Prof. Chris Koen
Permanent URI for this collection
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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Item Modelling the rotation period distribution of M dwarfs in the Kepler field(Springer Verlag, 2018) Koen, ChrisMcQuillan et al. (Mon. Not. R. Astron. Soc.432:1203, 2013) presented 1570 periods P of M dwarf stars in the field of view of the Kepler telescope. It is expected that most of these reflect rotation periods, due to starspots. It is shown here that the data can be modelled as a mixture of four subpopulations, three of which are overlapping log-normal distributions. The fourth subpopulation has a power law distribution, with P −1/2. It is also demonstrated that the bulk of the longer periods, representing the two major sub-populations, could be drawn from a single subpopulation, but with a period-dependent probability of observing half the true period.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 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 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.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 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 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 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 Multivariate comparisons of the period–light-curve shape distributions of Cepheids in five galaxies(Oxford University Press, 2007) Koen, Chris; Siluyele, I.A number of published tests suitable for the comparison of multivariate distributions are described. The results of a small power study, based on realistic Cepheid log period – Fourier coefficient data, are presented. It is found that a statistic due to Henze has good general performance. The tests are applied to Cepheid observations in the Milky Way galaxy, Large Magellanic Cloud, Small Magellanic Cloud, IC 1613 and NGC 6822. The null hypothesis of equal populations is rejected for all pairs compared, except IC 1613 – NGC 6822.Item Multicolour time series photometry of three periodic ultracool dwarfs(Oxford University Press, 2013) Koen, ChrisPhotometry in I, or contemporaneously in I and R, of the known variable ultracool dwarfs Kelu-1 and 2MASS J11553952−3727350 is presented. The nature of the variability of Kelu-1 appears to evolve on time-scales of a day or less. Both the period and amplitude of the variability of 2MASS J11553952−3727350 have changed substantially since publication of earlier observations of the object. DENIS 1454−6604 is a new variable ultracool dwarf, with persistent and prominent brightness modulations at a period of 2.6 h.Item HE0230–4323: an unusual pulsating hot subdwarf star(Oxford University Press, 2007) Koen, ChrisHE 0230−4323 is a known binary, consisting of a subdwarf star and a companion which is not observable in the optical. Photometric measurements reported in this paper have shown it to be both a reflection-effect and a pulsating variable. The dominant pulsation frequencies changed over the course of several nights of observing, from ∼32–39 d−1 to ∼8–16 d−1. Observations were obtained through B and V filters, and the variations in the two wavebands appear to be approximately 180◦ out of phase.Item The Nyquist frequency for time series with slight deviations from regular spacing(Oxford University Press, 2009) Koen, ChrisThe paper is based on the notion that the Nyquist frequency νN is a symmetry point of the periodogram of a time series: the power spectrum at frequencies above νN is a mirror image of that below νN. Koen showed that the sum SS(ν) = k, [sin 2πν(tk −t )]2 (where tk and t range over the time points of observation) is zero when the frequency ν = νN. This property is used to investigate the Nyquist frequency for data which are almost regularly spaced in time. For some configurations, there are deep minima of SS at frequencies νP νN; such νP are dubbed ‘pseudo-Nyquist’ frequencies: the implication is that most of the information about the frequency content of the data is available in the spectrum over (0, νP). Systematic simulation results are presented for two configurations – small random variations in respectively the time points of observation and the lengths of the intervals between successive observations. A few real examples of CCD time series photometry obtained over several hours are also discussed.Item Fitting power-law distributions to data with measurement errors(Oxford University Press, 2009) Koen, Chris; Kondlo, LIf X, which follows a power-law distribution, is observed subject to Gaussian measurement error e, thenX+e is distributed as the convolution of the power-lawand Gaussian distributions. Maximum-likelihood estimation of the parameters of the two distributions is considered. Large-sample formulae are given for the covariance matrix of the estimated parameters, and implementation of a small-sample method (the jackknife) is also described. Other topics dealt with are tests for goodness of fit of the posited distribution, and tests whether special cases (no measurement errors or an infinite upper limit to the power-law