Accurate Distance Determination Research Articles

Calibrating the Color–Magnitude Relation of M Giants by Using Open Clusters

Abstract M giants, with their distinctive properties such as high luminosity, serve as excellent indicators for mapping the structure of the Milky Way. The distance to distant M giants can be determined by using the color–magnitude relation (CMR), which is derived from color–magnitude diagrams of specific systems in previous studies. In this work, we aimed to achieve more accurate distance determination for M giants by focusing on open clusters (OCs) with a large number of member stars and thus improve the CMR. For the first time, we compiled a census of OCs harboring M giants using Gaia Data Release 3 (DR3) and Large Sky Area Multi-Object Fiber Spectroscopic Telescope Data Release 9. We identified 58 M giants associated with 43 OCs and obtained their astrometric and photometric parameters from Gaia DR3. Using the distances of these OCs, we derived the CMR for M giants as a linear correlation, expressed as M K s = 3.85 − 8.26 ( J − K s ) . This linear relation proved superior to the empirical distance relation in characterizing the CMR of M giants. The photometric distances of M giants derived from the CMR are consistent with the parallax distances from Gaia and known spectroscopic distances, with median deviations of 1.5% and 2.3%, respectively. Using the distances of M giants derived from the CMR, we computed their radial velocity (V R ), azimuthal velocity (V ϕ ), and vertical velocity (V Z ), respectively. The distributions of these velocities revealed key features of the Galactic disk, including oscillation, north–south rotational asymmetry, and warp. These findings are consistent with previous studies and further validate the reliability of the derived CMR.

Precessing binary black holes as better dark sirens

ABSTRACT Gravitational waves (GWs) from binary black hole mergers provide unique opportunities for cosmological inference such as standard sirens. However, the accurate determination of the luminosity distance of the event is limited by the correlation between the distance and the angle between the binary’s orbital angular momentum and the observer’s line of sight. In the letter, we investigate the effect of precession on the distance estimation of binary black hole events for the third-generation (3G) GW detectors. We find that the precession can enhance the precision of distance inference by one order of magnitude compared to the scenario where precession is absent. The constraint on the host galaxies can be improved due to the improved distance measurement, therefore the Hubble constant can be measured with higher precision and accuracy. These findings underscore the noteworthy impact of precession on the precision of distance estimation for 3G ground-based GW detectors, which can serve as highly accurate probes of the Universe.

Measurement of the matter-radiation equality scale using the extended baryon oscillation spectroscopic survey quasar sample

ABSTRACT The position of the peak of the matter power spectrum, the so-called turnover scale, is set by the horizon size at the epoch of matter-radiation equality. It can easily be predicted in terms of the physics of the universe in the relativistic era, and so can be used as a standard ruler, independent of other features present in the matter power spectrum, such as baryon acoustic oscillations (BAOs). We use the distribution of quasars measured by the extended Baryon Oscillation Spectroscopic Survey (eBOSS) to determine the turnover scale in a model-independent fashion statistically. We avoid modelling the BAO by down-weighting affected scales in the covariance matrix using the mode deprojection technique. We measure the wavenumber of the peak to be $k_\mathrm{TO} = \left(17.6^{+1.9}_{-1.8} \right) \times 10^{-3}h/\mathrm{Mpc}$, corresponding to a dilation scale of $D_\mathrm{V}(z_\mathrm{eff} = 1.48) = \left(31.1^{+4.1}_{-3.4}\right)r_\mathrm{H}$. This is not competitive with current BAO distance measures in terms of determining the expansion history but does provide a useful cross-check. We combine this measurement with low-redshift distance measurements from type-Ia supernova data from Pantheon and BAO data from eBOSS to make a sound-horizon free estimate of the Hubble–Lemaître parameter and find it to be $H_0=64.8^{+8.4}_{-7.8} \ \mathrm{km/s/Mpc}$ with Pantheon, and $H_0=63.3^{+8.2}_{-6.9} \ \mathrm{km/s/Mpc}$ with eBOSS BAO. We make predictions for the measurement of the turnover scale by the Dark Energy Spectroscopic Instrument (DESI) survey, the Maunakea Spectroscopic Explorer (MSE), and MegaMapper, which will make more precise and accurate distance determinations.

