arXiv subjects

René Heller

Publications and source records attributed to René Heller.

At least 37 records · Page 2Linked to original sources

arXiv2021

Digital color codes of stars

Publications in astrophysics are nowadays mainly published and read in digitized formats. Astrophysical publications in both research and in popular outreach often use colorful representations of stars to indicate various stellar types, that is, different spectral types or effective temperatures. Computer generated and computer displayed imagery has become an integral part of stellar astrophysics communication. There is, however, no astrophysically motivated standard color palette for illustrative representations of stars and some stars are actually represented in misleading colors. We use pre-computed PHOENIX and TLUSTY stellar model spectra and convolve them with the three standard color matching functions for human color perception between 360$\,$nm and 830$\,$nm. The color matching functions represent the three sets of receptors in the eye that respond to red, green, and blue light. For a grid of main sequence stars with effective temperatures between 2300$\,$K and 55,000$\,$K of different metallicities we present the red-blue-green and hexadecimal color codes that can be used for digitized color representations of stars as if seen from space. We find significant deviations between the color codes of stars computed from stellar spectra and from a black body radiator of the same effective temperature. We illustrate the main sequence in the color wheel and demonstrate that there are no yellow, green, cyan, or purple stars. Red dwarf stars (spectral types M0V - M9V) actually look orange to the human eye. Old white dwarfs such as WD$\,$1856$+$534, host to a newly discovered transiting giant planet candidate, occur pale orange to the human eye, not white. Our freely available software can be used to generate color codes for any input spectrum such as those from planets, galaxies, quasars etc.

astro-ph.SR↗

arXiv2020

Astrophysical Simulations and Data Analyses on the Formation, Detection, and Habitability of Moons Around Extrasolar Planets

While the solar system contains as many as about 20 times more moons than planets, no moon has been definitively detected around any of the thousands of extrasolar planets so far. The question naturally arises why an exomoon detection has not yet been achieved. This cumulative habilitation thesis covers three of the key aspects related to the ongoing search for extrasolar moons: 1. the possible formation scenarios for moons around extrasolar planets; 2. new detection strategies for these moons; and 3. the potential of exomoons as hosts to extrasolar life. This work is structured as follows. Part I gives a broad introduction to the field of extrasolar moons with special attention to their formation, detection, and habitability. Part II presents the cumulative part of this thesis with a total of 16 peer-reviewed journal publications listing the author of this thesis as a lead author, and six publications with the author of this thesis as a co-author. Part III shares some insights into our ongoing research on exomoons in collaboration with master student Anina Timmermann at the Georg-August University of Göttingen and former PhD student Kai Rodenbeck at the International Max Planck Research School for Solar System Science and the University of Göttingen. The Appendix is a collection of non-peer-reviewed conference proceedings and popular science publications by the author that further disseminate our research of extrasolar moons.

astro-ph.EP↗

arXiv2020

Low-cost precursor of an interstellar mission

The solar photon pressure provides a viable source of thrust for spacecraft in the solar system. Theoretically it could also enable interstellar missions, but an extremely small mass per cross section area is required to overcome the solar gravity. We identify aerographite, a synthetic carbon-based foam with a density of 0.18 kg/m^3 (15,000 times more lightweight than aluminum) as a versatile material for highly efficient propulsion with sunlight. A hollow aerographite sphere with a shell thickness eps_shl = 1 mm could go interstellar upon submission to the solar radiation in interplanetary space. Upon launch at 1 AU from the Sun, an aerographite shell with eps_shl = 0.5 mm arrives at the orbit of Mars in 60 d and at Pluto's orbit in 4.3 yr. Release of an aerographite hollow sphere, whose shell is 1 micrometer thick, at 0.04 AU (the closest approach of the Parker Solar Probe) results in an escape speed of nearly 6900 km/s and 185 yr of travel to the distance of our nearest star, Proxima Centauri. The infrared signature of a meter-sized aerographite sail could be observed with JWST up to 2 AU from the Sun, beyond the orbit of Mars. An aerographite hollow sphere with eps_shl = 100 micrometer and a radius of 1 m (5 m) weighs 230 mg (5.7 g) and has a 2.2 g (55 g) mass margin for interstellar escape. The payload margin is ten times the mass of the spacecraft, whereas the payload on chemical interstellar rockets is typically a thousandth of the weight of the rocket. Simplistic communication would enable studies of the interplanetary medium and a search for the suspected Planet Nine, and would serve as a precursor mission to alpha Centauri. We estimate prototype developments costs of 1 million USD, a price of 1000 USD per sail, and a total of <10 million USD including launch for a piggyback concept with an interplanetary mission.

