dataesr/scientific-paragraphs-categorization huggingface dataset:
3] [14]  ). Owing to the sin 3 i scaling, a systematic error in the estimated inclination angle due to an incomplete heating model can lead to a large bias in the resulting pulsar mass estimate. Millisecond pulsars (MSPs) also emit gamma-ray pulsations, as revealed by the Large Area Telescope (LAT)  15  onboard the Fermi Gamma-ray Space Telescope. Gamma rays are particularly helpful in discovering and studying spider pulsars because, unlike radio waves, they are not absorbed in the diffuse intra-binary material. Partially as a result of radio searches repeatedly targeting unidentified Fermi-LAT sources  16  , the number of known Galactic spider systems has increased tenfold since Fermi's launch. The LAT data also offer a new and independent means to constrain binary inclination angles and pulsar masses in spider systems by enabling searches for, and studies of, gamma-ray eclipses.
Strader et al. 17  found evidence in the Fermi-LAT data, later confirmed by Kennedy et al. 18  using a longer dataset, for the first such gamma-ray eclipse in a candidate accreting transitional MSP. In this Article we present a systematic search for gamma-ray eclipses from 49 confirmed/candidate spider pulsar systems. We first searched for eclipses in 42 Fermi-LAT detected confirmed spider pulsars, and found significant gamma-ray eclipses from five pulsars: PSRs B1957+20, J1048+2339, J1555-2908, J1816+4510 and J2129-0429. This number of detected eclipses is consistent with the number we would expect to observe from the tested population, assuming randomly distributed orbital axes and nearly Roche-lobe filling companion stars. The orbital gamma-ray light curves for these systems are shown in Fig.
1 , and the results of Monte Carlo simulations used to estimate their significance (see 'Significance calibration via Monte Carlo simulations' in the Methods) are shown in Fig. 2. Of these, the eclipse in PSR J1555-2908 has the lowest significance, but still has a false-alarm probability of 4 × 10 -5 after accounting for the trials factor introduced by testing a range of possible eclipse widths. The most significant eclipse, from PSR J2129 - 0429, represents a deficit of no more than 20 (weighted) photons over the 11. 4 yr of LAT data considered here. For 32 of the pulsars without detected eclipses the gamma-ray data significantly exclude otherwise feasible eclipses above a certain duration, but the faintest five systems yield no such constraints. In one of these, PSR J0251+2606, there is marginal evidence for an eclipse, with a false-alarm probability of 0.
For PSR J2215+5135, Romani, Graham, Filippenko and Kerr  31  inferred a high inclination from optical modelling, and even found marginal evidence for a low-significance gamma-ray eclipse in the Fermi-LAT data. However, eclipses in this system lasting longer than 0. 1% of an orbit are strongly ruled out by our longer dataset, showing that this earlier hint was likely to be a chance false-alarm, and indeed more recent modelling by Linares, Shahbaz and Casares 7 and Kandel and Romani  32  found lower, non-eclipsing inclinations. Finally, we note that pulsars that are eclipsed by their companion stars also necessarily pass in front of the heated face of the companion star half an orbit later. 4] [35]  ). The exact degree of the magnification depends only on the pulsar mass and the orbital separation.
To estimate their false-alarm probabilities, we therefore performed a simple linear fit to the observed δ log ℒ versus log(P FA ) curves for these pulsars, and extrapolated to the observed values. In Fig. 2 , we also show the empirical survival function; that is, the fraction of pulsars whose measured eclipse log-likelihoods would survive a given threshold. If there were no eclipses in our dataset, then the set of measured log-likelihood values would be drawn from the null-hypothesis distribution and this empirical survival function curve would closely follow the simulated curves. The ratio between the empirical and simulated curves at the highest measured log-likelihood value illustrates the significance of the largest outlier, given the number of pulsars included in the sample. If we removed the five eclipsing systems, then the empirical survival function curve did closely follow the simulated null-hypothesis curve, and only started to deviate for the final pulsar, PSR J0251 + 2606, which had a false-alarm probability of around 0.
