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At least 109 records · Page 6

Ultrafast dynamics of CN radical reactions with chloroform solvent under vibrational strong coupling

Polariton chemistry may provide a new means to control molecular reactivity, permitting remote, reversible modification of reaction energetics, kinetics, and product yields. A considerable body of experimental and theoretical work has already demonstrated that strong coupling between a molecular vibrational mode and the confined electromagnetic field of an optical cavity can alter chemical reactivity without external illumination. However, the mechanisms underlying cavity-altered chemistry remain unclear in large part because the experimental systems examined previously are too complex for detailed analysis of their reaction dynamics. Here, we experimentally investigate photolysis-induced reactions of cyanide radicals with strongly-coupled chloroform (CHCl 3 ) solvent molecules and examine the intracavity rates of photofragment recombination, solvent complexation, and hydrogen abstraction. Here we use a microfluidic optical cavity fitted with dichroic mirrors to facilitate vibrational strong coupling (VSC) of the C–H stretching mode of CHCl 3 while simultaneously permitting optical access at visible wavelengths. Ultrafast transient absorption experiments performed with cavities tuned on- and off-resonance reveal that VSC of the CHCl 3 C–H stretching transition does not significantly modify any measured rate constants, including those associated with the hydrogen abstraction reaction. This work represents, to the best of our knowledge, the first experimental study of an elementary bimolecular reaction under VSC. We discuss how the conspicuous absence of cavity-altered effects in this system may provide insights into the mechanisms of modified ground state reactivity under VSC and help bridge the divide between experimental results and theoretical predictions in vibrational polariton chemistry.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Insensitivity of Magnetic Coupling to Ligand Substitution in a Series of Tetraoxolene Radical-Bridged Fe 2 Complexes

The elucidation of magnetostructural correlations between bridging ligand substitution and strength of magnetic coupling is essential to the development of high-temperature molecule-based magnetic materials. Toward this end, we report the series of tetraoxolene-bridged Fe II 2 complexes [(Me 3 TPyA) 2 Fe 2 ( R L)] n + (Me 3 TPyA = tris(6-methyl-2-pyridylmethyl)amine; n = 2: OMe LH 2 = 3,6-dimethoxy-2,5-dihydroxo-1,4-benzoquinone, Cl LH 2 = 3,6-dichloro-2,5-dihydroxo-1,4-benzoquinone, Na 2 [ NO 2 L] = sodium 3,6-dinitro-2,5-dihydroxo-1,4-benzoquinone; n = 4: SMe 2 L = 3,6-bis(dimethylsulfonium)-2,5-dihydroxo-1,4-benzoquinone diylide) and their one-electron-reduced analogues. Furthermore, variable-temperature dc magnetic susceptibility data reveal the presence of weak ferromagnetic superexchange between Fe II centers in the oxidized species, with exchange constants of J = +1.2(2) (R = OMe, Cl) and +0.3(1) (R = NO 2 , SMe 2 ) cm –1 . In contrast, X-ray diffraction, cyclic voltammetry, and Mössbauer spectroscopy establish a ligand-centered radical in the reduced complexes. Magnetic measurements for the radical-bridged species reveal the presence of strong antiferromagnetic metal–radical coupling, with J = -57(10), -60(7), -58(6), and -65(8) cm –1 for R = OMe, Cl, NO 2 , and SMe 2 , respectively. The minimal effects of substituents in the 3- and 6-positions of R L x –• on the magnetic coupling strength is understood through electronic structure calculations, which show negligible spin density on the substituents and associated C atoms of the ring. Finally, the radical-bridged complexes are single-molecule magnets, with relaxation barriers of U eff = 50(1), 41(1), 38(1), and 33(1) cm –1 for R = OMe, Cl, NO 2 , and SMe 2 , respectively. Taken together, these results provide the first examination of how bridging ligand substitution influences magnetic coupling in semiquinoid-bridged compounds, and they establish design criteria for the synthesis of semiquinoid-based molecules and materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

The Southern hemisphere midlatitude circulation response to rapid adjustments and sea surface temperature driven feedbacks

