dataesr/scientific-paragraphs-categorization huggingface dataset:
( 100 ) The topologies (and therefore labelling of the couplings) are the same in Landau gauge as for our Feynman-gauge results in the appendix, but we add the superscript ξ = 0 here. We do not give the explicit expressions for these, since several are rather long-they contain many more integrals than the Feynman-gauge case-but they are provided as part of TLDR. Ignoring for the moment cases where some masses vanish, and using the loop functions defined in Ref. [110]  and the notation D x,y [f (x)] ≡ f (x) -f (y) x -y , (101a) D x,x [f (x)] ≡ lim y→x D x,y [f (x)] , (101b) we find the following expressions for the tadpoles: Tadpole topology Label Finite Part Our function I (1) 01 T ξ=0 SS -1 4 a (i1)ij λ ijkk D m 2 i ,m 2 j [f SS (m 2 i , m 2 k )] a (i1)ij λ ijkk t 1 (i, k, j) I (1) 24 T ξ=0 SSS -1 6 λ (i1)ijk a ijk f SSS (m 2 i , m 2 j , m 2 k ) λ (i1)ijk a ijk t 24 (i, j, k) I (1) 07 T ξ=0 SSSS -1 4 a (i1)ij a ikl a jkl D m 2 i ,m 2 j [f SSS (m 2 i , m 2 k , m 2 l )] a (i1)ij a ikl a jkl t 7 (i, k, l, j).
However, the expressions in SMH are actually written in a sufficiently convenient form to be translated into code readable by Mathematica, and so we were able to use it for an analytical cross-check of our results. On the other hand, the result there is in Landau gauge, and combines the tadpoles with self-energy contributions via Eq. (  7 ). Therefore we have cross-checked our results against the Standard Model by the following procedure: • We calculated the tadpoles and Higgs self-energies in the Landau gauge using the FeynArts model file for the SM (with some modifications that will be described elsewhere), and using TwoCalc, TARCER and our own reduction to reduce the basis of integrals to those that can be evaluated by TSIL. We compared the analytic expressions with those in SMH and found perfect agreement in all terms.
Conclusions We have given expressions for scalar self-energies and tadpoles at the complete two-loop order in Feynman gauge. With the aim of being flexible, we have given the results for all renormalised component diagrams, and also a much shorter version where the diagrams are combined into just 16 tadpole and 58 self-energy topologies, provided that the external scalars are not (would-be) Goldstone bosons. The results are provided in the most compact analytical form that we could give, but are also available electronically as a new package TLDR at http://tldr. hepforge. org (where more tools and calculations will be added over time) so that they can be easily applied. We also include online all of the replacement rules and degeneracies for each diagram with routines for extracting the finite part.
General relations Our aim is to reduce all scalar two-loop integrals into the basis of integrals that can be evaluated numerically by the code TSIL  [124]. We begin by reducing to the unrenormalised basis T 134 = -I m 2 1 , m 2 3 , m 2 4 , T 1234 = U m 2 2 , m 2 1 , m 2 3 , m 2 4 , T 11234 = -V m 2 2 , m 2 1 , m 2 3 , m 2 4 , T 234 = -S m 2 2 , m 2 3 , m 2 4 , T 2234 = T m 2 2 , m 2 3 , m 2 4 , T 12345 = -M m 2 1 , m 2 5 , m 2 2 , m 2 4 , m 2 3 , 0 T i 1 = -A(m 2 1 ) , 0 T 12 = B(m 2 1 , m 2 2 ) , (114) where we include the one-loop integrals A and B that are known analytically. While TSIL is capable of delivering these bare integrals, it finds them by solving differential equations for "renormalised" versions; and indeed it is these renormalised integrals that we actually need for practical applications.