astro-ph.IM↗

arXiv2020

Habitability Models for Planetary Sciences

Habitability has been generally defined as the capability of an environment to support life. Ecologists have been using Habitat Suitability Models (HSMs) for more than four decades to study the habitability of Earth from local to global scales. Astrobiologists have been proposing different habitability models for some time, with little integration and consistency between them and different in function to those used by ecologists. In this white paper, we suggest a mass-energy habitability model as an example of how to adapt and expand the models used by ecologists to the astrobiology field. We propose to implement these models into a NASA Habitability Standard (NHS) to standardize the habitability objectives of planetary missions. These standards will help to compare and characterize potentially habitable environments, prioritize target selections, and study correlations between habitability and biosignatures. Habitability models are the foundation of planetary habitability science. The synergy between the methods used by ecologists and astrobiologists will help to integrate and expand our understanding of the habitability of Earth, the Solar System, and exoplanets.

astro-ph.IM↗

arXiv2020

Transit least-squares survey -- III. A $1.9\,R_\oplus$ transit candidate in the habitable zone of Kepler-160 and a nontransiting planet characterized by transit-timing variations

The Sun-like star Kepler-160 (KOI-456) has been known to host two transiting planets, Kepler-160 b and c, of which planet c shows substantial transit-timing variations (TTVs). We used the archival Kepler photometry of Kepler-160 to search for additional transiting planets using a combination of our Wotan detrending algorithm and our transit least-squares (TLS) detection algorithm. We also used the Mercury N-body gravity code to study the orbital dynamics of the system. First, we recovered the known transit series of planets Kepler-160 b and c. Then we found a new transiting candidate with a radius of 1.91 (+0.17, -0.14) Earth radii (R_ear), an orbital period of 378.417 (+0.028, -0.025) d, and Earth-like insolation. The vespa software predicts that this signal has an astrophysical false-positive probability of FPP_3 = 1.8e-3 when the multiplicity of the system is taken into account. Kepler vetting diagnostics yield a multiple event statistic of MES = 10.7, which corresponds to an ~85 % reliability against false alarms due to instrumental artifacts such as rolling bands. We are also able to explain the observed TTVs of planet c with the presence of a previously unknown planet. The period and mass of this new planet, however, do not match the period and mass of the new transit candidate. Our Markov chain Monte Carlo simulations of the TTVs of Kepler-160 c can be conclusively explained by a new nontransiting planet with a mass between about 1 and 100 Earth masses and an orbital period between about 7 and 50 d. We conclude that Kepler-160 has at least three planets, one of which is the nontransiting planet Kepler-160 d. The expected stellar radial velocity amplitude caused by this new planet ranges between about 1 and 20 m/s. We also find the super-Earth-sized transiting planet candidate KOI-456.04 in the habitable zone of this system, which could be the fourth planet.

astro-ph.EP↗

arXiv2020

A possible transit of a disintegrating exoplanet in the nearby multiplanet system DMPP-1

We analyse TESS photometry of DMPP-1 (HD 38677; TIC 66560666), a nearby F8V star hosting hot super-Earth planets and a warm Neptune. Using the Transit Least Squares algorithm and other methods we find a transit signal at $P=3.2854^{+0.0032}_{-0.0025}$ d with depth 87$^{+25}_{-30}$ ppm and false alarm probability 1.6%. This is shallower than hitherto published TESS discoveries. The 3.285 d signal is recovered for several, but not all, methods for detrending stellar astrophysical variability. Further observations are needed to improve the significance of the detection. If this transit were due to an Earth-like rocky planet it would have been detected in the RV data, but it is not. The TESS data cover seven individual transits, one of which is consistent with zero depth. The insolation of the putative planet is $990 {\rm S_{\oplus}}$, typical of fluxes experienced by the three known catastrophically disintegrating exoplanets (CDEs). The transits can be self-consistently attributed to a CDE with a mass below the RV detection threshold. We searched for transits of the known RV planets, finding null results and detection thresholds of $< 100$ ppm, which we quantify for each. The DMPP-1 planetary system was discovered as a consequence of circumstellar gas attributed to ablation of hot planets. The RV planets may have been ablated to near-pure iron cores. We place limits on the orbital inclinations of the RV planets where the expected transit depth exceeds the detection threshold. If the 3.2854 day transit detection is confirmed, e.g. with CHEOPS photometry, DMPP-1 would be a first-rate target for JWST spectroscopy.

