Models to predict the parameters of ship voyages in the Arctic: existing approaches and possible ways of development

Any information support system for Arctic shipping requires a ship transit model as one of the key elements that allows for strategic analysis, operational planning of vessel voyages, and ice routing of a ship. At the same time, there is no single recognized approach to develop such a model, due to the complexity of ice cover in terms of its impact on shipping. In this article, we have identified and analyzed three principal approaches to predict the parameters of vessel voyages in the Arctic. They are (1) semi-empirical models to estimate the vessel resistance in ice and then calculate propulsion performance, (2) numerical methods to model ship-ice interaction and calculate ice resistance, (3) statistical models to assess the ship speed based on regression equations or neural networks. Analysis of the strengths and weaknesses of each approach allowed us to propose a concept to develop the ship transit model for practical application.

Going back to basics: accelerating exoplanet transit modelling using Taylor-series expansion of the orbital motion

ABSTRACT A significant fraction of an exoplanet transit model evaluation time is spent calculating projected distances between the planet and its host star. This is a relatively fast operation for a circular orbit, but slower for an eccentric one. However, because the planet’s position and its time derivatives are constant for any specific point in orbital phase, the projected distance can be calculated rapidly and accurately in the vicinity of the transit by expanding the planet’s x and y positions in the sky plane into a Taylor series at mid-transit. Calculating the projected distance for an elliptical orbit using the four first time derivatives of the position vector (velocity, acceleration, jerk, and snap) is ∼100 times faster than calculating it using the Newton’s method, and also significantly faster than calculating z for a circular orbit because the approach does not use numerically expensive trigonometric functions. The speed gain in the projected distance calculation leads to 2–25 times faster transit model evaluation speed, depending on the transit model complexity and orbital eccentricity. Calculation of the four position derivatives using numerical differentiation takes $\sim 1\, \mu$s with a modern laptop and needs to be done only once for a given orbit, and the maximum error the approximation introduces to a transit light curve is below 1 ppm for the major part of the physically plausible orbital parameter space.

RoadRunner: a fast and flexible exoplanet transit model

I present RoadRunner, a fast exoplanet transit model that can use any radially symmetric function to model stellar limb darkening while still being faster to evaluate than the analytical transit model for quadratic limb darkening by Mandel & Agol (2002). CPU and GPU implementations of the model are available in the PyTransit transit modelling package, and come with platform-independent parallelisation, supersampling, and support for modelling complex heterogeneous time series. The code is written in numba-accelerated Python (and the GPU model in OpenCL) without c or Fortran dependencies, which allows for the limb darkening model to be given as any Python-callable function. Finally, as an example of the flexibility of the approach, the latest version of PyTransit comes with a numerical limb darkening model that uses LDTk-generated limb darkening profiles directly without approximating them by analytical models.

Exomoon indicators in high-precision transit light curves

Context. While the Solar System contains about 20 times more moons than planets, no moon has been confirmed around any of the thousands of extrasolar planets discovered so far. Considering the large computational load required for the statistical vetting of exomoon candidates in a star–planet–moon framework, tools for an uncomplicated identification of the most promising exomoon candidates could be beneficial to streamline follow-up studies. Aims. Here we study three exomoon indicators that emerge if well-established planet-only models are fitted to a planet–moon transit light curve: transit timing variations (TTVs), transit duration variations (TDVs), and apparent planetary transit radius variations (TRVs). We re-evaluate under realistic conditions the previously proposed exomoon signatures in the TTV and TDV series. Methods. We simulated light curves of a transiting exoplanet with a single moon, taking into account stellar limb darkening, orbital inclinations, planet–moon occultations, and noise from both stellar granulation and instrumental effects. These model light curves were then fitted with a planet-only transit model whilst pretending there were no moon, and we explored the resulting TTV, TDV, and TRV series for evidence of the moon. Results. The previously described ellipse in the TTV-TDV diagram of an exoplanet with a moon emerges only for high-density moons. However, low-density moons distort the sinusoidal shapes of the TTV and the TDV series due to their photometric contribution to the combined planet–moon transit. Sufficiently large moons can nevertheless produce periodic apparent TRVs of their host planets that could be observable. We find that Kepler and PLATO have similar performances in detecting the exomoon-induced TRV effect around simulated bright (mV = 8) stars. Although these stars are rare in the Kepler sample, they will be abundant in the PLATO sample. Moreover, PLATO’s higher cadence yields a stronger TTV signal. We detect substantial TRVs of the Saturn-sized planet Kepler-856 b although an exomoon could only ensure Hill stability in a very narrow orbital range. Conclusions. The periodogram of the sequence of transit radius measurements can indicate the presence of a moon. The TTV and TDV series of exoplanets with moons could be more complex than previously assumed. We propose that TRVs could be a more promising means to identify exomoons in large exoplanet surveys.

MuSCAT2 multicolour validation of TESS candidates: an ultra-short-period substellar object around an M dwarf

Context. We report the discovery of TOI 263.01 (TIC 120916706), a transiting substellar object (R = 0.87 RJup) orbiting a faint M3.5 V dwarf (V = 18.97) on a 0.56 d orbit. Aims. We setout to determine the nature of the Transiting Exoplanet Survey Satellite (TESS) planet candidate TOI 263.01 using ground-based multicolour transit photometry. The host star is faint, which makes radial-velocity confirmation challenging, but the large transit depth makes the candidate suitable for validation through multicolour photometry. Methods. Our analysis combines three transits observed simultaneously in r′, i′, and zs bands usingthe MuSCAT2 multicolour imager, three LCOGT-observed transit light curves in g′, r′, and i′ bands, a TESS light curve from Sector 3, and a low-resolution spectrum for stellar characterisation observed with the ALFOSC spectrograph. We modelled the light curves with PYTRANSIT using a transit model that includes a physics-based light contamination component, allowing us to estimate the contamination from unresolved sources from the multicolour photometry. Using this information we were able to derive the true planet–star radius ratio marginalised over the contamination allowed by the photometry.Combining this with the stellar radius, we were able to make a reliable estimate of the absolute radius of the object. Results. The ground-based photometry strongly excludes contamination from unresolved sources with a significant colour difference to TOI 263. Furthermore, contamination from sources of the same stellar type as the host is constrained to levels where the true radius ratio posterior has a median of 0.217 and a 99 percentile of0.286. The median and maximum radius ratios correspond to absolute planet radii of 0.87 and 1.41 RJup, respectively,which confirms the substellar nature of the planet candidate. The object is either a giant planetor a brown dwarf (BD) located deep inside the so-called “brown dwarf desert”. Both possibilities offer a challenge to current planet/BD formation models and make TOI 263.01 an object that merits in-depth follow-up studies.