(136c) A. 5. UV divergences The remaining scalar integrals are UV divergent in general. In dimensional regularisation, these UV divergences can be parametrised by the regulator. For the two-loop two-point integrals appearing in this article, the terms that diverge in the limit → 0 are known analytically; the finite terms are evaluated numerically with the help of TSIL. In the following we list these UV divergences explicitly with the considered order in indicated in the superscript of the integrals: T 134 : T | -2 134 = 1 2 m 2 1 + m 2 3 + m 2 4 , (137a) T | -1 134 = 1 2 m 2 1 + m 2 3 + m 2 4 + A | 0 0 m 2 1 + A | 0 0 m 2 3 + A | 0 0 m 2 4 , (137b) T 234 : T | -2 234 = 1 2 m 2 2 + m 2 3 + m 2 4 , (138a) T | -1 234 = 1 2 m 2 2 + m 2 3 + m 2 4 + A | 0 0 m 2 2 + A | 0 0 m 2 3 + A | 0 0 m 2 4 - 1 4 p 2 , (138b) T 1234 : T | -2 1234 = 1 2 , (139a) T | -1 1234 = 1 2 + B | 0 0 p 2 , m 2 1 , m 2 2 , (139b) T 2234 and T 2 2 34 : T | -2 2234 = 1 2 , ( 140a ) T | -1 2234 = - 1 2 + 1 m 2 2 A | 0 0 m 2 2 , (140b) T | -2 2 2 34 = - 1 2 , (140c) T | -1 2 2 34 = 1 2 -B | 0 0 p 2 , m 2 3 , m 2 4 , (140d) T 11234 : T | -2 11234 = 0 , (141a) T | -1 11234 = 1 ∆ m 2 1 ,m 2 2 ,p 2 u p 2 ,m 2 1 ,m 2 2 m 2 1 A | 0 0 m 2 1 + 2 A | 0 0 m 2 2 + u m 2 1 ,m 2 2 ,p 2 B | 0 0 p 2 , m 2 1 , m 2 2 -1 , (141b) T |p 2 =m 2 1 , -2 112 34 = 1 2 m 2 1 , (141c) T |p 2 =m 2 1 , -1 112 34 = 1 m 2 1 1 ∆ m 2 1 ,m 2 3 ,m 2 4 3 8 u m 2 1 ,m 2 3 ,m 2 4 m 2 1 + 4 A | 0 0 m 2 3 + 4 A | 0 0 m 2 4 -4 m 2 3 m 2 4 -A | 0 0 m 2 3 A | 0 0 m 2 4 + 1 2 m 2 1 A | 0 0 m 2 1 - 3 2 , (141d) T |p 2 =m 2 1 ,m 2 3 =m 2 1 , -1 112 34 = 1 m 4 1 A | 0 0 m 2 1 , (141e) T 1 1 234 : T | -2 1 1 234 = 1 m 2 2 -p 2 , (142a) T | -1 1 1 234 = 1 m 2 2 -p 2 B | 0 0 0, m 2 3 , m 2 4 + 1 (m 2 2 -p 2 ) 2 2 p 2 + 2 A | 0 0 m 2 2 -m 2 2 + p 2 B | 0 0 p 2 , 0, m 2 2 , (142b) T |p 2 =m 2 2 , -2 1 1 234 = - 1 2 m 2 2 , (142c) T |p 2 =m 2 2 , -1 1 1 234 = - 1 2 m 2 2 1 m 2 2 A | 0 0 m 2 2 + B | 0 0 0, m 2 3 , m 2 4 -3 , (142d) T | -2 1 1 23 4 = 1 2 (m 2 2 -p 2 ) , (142e) T | -1 1 1 23 4 = 1 2 (m 2 2 -p 2 ) + 1 (m 2 2 -p 2 ) 2 2 p 2 + 2 A | 0 0 m 2 2 -m 2 2 + p 2 B | 0 0 p 2 , 0, m 2 2 , (142f) T |p 2 =m 2 2 , -2 1 1 23 4 = - 1 4 m 2 2 , (142g) T |p 2 =m 2 2 , -1 1 1 23 4 = - 1 2 m 2 2 1 m 2 2 A | 0 0 m 2 2 -2 , (142h) T 12345 : T | -2 12345 = 0 , (143a) T | -1 12345 = 0.