astro-ph.EP↗

arXiv2020

Habitability is a continuous property of nature

In their recent comment, Cockell et al. argue that the habitability of an environment is fundamentally a binary property; that is to say, an environment can either support the metabolic processes of a given organism or not. The habitability of different environments, they argue, may have different degrees that could be determined at least in theory by answering the question: 'is this environment habitable to a given organism?' 'More' or 'less' habitable environments could then be related by the number of yes or no answers given to what is fundamentally a series of binary questions and decisions. In my opinion, there are at least three implicit assumptions made for this line of reasoning that are implausible and that sabotage the conclusions. The first is in the genetic diversity of the organisms, which I argue is fundamentally continuous in nature and a binary construction of the sample is not meaningful. The second misconception is in the assumption that an ecosystem can be decomposed into subsets of independent samples. The third problem is in the definition of an environment. The question of the environment is a continuous one in both space and time and thus any concept constructed to be applicable to a sample of environments must be continuous as well. In summary, the question of whether habitability is a binary quantity or not brings us back to the question of whether our concepts of life and of the environments that life thrives in (or not) are binary or non-binary. I argue that the latter is the case, and hence any modern concept of habitability must be continuous too.

physics.pop-ph↗

arXiv2020

Exomoon indicators in high-precision transit light curves

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 known so far. Tools for an uncomplicated identification of the most promising exomoon candidates could be beneficial to streamline follow-up studies.} 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. We simulate light curves of a transiting exoplanet with a single moon. These model light curves are then fitted with a planet-only transit model, pretending there were no moon, and we explore the resulting TTV, TDV, and TRV series for evidence of the moon. The previously described ellipse in the TTV-TDV diagram of an exoplanet with a moon emerges only for high-density moons. 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 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 ($m_V=8$) stars. These stars, however, are rare in the Kepler sample but will be abundant in the PLATO sample. Moreover, PLATO's higher cadence yields a stronger TTV signal. 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 can be more complex than previously assumed. We propose that TRVs could be a more promising means to identify exomoons in large exoplanet surveys.

astro-ph.EP↗

arXiv2020

Radial velocity constraints on the long-period transiting planet Kepler-1625 b with CARMENES

The star Kepler-1625 recently attracted considerable attention when an analysis of the stellar photometric time series from the Kepler mission was interpreted as showing evidence of a large exomoon around the transiting Jupiter-sized planet candidate Kepler-1625b. We aim to detect the radial velocity (RV) signal imposed by Kepler-1625b (and its putative moon) on the host star or, as the case may be, determine an upper limit on the mass of the transiting object. We took a total of 22 spectra of Kepler-1625 using CARMENES, 20 of which were useful. Observations were spread over a total of seven nights between October 2017 and October 2018, covering $125\%$ of one full orbit of Kepler-1625b. We used the automatic Spectral Radial Velocity Analyser (SERVAL) pipeline to deduce the stellar RVs and uncertainties. Then we fitted the RV curve model of a single planet on a Keplerian orbit to the observed RVs using a $χ^2$ minimisation procedure. We derive upper limits on the mass of Kepler-1625b under the assumption of a single planet on a circular orbit. In this scenario, the $1\,σ$, $2\,σ$, and $3\,σ$ confidence upper limits for the mass of Kepler-1625b are $2.90\,M_{\rm J}$, $7.15\,M_{\rm J}$, and $11.60\,M_{\rm J}$, respectively. We present strong evidence for the planetary nature of Kepler-1625b, making it the 10th most long-period confirmed planet known today. Our data does not answer the question about a second, possibly more short-period planet that could be responsible for the observed transit timing variation of Kepler-1625b.

