dataesr/scientific-paragraphs-categorization huggingface dataset:
When the orbital period of a companion is much shorter than the Gaia DR3 observing window (1038 days), the PMa does not allow us to constrain the orbital inclination. In such cases, we fit Keplerian orbits with our MCMC, considering only the RV data points. We then used GASTON (Gaia Astrometric Noise Simulation to derive Orbit incliNation;  (Kiefer et al. 2019 (Kiefer et al. , 2021)) , updated to the improved Gaia DR3 accuracy, to model the DR3 astrometric excess noise (hereafter AEN) with a motion of the system's photocenter induced by the orbiting RV companion at an optimal orbital inclination. This leads to a new estimate of the true mass of the companion. The principle of GASTON is to assume the presence of this companion and (i) simulate Gaia's observations of the system with many possible orbits of the photocenter, (ii) fit out the 5-parameters linear model, as performed by Gaia, that includes position, proper motion, and parallax, (iii) calculate the AEN from the residuals, and (iv) compare the DR3 AEN to the outcomes of the simulations and perform an optimization of the orbital inclination.
The posteriors obtained for each free parameter of the MCMC are reported in Table  3    a minimum mass of 5. 3 M Jup , and an eccentricity of 0. 88. However, we observe a significant correlation between RV variations and bisector velocity span (BVS) variations (Fig. D. 9), indicating a possible stellar activity signal. Correcting the RV data with the linear regression between RVs and the bisector velocity span  (Melo et al. 2007) , we obtain a new RV dataset, for which a strong peak is present in the periodogram around 3000 days. Considering these data corrected for the stellar activity, we find the best solution for the companion corresponding to a planet that is less massive and eccentric (m p sin i = 2. 7 M Jup and e = 0. 44) but that has a similar period  (Fig. D. 11). Combining the corrected RV data with absolute astrometry with our MCMC (Fig.
HD 89839 Ninety-eight RV data points were obtained with HARPS between 2004 and 2021 for the F7V star HD 89839. Moutou et al. (2011)  reported a giant planet candidate based on the RV HARPS measurements obtained before June 2010 (Julian day: 2 455 353). However, this dataset does not fully cover the orbit of the companion, which is consequently poorly characterized. The reported orbital parameters are therefore poorly constrained, with a semi-major axis of 6. 8 +3. 3  -2. 4 au and an eccentricity of 0. 32 ± 0. 20. The available data allow us to reasonably well constrain the amplitude of RV variations, corresponding to a minimum mass of 3. 9 ± 0. 4 M Jup. The additional data points obtained between 2010 and 2021 now allow us to properly constrain the orbital parameters of HD 89839 b and, by simultaneously fitting all the RV data points available with the absolute astrometry with our MCMC (Figs.
It is not possible to confirm the presence of the planet. A107, page 11 of 71  Philipot, F. , et al. : A&A, 678, A107 (2023)  In any case, as the orbital period of the planet candidate is much smaller than the duration of Gaia DR3, the proper motion induced by this potential planet is negligible. Thus, by simultaneously fitting the same RV dataset as  Feng et al. (2022)  and the absolute astrometry with our MCMC  (Figs. D. 33 and D. 34) , and by considering 400 000 iterations (burn-in = 100 000) and 1000 walkers, we find a semi-major axis of 11. 8 +4. 1 -2. 5 au (P = 14 386 +8099 -4415 d), an inclination of either 40 +18 -11 °or 138 +12 -21 °, a mass of 1. 8 ± 0. 5 M Jup , and an eccentricity of 0. 77 +0. 06  -0. 07. This solution is within the error bars associated with the values found by  Feng et al.
035 -0. 036 au, and an eccentricity of 0. 257 ± 0. 019 for HD 169830 c. Recently, combining all the RV data points with absolute astrometry,  Feng et al. (2022)  report an orbital inclination of 24. 47 +12. 74  -7. 21 °and a true mass of 7. 67 +1. 94  -2. 76 M Jup for HD 169830 c 7. By simultaneously fitting the same RV dataset as  Feng et al. (2022) , corrected for the signal of HD 169830 b, and the absolute astrometry with our MCMC (Figs. D. 39 and D. 40), and considering 300 000 iterations (burn-in = 50 000) and 1000 walkers, we find a semi-major axis of 3. 29 +0. 04 -0. 05 au (P = 1832 ± 7 d), an inclination of either 23 +12 -6 °or 158 +5 -9 °, a mass of 8. 9 +2. 8 -2. 6 M Jup , and an eccentricity of 0. 23 +0. 03  -0. 02. This solution is within the error bars associated with the values found by  Feng et al.
