Prof. Chris Koen
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Position: | Senior Professor |
Department: | Statistics and Population Studies Programme |
Faculty: | Faculty of Natural Sciences |
Qualifications: | PhD (Astronomy), PhD (Mathematical Statistics) |
Research publications in this repository | |
ORCID iD | 0000 0003 2291 2660 |
Tel: | 021 959 3258 |
Fax: | 021 959 2909 |
Email: | ckoen@uwc.ac.za |
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Browsing by Subject "Astronomy"
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Item The analysis of indexed astronomical time series – XI. The statistics of oversampled white noise periodograms(Oxford University Press, 2015) Koen, ChrisThe distribution of the maxima of periodograms is considered in the case where the time series is made up of regularly sampled, uncorrelated Gaussians. It is pointed out that if there is no oversampling, then for large data sets, the known distribution of maxima tends to a oneparameter Gumbel distribution. Simulations are used to demonstrate that for oversampling by large factors, a two-parameter Gumbel distribution provides a highly accurate representation of the simulation results. As the oversampling approaches the continuous limit, the twoparameter Gumbel distribution takes on a simple form which depends only on the logarithm of the number of data. Subsidiary results are the autocorrelation function of the oversampled periodogram; expressions for the accuracy of simulated percentiles; and the relation between percentiles of the periodogram and the amplitude spectrum.Item The analysis of indexed astronomical time series – XII. The statistics of oversampled Fourier spectra of noise plus a single sinusoid(Oxford University Press, 2015) Koen, ChrisWith few exceptions, theoretical studies of periodogram properties focus on pure noise time series. This paper considers the case in which the time series consists of noise together with a single sinusoid, observed at regularly spaced time points. The distribution of the periodogram ordinates in this case is shown to be of exponentially modified Gaussian form. Simulations are used to demonstrate that if the periodogram is substantially oversampled (i.e. calculated in a dense grid of frequencies), then the distribution of the periodogram maxima can be accurately approximated by a simple form (at least at moderate signal-to-noise ratios). This result can be used to derive a calculation formula for the probability of correct signal frequency identification at given values of the time series length and (true) signal-to-noise ratio. A set of curves is presented which can be used to apply the theory to, for example, asteroseismic data. An illustrative application to Kepler data is given.Item A detection threshold in the amplitude spectra calculated from Kepler data obtained during K2 mission.(Oxford University Press, 2015) Baran, A.C.; Koen, Chris; Pokrzywka, B.We present our analysis of simulated data in order to derive a detection threshold which can be used in the pre-whitening process of amplitude spectra. In case of ground-based data of pulsating stars, this threshold is conventionally taken to be four times the mean noise level in an amplitude spectrum. This threshold is questionable when space-based data are analysed. Our effort is aimed at revising this threshold in the case of continuous 90-d Kepler K2 phase observations. Our result clearly shows that a 95 per cent confidence level, common for ground observations, can be reached at 5.4 times the mean noise level and is coverage dependent. In addition, this threshold varies between 4.8 and 5.7, if the number of cadences is changed. This conclusion should secure further pre-whitening and helps to avoid over-interpretation of spectra of pulsating stars observed with the Kepler spacecraft during K2 phase. We compare our results with the standard approach widely used in the literature.Item Multicolour time series photometry of four short-period weak-lined T Tauri stars(Oxford University Press, 2015) Koen, ChrisThe paper describes continuous photometric monitoring of four pre-main-sequence stars, probable members of young stellar associations. Measurements, covering at least four nights per star, were obtained by cycling through several filters. The data could be used to choose between aliases of rotation periods quoted in the literature. As expected, the amplitudes of sinusoidal variations decline with increasing wavelength, mildly enough to indicate the presence of coolspots on the stellar surfaces. Variability amplitudes can dwindle from a 0.1mag level to virtually zero on a time-scale of one or two days. A flare observed in CD-36 3202 is discussed in some detail, and a useful mathematical model for its shape is introduced. It is demonstrated that accurate colour indices (σ <5–6 mmag, typically) can be derived from the photometry. The magnitude variations as measured through different filters are linearly related. This is exploited to calculate spot temperatures (800–1150K below photospheric for the different stars) and the ranges of variation of the spot filling factors (roughly 10– 20 per cent). The available All Sky Automated Survey measurements of the stars are analysed, and it is concluded that there is good evidence for differential rotation in all four stars.Item Multicolour time series photometry of the T Tauri star CVSO 30(Oxford University Press, 2015) Koen, ChrisFive consecutive runs of at least five hours, and two shorter runs, of V(RI)C time series photometry of CVSO 30 are presented. No evidence could be seen for planetary transits, previously claimed in the literature for this star. The photometry described in this paper, as well as earlier observations, can be modelled by two non-sinusoidal periodicities of 8 and 10.8 h (frequencies 3 and 2.23 d−1) or their 1 d−1 aliases. The possibility is discussed that star-spots at different latitudes of a differentially rotating star is responsible for the brightness modulations. The steep wavelength dependence of the variability amplitudes is best described by hot star-spots.Item Multicolour time series photometry of the variable star 1SWASP J234401.81−212229.1(Oxford University Press, 2014) Koen, Chris1SWASP J234401.81-212229.1 may be one of a handful of contact binaries comprising two Mdwarfs. Modelling of the available observations is complicated by the fact that the radiation of the eclipsing system is dominated by a third star, a K dwarf. New photometry, presented in this paper, strengthens this interpretation of the data. The existence of such systems will have implications for the statistical distributions of masses in hierarchical multiple star systems.Item An O−C (and light travel time) method suitable for application to large photometric databases(Oxford University Press, 2014) Koen, ChrisThe standard method of studying period changes in variable stars is to study the timing residuals or O−C values of light-curve maxima or minima. The advent of photometric surveys for variability, covering large parts of the sky and stretching over years, has made available measurements of probably hundreds of thousands of variable stars, observed at random phases. Simple methodology is described which can be used to quickly check such measurements of a star for indications of period changes. Effectively, the low-frequency periodogram of a first-order estimate of the O−C function is calculated. In the case of light travel time (LTT) effects, the projected orbital amplitude follows by robust regression of a sinusoid on the O−C. The results can be used as input into a full non-linear least-squares regression directly on the observations. Extensive simulations of LTT configurations are used to explore the sensitivity of results to various parameter values (period of the variable star and signal to noise of measurements; orbital period and amplitude; number and time baseline ofItem A search for p-mode pulsations in white dwarf stars using the Berkeley Visible Imaging Tube detector(Oxford University Press, 2014) Kilkenny, David; Welsh, B.Y.; Koen, Chris; Gulbis, A.A.S.; Kotze, M.M.We present high-speed photometry (resolution 0.1 s) obtained during the commissioning of the Berkely Visible Imaging Tube system on the Southern African Large Telescope (SALT). The observations were an attempt to search for very rapid p-mode oscillations in white dwarf stars and included three DA stars known to be g-mode pulsators (ZZ Cet, HK Cet and AF Pic), one other DA star (WD 1056-384) not known to be variable and one AM Cvn star (HP Lib). No evidence was found for any variations greater than about 1 mmag in amplitude (∼0.1 per cent) at frequencies in excess of 60 mHz (periods <17 s) in any of the target stars, though several previously known g-mode frequencies were recovered.