distribution) may be preferred. The application of the methodology is illustrated by fitting convolved distributions to masses of giant molecular clouds in M33 and the Large Magellanic Cloud (LMC), and to HI cloud masses in the LMC.Item The analysis of indexed astronomical time series – X. Significance testing of O − C data(Oxford University Press, 2006) Koen, ChrisIt is assumed that O − C (‘observed minus calculated’) values of periodic variable stars are determined by three processes, namely measurement errors, random cycle-to-cycle jitter in the period, and possibly long-term changes in the mean period. By modelling the latter as a random walk, the covariances of all O − C values can be calculated. The covariances can then be used to estimate unknown model parameters, and to choose between alternative models. Pseudo-residuals which could be used in model fit assessment are also defined. The theory is illustrated by four applications to spotted stars in eclipsing binaries.Item Estimation of the coherence time of stochastic oscillations from modest samples(Oxford University Press, 2012) Koen, Chris‘Quasi-periodic’ or ‘solar-like’ oscillations can be described by three parameters – a characteristic frequency, a coherence time (or ‘quality factor’) and the variance of the random driving process. This paper is concerned with the estimation of these quantities, particularly the coherence time, from modest sample sizes (observations covering of the order of a hundred or fewer oscillation periods). Under these circumstances, finite sample properties of the periodogram (bias and covariance) formally invalidate the commonly used maximum-likelihood procedure. It is shown that it none the less gives reasonable results, although an appropriate covariance matrix should be used for the standard errors of the estimates. Tailoring the frequency interval used, and oversampling the periodogram, can substantially improve parameter estimation. Maximum-likelihood estimation in the time-domain has simpler statistical properties, and generally performs better for the parameter values considered in this paper. The effects of added measurement errors are also studied. An example analysis of pulsating star data is given.Item Detection of an increasing orbital period in the subdwarf B eclipsing system NSVS 14256825(Oxford University Press, 2012) Kilkenny, David; Koen, ChrisNew timings of eclipses made in 2010 and 2011 are presented for the hot subdwarf B (sdB) eclipsing binary NSVS 14256825. Composed of an sdB star and a much cooler companion, with a period near 0.1104 days, this system is very similar to the prototype sdB eclipsing binary HW Vir. The new observations show that the binary period of NSVS 14256825 is rapidly increasing at a rate of about 12 × 10−12 days orbit−1.Item Photometry of the magnetic white dwarf SDSS 121209.31+013627.7(Oxford University Press, 2006) Koen, Chris; Maxted, P.F.L.The results of 27 h of time series photometry of SDSS 121209.31+013627.7 are presented. The binary period established from spectroscopy is confirmed and refined to 0.061 412 d (88.43 min). The photometric variations are dominated by a brightening of about 16 mmag, lasting a little less than half a binary cycle. The amplitude is approximately the same in V, R and white light. A secondary small brightness increase during each cycle may also be present. We speculate that SDSS 121209.31+013627.7 may be a polar in a low state.Item The analysis of irregularly observed stochastic astronomical time-series – I. Basics of linear stochastic differential equations(Oxford University Press, 2005) Koen, ChrisThe theory of low-order linear stochastic differential equations is reviewed. Solutions to these equations give the continuous time analogues of discrete time autoregressive time-series. Explicit forms for the power spectra and covariance functions of first- and second-order forms are given. A conceptually simple method is described for fitting continuous time autoregressive models to data. Formulae giving the standard errors of the parameter estimates are derived. Simulated data are used to verify the performance of the methods. Irregularly spaced observations of the two hydrogen-deficient stars FQ Aqr and NO Ser are analysed. In the case of FQ Aqr the best-fitting model is of second order, and describes a quasi-periodicity of about 20 d with an e-folding time of 3.7 d. The NO Ser data are best fitted by a first-order model with an e-folding time of 7.2 d.Item Improved SAAO–2MASS photometry transformations(Oxford University Press, 2007) Koen, Chris; Marang, F.; Kilkenny, David; Jacobs, C.Near-infrared photometry of 599 stars is used to calculate transformations from the South African Astronomical Observatory (SAAO) JHK system to the Two-Micron All-Sky Survey (2MASS) JHKS system. Both several-term formal regression relations and simplified transformations are presented. Inverse transformations (i.e. 2MASS to SAAO) are also given. The presence of non-linearities in some colour terms is highlighted.
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