Rapid adjustments – the response of meteorology to external forcing while sea surface temperatures (SST) and sea ice are held fixed – can affect the midlatitude circulation and contribute to long-term forced circulation responses in climate simulations. This study examines rapid adjustments in the Southern hemisphere (SH) circulation using nine models from the Precipitation Driver and Response Model Intercomparison Project (PDRMIP), which perform fixed SST and coupled ocean experiments for five perturbations: a doubling of carbon dioxide (2xCO2), a tripling of methane (3xCH4), a five-fold increase in sulphate aerosol (5xSO4), a ten-fold increase in black carbon aerosol (10xBC) and a 2% increase in solar constant (2%Sol). In the coupled experiments, the SH eddy-driven jet shifts poleward and strengthens for forcings that produce global warming (and vice versa for 5xSO4), with the strongest response found in austral summer. In austral winter, the responses project more strongly onto a change in jet strength. For 10xBC, which induces strong shortwave absorption, the multi-model mean (MMM) rapid adjustment in DJF jet latitude is ~75% of the change in the coupled simulations. For the other forcings, which induce larger SST changes, the effect of SST-mediated feedbacks on the SH circulation is larger than the rapid adjustment. Nevertheless, for these perturbations the magnitude of the MMM jet shift due to the rapid adjustment is still around 25-33% of that in the coupled experiments. The results demonstrate the need to understand the mechanisms for rapid adjustments in the midlatitude circulation, in addition to the effect of changing SSTs.

Wood, Thomas↗

Influence of solvents on electrochemical stability window of ionic liquid solutions

The electrochemical stability window (ESW) defines the voltage range within which an electrolyte remains stable against oxidation and reduction, serving as a key descriptor for ionic liquid (IL)-based systems. The ESWs of 15 ILs with diverse cation-anion combinations were systematically investigated, both in their neat forms and as binary mixtures with three representative solvents, i.e., propylene carbonate (PC), ethylene glycol (EG), and tetrahydrofuran (THF). Cyclic voltammetry on a glassy carbon electrode determined anodic and cathodic stability limits, revealing that ESW protection in IL-solvent mixtures strongly depends on solvent polarity, proticity, and IL compatibility. PC, with a high dielectric constant and aprotic character, broadened anodic limits and moderately stabilized cathodic limits. THF maintained compact interfacial structure, offering additional cathodic protection, whereas EG, being protic, reduced ESWs via proton-coupled electron transfer and hydrogen evolution. The solvent protection trend followed by PC > THF > EG, with bulky, hydrophobic cations ([HMIM] + , [BMPYRR] + ) and weakly coordinating anions ([NTF 2 ] - , [DCA] - , [DEP] - ) showing the highest ESW protection for 50 mol% IL in these solvents. Among the neat ILs, [EMIM][DEP], [HMIM][PF 6 ], and [BMPYRR][DCA] showed wide ESWs of ∼5.5 V. These results provide valuable insight into solvent-modulated electrochemical stability, enabling rational design of IL-based electrolytes for energy storage and electrosynthesis.

25 ENERGY STORAGE↗

Analysis of the rotationally-resolved infrared spectrum of CD 3 79 Br and CD 3 81 Br between 900 and 1400 cm -1

We report the infrared spectrum of CD 3 79 Br and CD 3 81 Br between 900 cm -1 and 1400 cm -1 has been analyzed at high resolution. In this region, two fundamental vibrational states, v 2 = 1 and v 5 = 1, an overtone state, v 3 = 2, and a combination state, v 3 = v 6 = 1, have been analyzed for both isotopologues. As found in other halomethane molecules, strong Coriolis resonances couple the v 2 = 1 state to the v 5 = 1 state, and similar resonances were also used to describe the coupling found between the v 5 = 1 state to the v 3 = 2 state. A new determination of the K-dependent constant A 0 was performed for each isotopologue through the use of perturbation-allowed transitions. The values for A 0 determined from the analysis are 2.6001898(26) and 2.6001905(27) for CD 3 79 Br and CD 3 81 Br, respectively. Ab initio calculations were performed to examine the efficacy of high-level theoretical calculations to accurately predict spectroscopic constants. The ab initio calculations had variable success with the largest errors associated with the prediction of the ΔB rotational constants of the interacting states

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Tensor network formulation of two-dimensional gravity

