In an earlier campaign to characterize the mass of the transiting temperate super-Earth K2-18b with HARPS, a second, non-transiting planet was posited to exist in the system at ~9 days. Further ...radial velocity follow-up with the CARMENES spectrograph visible channel revealed a much weaker signal at 9 days, which also appeared to vary chromatically and temporally, leading to the conclusion that the origin of the 9-day signal was more likely related to stellar activity than to a planetary presence. Here we conduct a detailed reanalysis of all available RV time-series – including a set of 31 previously unpublished HARPS measurements – to investigate the effects of time-sampling and of simultaneous modelling of planetary plus activity signals on the existence and origin of the curious 9-day signal. We conclude that the 9-day signal is real and was initially seen to be suppressed in the CARMENES data due to a small number of anomalous measurements, although the exact cause of these anomalies remains unknown. Investigation of the signal’s evolution in time with wavelength and detailed model comparison reveals that the 9-day signal is most likely planetary in nature. Using this analysis, we reconcile the conflicting HARPS and CARMENES results and measure precise and self-consistent planet masses of mp,b = 8.63 ± 1.35 and mp,c sinic = 5.62 ± 0.84 Earth masses. This work, along with the previously published RV papers on the K2-18 planetary system, highlights the importance of understanding the time-sampling and of modelling the simultaneous planet plus stochastic activity, particularly when searching for sub-Neptune-sized planets with radial velocities.
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The source GJ1132 is a nearby red dwarf known to host a transiting Earth-size planet. After its initial detection, we pursued an intense follow-up with the HARPS velocimeter. We now confirm the ...detection of GJ1132b with radial velocities alone. We refined its orbital parameters, and in particular, its mass (
m
b
= 1.66 ± 0.23
M
⊕
), density (
ρ
b
= 6.3 ± 1.3 g cm
−3
), and eccentricity (
e
b
< 0.22; 95%). We also detected at least one more planet in the system. GJ1132c is a super-Earth with period
P
c
= 8.93 ± 0.01 days and minimum mass
m
c
sin
i
c
= 2.64 ± 0.44
M
⊕
. Receiving about 1.9 times more flux than Earth in our solar system, its equilibrium temperature is that of a temperate planet (
T
eq
= 230−300 K for albedos
A
= 0.75 − 0.00), which places GJ1132c near the inner edge of the so-called habitable zone. Despite an a priori favorable orientation for the system,
Spitzer
observations reject most transit configurations, leaving a posterior probability <1% that GJ1132c transits. GJ1132(d) is a third signal with period
P
d
= 177 ± 5 days attributed to either a planet candidate with minimum mass
m
d
sin
i
d
= 8.4
−2.5
+1.7
M
⊕
or stellar activity. Its Doppler signal is the most powerful in our HARPS time series but appears on a timescale where either the stellar rotation or a magnetic cycle are viable alternatives to the planet hypothesis. On the one hand, the period is different than that measured for the stellar rotation (~125 days), and a Bayesian statistical analysis we performed with a Markov chain Monte Carlo and Gaussian processes demonstrates that the signal is better described by a Keplerian function than by correlated noise. On the other hand, periodograms of spectral indices sensitive to stellar activity show power excess at similar periods to that of this third signal, and radial velocity shifts induced by stellar activity can also match a Keplerian function. We, therefore, prefer to leave the status of GJ1132(d) undecided.
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Using the non-negativity of Gram determinants of arbitrary order, we derive higher-order uncertainty relations for the symmetric uncertainty matrices of corresponding order n > 2 to n Hermitean ...operators (n =
2
is the usual case). The special cases of third-order and fourth-order uncertainty relations are considered in detail. The obtained third-order uncertainty relations are applied to the Lie groups SU(1,1) with three Hermitean basis operators (K
1
,K
2
,K
0
) and SU(2) with three Hermitean basis operators (J
1
,J
2
,J
3
) where, in particular, the group-coherent states of Perelomov type and of Barut-Girardello type for SU(1,1) and the spin or atomic coherent states for SU(2) are investigated. The uncertainty relations for the determinant of the third-order uncertainty matrix are satisfied with the equality sign for coherent states and this determinant becomes vanishing for the Perelomov type of coherent states for SU(1,1) and SU(2). As an example of the application of fourth-order uncertainty relations, we consider the canonical operators (Q
1
,P
1
,Q
2
,P
2
) of two boson modes and the corresponding uncertainty matrix formed by the operators of the corresponding mean deviations, taking into account the correlations between the two modes. In two mathematical appendices, we prove the non-negativity of the determinant of correlation matrices of arbitrary order and clarify the principal structure of higher-order uncertainty relations.
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ABSTRACT
We study the transit timings of 10 exoplanets in order to investigate potential transit timing variations in them. We model their available ground-based light curves, some presented here and ...others taken from the literature, and homogeneously measure the mid-transit times. We statistically compare our results with published values and find that the measurement errors agree. However, in terms of recovering the possible frequencies, homogeneous sets can be found to be more useful, of which no statistically relevant example has been found for the planets in our study. We corrected the ephemeris information of all 10 planets we studied and provide these most precise light elements as references for future transit observations with space-borne and ground-based instruments. We found no evidence for secular or periodic changes in the orbital periods of the planets in our sample, including the ultra-short period WASP-103 b, whose orbit is expected to decay on an observable time-scale. Therefore, we derive the lower limits for the reduced tidal quality factors (Q$^{\prime }_{\star }$) for the host stars based on best-fitting quadratic functions to their timing data. We also present a global model of all available data for WASP-74 b, which has a Gaia parallax-based distance value ∼25 per cent larger than the published value.