astro-ph.EP↗

arXiv2019

Exoplanet Vision 2050

Is there any hope for us to draw a plausible picture of the future of exoplanet research? Here we extrapolate from the first 25 years of exoplanet discovery into the year 2050. If the power law for the cumulative exoplanet count continues, then almost 100,000,000 exoplanets would be known by 2050. Although this number sounds ridiculously large, we find that the power law could plausibly continue until at least as far as 2030, when Gaia and WFIRST will have discovered on the order of 100,000 exoplanets. After an early era of radial velocity detection, we are now in the transit era, which might be followed by a transit and astrometry era dominated by the WFIRST and Gaia missions. And then? Maybe more is not better. A small and informal survey among astronomers at the "Exoplanet Vision 2050" workshop in Budapest suggests that astrobiological topics might influence the future of exoplanet research.

astro-ph.EP↗

arXiv2019

p-type codoping effect in (Ga,Mn)As: Mn lattice location versus magnetic properties

In the present work, we perform a systematic investigation on p-type codoping in (Ga,Mn)As. Through gradually increasing Zn doping concentration, the hole concentration increases, which should theoretically lead to an increase of the Curie temperature (TC) according to the p-d Zener model. Unexpectedly, although the film keeps its epitaxial structure, both TC and the magnetization decrease. The samples present a phase transition from ferromagnetism to paramagnetism upon increasing hole concentration. In the intermediate regime, we observe a signature of antiferromagnetism. By using channeling Rutherford backscattering spectrometry and particle-induced x-ray emission, the substitutional Mn atoms are observed to shift to interstitial sites, while more Zn atoms occupy Ga sites, which explains the observed behavior. This is also consistent with first-principles calculations, showing that the complex of substitutional Zn and interstitial Mn has the lowest formation energy.

cond-mat.mtrl-sci↗

arXiv2019

Wotan: Comprehensive time-series de-trending in Python

The detection of transiting exoplanets in time-series photometry requires the removal or modeling of instrumental and stellar noise. While instrumental systematics can be reduced using methods such as pixel level decorrelation, removing stellar trends while preserving transit signals proves challenging. Due to vast archives of light curves from recent transit surveys, there is a strong need for accurate automatic detrending, without human intervention. A large variety of detrending algorithms are in active use, but their comparative performance for transit discovery is unexplored. We benchmark all commonly used detrending methods against hundreds of Kepler, K2, and TESS planets, selected to represent the most difficult cases for systems with small planet-to-star radius ratios. The full parameter range is explored for each method to determine the best choices for planet discovery. We conclude that the ideal method is a time-windowed slider with an iterative robust location estimator based on Tukey's biweight. This method recovers 99% and 94% of the shallowest Kepler and K2 planets, respectively. We include an additional analysis for young stars with extreme variability and conclude they are best treated using a spline-based method with a robust Huber estimator. All stellar detrending methods explored are available for public use in wotan, an open-source Python package on GitHub (see https://github.com/hippke/wotan).

astro-ph.EP↗

arXiv2019

Transit least-squares survey -- II. Discovery and validation of 17 new sub- to super-Earth-sized planets in multi-planet systems from K2

The extended Kepler mission (K2) has revealed more than 500 transiting planets in roughly 500,000 stellar light curves. All of these were found either with the box least-squares algorithm or by visual inspection. Here we use our new transit least-squares (TLS) algorithm to search for additional planets around all K2 stars that are currently known to host at least one planet. We discover and statistically validate 17 new planets with radii ranging from about 0.7 Earth radii to roughly 2.2 Earth radii and a median radius of 1.18 Earth radii. EPIC201497682.03, with a radius of 0.692 (-0.048, +0.059) Earth radii, is the second smallest planet ever discovered with K2. The transit signatures of these 17 planets are typically 200 ppm deep (ranging from 100 ppm to 2000 ppm), and their orbital periods extend from about 0.7 d to 34 d with a median value of about 4 d. Fourteen of these 17 systems only had one known planet before, and they now join the growing number of multi-planet systems. Most stars in our sample have subsolar masses and radii. The small planetary radii in our sample are a direct result of the higher signal detection efficiency that TLS has compared to box-fitting algorithms in the shallow-transit regime. Our findings help in populating the period-radius diagram with small planets. Our discovery rate of about 3.7 % within the group of previously known K2 systems suggests that TLS can find over 100 additional Earth-sized planets in the data of the Kepler primary mission.