DDT run-up distance in an obstructed tube

Self-luminous high-speed photography was used to study flame acceleration and deflagration-to-detonation transition (DDT) in a clear polycarbonate round tube equipped with orifice plates. The 288 cm long, 7.6 cm inner-diameter tube was equipped with equally spaced 50% and 75% area-blockage orifice plates. The primary test mixture was stoichiometric ethylene–oxygen diluted with varying amounts of nitrogen, and the initial pressure was varied between 5 and 90 kPa. Tests were also performed with stoichiometric hydrogen–oxygen with large argon dilution to study the effect of detonation cell structure regularity. High-speed video showed that the initial DDT always occurred following shock reflection off an obstacle, allowing an accurate determination of the DDT run-up distance. Soot foils were used to measure cell size at the end of the obstacle-free tube. A correlation for flame acceleration to one-half the Chapman–Jouguet detonation velocity (VCJ) predicted the measured DDT run-up distance successfully for the most reactive mixture conditions. However, the measured DDT run-up distance increasingly deviated from the correlation with decreasing initial pressure, significantly under predicting the run-up distance at the DDT limit. A correlation for the DDT run-up distance was proposed based on the concept of flame acceleration to one-half VCJ followed by an induction phase that ends with the transition to detonation. For a given tube and obstacle configuration, the flame acceleration distance depends on the flame properties, and the DDT induction distance depends on the properties that quantify the detonation length-scale and stability.

An Independent Determination of the Distance to Supernova SN 1987A by Means of the Light Echo AT 2019xis

Accurate distance determination to astrophysical objects is essential for the understanding of their intrinsic brightness and size. The distance to SN 1987A has been previously measured by the expanding photosphere method and by using the angular size of the circumstellar rings with absolute sizes derived from light curves of narrow UV emission lines, with reported distances ranging from 46.77 to 55 kpc. In this study, we independently determined the distance to SN 1987A using photometry and imaging polarimetry observations of AT 2019xis, a light echo of SN 1987A, by adopting a radiative transfer model of the light echo developed in Ding et al. We obtained distances to SN 1987A in the range from 49.09 ± 2.16 kpc to 59.39 ± 3.27 kpc, depending on the interstellar polarization and extinction corrections, which are consistent with the literature values. This study demonstrates the potential of using light echoes as a tool for distance determination to astrophysical objects in the Milky Way, up to kiloparsec level scales.

Megamaser Cosmology Project II : The prospects for measuring a 1% Ho and distances to high-z galaxies

AbstractH2O megamaser emission from sub-parsec circumnuclear disks at the center of active galaxies allows a single-step, direct distance measurements to galaxies in the Hubble flow without any external calibration. Based on accurate distance determinations of six maser galaxies within 150 Mpc, the Megamaser Cosmology Project (MCP) team recently obtained H0 = 73.9± 3.0 km/s/Mpc (‘∼ 4% accuracy), independent of distance ladders and the cosmic microwave background. To further applying the megamaser technique to attain a 1% Ho measurement, detecting more high-quality disk maser systems is crucial. In this conference proceeding, we update the status of the MCP and discuss strategies of detecting additional high-quality disk maser galaxies within z ∼ 0.1. In addition, we show the prospects of reaching a 1% Ho measurement with the supreme sensitivity of the ngVLA. Finally, we demonstrate that applying the maser technique to distance measurements of high-z galaxies with future submm VLBI systems is promising and this will allow for investigation of the new tension between the ΛCDM model and the high-z Hubble diagram.