The Roche-lobe filling factor can be estimated from rotational broadening or surface gravity measurements via optical spectroscopy (for example ref. 47  ) or from the amplitude of the 'ellipsoidal' component of an observed optical light curve  48. However, this parameter is often correlated with the estimated inclination, and so previous estimates of f RL are not necessarily consistent with new inclination constraints from an eclipse detection or exclusion. To compute expected eclipse durations, we generated model stars using the Icarus 48 binary modelling software. Icarus assumes that the surface of the star follows an equipotential contour within its Roche lobe, and therefore the simulated surface accounts for the non-spherical shape of the star due to tidal and rotational deformation. For a given binary mass ratio and Roche-lobe filling factor we could then compute the range of orbital phases at which the pulsar is eclipsed by the model star, when viewed from a given inclination.
To search for gamma-ray eclipses in these systems, we prepared Fermi-LAT datasets in the same way as for the confirmed spider cases, but included 12. 4 yr of data. As these datasets were not bound to the validity period of a pulsar timing ephemeris, we included this extra year of data to allow for stronger detections to partially mitigate the large trials factor (see below). For these datasets we used gtsrcprob to compute the photon weights, rather than optimizing these to maximize the pulsation significance (since this optimization is not possible here without a gamma-ray pulsation detection), and used the prior probability weights, since posterior weights are unavailable in the absence of pulsations. Unlike the majority of systems studied here, where the pulsar's timing ephemeris provides precise orbital period and phase measurements over the Fermi-LAT dataset, for these systems we have only https://doi.
Acknowledgements C. J. C. thanks  B. Allen  for useful discussions that led to the use of posterior weights that increased the significances of the detected eclipses. We thank  S. Digel ,  T. Johnson ,  M. Pesce-Rollins ,  D. Thompson  and  Z. Wadiasingh  for carefully reviewing the manuscript on behalf of the  Fermi-LAT collaboration. C. J. C. , R. P. B, M. R. K. , D. M. S. and G. V. acknowledge support from the  ERC  under the European Union's  Horizon 2020 research and innovation programme  (grant agreement no. 715051 ; Spiders). This work was supported by the  Max-Planck-Gesellschaft (MPG). B. B. acknowledges the support of the  Department of Atomic Energy, Government of India , under project no. 12-R&D-TFR-5. 02-0700. H. T. C. is a  Hubble Fellowship Program Einstein Postdoctoral Fellow.
Support for H. T. C. was provided by  NASA  through the  NASA Hubble Fellowship Program  grant no. HST-HF2-51453. 001  awarded by the  Space Telescope Science Institute , which is operated by the  Association of Universities for Research in Astronomy, Inc. , for  NASA , under contract no. NAS5-26555. V. S. D. was supported by the  STFC. M. R. K. acknowledges support from the  Irish Research Council  in the form of a  Government of Ireland Postdoctoral Fellowship  ( GOIPD/2021/670 :  Invisible Monsters ). S. M. R. is a CIFAR Fellow and is supported by the  NSF Physics Frontiers Center  award no. 1430284. D. M. S. also acknowledges the  Fondo Europeo de Desarrollo Regional (FEDER)  and the  Canary Islands government  for the financial support received in the form of grant no. PROID2020010104.
Data availability The Fermi-LAT data are available from the Fermi Science Support Center at http://fermi. gsfc. nasa. gov/ssc. Ephemerides and folded Fermi-LAT datasets, including prior and posterior photon weights for systems with detected eclipses, are available via Zenodo at https://doi. org/10. 5281/zenodo. 7133502. Ephemerides and folded datasets for other pulsars included in this study may contain unpublished information about unrelated scientific results; these are available from the corresponding author upon request.
Code availability The Fermitools, including gtsrcprob, used to analyse Fermi-LAT data are available at https://fermi. gsfc. nasa. gov/ssc/data/analysis/software/. TEMPO  45  , used to compute rotational and orbital photon phases, is available via Bitbucket at https://bitbucket. org/psrsoft/tempo2. Icarus  48  , used to commpute expected eclipse durations to derive pulsar mass estimates, is available via GitHub at https://github. com/bretonr/ Icarus. Godot  39  , used to compute Fermi-LAT exposure, is available via GitHub at https://github. com/kerrm/godot. PINT  65  , used to evaluate template pulse profiles to derive posterior weights, is available via GitHub at https://github. com/nanograv/PINT. The scripts used to perform the eclipse searches and false-alarm calibrations are available via Zenodo at https://doi.