astro-ph.EP↗

arXiv2019

Formation of hot Jupiters through disk migration and evolving stellar tides

Here we address the hot Jupiter (hJ) pile-up at 0.05 AU around young solar-type stars observed in stellar radial velocity surveys, the hJ longterm orbital stability in the presence of stellar tides, and the hJ occurrence rate of 1.2 (+-0.38)% in one framework. We calculate the combined torques on the planet from the stellar dynamical tide and from the protoplanetary disk in the type II migration regime. We model a 2D nonisothermal viscous disk parameterized to reproduce the minimum-mass solar nebula and simulate an inner disk cavity at various radial positions near the star. We choose stellar rotation periods according to observations of young star clusters. The planet is on a circular orbit in the disk midplane and in the star's equatorial plane. We show that the torques can add up to zero beyond the corotation radius around young stars and stop inward migration. Monte Carlo simulations predict hot Jupiter survival rates between ~3% (alpha disk viscosity of 1e-1) and 15% (alpha = 1e-3). Once the protoplanetary disk has been fully accreted, the surviving hJs are pushed outward from their tidal migration barrier and pile up near 0.05 AU, as we demonstrate using a numerical implementation of a stellar dynamical tide model. Orbital decay is negligible on a one-billion-year timescale due to the contraction of the highly dissipative convective envelopes in young Sun-like stars. We find that the higher pile-up efficiency around metal-rich stars can at least partly explain the observed positive correlation between stellar metallicity and hJ occurrence. Combined with the observed hJ occurrence rate, our results for the survival rate imply that <8 % (alpha = 1e-3) to <43 % (alpha = 1e-1) of sun-like stars initially encounter an inward migrating hJ. This reconciles models and observations of young spinning stars with the observed hJ pile up and hJ occurrence rates.

astro-ph.EP↗

arXiv2019

Transit least-squares survey - I. Discovery and validation of an Earth-sized planet in the four-planet system K2-32 near the 1:2:5:7 resonance

We apply, for the first time, the Transit Least Squares (TLS) algorithm to search for new transiting exoplanets. TLS is a successor to the Box Least Squares (BLS) algorithm, which has served as a standard tool for the detection of periodic transits. In this proof-of-concept paper, we demonstrate how TLS finds small planets that have previously been missed. We showcase TLS' capabilities using the K2 EVEREST-detrended light curve of the star K2-32 (EPIC205071984) that was known to have three transiting planets. TLS detects these known Neptune-sized planets K2-32b, d, and c in an iterative search and finds an additional transit signal with a high signal detection efficiency (SDE_TLS) of 26.1 at a period of 4.34882 (-0.00075, +0.00069) d. We show that this signal remains detectable (SDE_TLS = 13.2) with TLS in the K2SFF light curve of K2-32, which includes a less optimal detrending of the systematic trends. The signal is below common detection thresholds, however, if searched with BLS in the K2SFF light curve (SDE_BLS = 8.9) as in previous searches. Markov Chain Monte Carlo sampling shows that the radius of this candidate is 1.01 (-0.09, +0.10) Earth radii. We analyze its phase-folded transit light curve using the vespa software and calculate a false positive probability FPP = 3.1e-3, formally validating K2-32e as a planet. Taking into account the multiplicity boost of the system, FPP < 3.1e-4. K2-32 now hosts at least four planets that are very close to a 1:2:5:7 mean motion resonance chain. The offset of the orbital periods of K2-32e and b from a 1:2 mean motion resonance is in very good agreement with the sample of transiting multi-planet systems from Kepler, lending further credence to the planetary nature of K2-32e. We expect that TLS can find many more transits of Earth-sized and smaller planets in the Kepler data that have hitherto remained undetected with BLS and similar algorithms.

astro-ph.EP↗

arXiv2019

An alternative interpretation of the exomoon candidate signal in the combined Kepler and Hubble data of Kepler-1625