Modified Gravity and the Flux-weighted Gravity–Luminosity Relationship of Blue Supergiant Stars

Abstract We calculate models of stellar evolution for very massive stars and include the effects of modified gravity to investigate the influence on the physical properties of blue supergiant stars and their use as extragalactic distance indicators. With shielding and fifth force parameters in a similar range as those in previous studies of Cepheid and tip of the red giant branch (TRGB) stars, we find clear effects on stellar luminosity and flux-weighted gravity. The relationship between flux-weighted gravity, g F ≡ g/ , and bolometric magnitude M bol, which has been used successfully for accurate distance determinations, is systematically affected. While the stellar evolution of flux-weighted gravity–luminosity relationships (FGLRs) show a systematic offset from the observed relation, we can use the differential shifts between models with Newtonian and modified gravity to estimate the influence on FGLR distance determinations. Modified gravity leads to an increase in distance of 0.05–0.15 magnitudes in distance modulus. These changes are comparable to the ones found for Cepheid stars. We compare observed FGLR and TRGB distances of nine galaxies to constrain the free parameters of modified gravity. Not accounting for systematic differences between TRGB and FGLR distances shielding parameters of 5 × 10−7 and 10−6 and fifth force parameters of 1/3 and 1 can be ruled out with about 90% confidence. Allowing for potential systematic offsets between TRGB and FGLR distances no determination is possible for a shielding parameter of 10−6. For 5 × 10−7 a fifth force parameter of 1 can be ruled out to 92% but 1/3 is unlikely only to 60%.

A Dual-Color Tyr-FISH Method for Visualizing Genes/Markers on Plant Chromosomes to Create Integrated Genetic and Cytogenetic Maps.

In situ imaging of molecular markers on a physical chromosome is an indispensable tool for refining genetic maps and validation genome assembly at the chromosomal level. Despite the tremendous progress in genome sequencing, the plant genome assembly at the chromosome level remains a challenge. Recently developed optical and Hi-C mapping are aimed at assistance in genome assembly. For high confidence in the genome assembly at chromosome level, more independent approaches are required. The present study is aimed at refining an ultrasensitive Tyr-FISH technique and developing a reliable and simple method of in situ mapping of a short unique DNA sequences on plant chromosomes. We have carefully analyzed the critical steps of the Tyr-FISH to find out the reasons behind the flaws of this technique. The accurate visualization of markers/genes appeared to be significantly dependent on the means of chromosome slide preparation, probe design and labeling, and high stringency washing. Appropriate adjustment of these steps allowed us to detect a short DNA sequence of 1.6 Kb with a frequency of 51.6%. Based on our results, we developed a more reliable and simple protocol for dual-color Tyr-FISH visualization of unique short DNA sequences on plant chromosomes. This new protocol can allow for more accurate determination of the physical distance between markers and can be applied for faster integration of genetic and cytogenetic maps.

Distance measurements to quadrupolar nuclei: Evolution of the rotational echo double resonance technique.

Molecular structure determination is the basis for understanding chemical processes and the property of materials. The direct dependence of the magnetic dipolar interaction on the distance makes solid-state nuclear magnetic resonance (NMR) an excellent tool to study molecular structure when X-ray crystallography fails to provide atomic-resolution data. Although techniques to measure distances between pairs of isolated nuclear spin-1/2 pairs are routine and easy to implement using the rotational echo double resonance (REDOR) experiment (Gullion & Schaefer, 1989), the existence of a nucleus with a spin > 1/2, appearing in approximately 75% of the elements in the periodic table, poses a challenge due to difficulties stemming from the large nuclear quadrupolar coupling constant (QCC). This mini-review presents the existing solid-state magic-angle spinning NMR techniques aimed toward the efficient and accurate determination of internuclear distances between a spin-1/2 and a "quadrupolar" nucleus having a spin larger than one half. Analytical expressions are provided for the various recoupling curves stemming from different techniques, and a coherent nomenclature for these various techniques is suggested. Treatment of some special cases such as multiple spin effects and spins with close Larmor frequencies is also discussed. The most advanced methods can recouple spins with quadrupolar frequencies up to tens of megahertz and beyond, expanding the distance measurement capabilities of solid-state NMR to an increasingly growing number of applications and nuclear spin systems.