We show how to formulate a lattice gauge theory whose naive continuum limit corresponds to two-dimensional (Euclidean) quantum gravity including a positive cosmological constant. More precisely the resultant continuum theory corresponds to gravity in a first-order formalism in which the local frame and spin connection are treated as independent fields. Recasting this lattice theory as a tensor network allows us to study the theory at strong coupling without encountering a sign problem. In two dimensions this tensor network is exactly soluble and we show that the system has a series of critical points that occur for pure imaginary coupling and are associated with first order phase transitions. We then augment the action with a Yang-Mills term which allows us to control the lattice spacing and show how to apply the tensor renormalization group to compute the free energy and look for critical behavior. Finally we perform an analytic continuation in the gravity coupling in this extended model and show that its critical behavior in a certain scaling limit depends only on the topology of the underlying lattice. We also show how the lattice gauge theory can be naturally generalized to generate the Polyakov or Liouville action for two dimensional quantum gravity.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Nonlocal Interactions in Moiré Hubbard Systems

Moiré materials formed in two-dimensional semiconductor heterobilayers are quantum simulators of Hubbard-like physics with unprecedented electron density and interaction strength tunability. Compared to atomic scale Hubbard-like systems, electrons or holes in moiré materials are less strongly attracted to their effective lattice sites because these are defined by finite-depth potential extrema. As a consequence, nonlocal interaction terms like interaction-assisted hopping and intersite exchange are more relevant. Here, we theoretically demonstrate the possibility of tuning the strength of these coupling constants to favor unusual states of matter, including spin liquids, insulating ferromagnets, and superconductors.

36 MATERIALS SCIENCE↗

In situ aerobic methane oxidation rates in a stratified lake

Abstract Microbial aerobic methane oxidation is an important sink for aquatic methane worldwide. Despite its importance to global methane fluxes, few aerobic methane oxidation rates have been obtained in freshwater or marine environments without imposing changes to the microbial community through use of ex situ methods. A novel in situ incubation method for continuous time‐series measurements was used in Jordan Lake, North Carolina, during 2020–2021, to determine reaction kinetics for aerobic methane oxidation rates across a wide range of naturally varying methane (55–1833 nM) and dissolved oxygen (DO; 28–366 μM) concentrations and temperatures (17–30°C). Methane oxidation began immediately at the start of each of 21 incubations and methane oxidation rates were 1 st order with respect to methane. The data density allowed for accurate calculation of 1 st ‐order rate constants,k, that ranged from 0.018 to 0.462 h −1 (R 2 > 0.967). Addition of ammonium (20–45 μM) to natural concentrations ranging from 0.057 to 2.4 μM did not change aerobic methane oxidation rate kinetics, suggesting that the natural population of aerobic methane oxidizers in this eutrophic lake was not nitrogen limited. Values ofkinversely correlated most strongly with initial DO concentrations (R 2 = 0.82) rather than temperature. Values forkincreased with Julian day throughout our sampling period, suggesting seasonal influences on methane oxidation via responses to geochemical changes or shifts in microbial community abundance and composition. These experiments demonstrate a high variability in the enzymatic capacity for 1 st ‐order methane oxidation rates in this eutrophic lake that is tightly and inversely coupled to oxygen concentrations. Measurements of in situ aerobic methane oxidation rate constants allow for the direct quantification and modeling of the microbial community's capacity for methane oxidation over a wide range of natural methane concentrations.