Kepler and Hubble photometry of a total of four transits by the Jupiter-sized Kepler-1625b have recently been interpreted to show evidence of a Neptune-sized exomoon. The profound implications of this first possible exomoon detection and the physical oddity of the proposed moon, that is, its giant radius prompt us to re-examine the data and the Bayesian Information Criterion (BIC) used for detection. We combine the Kepler data with the previously published Hubble light curve. In an alternative approach, we perform a synchronous polynomial detrending and fitting of the Kepler data combined with our own extraction of the Hubble photometry. We generate five million MCMC realizations of the data with both a planet-only model and a planet-moon model and compute the BIC difference (DeltaBIC) between the most likely models, respectively. DeltaBIC values of -44.5 (using previously published Hubble data) and -31.0 (using our own detrending) yield strongly support the exomoon interpretation. Most of our orbital realizations, however, are very different from the best-fit solutions, suggesting that the likelihood function that best describes the data is non-Gaussian. We measure a 73.7min early arrival of Kepler-1625b for its Hubble transit at the 3 sigma level, possibly caused by a 1 day data gap near the first Kepler transit, stellar activity, or unknown systematics. The radial velocity amplitude of a possible unseen hot Jupiter causing Kepler-1625b's transit timing variation could be some 100m/s. Although we find a similar solution to the planet-moon model as previously proposed, careful consideration of its statistical evidence leads us to believe that this is not a secure exomoon detection. Unknown systematic errors in the Kepler/Hubble data make the DeltaBIC an unreliable metric for an exomoon search around Kepler-1625b, allowing for alternative interpretations of the signal.

astro-ph.EP↗

arXiv2019

Analytic solutions to the maximum and average exoplanet transit depth for common stellar limb darkening laws

The depth of an exoplanetary transit in the light curve of a distant star is commonly approximated as the squared planet-to-star radius ratio, (R_p/R_s)^2. Stellar limb darkening, however, results in significantly deeper transits. Here we derive analytical solutions to the overshoot of the mid-transit depth caused by stellar limb darkening compared to the (R_p/R_s)^2 estimate for arbitrary transit impact parameters. In turn, this allows us to compute the true planet-to-star radius ratio from the transit depth for a given parameterization of a limb darkening law and for a known transit impact parameter. We calculate the maximum emerging specific stellar intensity covered by the planet in transit and derive analytic solutions for the transit depth overshoot. Solutions are presented for the linear, quadratic, square-root, logarithmic, and non-linear stellar limb darkening with arbitrary transit impact parameters. We also derive formulae to calculate the average intensity along the transit chord, which allows us to estimate the actual transit depth (and therefore R_p/R_s) from the mean in-transit flux. The transit depth overshoot of exoplanets compared to the (R_p/R_s)^2 estimate increases from about 15% for A main-sequence stars to roughly 20% for sun-like stars and some 30% for K and M stars. The error in our analytical solutions for R_p/R_s from the small planet approximation is orders of magnitude smaller than the uncertainties arising from typical noise in real light curves and from the uncertain limb darkening. Our equations can be used to predict with high accuracy the expected transit depth of extrasolar planets. The actual planet radius can be calculated from the measured transit depth or from the mean in-transit flux if the stellar limb darkening can be properly parameterized and if the transit impact parameter is known. Light curve fitting is not required.

astro-ph.EP↗

arXiv2019

Transit Least Squares: Optimized transit detection algorithm to search for periodic transits of small planets

We present a new method to detect planetary transits from time-series photometry, the Transit Least Squares (TLS) algorithm. TLS searches for transit-like features while taking the stellar limb darkening and planetary ingress and egress into account. We have optimized TLS for both signal detection efficiency (SDE) of small planets and computational speed. TLS analyses the entire, unbinned phase-folded light curve. We compensate for the higher computational load by (i.) using algorithms like "Mergesort" (for the trial orbital phases) and by (ii.) restricting the trial transit durations to a smaller range that encompasses all known planets, and using stellar density priors where available. A typical K2 light curve, including 80d of observations at a cadence of 30min, can be searched with TLS in ~10s real time on a standard laptop computer, as fast as the widely used Box Least Squares (BLS) algorithm. We perform a transit injection-retrieval experiment of Earth-sized planets around sun-like stars using synthetic light curves with 110ppm white noise per 30min cadence, corresponding to a photometrically quiet KP=12 star observed with Kepler. We determine the SDE thresholds for both BLS and TLS to reach a false positive rate of 1% to be SDE~7 in both cases. The resulting true positive (or recovery) rates are ~93% for TLS and ~76% for BLS, implying more reliable detections with TLS. We also test TLS with the K2 light curve of the TRAPPIST-1 system and find six of seven Earth-sized planets using an iterative search for increasingly lower signal detection efficiency, the phase-folded transit of the seventh planet being affected by a stellar flare. TLS is more reliable than BLS in finding any kind of transiting planet but it is particularly suited for the detection of small planets in long time series from Kepler, TESS, and PLATO. We make our Python implementation of TLS publicly available.

astro-ph.EP↗