HD 100777 Thirty-seven RV data points were obtained with HARPS between 2004 and 2007 for the G8V star HD 100777. Naef et al. (2007)  reported a giant planet candidate with a minimum mass of 1. 16 ± 0. 03 M Jup , a semi-major axis of 1. 03 ± 0. 03 au, and an eccentricity of 0. 36 ± 0. 02, considering all the available HARPS data. By fitting the same dataset as the one considered by  Naef et al. (2007)  with our MCMC, and considering 200 000 iterations (burn-in = 50 000) and 1000 walkers (Fig. D. 50), we find orbital parameters close to those reported by  Naef et al. (2007) , with a semi-major axis of 1. 06 +0. 02 -0. 01 au (P = 383 ± 1 d) and an eccentricity of 0. 38 ± 0. 02. Using Gaston, we could estimate that the orbital inclination of HD 100777 b is between 4°and 176°( confidence interval at 3σ), and thus that the maximum mass of the planet is 18 M Jup.
HD 111998 One hundred and fifty RV data points were obtained with the HARPS spectrograph between 2006 and 2014 for HD 111998. As HD 111998 is a fast-rotating F6V star, the HARPS DRS is not able to properly compute the radial velocity of the star. For this reason,  Borgniet et al. (2017)  used the SAFIR (Spectroscopic data via Analysis of the Fourier Interspectrum Radial velocities) software  (Galland et al. 2005)  to compute the RV. They report a giant planet candidate with a minimum mass of 4. 51 ± 0. 50 M Jup , a semi-major axis of 1. 82 ± 0. 07 au, and an eccentricity of 0. 03 ± 0. 04. By fitting the same dataset as the one considered by  Borgniet et al. (2017)  with our MCMC, and considering 300 000 iterations (burn-in = 100 000) and 1000 walkers (Fig. D. 50), we find orbital parameters close to those reported by  Borgniet et al.
Moreover, in most cases, when the period of the companion is much larger than the available RV baseline, the orbital parameters and the mass of the companion cannot be properly characterized. In these cases, the addition of relative astrometry significantly improves the constraint on the orbit of the companion and, consequently, its mass. Good examples are the cases of GJ680 B and HD 111031 B. Feng et al. (2022)  combine RV data points obtained with HARPS between 2004 and 2012 for GJ680, and with HIRES between 1997 and 2016 for HD 111031, and absolute astrometry. They report a semi-major axis of 10. 1 +1. 8 -1. 7 and 13. 1   (Dalba et al. 2021). In this study, we consider the same RV dataset for GJ680 and, for HD 111031, we consider the RV HARPS measurements obtained between 2004 and 2013, the RV HIRES data obtained between 1997 and 2020, the RV APF measurements obtained between 2013 and 2020, and the RV LICK measurements obtained in 2001.
We thus determine their true mass and their exact nature. Moreover, by applying the same method, we are able to improve the characterization and determine precisely the true mass of ten known substellar companions and, using GASTON, we are able to confirm the planetary nature of three known candidate planets (Fig. 11 ). We determined the properties of 25 stellar companions, A107, page 15 of 71  Philipot, F. , et al. : A&A, 678, A107 (2023)  including 12 new detections. We show also that five companions previously reported as brown dwarfs are indeed low-mass stars: GJ 680 B, HD 56380 B, HD 111031 B, HD 131664 B, and HD 221638 B. The coupling of HIPPARCOS/Gaia measurements with RV data does not always permit the accurate characterization of the orbit of a companion, in particular when its period is not completely covered by the RV data.
The addition of HCI data allows for better constraining of the orbit of the companion and, consequently, measuring its mass. However, most of the companions revealed in this study have not been detected or observed in imaging. Thus, neither the orbital parameters nor the exact nature of 27 of the 80 single companions found in our sample can be determined. In summary, we conclude that studying the PMa of stars allows the search for substellar companions in RV to be optimized so that they can then be properly characterized by combining RV, absolute astrometry, and, when available, relative astrometry data. However, this method is not sensitive to lowmass planets and therefore does not enable Earth-like planets to be searched for. Ghazaryan et al. (2019). 16 Ammler-von Eiff & Reiners (2012). 17 Rice & Brewer (2020).