Aims. We present the design and pre-launch performance of the Solar Orbiter Heliospheric Imager (SoloHI) which is an instrument prepared for inclusion in the ESA/NASA Solar Orbiter mission, currently scheduled for launch in 2020. Methods. The goal of this paper is to provide details of the SoloHI instrument concept, design, and pre-flight performance to give the potential user of the data a better understanding of how the observations are collected and the sources that contribute to the signal. Results. The paper discusses the science objectives, including the SoloHI-specific aspects, before presenting the design concepts, which include the optics, mechanical, thermal, electrical, and ground processing. Finally, a list of planned data products is also presented. Conclusions. The performance measurements of the various instrument parameters meet or exceed the requirements derived from the mission science objectives.
In the following sections we describe the SoloHI instrument. In Sect. 2 we present the Solar Orbiter science objectives, including the objectives unique to SoloHI. In Sect. 3 we present an overview of the instrument. In Sect. 4, we describe the instrument design. In Sect. 5, we describe the operations concept, the data processing and the data products, and the ground system. Finally, we summarise in Sect. 6.
SoloHI is comprised of the SoloHI Instrument Module (SIM) and the SoloHI Power System box (SPS). The SoloHI functional block diagram (Fig. 5 ) shows the components of the SIM and SPS. An interconnect harness (not shown) connects the SIM and the SPS and a spacecraft harness (not shown) connects SoloHI to the spacecraft. Both SoloHI instrument units, the SIM and the SPS, are mounted on the exterior of the Solar Orbiter +Y panel. The SPS is located underneath the SIM and between the forward and aft SIM brackets that support the SIM. Figure  6  (top) shows the orientation of SoloHI with respect to the Solar Orbiter. The origin of the SIM physical reference frame is located at the centre of the aft SIM rigid instrument mount projected down to the base of the aft SIM bracket at the SIM mounting interface plane with the spacecraft deck.
The survival heaters are controlled by thermostats and operate when the SoloHI is powered off and thus are unable to be controlled by instrument software. Each survival heater was split into a trim and a bias heater. The trim heater cycles frequently to maintain the temperature above the survival temperature but draws less power than the 100 mA requirement. When the trim heater is unable to maintain the desired temperature, the bias heater is powered on by ground command to bias the temperature higher so that the trim heater can again maintain the survival temperature. In the current orbit scenario, the bias heater is not needed. Contamination sensitivity. SoloHI is very susceptible to contamination from dust particles on the edges of the baffles and the lenses but is insensitive to contamination from organic compounds.
Electrical design The SoloHI electrical design (Fig. 15 ) consists of four subsystems: the SoloHI Power System (SPS), the SoloHI Camera Electronics (SCE), the Detector Readout Board (DRB), and the Detector Interface Board (DIB). Each component comprises several subsystems, which we describe briefly below. To meet the requirements for mass and power, for the main CPU located on the PC, SoloHI chose a light-weight, lower-power CPU: the LEON3FT with 20 MIPS. Since a C++ compiler and board support package for the LEON3FT was available, RTEMS 4. 10 was chosen as the real time operating system. Using the RTEMS and C++ combination allows the same basic design of the heritage STEREO/SECCHI software to be used. There is a near one-to-one correspondence of system calls between VxWorks used with the SECCHI RTEMS and the SoloHI RTEMS.
Flight software SoloHI is the latest in a series of coronagraphs and heliospheric imagers for which NRL provided the software. The SoloHI flight software has its heritage in the STEREO SECCHI telescope suites, NASA Small Explorer (SMEX) satellites, and the SOHO LASCO/EIT telescopes. The starting point for the SoloHI flight software (Fig. 22 ) was the SECCHI flight software, which satisfied many of the basic scientific requirements for space coronagraphs. The requirements for basic functions such as telemetry, command handling, health and safety, and heater control are generally very similar from instrument to instrument. Modifications of the software requirements were needed primarily because of different specific hardware (CPU, camera, heater, and thermistors) and spacecraft-interface requirements.