Solubilization properties and structural characterization of dissociated HgO and HgCl2 in deep eutectic solvents

A synergic approach combining X-ray absorption near-edge structure (XANES) and extended X-ray absorption fine structure (EXAFS) spectroscopies together with quantum mechanical (QM) calculations on cluster models has been used to investigate the solvation properties of the HgCl2 salt and of HgO dissolved in deep eutectic solvents (DESs). Choline chloride (ChCl)-based DESs were prepared using different hydrogen bond donors, namely 1:2 mixtures of ChCl and either urea, acetylsalicylic acid (ASA) or sesamol (SES) and a 1:1 mixture of ChCl and pyrogallol (PYR). The XANES results show that both HgCl2 and HgO molecules are completely dissociated in all the investigated DESs and the Hg2+ first coordination shell is composed only of Cl− anions in all the systems, with a local structure of Cl− ligands around the Hg2+ ion that is the same independently of the DES solvent and of the nature of the dissolved species. By applying a deconvolution procedure on the Hg L3-edge raw XANES experimental data and carrying out fitting procedures of the deconvolved XANES data using different coordination models for the Cl− anions surrounding Hg2+, we were able to unambigously determine the coordination number and the geometry of the Hg2+ first shell complex, namely a [HgCl4]2− tetrahedral coordination model. The analysis of the EXAFS spectra of HgCl2 salt in ChCl-Urea, ChCl-ASA, ChCl-SES and ChCl-PYR and of HgO dissolved in ChCl-ASA allowed us to obtain a very accurate determination of the HgCl first shell average distance (2.47–2.48 Å), in agreement with the XANES determinations. Moreover, ab initio calculations of different [HgCln](2−n)+ clusters carried out both in vacuum and simulating bulk solvent effects by means of the SMD solvation model strongly support the experimental findings that, in DESs, Hg2+ forms a complex with four chloride ions arranged in a tetrahedral geometry. The Cl− ion is thus shown to form such strong interactions with Hg2+ that none of the DES hydrogen bond donors is able to compete with it and act as a ligand for Hg2+. The strong solvation ability of the Cl− anions towards metal ions can be at the origin of the high solubility of metal oxides in chloride-based DESs, which is crucial in several important processes such as metal winning, corrosion remediation and catalyst preparation.

Transferred-Rotational-Echo Double Resonance.

Internuclear distance determination is the foundation for NMR-based structure calculation. However, high-precision distance measurement is a laborious process requiring lengthy data acquisitions due to the large set of multidimensional spectra needed at different mixing times. This prevents application to large or challenging molecular systems. Here, we present a new approach, transferred-rotational-echo double resonance (TREDOR), a heteronuclear transfer method in which we simultaneously detect both starting and transferred signals in a single spectrum. This co-acquisition is used to compensate for coherence decay, resulting in accurate and precise distance determination by a single parameter fit using a single spectrum recorded at an ideal mixing time. We showcase TREDOR with the microcrystalline SH3 protein using 3D spectra to resolve resonances. By combining the measured N–C and H–C distances, we calculate the structure of SH3, which converges to the correct fold, with a root-mean-square deviation of 2.1 Å compared to a reference X-ray structure. The TREDOR data used in the structure calculation were acquired in only 4 days on a 600 MHz instrument. This is achieved due to the more than 2-fold time saving afforded by co-acquisition of additional information and demonstrates TREDOR as a fast and straightforward method for determining structures via magic-angle spinning NMR.

