Predictions on the detectability of short timescale variability with Gaia
3.3 Detectability results in an ideal situation
685.18 685.20 685.22 685.24 685.26
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Kepler Mflare 9726699
Relative times [d]
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Figure 3.5: Examples of transient light-curve templates. Left: M dwarf flare template fromKepler optical light-curve. Right: SN template fromAAVSO, inV band.
the time between the beginning of the event and its peak, the time between the peak and the return to quiescent magnitude, and the sum of the increase and decrease durations.
The magnitude of the simulated transient source is taken equal to the quiescent mag-nitude of real astronomical object associated with the template used.
Finally, I generate the set of observation times following the appropriate time sampling and over the required timespan, and I compute the corresponding magnitudes from my smoothed template. Similarly to what is done in the periodic case, from each transient template I generate two different light-curves:
• Thecontinuouslight-curve, noiseless, with a dense and perfectly regular time sam-pling, over a timespan of∆t∼τtotthe total duration of the transient event, with 1000 points per light-curve,
• TheGaia-likelight-curve, with a time sampling following the Gaia scanning law for a random position in the sky, over a5year timespan, adding noise according to the realGaiamagnitude-error distribution (see Figure 3.4).
Note that, for transientGaia-like light-curves, I ensure that at least a part of the tran-sient event is sampled, and not falling completely in a gap between two successive mea-surements.
3.3 Detectability results in an ideal situation
For each simulated continuous light-curve, I calculate the associated variogram, for the appropriate lag values defined by the underlying time sampling (i.e. explored lags are multiples of the time intervalδt). Here, because the continuous time sampling is perfectly regular, no binning of the time differences is required to form the magnitude pairs and calculate the variogram values. Figures 3.6 and 3.7 show one example of continuous light-curve simulated, for each of the periodic variable types listed in Table 3.1, together with the corresponding variograms, referred to as theoretical variograms. Similarly, Figure 3.8 represents examples of simulated M dwarf flare and SN simulated continuous light-curves and their theoretical variograms.
Then, I apply the short timescale detection criterion described in Section 3.1, with γdet = 10−3mag2, which corresponds to a standard deviation around 0.03mag, and the
52
short timescale limit fixed atτdet ≤0.5d. As shown in Figures 3.6, 3.7 and 3.8, all the vari-able examples presented here are flagged as short timescale candidates with the adopted criterion, withτdet ≈91min for theβCephei example,τdet≈9.1min for theδScuti exam-ple,τdet ≈18min for the Algol binary example,τdet ≈11min for the contact binary exam-ple,τdet ≈14min for the RRab example,τdet ≈11min for the RRc example,τdet ≈ 3.6min for the ZZ Ceti example,τdet ≈ 24s for the AM CVn example,τdet ≈ 86s for the M dwarf flare example andτdet ≈9.6h for the supernova example.
3.3.1 Periodic variations
Among the 800 periodic variable simulations in the continuous data set, 603 (75.4%) are flagged as short timescale variable with the adopted criterion, and 197 (25.4%) are missed. The main discriminating pattern between the flagged and missed sources is the simulation amplitudeA, which strongly influences the maximum variogram value in the variogram plot, as can be seen in Figure 3.9. With our choice ofγdet, the amplitude limits for detecting short timescale variables in an ideal noiseless case are:
• A&0.14mag for the AM CVn stars,
• A&0.1046mag for the seven other periodic variable types simulated.
This limit is different for AM CVn stars because their eclipses are very brief, so there are many more points sampling the quiescent phase than the eclipses in their time series, which results in variogram values lower than those of other variable types with more sinusoidal-like light-curves. Because of their relatively small variation amplitudes, the β Cephei and ZZ Ceti variable stars appear to be the hardest to detect among the periodic continuous sample, with only a few percents retrieved withγdet = 10−3mag2.
Figure 3.10 represents the distribution of the detection timescale τdet obtained with γdet = 10−3mag2, as function of the so-calledmaximum variation ratein the light-curve, for each periodic type simulated. This maximum variation rate is defined as
maxi>j (|mti−mj
i−tj |)
Globally, there is a tendency for the detection timescale to decrease as the maximum vari-ation rate increases, and the typical range occupied byτdet values is somehow correlated to the variable type. For example, when flagged, ZZ Ceti variables are detected at shorter time lags thanδScuti stars.