C. License and Distribution The Enrico's Chart is a digital object (pdf file) released under the Creative Commons 4. 0 CC-BY-NC-ND license available from Zenodo as DOI 10. 5281/zenodo. 4399218. The latter is called concept DOI and always resolves to the latest version. Because Zenodo delivers a separate DOI for each version, the 'version DOI' should be used only in special cases. The QR codes of Fig. 1  point to the Chart and to this article. Redistribution is encouraged as the Internet link or as the QR code, not as a file. The NC copyright attribution deserves a comment. This restriction is mainly intended to prevent selling the Chart for profit. By contrast, giving the Chart for free with way more expensive goods is not considered commercial use, and we encourage this practice. The electronic equipment more or less related to our field is a notable example.
People interested in the rise of the scientific ideas beyond phase noise should go for Chi (Ed. ) 1965  [28]. This is the Proceedings book of a one-time NASA conference, which in our opinion is where the awareness of phase noise started with. The PDF is available for free from the IEEE. Rutman 1978 [112]  is a review article about the progress on the concepts of phase noise and frequency stability after the early ideas. See also  Rutman & Walls 1991 [113]. A report of the CCIR on frequency and phase noise is also available  [27]. Turning our attention to books and booklets, Riley 2008  [101]  is free available and sponsored by NIST. Emphasis is on Allan and Allan-like variances, rather than noise spectra, making extensive use of the Stable32 software package. Owen 2004  [98]  is a rather extensive practical guide about phase noise, albeit elderly.
number of samples is 389998, for a total duration T ≈ 4. 5 days. Figure  8  shows the MDEV of the experiment described, processed with the SigmaTheta software tool. Starting from uniformly averaged data, a practical minimum of 8-10 samples is needed to approximate the triangular average (Regions 2. 1 and 2. 2. ). Thus, MDEV is plotted in powers of 2 starting from τ = 8τ 0 = 8 s. At the scale of this experiment, the H maser used as the reference can be considered ideally stable, and the noise of the instrument is negligible as well. The SigmaTheta software package provides the following pieces of information (see Sections IX and XI) • The values of σ y (τ ) shown as crosses, • The Bayesian estimates of σ y (τ ), shown as green, donuts, • The uncertainty bars, • The identification of the most relevant noise processes, shown as the colored straight lines of slope 1/ √ τ , constant vs τ and τ.
It was used in the HP5371A HP5372A time interval analyzers 6 in the late 1980s, and by  Johansson 2005 [71]  at Pendulum. The name "Ω counter" comes from Rubiola & al. [110] , which introduces the related mathematical framework for frequency metrology. Feeding the linear-regression estimates into (30), we get PVAR. This idea came independently from  Benkler & al. 2015 [13] , PTB, and Vernotte & al. 2016  [125] , FEMTO-ST Institute, and the name PVAR was decided together by the two teams. Reference  [125]  digresses the advanced statistical properties of PVAR, including the Bayesian statistics and the minimum duration of the data record to detect a noise process. 4) Aliasing: Vernotte 1998  [123]  provides theory and insight on spectral aliasing. Calosso & al. 2016 [22]  gives an interesting perspective about aliasing in the AVAR and MVAR, covering the effect of spectral bumps and 'blue noise,' often found in optical systems.
H. Suggested Readings About Experimental Methods 1) Mathematical methods: The algorithm commonly used for the estimation of power spectra, known as the Welch algorithm, is introduced in Welch 1967  [132]. In several software packages libraries, the PSD function takes a name which recalls Welch. This is the case of Matlab, Octave and Python (SciPy). Brigham 1988  [19]  is the Enrico's favorite reference about the Fast Fourier Transform. The FFT is a fast algorithm for the evaluation of the Discrete Fourier Transform (DFT), and gives the same result. The algorithm generally used in software packages and libraries is now the 'Fastest Fourier Transform of the West' FFTW3, published in 2005 by Matteo Frigo & Steven B. Johnson, MIT,  [46]. With a bit of humor, we note that the FFTW comes from the Eastern USA.
To the best of our knowledge, noise analyzers do not save or transfer raw data of this size and at this rate. TimeLab is no exception, to the extent that the spectra up to 1 MHz are pre-processed inside the instrument, and only lowrate time samples are transferred to the external computer for the evaluation of the two-sample variances. Y Y 2 Y CGODEV beta Y - - GRADEV Y - - - HDEV Y 2 Y Y 2 Y MDEV Y Y Y Y PDEV - Y - - Thêo1 Y - Y - ThêoH - - Y - TOTDEV Y - Y - Time MTIE Y - Y Y TDEV Y - Y Y TIErms Y - Y - Other Estimator direct Bayes direct direct Error bars LA & GR GR GR LA Fit - Y - - General We present a selection of software packages (Table  II ), chosen for their scientific value or for their wide use. The grayed area highlight some interesting features. A. Features 1) Main purposes: AllanTools, SigmaTheta and Stable32 are intended for data analysis.