Transit events of extrasolar planets offer a wealth of information for planetary characterization. However, for many known targets, the uncertainty of their predicted transit windows prohibits an ...accurate scheduling of follow-up observations. In this work, we refine the ephemerides of 21 hot Jupiter exoplanets with the largest timing uncertainties. We collected 120 professional and amateur transit light curves of the targets of interest, observed with a range of telescopes of 0.3 m–2.2 m, and analyzed them along with the timing information of the planets discovery papers. In the case of WASP-117b, we measured a timing deviation compared to the known ephemeris of about 3.5 h, and for HAT-P-29b and HAT-P-31b the deviation amounted to about 2 h and more. For all targets, the new ephemeris predicts transit timings with uncertainties of less than 6 min in the year 2018 and less than 13 min until 2025. Thus, our results allow for an accurate scheduling of follow-up observations in the next decade.
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Phosphoniumylidyl and phosphazenyl groups are effective substituents to increase the electron‐donating ability of tertiary phosphines. However, the influence of structural variations among those ...substituents on the electronic properties of the phosphines is little explored. Herein, we show that protonation of the ylidic carbon atom of phosphoniumylidyl phosphines increases the Tolman electronic parameter (TEP) by ΔTEP = 16.0–18.8 cm–1. Furthermore, phosphazenyl phosphines were synthesized with isopropyl groups (NP{iPr}3) and tetramethylguanidino groups (NP{tmg}3) at the phosphonium center. Determination of their TEP values reveals a remarkable low substituent parameter of χ = –18.5 cm–1 for the NP(tmg)3 group. In addition, we prepared the corresponding gold(I) complexes and determined their solid‐state structures using single‐crystal X‐ray diffraction studies to analyze the steric profile of the new phosphine ligands.
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Isolable singlet carbenes are among the most important tools in chemistry, but generally require the interaction of two substituents with the electron deficient carbon atom. We herein report a ...synthetic approach to monosubstituted phosphinocarbenes
via
deprotonation of hitherto unknown diprotic terminal methylene phosphonium ions. Two methylene phosphonium salts bearing bulky
N
-heterocyclic imine substituents at the phosphorus atom were isolated and fully characterized. Deprotonation studies indicate the formation of transient monosubstituted carbenes that undergo intermolecular cycloadditions or intramolecular Buchner ring expansion to afford a cycloheptatriene derivative. The reaction mechanism of the latter transformation was elucidated using DFT calculations, which reveal the ambiphilic nature of the phosphinocarbene enabling the insertion into the aromatic C-C bond. Additional computational studies on the role of substituent effects are presented.
Diprotic terminal methylene phosphonium ions were prepared using bulky
N
-heterocyclic imine substituents. Deprotonation yields transient monosubstituted phosphinocarbenes, which insert into the C&z.dbd;C bond of a phenyl ring
via
a Buchner ring expansion.
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Oxophosphoniumionen (R2P=O)+ sind faszinierende chemische Intermediate, die mit den bekannten Acyliumkationen (RC=O)+ verwandt sind. Sie bestehen aus einem dreifach koordinierten Phosphor(V)‐Zentrum ...mit einer Phosphor‐Sauerstoff‐Doppelbindung. Hier wird die Synthese zweier Oxophosphoniumionen vorgestellt, die durch sterisch anspruchsvolle Imidazolin‐2‐imin‐ und Imidazolidin‐2‐olefin‐Substituenten am Phosphorzentrum stabilisiert sind. Diese neuen Verbindungen wurden durch NMR‐Spektroskopie und Einkristallröntgenstrukturanalyse charakterisiert, und die Bindungssituation wurde mittels DFT‐Rechnungen untersucht. Die Bestimmung der Akzeptornummer und der Fluoridionenaffinität zeigte, dass die Wahl der Substituenten starken Einfluss auf die Elektrophilie des Phosphorzentrums hat. Darüber hinaus wurden die Bildung von Lewis‐Base‐Addukten mit Pyridinderivaten sowie die Reaktivität gegen Isopropylalkohol untersucht.
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Associated Hermite polynomials
He
ν
n
(
z) which generalize the usual (scaled) Hermite polynomials
He
n
(
z) corresponding to
ν=0 are introduced for the purpose to represent the raising and lowering ...of the indices of functions of the parabolic cylinder
D
ν
(
z) in finite integer steps. Properties of these polynomials such as recursion relations, explicit representations and the differential equation are derived. The generation of the associated Hermite polynomials from the usual Hermite polynomials by differential operators representable by means of the confluent hypergeometric function is given. An application for the explicit calculation of the functions of the parabolic cylinder for negative integer indices is discussed. Other applications are visible for the investigation of the zeros of the functions of the parabolic cylinder.
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