Acknowledgements. This study was funded by a grant from  PSL/OCAV. This project has also received funding from the  European Research Council (ERC)  under the  European Union 's  Horizon 2020 research and innovation programme ( COBREX ; grant agreement  n°885593 ). This work presents results from the  European Space Agency (ESA)  space mission Gaia. Gaia data are being processed by the  Gaia Data Processing and Analysis Consortium (DPAC). Funding for the DPAC is provided by national institutions, in particular the institutions participating in the Gaia MultiLateral Agreement (MLA). The Gaia mission website is https://www. cosmos. esa. int/Gaia. The Gaia archive website is https://archives. esac. esa. int/Gaia. This publication makes use of The Data & Analysis Center for Exoplanets (DACE), which is a facility based at the  University of Geneva (CH)  dedicated to extrasolar planet data visualisation, exchange, and analysis.
DACE is a platform of the  Swiss National Centre of Competence in Research (NCCR) PlanetS , federating Swiss expertise in exoplanet research. The DACE platform is available at ttps://dace. unige. ch. This work has made use of the  SPHERE Data Center , jointly operated by  OSUG/IPAG (Grenoble) ,  PYTHEAS/LAM/CeSAM (Marseille) ,  OCA/Lagrange (Nice) ,  Observatoire de Paris/LESIA (Paris) , and  Observatoire de Lyon (OSUL/CRAL). This research has made use of the SIMBAD database and VizieR catalogue access tool, operated at  CDS in Strasbourg, France. It is also based on data retrieved from the SOPHIE archive at  Observatoire de Haute-Provence (OHP) , available at atlas. obs-hp. fr/sophie, on spectral data retrieved from the ELODIE archive at  Observatoire de Haute-Provence (OHP) , and on observations collected at the  European Southern Observatory  under ESO programmes.
ucl. ac. uk/neomine; Figure  1 ). The combination of datasets with different raw materials enables the reconstruction of more complex relations, such as economic choices, where certain raw materials are substituted for others (cf. Knappet 2021). Here, the data science part of the project comes in: the data integration process focuses on potential for automation as well as domain and research data management requirements. The integrated relational data are mapped to a Heterogeneous Information Network (HIN) to enable the exploration of relationship patterns with a variety of graphical and data mining techniques (Shi 2017). Regional LBK groups can be distinguished by ceramics. The north-western LBK (NW group) is characterised by a good supply of flint of Rijckholt origin  (Zimmermann 1995) , but the absence of materials that are otherwise widespread in Central Europe is now becoming apparent; the lack of Spondylus, for example (method: Figure  3 ), in the north-west was suspected to result from local poor preservation conditions (cf.
54 Landeros-Rivera, Contreras-García, and Dominiak recently argued that this is due to the sensitivity of the XCW fitting procedure to the data treatment, which is particularly reflected in the experimental standard uncertainties. 68 Subsequently, in a study using 14 different datasets of oxalic acid dihydrate (none of them of the usual high quality used for experimental charge-density determinations), some of us have tested the reproducibility and reliability of the information extracted from an XCW fitting. 25 The result was that there were consistent systematic effects preserved in every dataset, some of which could be rationalized to be electron correlation and polarization effects, but others must have been caused by systematic errors in the data. We note that XCW fitting always deals with information that are just above the noise level as discussed in Ref.
26. Based on these findings and problems, we have chosen to use x-ray diffraction datasets that are well-known to be of superb quality and have been used for similar proof-of-concept studies in the past: urea measured by Birkedal et al. 69  and used, e. g. , in Refs. 70-72, as well as L-alanine measured by Destro et al. 73  and used, e. g. , in Refs. 74-78. Here-unlike in any other XCW fitting study that discussed the effects I to III-after a theoretical evaluation of the effects I and II, we proceed to the experimental datasets of urea and L-alanine with real experimental errors: In the first and second part of this study, we will investigate to which extent and percentage XCW fitting is able to retrieve electron correlation and polarization from theoretical x-ray structure factors that include either of these two effects exclusively.
A self-consistent cluster of point charges and dipoles around the central molecule for every symmetry-generated molecule within a radius of 8 Å was used in the crystallographic refinement to simulate the crystal field. This procedure ensures the best possible experimental structures available today from x-ray diffraction data, including A-H bond lengths similar to those derived from neutron-diffraction studies and anisotropic displacement parameters for hydrogen atoms. 93, 94  Figure  1  shows the experimental structures after HAR at the HF/pob-TZVP level of theory, with refinement details summarized in the caption. The resulting HAR CIFs at this level of theory are deposited with the Cambridge Structural Database under the deposition numbers CCDC-2182609 (urea) and 2182613 (L-alanine) and can be obtained free of charge via https://www.