Marine & Freshwater Biology↗

Soft-mode enhanced type-I superconductivity in LiPd 2 Ge

The synthesis, crystal structure, and physical properties (magnetization, resistivity, heat capacity) in combination with theoretical calculations of the electronic structure and phonon properties are reported for intermetallic compounds LiPd 2 X ( X = Si, Ge, and Sn). LeBail refinement of powder x-ray diffraction data confirms that all compounds belong to the Heusler family (space group $\textit{F m-3m}$, No. 225). The lattice parameter increases with atomic size of X , and its value varies from $\textit{a}$ = 5.9059(4) Å for LiPd 2 Si and $\textit{a}$ = 6.0082(3)Å for LiPd 2 Ge, to $\textit{a}$ = 6.2644(1) Å for LiPd 2 Sn. The first compound, LiPd 2 Si, has apparently not been previously reported. All measured quantities demonstrate that LiPd 2 Ge exhibits superconductivity below $T_c$ = 1.96 K and the normal- and superconducting-state data indicate that it is a weak-strength type-I superconductor ($C/γT_c$ = 1.38) with electron-phonon coupling constant $λ_{e–p}$ = (0.53–0.56). LiPd 2 Si and LiPd 2 Sn are not superconducting above 1.68 K. The experimental observations are supported by theoretical calculations which show that LiPd 2 Ge has the highest computed $λ_{e–p}$ and $T_c$ of the group. A strong softening of the acoustic phonon mode is calculated, and in the case of X = Ge and Sn, imaginary phonon frequencies were computed. In this work, the soft mode is most pronounced in the case of LiPd 2 Ge, which suggests its correlation with superconductivity.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Estimation of biquadratic and bicubic Heisenberg effective couplings from multiorbital Hubbard models

Abstract We studied a multi-orbital Hubbard model at half-filling for two and three orbitals per site on a two-site cluster via full exact diagonalization, in a wide range for the onsite repulsion U , from weak to strong coupling, and multiple ratios of the Hund coupling J H to U . The hopping matrix elements among the orbitals were also varied extensively. At intermediate and large U , we mapped the results into a Heisenberg model. For two orbitals per site, the mapping is into a S = 1 Heisenberg model where by symmetry both nearest-neighbor ( S i ⋅ S j ) and ( S i ⋅ S j ) 2 are allowed, with respective couplings J 1 and J 2 . For the case of three orbitals per site, the mapping is into a S = 3/2 Heisenberg model with ( S i ⋅ S j ), ( S i ⋅ S j ) 2 , and ( S i ⋅ S j ) 3 terms, and respective couplings J 1 , J 2 , and J 3 . The strength of these coupling constants in the Heisenberg models depend on the U , J H , and hopping amplitudes of the underlying Hubbard model. Our study provides a first crude estimate to establish bounds on how large the ratios J 2 / J 1 and J 3 / J 1 can be. We show that those ratios appear rather limited and, as a qualitative guidance, we conclude that J 2 / J 1 is less than 0.4 and J 3 / J 1 is less than 0.2, establishing bounds on effective models for strongly correlated Hubbard systems. Moreover, the intermediate Hubbard U regime was found to be the most promising to enhance J 2 / J 1 and J 3 / J 1 .

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Photon induced $K\Lambda $ production on the proton at $E_{\gamma} < 3$ GeV

The associated photoproduction of $K\Lambda$ from the proton for $E_{\gamma} < 3$ GeV is studied using an isobar model in which the non-resonant contributions corresponding to $s$, $t$, $u$ channel diagrams are obtained from a non-linear sigma model with chiral SU(3) symmetry. The model also predicts a contact term and its coupling strength in a natural way to preserve gauge symmetry. The parameters used are the pion decay constant $f_{\pi}$, vector and axial vector current couplings of the baryon octet in terms of the symmetric and antisymmetric couplings $D$ and $F$. In the non-resonant sector, the model is almost parameter free except a common cut-off parameter $\Lambda_{B}$, to describe the hadronic form factors at the strong kaon-nucleon-hyperon($KN\Lambda$) vertices. In the resonance sector, contribution from the various nucleon resonances($R$) in the $s$ channel, hyperon resonances($Y^{*}$) in the $u$ channel, and the kaon resonances($K^{*}$ and $K_{1}$) in the $t$ channel, which are present in the PDG having spin $\le \frac{3}{2}$ and mass $<2$ GeV with significant branching ratio in $K\Lambda$ decay mode have been considered. In the case of the nucleon resonances($R$), the couplings $\gamma NR$ at the electromagnetic vertices are determined in terms of the helicity amplitudes and the $RK\Lambda$ couplings at the strong vertices are determined by the partial decay width of the resonances($R$) decaying to $K\Lambda$. The strong and the electromagnetic couplings of $u$ and $t$ channel resonances are fitted to reproduce the experimental data of CLAS and SAPHIR. The numerical results are presented for the total and differential scattering cross sections and are compared with the available experimental data from CLAS and SAPHIR as well as with some of the recent theoretical models.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Polarity-dependence of the nonlinear dielectric response in interfacial water