The camera FPGA can do many image processing functions including summing of multiple images, binning 2 × 2, 4 × 4, or 8 × 8 pixels, truncation, and cosmic ray scrubbing. The camera can handle up to four different images from each detector, each with different image-processing parameters, that is, a total of up to 16 images at once. The major resources to be managed are the camera memory and timing of the images. It is quite possible to take images faster than they can be processed so any new microcode must be carefully tested. The microcode generates a sequence of images that is predictable and the LEON3FT software uses this information to set the registers in the camera FPGA. The pre-processed image is then transferred from the CC to the LEON3FT for final image processing and compression.
Telemetry data processing The playback telemetry, Level-0 files, are transferred by Secure File Transfer Protocol (SFTP), via the ESA Ground Operations System (EGOS) Data Distribution System (EDDS), to the ISOC. At ISOC, the ITOS ground system is used to translate housekeeping telemetry into database scripts that populate a MYSQL 1  relational database. The ITOS captures science telemetry from Level-0 packet files and converts these into compressed-imagefiles, which are then processed in the Image Processing Pipeline (IPP) to Level-1 Flexible Image Transport System (FITS) files. These files, along with browse data and other data products, will be made available publicly via the SoloHI website and the ESAC Solar Orbiter Archive (SOAR). The SOAR is the primary source for all Solar Orbiter data  (Sanchez et al.
Data products The routine processing pipeline will automatically process the science and housekeeping telemetry packets, that is, the Level-0 data, and make the data available to the public. The science data from SoloHI are images and will be converted from the compressed format into decompressed FITS files. One FITS file will be generated for each image file. The FITS file headers will include instrument orbit and attitude information (if available), all instrument settings associated with the image, information on all onboard and ground processing steps, image statistics, and any other ancillary information necessary to interpret the image data. The metadata of the images and the housekeeping parameters will each be stored in a MYSQL database that can be searched via the SoloHI website. The routine processing pipeline will produce the various standard data products listed in Table  5.
The SoloHI data policy dictates completely open access to all data, including planning, quick-look, and final data products, the calibration data, and all procedures to calibrate and perform high-level processing of the data. The NRL will maintain a web interface to a database of all science and housekeeping data that will permit users to search for data corresponding to time periods or events of interest using selected values from the image header, as well as to perform trend analysis of instrument housekeeping parameters such as temperatures and voltages. Validated science data will be distributed directly from NRL to the requester based on the results of a database query.
Data catalogs and documentation The SoloHI project will use the open source database program, MYSQL, which is currently being used to manage the housekeeping and image header information on both SECCHI and LASCO. A web-based tool enables searches of the image header database with the ability to select FITS files for download to the computer of the user. The database table structures are similar to the existing database tables, but there will be keywords that are unique to SoloHI and/or Solar Orbiter. For example, the existing IDL tools (in SolarSoft) include the ability to extract any parameter(s) of interest and to generate plots against time or to correlate one parameter against another. It is our intention that the FITS image header will mirror the SPASE 3  catalog. Keywords, if known, will be incorporated into the image FITS headers.
All calibration data necessary for these corrections will be included as part of the Solarsoft distribution which is publicly available 5. This approach has been used successfully for both LASCO and SECCHI. Software tools for common analysis tasks that are in use for LASCO, SECCHI, and WISPR will be extended to incorporate SoloHI data. These include image visualisation, generation of movies, feature tracking, structure measurement, and combining datasets from multiple remote-sensing and in-situ instruments and spacecraft. Forward fitting of 3D models to heliospheric features such as streamers and CMEs will also be provided in SolarSoft. A significant difference between the analysis of the SoloHI images and previous images from LASCO or SECCHI is that the backgrounds must be computed differently.