C. Electron correlation The software Gaussian09 95 was used to calculate the reference electron correlation effects for urea and L-alanine. The coordinates of the HAR-refined final geometries were used as input geometries for coupled-cluster singles and doubles (CCSD) (no frozen core) and HF single-point calculations, respectively. The basis sets def 2-TZVP and pob-TZVP (with the exact coefficients as implemented in CRYSTAL14)  92  were used to test basis-set dependencies of the electron correlation effects. However, the basis set comparison is only discussed in the supplementary material. In the following, all results are described based on the pob-TZVP basis set only, which is implemented in CRYSTAL14 and was explicitly defined by us for the software programs TONTO and Gaussian09. The software denprop 96 was employed to calculate the hkl indices and static structure factor magnitudes that include the effect of electron correlation.
For this purpose, the Gaussian09 wavefunction output (. wfn file) of the CCSD calculation was used as input for a model pseudo-periodic system with cell constants of 10 × 10 × 10 Å 3 (cubic cell) and a resolution of 0. 7, 1. 4417, and 2. 0 Å -1 for urea and 20 × 20 × 20 Å 3 (cubic cell) with a resolution of 0. 7, 1. 0778, and 2. 0 Å -1 for L-alanine. In each case, the medium resolution agrees with the resolution of the experimental. hkl file. Effects of atomic displacement were not simulated, and the artificially large unit cell constants prevent intermolecular interactions to play any role. The software TONTO 91 was used for the XCW fitting against the theoretical structure factors. A. cif file was manually written with the coordinates from the Gaussian09. wfn file and the cell as specified in denprop.
The obtained grid points containing the difference electron density were then written to a file in the same Gaussian cube file format. Restrictions to this script are that the geometry of the molecule and the orientation of that molecule toward the cube borders must be exactly the same in both cubes. With a second script, the absolute values of each grid point (r i ) of the difference density grids were summed up and then divided by two to obtain the total electron count of the difference, namely, the total magnitude of the electron correlation effect as it impacts on the electron density (Ne = (∑ n p i=1 |ρ method1 (ri) -ρ method2 (ri)|)/2). To obtain the percentage reconstruction (PR) of the XCW fitting procedure [Eq. (  3 )], the difference between the TONTO_λ=x. cube with electron density values ρ λ=x (ri) and the unconstrained values ρ λ=0 (ri) in the TONTO_λ=0.
D. Polarization The software CRYSTAL14 100 was used to calculate the reference polarization effects of urea and L-alanine. The coordinates of the HAR were used as input geometry for a fully periodic single-point calculation at the experimental crystal symmetry and crystal lattice with the HF/pob-TZVP level of theory, termed the 3D model. In a separate calculation, the keyword MOLSPLIT was used to obtain the molecule-based procrystal electron density that does not include polarization effects. The software denprop was used only to calculate the list of hkl indices for a certain resolution, given the experimental lattice parameters. The considered resolutions are 0. 7, 1. 4417, and 2. 0 Å -1 for urea as well as 0. 7, 1. 0778, and 2. 0 Å -1 for L-alanine. The predicted hkl indices were then used as input (.
d3 file) for the calculation of the respective structure factor magnitudes for the 3D model with the runprop14 utility as implemented in CRYSTAL14. The effects of atomic displacement were not simulated; the resulting structure factor magnitudes are static. The software TONTO was used for the XCW fitting, and the procedure is similar to the one described for obtaining the correlation effects. The CYRSTAL14-obtained structure factors of the 3D model served as input to be fitted against with a molecular HF/pob-TZVP wavefunction as ansatz. The XCW fitting was performed from λ = 0 to the indicated maximum λ-values in steps of 0. 5 (for resolutions of 1. 4417 and 2. 0 Å -1 for urea), 0. 2 (for resolutions of 0. 7 Å -1 for urea as well as 1. 0778 and 2. 0 Å -1 for L-alanine), or 0. 02 (0. 7 Å -1 for L-alanine) applying a uniform structure factor error of 0.
The resolution dependence of the fitting of the polarization effect  59, 60  agrees with the trends observed for electron correlation but is less pronounced (see Table  II ). With low-resolution data, the physical effect is incorporated into the wavefunction at lower λ-values more quickly. From the higher exponential coefficients b 1 of the higher resolution datasets, it is quite clear that these datasets contain less information about polarization per value of λ. This means, on the other hand, that convergence ceases much earlier for low-resolution datasets. The resolution dependence of the maximum achievable PR value on resolution is clearly less pronounced than for electron correlation (compare Table  II  with Table  I ).