Molecular dynamics simulations are used to study the nonlinear dielectric responses of a confined aqueous film in a planar nanopore under perpendicular electric fields at varied voltages between confining graphene sheets. Dielectric saturation reminiscent of the bulk phase behavior is prevalent at very strong fields, whereas we observe a nonmonotonic permittivity dependence on the electric field at intermediate strengths where field-alignment and spontaneous polarization of interfacial water are of comparable magnitude. The coupling between the two effects results in distinct dielectric responses at opposite confinement walls. The normal component of both the differential dielectric constant and dielectric difference constant tensors averaged over the region closer to the wall under an incoming electric field (field pointing from the liquid to the solid phase) initially increases with the strength of the imposed field. The differential permittivity peaks at a field strength previously shown to offset the surface-induced orientation bias of hydration molecules at this wall. Further strengthening of the field results in a conventional saturation behavior. At the opposite wall (subject to outgoing field) and in the central region of the water slab, the nonlinear dielectric response resembles bulklike saturation. The conditions at the permittivity extremum coincide with the window of accelerated reorientation rates of interfacial water molecules under an incoming field we uncovered in earlier molecular dynamics analyses.

Chemistry↗

Evidence of Polaron Formation in Halide Perovskites via Carrier Effective Mass Measurements

Carrier effective mass is a central parameter in solid-state physics. It is a measure of the strength of the coupling between a carrier and excitations arising from its surrounding medium, and features prominently in transport and optical calculations. Experimental techniques employed to determine it are steady-state ones, and so are unable to detect any change in the effective mass after a strong perturbation to the system, e.g., strong optical excitation. By combining time-resolved terahertz spectroscopy and transient absorption spectroscopy, on a mixed-cation mixed-halide perovskite thin film, we observe a large and long-lived photoinduced enhancement of the carrier effective mass, and from it deduce a twofold increase of the carrier-phonon coupling constant, giving evidence of polaron formation. Our work demonstrates a new approach to track the strength and ultrafast lifetimes of photoinduced carrier-boson interactions down to picosecond timescales that can be applied to a wide range of solid-state systems.

36 MATERIALS SCIENCE↗

Thickness and temperature dependence of the atomic-scale structure of SrRuO 3 thin films

The temperature-dependent layer-resolved structure of 3 to 44 unit cell thick SrRuO 3 (SRO) films grown on Nb-doped SrTiO 3 substrates is investigated using a combination of high-resolution synchrotron x-ray diffraction and high-resolution electron microscopy to understand the role that structural distortions play in suppressing ferromagnetism in ultra-thin SRO films. The oxygen octahedral tilts and rotations and Sr displacements characteristic of the bulk orthorhombic phase are found to be strongly dependent on temperature, the film thickness, and the distance away from the film–substrate interface. For thicknesses, t, above the critical thickness for ferromagnetism (t > 3 uc), the orthorhombic distortions decrease with increasing temperature above T C . Below T C , the structure of the films remains constant due to the magneto-structural coupling observed in bulk SRO. The orthorhombic distortions are found to be suppressed in the 2–3 interfacial layers due to structural coupling with the SrTiO 3 substrate and correlate with the critical thickness for ferromagnetism in uncapped SRO films.

36 MATERIALS SCIENCE↗

R -parity violation axiogenesis

We show that the rotation of the QCD axion field, aided by B–L violation from supersymmetric R-parity violating couplings, can yield the observed baryon abundance. Strong sphaleron processes transfer the angular momentum of the axion field into a quark chiral asymmetry, which R-parity violating couplings convert to the baryon asymmetry of the Universe. We focus on the case of dimensionless R-parity violating couplings with textures motivated by grand unified theories and comment on more general scenarios. The axion decay constant and mass spectrum of supersymmetric particles are constrained by Big Bang nucleosynthesis, proton decay from the R-parity violation, and successful thermalization of the Peccei-Quinn symmetry breaking field. Axion dark matter may be produced by the axion rotation via the kinetic misalignment mechanism for axion decay constants below 10 10 GeV, or by the conventional misalignment mechanism for 10 11-12 GeV. The viable parameter region can be probed by proton decay and axion searches. This scenario may also have connections with collider experiments, including searches for long-lived particles, and observations of gravitational waves.