From a more practical point of view, the detection timescale can be interpreted in terms of required time sampling for short timescale variable source identification with the var-iogram method. Hence, if one plans to perform high cadence photometric monitoring of some astronomical target, and if the instrument accuracy is around 30mmag (which correspond to the detection threshold value used), then the required imaging cadence to enable the detection of a ZZ Ceti star can be as fast as one image every 3 min, depending on its variation amplitude. Actually, the smaller the amplitude, the faster the cadence should be. For AM CVn stars, the τdet range is very wide, and the required cadence for detection with the variogram approach can go down to a few tens of seconds.
As part of the variogram short timescale analysis, I also implemented an automated method to estimate the typical timescaleτtyp of the variation, which in the periodic case should approximate the period P of variability. The idea here is to identify the smallest
54CHAPTER 3. PREDICTIONS ON THE DETECTABILITY OF SHORT TIMESCALE VARIABILITY WITHGAIA
BCEP84 P=0.19519d A=0.05634mag faintMag=15.362mag
P = 0.19519270862622 d
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BCEP84 P=0.19519d A=0.05634mag faintMag=15.362mag
Log(h [d]) Log(γ [mag2])
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DSCT84 P=0.15725d A=0.34478mag faintMag=12.892mag
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DSCT84 P=0.15725d A=0.34478mag faintMag=12.892mag
Log(h [d]) Log(γ [mag2])
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Algol6 P=0.44907d A=0.2994mag faintMag=14.363mag
P = 0.449071273288595 d
Phase
Algol6 P=0.44907d A=0.2994mag faintMag=14.363mag
Log(h [d]) Log(γ [mag2])
Pτtyp
ContactBinary7 P=0.26727d A=0.38012mag faintMag=11.87mag
P = 0.267272314520932 d
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ContactBinary7 P=0.26727d A=0.38012mag faintMag=11.87mag
Log(h [d]) Log(γ [mag2])
Pτtyp
Figure 3.6: Example of continuous phase-folded light-curves (left) and associated theoretical var-iograms (right) for different short timescale periodic variable types. The period used for phase folding is the simulation input periodP. The blue dotted lines show the detection threshold used, and the correspondingτdetfor the considered source. The green line points the simulation period P, and the orange dashed line the typical timescaleτtyp estimated from the variogram analysis.
From top to bottom: βCephei star,δScuti star, Algol-like binary, contact binary.
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RRab1 P=0.4589d A=0.50091mag faintMag=13.812mag
P = 0.458895850096774 d
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RRab1 P=0.4589d A=0.50091mag faintMag=13.812mag
Log(h [d]) Log(γ [mag2])
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RRc1 P=0.28736d A=0.42133mag faintMag=14.805mag
P = 0.287364289829751 d
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RRc1 P=0.28736d A=0.42133mag faintMag=14.805mag
Log(h [d]) Log(γ [mag2])
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ZZCeti94 P=0.0087d A=0.06252mag faintMag=16.92mag
P = 0.00870044477670823 d
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Log(h [d]) Log(γ [mag2])
Pτtyp
AMCVn5 P=0.01197d A=0.20491mag faintMag=15.43mag
P = 0.0119744966925484 d
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AMCVn5 P=0.01197d A=0.20491mag faintMag=15.43mag
Log(h [d]) Log(γ [mag2])
Pτtyp
Figure 3.7: Same as Figure 3.6, but this time for RRab, RRc, ZZ Ceti and AM CVn variable types, from top to bottom.
56CHAPTER 3. PREDICTIONS ON THE DETECTABILITY OF SHORT TIMESCALE VARIABILITY WITHGAIA
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Figure 3.8: Example of continuous simulated transient light-curves (left) and associated theoretical variograms (right), respectively for an M dwarf flare (top) and for a supernova (bottom). The blue dashed lines point the detection threshold used and the corresponding τdet for the considered simulation.
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Figure 3.10: Detection timescale as function of the maximum variation rate, for the continuous data set and for each of the ten simulated variable types. The green dashed line represents the short timescale limit of0.5d. The crosses indicate the sources that are detected (max(γ)≥γ ) but
3.3. Detectability results in an ideal situation
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Figure 3.11: Typical timescale τtyp as function of the simulation period P, for the periodic con-tinuous simulations flagged as short timescale candidates withγdet = 10−3mag2. The black line indicates the first bisector, the grey line corresponds toτtyp =P/2and the green dashed line cor-responds to the short timescale limit of0.5d
lag whose corresponding variogram value is greater than 80% of the absolute maximum of the variogram. Thenτtypis defined by the first local minimum ofγ at lags greater than the lag of this percentaged maximum.