By contrast, TimeLab is a tool for data acquisition, with limited analysis capabilities. It supports the phase noise analyzers from Jackson Lab and Microchip (formerly Microsemi), and a few frequency counters. 2) Graphical interface versus scripting: Albeit elderly, Stable32 has an efficient graphical interface, which makes it a great choice for occasional users. For this reason, it is by far the most widely used. AllanTools and SigmaTheta require programming skills. Scripting is great in that it enables the analysis of a bulk of data sets at once. 3) Mathematical functions: All the packages provide ADEV, MDEV and the other mostly-used functions. For simplicity, DEV in Tab. II stands for DEV or VAR. When it comes to more exotic functions like Thêo and the Groslambert covariance, the choice of packages is smaller.
4) Estimator: The unique feature of SigmaTheta is that the evaluation is based on the Bayesian statistics (inverse problem), which consists of estimating the most probable value from the experimental data. The other packages evaluate the average value using the classical formulae like (32) for AVAR. 5) Missing data: The Gap Resistant ADEV (GRADEV), included only in AllanTools, enables the evaluation of ADEV in the case of missing data during the measurement. 6) Error bars: The choice is between the classical Lesage-Audoin algorithm  [87] , and the more sophisticated Greenhall-Riley algorithm  [52]. The LA algorithm uses the square root of the 4th moment, assuming that the error distribution is Gaussian centered around the estimate. By contrast, the GR algorithm estimates the degrees of freedom using the χ 2 distribution.
B. Availability The availability is summarized in Tab. III. AllanTools and SigmaTheta are open code released to public domain under very similar licenses. Stable32 is © IEEE. The developers informed us that the code itself is covered by the MIT license, but compiling needs code for other sources. They are trying to clean the code for it to be released into the public domain, provided the IEEE agrees, with the ultimate goal of having at least Linux, macOS and Windows distributions available.
ACKNOWLEDGMENTS We express gratitude to John Lewis "Jan" Hall for his authoritative and friendly encouragement. On February 5, 2020, he wrote in a private communication. But the best thing for me is the link to your new charts, collecting the multiple informations about how to analyze measured phasenoise spectra to begin to grasp the underlying causes. I have been using a 10th-generation photocopy of an early precursor to your chart, which came many years ago from either Don Halford or Helmut Hellwig at the NBS/NIST. We thanks the users of the earlier versions of the Chart for feedback and corrections. This.
Off-axis objects can either take the form of point-like sources or that of spatially extended features like circumstellar disks. In this paper, we focus on the detection of point-like sources, leaving the problem of disk reconstruction for future work. In order to unmix the sought objects from the nuisance component, high-contrast observations are performed with dedicated strategies like angular differential imaging (ADI;  Marois et al. (2006) ), that we consider in this paper. ADI consists in tracking the observed target over time, with the telescope derotator tuned to keep the telescope pupil stable while the field of view rotates around the host star. Consequently, in the resulting 3-D datasets (2-D + time), the objects of interest follow an apparent motion along a deterministic circular trajectory centered on the star while the telescope pupil remains static.
The classical principle is to estimate a reference image (so-called on-axis PSF) of the nuisance component, that can be subtracted from the data in order to unveil the sought objects. A simple practical implementation of this general strategy consists in subtracting the temporal mean or median of the dataset from each frame of the ADI stack. The residual images are then co-aligned to the true-North so that the signals of the sought objects are superimposed and can be combined by temporal stacking. This is the principle of the cADI method designed to process the first direct imaging observations  (Marois et al. 2006; Lagrange et al. 2009 ). In the last decade, several more advanced methods have been developed, see, e. g. ,  Pueyo (2018)  for a review. In particular, TLOCI  (Marois et al. 2013 (Marois et al.
In the same vein, the LLSG algorithm  (Gonzalez et al. 2016)  decomposes the dataset into low-rank, sparse and Gaussian components. Because few sources are expected in the field of view, their signatures are mainly recovered in the sparse component. The RSM algorithm  (Dahlqvist et al. 2020 (Dahlqvist et al. , 2021a,b) ,b)  combines residual images obtained with different post-processing algorithms (e. g. , cADI and PCA) to leverage their specific benefits and mitigate their respective drawbacks. Since all of these algorithms are based on the estimation and subtraction of an off-axis PSF, they are facing a common pitfall: they fail in deriving a statistically grounded detection map, especially at short angular separations. As a consequence, the identification of candidate sources partly relies on visual inspection of the detection map.