Beyond Standard Model↗

High-temperature superconductivity in LaH 10

The recent discovery of a high critical temperature $T_c$ in compressed H 3 S has been followed by the prediction of Liu et al. of $T_c$ ≈ 250 K in the clathrate LaH 10 structure. This report has been confirmed experimentally by Somayazulu et al. and Drozdov et al. Additional theoretical work by Wang et al. and Quan et al. further established the mechanism of electron-phonon interaction and the dominant role of hydrogen. In the present Rapid Communication we follow the classic McMillan paper, which separates the electron and phonon contributions to the electron-phonon coupling λ. We first compute the numerator of McMillan's expression, the Hopfield parameter η, using the theory of Gaspari and Gyorffy (GG), and obtain the force constants in the denominator from Wang et al. and Quan et al. The resulting λ is used in the Allen-Dynes equation to calculate $T_c$. The value of $T_c$ reaches a maximum in the range of 236–263 K at pressures of 255 GPa and decreases for smaller or larger pressures. Further, we provide a thorough analysis of the different terms of the GG equation and draw the conclusion that the $\textit{sp}$ channel of the hydrogen is the most important contribution to obtain high values of $T_c$ in this material. Consistent with Wang et al., we find large values of λ that decrease with increasing pressure. In addition, we find that the hydrogen sites are the largest contributors to the total value of the coupling constant λ. That is, the acoustic mode associated with La contributes only 2% to the total λ, while the optic modes associated with H contribute 18% for the H1 site and 80% for the H2 site. These relative contributions to λ are consistent with those given by Wang et al. and by Quan et al. Thus, our results strongly support the view that LaH 10 is a metallic hydrogen superconductor.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Gapless Dirac magnons in CrCl3

Abstract Bosonic Dirac materials are testbeds for dissipationless spin-based electronics. In the quasi two-dimensional honeycomb lattice of CrX 3 (X = Cl, Br, I), Dirac magnons have been predicted at the crossing of acoustical and optical spin waves, analogous to Dirac fermions in graphene. Here we show that, distinct from CrBr 3 and CrI 3 , gapless Dirac magnons are present in bulk CrCl 3 , with inelastic neutron scattering intensity at low temperatures approaching zero at the Dirac K point. Upon warming, magnon-magnon interactions induce strong renormalization and decreased lifetimes, with a ~25% softening of the upper magnon branch intensity from 5 to 50 K, though magnon features persist well above T N . Moreover, on cooling below ~50 K, an anomalous increase in the a -axis lattice constant and a hardening of a ~26 meV phonon feature are observed, indicating magnetoelastic and spin-phonon coupling arising from an increase in the in-plane spin correlations that begins tens of Kelvin above T N .

36 MATERIALS SCIENCE↗

Further Evidence of Modified Spin-down in Sun-like Stars: Pileups in the Temperature–Period Distribution

We combine stellar surface rotation periods determined from NASA's Kepler mission with spectroscopic temperatures to demonstrate the existence of pileups at the long-period and short-period edges of the temperature–period distribution for main-sequence stars with temperatures exceeding ~5500 K. The long-period pileup is well described by a curve of constant Rossby number, with a critical value of Ro crit ≲ Ro ⊙ . The long-period pileup was predicted by van Saders et al. as a consequence of weakened magnetic braking, in which wind-driven angular momentum losses cease once stars reach a critical Rossby number. Stars in the long-period pileup are found to have a wide range of ages (~2–6 Gyr), meaning that, along the pileup, rotation period is strongly predictive of a star's surface temperature but weakly predictive of its age. The short-period pileup, which is also well described by a curve of constant Rossby number, is not a prediction of the weakened magnetic braking hypothesis but may instead be related to a phase of slowed surface spin-down due to core-envelope coupling. The same mechanism was proposed by Curtis et al. to explain the overlapping rotation sequences of low-mass members of differently aged open clusters. The relative dearth of stars with intermediate rotation periods between the short- and long-period pileups is also well described by a curve of constant Rossby number, which aligns with the period gap initially discovered by McQuillan et al. in M-type stars. These observations provide further support for the hypothesis that the period gap is due to stellar astrophysics, rather than a nonuniform star formation history in the Kepler field.

79 ASTRONOMY AND ASTROPHYSICS↗