Acknowledgements. We are very appreciative of the excellent review provided by the anonymous referee, which significantly improved the manuscript. We gratefully acknowledge the hard work and dedication of the literally hundreds of people who contributed to the  SoloHI program. We would like to acknowledge the enthusiastic support from our colleague  Dr. Eric M. DeJong , deceased. We also acknowledge the support of the  NASA Heliophysics Division , Solar Orbiter Collaboration Office under DPR  NNG09EK11I. The NRL effort was also supported by the  Office of Naval Research. The participation of A. V in the program is supported by  NRL  grant  N00173-16-1-G029. The CSL effort was also supported by the  BELSPO/PRODEX.
5-5617 in the RoI model with a point source at the Gaia DR2 position of the optical source. To model the source spectrum, we used a subexponentially-cutoff power-law spectrum typical for gamma-ray pulsars (4FGL), 𝑑𝑁 𝑑𝐸 = 𝐾 𝐸 𝐸 0 -Γ exp -𝑎 𝐸 1 MeV 𝑏 , (1) where the parameters  0 = 1 GeV ("pivot energy") and  = 2/3 (exponential index) were fixed at their 4FGL values, while the parameters  (normalisation), Γ (low-energy spectral index) and  (exponential factor) were free to vary during fitting. We performed a binned likelihood analysis using fermipy  (Wood et al. 2017 ) version 0. 18. 0, with 0. 05°× 0. 05°bins and 10 logarithmic energy bins per decade. For this analysis we utilised the "PSF" event types and corresponding IRFs, which partition the LAT data into quartiles based on the quality of the reconstructed photon arrival directions.
Within this region, there were 181, 813 photons in total, with    = 3850 "effective" photons. To speed up our timing analyses (Section 3. 2) we additionally removed photons with  < 0. 1, leaving 6571 photons which account for 93% of the expected pulsation signal-to-noise ratio (which is proportional to   2  ,  Clark et al. 2017 ). The data set described above was used for the timing (Section 3. 2) and orbital modulation analyses (Section 3. 3) presented in this paper. For the pulsation search described in Section 3. 1, we used an earlier data set which only covered data up to 2019 January 10 and used spectral parameters from a preliminary version 3 of the 4FGL catalogue when computing photon weights.
Gamma-ray Timing Following the discovery of gamma-ray pulsations, we used the Fermi-LAT data set to obtain a rotational ephemeris spanning 11 years. To do so, we followed the principles described by  Kerr et al. (2015) , in which a template pulse profile  () is produced, and the parameters  of a phase model ( | ), are fit to maximise the Poisson log-likelihood of the unbinned photon phases. Assuming that the weights derived in Section 3 represent the probability that each photon was emitted by the pulsar, then the contribution to the pulsation log-likelihood from the -th photon, with weight   , is a mixture model between a constant (i. e. uniform in phase) background rate and the template pulse profile, with mixture weights of 1 -  and   respectively. Hence, the overall log-likelihood is log 𝐿 (𝝀 | 𝑡 𝑗 , 𝑤 𝑗 , 𝐹) = 𝑁 ∑︁ 𝑗=1 log 𝑤 𝑗 𝐹 𝜙 𝑡 𝑗 | 𝝀 + (1 -𝑤 𝑗 ) (2) where   denotes the measured arrival time of the -th detected gamma-ray photon.
Gamma-ray Variability The subset of transitional redback systems has been seen to transition to and from long-lasting accretion-powered states, in which their gamma-ray flux is significantly enhanced  (Stappers et al. 2014; Johnson et al. 2015; Torres et al. 2017). To check for such behaviour from J2039, we investigated potential gamma-ray variability over the course of the Fermi-LAT data span. In 4FGL, J2039 has two-month and one-year variability indices (chi-squared variability tests applied to the gamma-ray flux measured in discrete time intervals) of 44 with 48 degrees of freedom, and 13 with 7 degrees of freedom, respectively. Although the 1-year variability index is slightly higher than expected for a steady source, we note that the gamma-ray light curves in  Ng et al. (2018)  indicate that a flare from a nearby variable blazar candidate, 4FGL J2052.
