Figures 5.22 and 5.23. The ∆m-∆ttimescale shows a weak correlation with both burst and fade width, but not with burst or fade separation. The peak-finding timescale may be very weakly correlated with event width, but it is not correlated with event separation. The Gaussian process timescale is not correlated at all with any of the by-eye timescales.

I also inspected several lightcurves — those for LkHα139, LkHα174, FHO 15, FHO 19, FHO 25, and FHO 26 — by eye to confirm whether the computed timescale metrics corresponded to real structure in the lightcurve. For the lightcurve of FHO 26, I refer the reader tosubsection 3.6.1. For ∆m-∆t timescales, the comparison was made by estimating the lightcurve amplitude by eye, then searching for pairs of observations (not necessarily associated with bursting or fading) separated by half that amplitude. The range of time separations between such pairs tended to include the ∆m-∆t

timescale, indicating that the timescale is at least roughly consistent with visual inspection of the lightcurve. For peak-finding timescales, I estimated the lightcurve amplitude by eye, then searched for local minima and maxima (again, not necessarily distinct bursting or fading events) separated by at least half that amplitude. Depending on the lightcurve, the separations between these manually identified peaks tended to be 2-3 times longer or 2-3 times shorter than the peak-finding timescale, leaving the peak-finding results difficult to interpret.

∆m-∆ttimescales seem easiest to relate to specific variations within the corresponding lightcurve. Peak-finding timescales are harder to associate with specific structures, and the best-fit timescales produced by Gaussian process models appear to have no correlation at all with any intuitive measure

Source Burst Burst Fade Fade ∆m-∆t Peak-Finding Gaussian Width(s) Separation(s) Width(s) Separation(s) Process 205032.32+442617.4 0.1-0.5 5-40 0.03 2 1.9±0.5 205036.93+442140.8 >352 >640 80 1,100 8.7±0.4 205040.29+443049.0 3.0 >165 1.8 11 0.48±0.04 205042.78+442155.8 0.04-0.12 1-313 0.02 3 26±4 205100.90+443149.8 2-3 13-39 1.3 10 1.06±0.04 205114.80+424819.8 47-56 96-334 10 100 10.2±0.6 205115.14+441817.4 120 >930 10 18 205119.43+441930.5 1-2 4-7 0.3 5 205120.99+442619.6 0.5-2.0 14-80 0.9 6 205123.59+441542.5 43 560 1.8 4 1.04±0.05 205124.70+441818.5 1-3 7-10 0.6 5 0.38±0.03 205139.26+442428.0 6-7 22-50 2.5 18 205139.93+443314.1 50-150 129-264 30 50 205145.99+442835.1 100 >630 3 9 0.85±0.05 205155.70+443352.6 4-6 9-25 1.3 12 205158.63+441456.7 0.5-3.0 7.0 4-16 83-327 1.3 8 0.52±0.04 205203.65+442838.1 36-119 685 0.01 9 2.1±0.2 205228.33+442114.7 1.5 5.78 205230.89+442011.3 3 7.71 0.6 5 0.52±0.02 205252.48+441424.9 2-6 11-21 1.8 9 0.96±0.04 205253.43+441936.3 2-4 11-28 4 8 1.16±0.09 205254.30+435216.3 30-100 298-348 7 13 0.82±0.05 205314.00+441257.8 2-80 29-337 0.9 6 0.59±0.04 205315.62+434422.8 0.5-150 25-610 40 17 1.05±0.03 205340.13+441045.6 2-20 11-31 3-10 11-80 1.8 10 0.90±0.04 205410.15+443103.0 3 8-10 0.9 6 0.64±0.04 205413.74+442432.4 2-5 2-19 1.3 7 205424.41+444817.3 5-11 250-330 0.6 6 205445.66+444341.8 3-20 45-300 0.9 6 0.75±0.06 205446.61+441205.7 2-6 13-62 1.8 6 0.96±0.05 205451.27+430622.6 5-30 30-250 7 50 4.0±0.3 205503.01+441051.9 6 >57 4 12 1.17±0.04 205534.30+432637.1 65 >680 7 4 13.3±1.8 205659.32+434752.9 3-4 11-12 3 11 1.06±0.05 205759.84+435326.5 2.2-18 >100 0.9 5 0.51±0.04 205801.36+434520.5 14-37 29-90 80 71 1.24±0.03 205806.10+435301.4 1.5-5.0 35 1.3 6 0.94±0.06 205825.55+435328.6 2-6 8-123 0.9 6 0.72±0.04 205839.73+440132.8 0.5-4.0 8-210 14 19 205905.98+442655.9 10-15 27-47 1.3 14 205906.69+441823.7 2-3 8-63 0.9 4 0.43±0.05

Table 5.3: The results of applying several timescale metrics to the sample of Table 3.3. All timescales are in days. The first four columns after the source name are the timescales estimated by eye as described inFigure 3.4.1. The last three columns are the timescales returned by ∆m-∆t plots, peak-finding, and Gaussian process fitting, as described in the text.

165

Figure 5.22: Comparison of the computed timescale metrics with timescales determined by eye, for sources showing bursting behavior. The dotted line indicates where the timescales on the two axes are equal. The vertical axis shows a timescale derived from ∆m-∆tplots in the top row, from peak-finding in the middle row, and from a Gaussian process fit in the bottom row. The spread in values along the Gaussian process axis represents the formal 1σuncertainty. The horizontal axis shows the full width at baseline of each bursting event in the left column, and the separation between consecutive peaks in the right column. The spread in values along the horizontal axis represents variation in properties among different bursting events in the same lightcurve.

167

of timescale. Although these results must be interpreted with caution, since I had preconceptions about the effectiveness of the timescale metrics at the time I tested them on specific lightcurves, the results are broadly consistent with the conclusion ofsection 5.9that ∆m-∆tplots are the most appropriate tool for this thesis.