IV. CONCLUSIONS A. Conclusions from XCW fitting against theoretical data The effect of polarization builds up in the fitted wavefunction more quickly, i. e. , at lower values of λ, than electron correlation. Nevertheless, if fitted to λmax, both polarization and electron correlation effects can be recovered to the same extent and with the same accuracy and reliability. An extrapolation to λ∞ shows that inherently XCW fitting is not more sensitive to the one or the other effect. The success of the reconstruction of both effects depends on the maximum resolution of the structure factors set; a mediumresolution dataset allows faster and more complete reconstruction than an ultra-high resolution dataset. We show for the first time how the flow-on effect of the fitting to correlated structure factors on the exchange-correlation potential looks like and that it is physically meaningful, even if a HF wavefunction is used for fitting.
C. Conditions and uncertainties The results in this paper are based on two datasets of high quality, extensively used as test sets for benchmarking new methods in the field of quantum crystallography for decades. In a different study,  25  some of us have recently demonstrated that with data of not the same high quality, the reproducibility of the fitted effects is limited. This has to do with the fact that the discussed effects are very small. For urea and L-alanine, they amount to roughly 0. 05 e per non-hydrogen atom per physical effect. Moreover, as a ballpark figure, 95% (corresponding to a crystallographically refined R-value of 5%) of the measured physical effects are reconstructed by simply summing up calculated spherical atomic electron densities, another few percent by accounting for atomic non-sphericity in the chemical and crystal field of neighbors (chemical bonding effect), so only a very small percentage of the reconstructed electron density is due to the discussed effects of polarization and electron correlation.
Therefore, as the next step toward the general use of experimental diffraction data in method development for quantum chemistry, a reproducibility study using very high-quality datasets is needed and envisaged. Although the effects are small on an electron-density scale relative to experimental uncertainties, one should not forget that such small permanent, fluctuating or induced electron-density differences give rise to very significant intermolecular forces (electrostatic, van-der-Waals, London dispersion etc. ). Roughly, already a change of 1% in the molecular energy of urea or L-alanine amounts to several thousand kJ/mol. Finally, we have shown that the approximation of the crystal effect with cluster charges is insufficient for XCW fitting so that better quantum-mechanical models must be tested in the future.
ACKNOWLEDGMENTS S. Grabowsky ,  E. Hupf , and F. Kleemiss thank the  German Research Foundation (Deutsche Forschungsgemeinschaft DFG)  for funding within the  Emmy-Noether scheme  (Grant No. GR 4451/1-1 ) (S. G. ), for a postdoctoral fellowship (Grant No. HU 2512/1-1 ) (E. H. ), and for a  Walter-Benjamin fellowship  (Grant No. KL 3500/1-1 ) (F. K. ). M. Woińska acknowledges financial support from the  Polish National Science Centre (NCN)  under Opus Grant No. DEC-2018/31/B/ST4/02142.
Inversion Method and Results We apply trans-dimensional Markov-chain Monte Carlo inversion to our surface-wave group-velocity measurements. To implement the inversion, we make use of the BayHunter  (Dreiling & Tilmann, 2019)  open-source inversion package. This package is developed for 1D isotropic velocity models, and the forward modeling module is from Computer Programs in Seismology  (Herrmann, 2013). For each model, the package allows the number of layers, the V S of each layer, and the layer thickness to evolve iteratively. We set the minimum layer thickness to be 2 km, as Shi et al. (  2022 ) report a ∼2-km-thickness layer beneath the InSight lander. We set one V P /V S ratio for each model, and this ratio is allowed to vary between 1. 70 and 1. 85 during the inversion. The density of each layer is determined by the V P -density relationship proposed by  Berteussen (1977).
Data Availability Statement The Martian topography data are from the NASA PDS Geosciences Node  (Neumann et al. , 2003). The InSight seismic waveform data are available from the IPGP Datacenter, IRIS-DMC and the NASA PDS (InSight Mars SEIS Data Service, 2019a, 2019b) and secondary data of S1222a (e. g. , location, arrival times) is available from MQS catalog (InSight Marsquake Service, 2023). The inversion package, BayHunter, is from  Dreiling and Tilmann (2019). The velocity models from the inversion are available from  Xu et al. (2023). The direct solution method  (Geller & Ohminato, 1994)  used in the Supporting Information S1 is from  Fuji et al. (2016).