Laser-induced Coulomb-explosion imaging of the CS2 dimer: The effect of non-Coulombic interactions

Carbon disulfide dimers ${({\mathrm{CS}}_{2})}_{2}$ are doubly ionized by an intense 40-fs laser pulse leading to fragmentation into a pair of ${{\mathrm{CS}}_{2}}^{+}$ cations. Unlike previous studies on atomic dimers, their kinetic energy, gained by mutual electrostatic repulsion, deviates strongly from the value determined by applying the Coulomb interaction approximation to the ${{({\mathrm{CS}}_{2})}_{2}}^{2+}$ ion. An ab initio calculation shows that inclusion of non-Coulombic interactions in ${{({\mathrm{CS}}_{2})}_{2}}^{2+}$ is crucial to account for the observed kinetic energy. These interactions result in 16 ${{({\mathrm{CS}}_{2})}_{2}}^{2+}$ electronic microstates, which obstructs accurate determination of intermolecular bond distances in ${({\mathrm{CS}}_{2})}_{2}$ from the fragments' kinetic energy. The situation will be similar for most other weakly bonded atomic and molecular complexes.

Kalkayotl: A cluster distance inference code

Context. The high-precision parallax data of the Gaia mission allows for significant improvements in the distance determination to stellar clusters and their stars. In order to obtain accurate and precise distance determinations, systematics such as parallax spatial correlations need to be accounted for, especially with regard to stars in small sky regions. Aims. Our aim is to provide the astrophysical community with a free and open code designed to simultaneously infer cluster parameters (i.e., distance and size) and distances to the cluster stars using Gaia parallax measurements. The code includes cluster-oriented prior families and it is specifically designed to deal with the Gaia parallax spatial correlations. Methods. A Bayesian hierarchical model is created to allow for the inference of both the cluster parameters and distances to its stars. Results. Using synthetic data that mimics Gaia parallax uncertainties and spatial correlations, we observe that our cluster-oriented prior families result in distance estimates with smaller errors than those obtained with an exponentially decreasing space density prior. In addition, the treatment of the parallax spatial correlations minimizes errors in the estimated cluster size and stellar distances, and avoids the underestimation of uncertainties. Although neglecting the parallax spatial correlations has no impact on the accuracy of cluster distance determinations, it underestimates the uncertainties and may result in measurements that are incompatible with the true value (i.e., falling beyond the 2σ uncertainties). Conclusions. The combination of prior knowledge with the treatment of Gaia parallax spatial correlations produces accurate (error < 10%) and trustworthy estimates (i.e., true values contained within the 2σ uncertainties) of cluster distances for clusters up to ∼5 kpc, along with cluster sizes for clusters up to ∼1 kpc.

Streams, Substructures, and the Early History of the Milky Way

The advent of the second data release of the Gaia mission, in combination with data from large spectroscopic surveys, is revolutionizing our understanding of the Galaxy. Thanks to these transformational data sets and the knowledge accumulated thus far, a new, more mature picture of the evolution of the early Milky Way is currently emerging. ▪ Two of the traditional Galactic components, namely, the stellar halo and the thick disk, appear to be intimately linked: Stars with halo-like kinematics originate in similar proportions from a heated (thick) disk and from debris from a system named Gaia-Enceladus. Gaia-Enceladus was the last big merger event experienced by the Milky Way and was completed around 10 Gyr ago. The puffed-up stars now present in the halo as a consequence of the merger have thus exposed the existence of a disk component at z ∼ 1.8. This is likely related to the previously known metal-weak thick disk and may be traceable to metallicities [Fe/H] [Formula: see text] −4. As importantly, there is evidence that the merger with Gaia-Enceladus triggered star formation in the early Milky Way, plausibly leading to the appearance of the thick disk as we know it. ▪ Other merger events have been characterized better, and new ones have been uncovered. These include, for example, the Helmi streams, Sequoia, and Thamnos, which add to the list of those discovered in wide-field photometric surveys, such as the Sagittarius streams. Current knowledge of their progenitors’ properties, star formation, and chemical evolutionary histories is still incomplete. ▪ Debris from different objects shows different degrees of overlap in phase-space. This sometimes confusing situation can be improved by determining membership probabilities via quantitative statistical methods. A task for the next few years will be to use ongoing and planned spectroscopic surveys for chemical labeling and to disentangle events from one another using dimensions other than phase-space, metallicity, or [α/Fe]. ▪ These large surveys will also provide line-of-sight velocities missing for faint stars in Gaia releases and more accurate distance determinations for distant objects, which in combination with other surveys could also lead to more accurate age dating. The resulting samples of stars will cover a much wider volume of the Galaxy, allowing, for example, the linking of kinematic substructures found in the inner halo to spatial overdensities in the outer halo. ▪ All the results obtained so far are in line with the expectations of current cosmological models. Nonetheless, tailored hydrodynamical simulations to reproduce in detail the properties of the merger debris, as well as constrained cosmological simulations of the Milky Way, are needed. Such simulations will undoubtedly unravel more connections between the different Galactic components and their substructures, and will aid in pushing our knowledge of the assembly of the Milky Way to the earliest times.