The green horizontal dot-dashed line shows the estimated measurement uncertainty level, to which the power spectrum breaks at high frequencies. The solid blue and red curves show the best-fitting Matérn covariance function model, and those of random samples from the MCMC process, respectively. The dashed blue line additionally includes the measurement noise level. The lower panels show the power spectra of the orbital phase residuals after whitening using the Cholesky decomposition of the model covariance matrix (i. e. accounting for the blue curve in the upper panel). The horizontal dotted line shows the estimated level which the noise power in 95% of independent trials should be below. The vertical line in both panels shows the time span covered by the Fermi-LAT data -noise power close to and below this frequency is suppressed by our inclusion of a single orbital period derivative in the timing model.
New optical observations We performed optical photometry of J2039 with the high-speed triple-beam CCD camera ULTRACAM  (Dhillon et al. 2007 ) on the NTT on 2017 June 18, 2018 June 02 and 2019 July 07. The first two observations each covered just over one full orbital period, while the third was affected by intermittent cloud cover throughout before being interrupted by thick clouds after 70% of an orbit had been observed. We observed simultaneously in   ,   and   4  , with 13 s exposures (65 s in   ) and negligible dead time between frames. Each image was calibrated using a bias frame taken on the same night and a flat-field frame taken during the same observing run. All reduction and calibration was performed using the ULTRA-CAM software pipeline 5  (GROND images were first converted to the ULTRACAM pipeline's data format).
Light curve modelling To estimate physical properties of the binary system, we fit a model of the binary system to the observed light curves using the Icarus binary light curve synthesis software  (Breton et al. 2012). Icarus assumes point masses at the location of the pulsar (with mass  psr ) and companion star centre-of-masses, and solves for the July 07 with ULTRACAM). For clarity, the ULTRACAM data points have been combined into 250 s integrations. The folded light curves are repeated twice, with uncertainties shown only in the first cycle. These are mostly smaller than the corresponding markers. Here, and throughout this paper, orbital phase zero corresponds to the pulsar's ascending node. The GROND light curves have been corrected to the ULTRACAM magnitude system via colour corrections computed from the magnitudes of comparison stars in the field.
The model fits were performed using the pymultinest Python interface  (Buchner et al. 2014)  to the Multinest nested sampling algorithm  (Feroz et al. 2013). The best fitting models and light curves are shown in Figure  7 , the posterior distributions for our model parameters are shown in Figures 8, 9 and 10, and numerical results are given in Table  3. While the inferred posterior distributions from each epoch generally overlap with each other (except for the spot and heating parameters encapsulating variability), in the following discussion we take the full range covered by the 95% confidence intervals of the three posterior distributions as estimates for the model uncertainty, in the hope that biases due to variability are contained within that range. 18. 1 +8. 3 -6. 5.
g. variable mass loss, or magnetic braking) then this would manifest as a random walk in the orbital period derivative or higher orders ( 5/2). Unfortunately, Figure  2  illustrates that we are insensitive to the value of , as the variability quickly falls below the measurement uncertainty level for periods shorter than ℓ ≈ 130 d, preventing measurement of the power-law slope above the corner frequency. We find only that a very shallow power-law spectrum  < 1 is ruled out with 95% confidence, but models with finite  > 1. 5 fit the data equally well as the squared exponential kernel corresponding to  → ∞. We also find marginal evidence for an excess in the noise power at periods longer than the 11-years of Fermi-LAT data. This is not well accounted for by a longer correlation timescale ℓ and shallower spectral index, as this leaves excess power at intermediate frequencies, and we do find that a break in the spectrum is preferred, with ℓ  obs.