As can be seen in Figure 3.11, the detection timescaleτtyp, deduced from the theoretical variograms of the 603 flagged sources, matches their periodP quite well. For about 54%
of them, we have τtyp ≈ P ±10%. The other 46% consist only in eclipsing binaries and AM CVn stars, and for most of them (35% of the flagged short timescale sources) we have τtyp ≈ P/2±10%, which was quite predictable. Algol-like and contact binary examples presented in Figure 3.7 illustrate this phenomenon. Indeed, during one cycle of an eclips-ing source, due to the presence of two minima (the primary and the secondary eclipse), pairs separated by P/2 have globally similar magnitudes, and therefore the variance of their magnitude difference is smaller, causing a decrease in the variogram plot. The re-maining 11% correspond to sources for which theτtypestimate method points a very local minimum in the variogram, due to small variations in brightness during the quiescence phase, instead of the true first significant dip.
Note that the linear features visible in Figure 3.11 are artefacts due to the simulation principle: the time stepδtis a fraction of the simulation periodP and the lagshare mul-tiples ofδt, hence eachhis also a fraction ofP.
All in all, at this point of my analysis, it appears that, in an ideal situation, the vari-ogram method enables to retrieve short timescale periodic variability, provided the am-plitude of variation is sufficiently large. In most cases, it is possible to deduce from the variograms a good estimate of the underlying period, or of the semi-period for eclipsing sources.
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Mflare SN Detected Not detected
Figure 3.12: Maximum variation rate as function of the amplitude, for the transient simulations in the continuous data set.
3.3.2 Transient variations
Among the 50 transient simulations in the continuous data set, 31 of the 38 simulated M dwarf flares are flagged as short timescale variables, as well as 5 of the 12 simulated SNe. After further investigation, I find that the 11 missed M dwarf flares are the ones with the smallest amplitudes among the simulated sample (Figure 3.12), and they are not detected at all (i.e. max(γ) < γdet). Typically, for the chosenγdet, the amplitude limit for detection of M dwarf flares is A & 0.12mag. As concerns the 7 missed SNe, they are associated to smaller maximum variation rates, with a limit value for being flagged of maxi>j (|mti−mj
i−tj |) & 0.15 mag.d−1. In this case, simulated sources are detected, but because
their detection timescale is longer than0.5d, they are not flagged as short timescale vari-ables.
Similarly to Section 3.3.1, the detection timescale can be interpreted as a prescription for future photometric follow-up. Thus, to detect an M dwarf flare from the ground with an instrument whose accuracy is around30mmag, the required observing cadence can be as high as every4min (Figure 3.10).
As for periodic variables, I estimate the different typical timescales revealed by the the-oretical variograms of the flagged transients. From visual inspection of these variograms, we note the following structures:
• A flattening in the variogram plot, at shorter lags, with associated timescaleτtyp,plateau. For e.g. the M dwarf flare example in Figure 3.8, this flattening occurs around 10−2.6d∼3min.
• A peak towards longer lags, occuring at timescaleτtyp,peak
3.3. Detectability results in an ideal situation
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Figure 3.13: Typical timescales as function of the event durations, for the transient continuous simulations flagged as short timescale candidates withγdet = 10−3mag2. The black line indicates the first bisector, and the green dashed line corresponds to the short timescale limit of0.5d
• A valley after the aforementioned peak, starting at timescaleτtyp,valley
These typical timescales trace the increase, decrease and total duration of the transient, respectively. As can be seen in Figure 3.13, the values obtained match quite well with the event durations, thoughτtyp,valley slightly overestimates the total duration.
To conclude, similar to Section 3.3.1, we see that in the ideal case, the variogram method enables to detect fast transient events such as M dwarf flares, provided their am-plitude is higher than about0.12mag, as well as some supernovae. Moreover, the typical timescale estimates retrieved from theoretical variograms recover the characteristic dura-tions of the simulated transient events quite well.
60