A large catalogue of molecular clouds with accurate distances within 4 kpc of the Galactic disc

ABSTRACT We present a large, homogeneous catalogue of molecular clouds within 4 kpc from the Sun at low Galactic latitudes (|b| < 10°) with unprecedented accurate distance determinations. Based on the 3D dust reddening map and estimates of colour excesses and distances of over 32 million stars presented in Chen et al., we have identified 567 dust/molecular clouds with a hierarchical structure identification method and obtained their distance estimates by a dust model fitting algorithm. The typical distance uncertainty is less than 5 per cent. As far as we know, this is the first large catalogue of molecular clouds in the Galactic plane with distances derived in a direct manner. The clouds are seen to lie along the Sagittarius, Local and Perseus Arms. In addition to the known structures, we propose the existence of a possible spur, with a pitch angle of about 34°, connecting the Local and the Sagittarius Arms in the fourth quadrant. We have also derived the physical properties of those molecular clouds. The distribution of cloud properties in different parameter spaces agrees grossly with the previous results. Our cloud sample is an ideal starting point to study the concentration of dust and gas in the solar vicinity and their star formation activities.

EXAFS of titanium LIII edge using a compact laboratory system based on a laser-plasma soft X-ray source

We present results of applying a compact laboratory system based on a laser-plasma soft X-ray (SXR) source to the extended X-ray absorption fine structure (EXAFS) spectroscopy of titanium in the vicinity of the LIII absorption edge. The source, operating with a plasma produced as a result of irradiation a krypton/helium double-stream gas-puff target, was optimized for an intense emission in the spectral range between 200 and 700 eV. A broad SXR spectrum and high photon flux are indispensable in the EXAFS studies. The experimental setup assured the simultaneous acquisition of both the reference and the absorption spectra. A grazing-incidence flat-field spectrometer was used to record the spectra. The absorption spectra of a thin (200-nm thick) titanium sample revealed the features in the EXAFS region allowing for quite accurate determination of the radial distances between the atoms. Results are in good agreement with the output of numerical modeling based on photoelectron wave function scattering and with the data reported for using a synchrotron source. This confirms the suitability of the source for using it in the standard EXAFS method.

Measurement of Accurate Interfluorine Distances in Crystalline Organic Solids: A High-Frequency Magic Angle Spinning NMR Approach.