The network is trained from scratch using full frame samples generated with a custom data augmentation strategy allowing to build a large training set from a single ADI dataset. Finally, the underlying discriminative model is applied to the pre-processed observations and delivers a detection map. Detected sources are then photometrically characterized by a second deep neural network, also trained from scratch using patch samples generated with a dedicated data augmentation step. On this latter part, while the recent astronomy literature reports several works for photometry estimation through deep learning models (see e. g. ,  Boucaud et al. (2020) ;  Cabayol et al. (2021) ; Huertas-Company & Lanusse (2022) for galaxie's photometry or red-shift estimation), to the best of your knowledge this is the first time that deep learning is employed to estimate the flux of detected sources in direct imaging at high-contrast.
Statistical model of the nuisance component A dataset 𝒓 in R 𝑁 ×𝑇 recorded with the ADI technique is formed by 𝑁-pixel images captured at different times 𝑡 in ⟦1; 𝑇⟧. The direct model for the observed intensity is: 𝒓 = 𝒇 + 𝑃 ∑︁ 𝑝=1 𝛼 𝑝 𝒉(𝜙 𝑝 ) , (1) where 𝒇 in R 𝑁 ×𝑇 is the nuisance component, and 𝒉 𝜙 𝑝 in R 𝑁 ×𝑇 stands for the contribution of a point source 𝑝 ∈ ⟦1; 𝑃⟧ with a contrast 𝛼 𝑝 in R + that is assumed constant during the few hours of the total observations. The contribution of a source 𝑝 takes the form of the off-axis PSF centered at location F 𝑡 (𝜙 𝑝 ) in the 𝑡-th image, where 𝜙 𝑝 is its initial location on an image at a reference time 𝑡 ref (e. g. , 𝑡 ref = 𝑡 1 ). The function F 𝑡 is a geometric transform (typically in ADI, a circular translation with respect to the star located at the center of the images) modeling the apparent motion of the field of view between the observation configurations at time 𝑡 ref and time 𝑡.
2. 1. 1 or in Appendix A1. It can be noted that overlapping patches should be used with this refinement, and that the patch shape can be either squared or circular. This alternative approach leads to a better stability and robustness of the method for datasets recorded under bad observing conditions 5. However, the computational burden of this variant is increased by a factor 2 × 𝐾, typically lying in ⟦100; 250⟧ for the VLT/SPHERE instrument. For these reasons, this variant is not applied by default in the following. We recommend to apply it, in a second step, when the training, validation, or inference results are clearly impacted by a significant number of false alarms, much higher than expected, which is an unambiguous sign of the limited fidelity to the observations of the pre-processing procedure used by default.
The ground truth map is built for a given (and arbitrary) orientation of the field of view, e. g. aligned with the true North. The implemented simulation process is quite realistic since the injected source signature corresponds to the off-axis PSF of the target star usually measured just before or just after the main sequence of observations by decentering the coronagraph. Second, the nuisance component varies drastically from one observation to the other, as it is highly dependent on the observing conditions, the magnitude of the star, and the instrument settings. As a consequence, we follow an observation-dependent approach, and train a different model on each observation. It means that the model parameters (except algorithmic and optimization hyper-parameters, see Sect. 2. 2. 4) are optimized from scratch for each dataset.
In practice, we found that this setting is suitable to detect both faint sources and bright sources without generating large number of false alarms. As the pre-processing is an expensive procedure and becomes the bottleneck during online data generation, we adopt a local update strategy to reduce its computational cost. Prior to the injection of synthetic sources, the whole dataset is pre-processed, i. e. centered and spatially whitened, see Fig. 1 (b). We denote by 𝒓 the pre-computed cube. After each batch 𝑠 of injections, the set S [𝑠] of locations impacted by the signal of the 𝑃 [𝑠] sources is determined. Outside S [𝑠] , the pre-processed images are obtained from the temporal permutation of 𝒓. Inside S [𝑠] , the statistics of the nuisance component are updated given the contamination of the 𝑃 [𝑠] injected sources, and the pre-processed images are updated with these refined statistics.