Long-range interatomic distance restraints are critical for the determination of molecular structures by NMR spectroscopy, both in solution and in the solid state. Fluorine is a powerful NMR probe in a wide variety of contexts, owing to its favorable magnetic properties, ease of incorporation into biological molecules, and ubiquitous use in synthetic organic molecules designed for diverse applications. Because of the large gyromagnetic ratio of the 100% naturally abundant 19F isotope, interfluorine distances as long as 20 Å are accessible in magic-angle spinning (MAS) dipolar recoupling experiments. Herein, we present an approach for the determination of accurate interfluorine distances in multispin systems, using the finite pulse radio frequency driven recoupling (fpRFDR) at high MAS frequencies of 40-60 kHz. We use a series of crystalline "molecular ruler" solids, difluorobenzoic acids and 7F-L-tryptophan, for which the intra- and intermolecular interfluorine distances are known. We describe the optimal experimental conditions for accurate distance determinations, including the choice of a phase cycle, the relative advantages of selective inversion one-dimensional versus two-dimensional correlation experiments, and the appropriate numerical simulation protocols. An optimal strategy for the analysis of RFDR exchange curves in organic solids with extended spin interaction networks is presented, which, even in the absence of crystal structures, can be potentially incorporated into NMR structure determination.

Globular clusters in the Fornax cluster: A report from the FDS survey

AbstractThe Fornax Deep Survey (FDS) is a multi-band imaging survey of the Fornax cluster of galaxies, executed with the ESO VLT Survey Telescope (VST). The survey is designed to reach unprecedented surface brightness and point-source magnitude depth over one virial radius of the cluster. The scientific objectives of the survey are numerous: the study of the galaxy luminosity function, derivation of galaxy scaling relations, determination of the properties of compact stellar systems, an accurate determination of distances and 3-D geometry of the Fornax cluster, analysis of diffuse stellar light and galaxy interactions, etc.In this contribute we give an overview on the interest of the survey on globular clusters (GC) populations, and present a report the status of the study of GCs also providing some preliminary results of our analysis, with particular regard to the two-dimensional distribution of GC candidates over ∼20 sq. degree area of Fornax centered on NGC 1399.

Xanes Specroscopic Diagnostics of the 3D Local Atomic Structure of Nanostructured Materials

A review of current works on XANES spectroscopy applied for the determination of parameters of a threedimensional local atomic structure of nanostructured materials is given. Special attention is paid to a new method based on the theoretical analysis of XANES spectra by means of multivariate interpolation. The uniqueness of the technique consists not only in the highly accurate (up to 0.01 A) determination of interatomic distances in materials without a long-range order in the atomic arrangement but also the estimation of the angular distribution of atoms (i.e. chemical bond angles) in any condensed materials. Several types of nanostructured materials, including coordination compounds, semiconductor quantum dots, nanosized structures in quasicrystals and extraterrestrial materials are given as examples.

Pushing the limit of NMR-based distance measurements – retrieving dipolar couplings to spins with extensively large quadrupolar frequencies

Dipolar recoupling under magic-angle spinning allows to measure accurate inter-nuclear distances provided that the two interacting spins can be efficiently and uniformly excited. Alexander (Lex) Vega has shown that adiabatic transfers of populations in quadrupolar spins during the application of constant-wave (cw) radio-frequency pulses lead to efficient and quantifiable dipolar recoupling curves. Accurate distance determination within and beyond the adiabatic regime using cw pulses is limited by the size of the quadrupolar coupling constant. Here we show that using the approach of long-pulse phase modulation, dipolar recoupling and accurate distances can be obtained for nuclei having extensively large quadrupolar frequencies of 5–10 MHz. We demonstrate such results by obtaining a 31P-79/81Br distance in a compound for which bromine-79 (spin-3/2) has a quadrupolar coupling constant of 11.3 MHz, and a 13C-209Bi distance where the bismuth (spin-9/2) has a quadrupolar coupling constant of 256 MHz, equaling a quadrupolar frequency of 10.7 MHz. For Bromine, we demonstrate that an analytical curve based on the assumption of complete spin saturation fits the data. In the case of bismuth acetate, a C-Bi3 spin system must be used in order to match the correct saturation recoupling curve, and results are in agreement with the crystallographic structure.