dataesr/scientific-paragraphs-categorization huggingface dataset:
Introduction The primary fission fragment (FF) entry zone in excitation energy and spin-parity (E*, J π ) is one of the key points in the simulation of the fission process leading to prompt particle emission. Theory as well as experiments are not yet able to clearly identify these initial primary FF nuclear states. Models that are used in Monte Carlo codes allow to reproduce the neutron multiplicity or the gamma multiplicity but it is quite difficult to achieve both of them in one shot. Neutron and gamma multiplicities are the end point of the whole de-excitation process. Several models have to be used in order to calculate level densities, photon strength functions, optical model potential for neutron transmission coefficients. At low energies the nuclear level scheme, that is to say the knowledge of level energies, spins, parities, half-lives, intensities of the transitions from level to level have to be accounted for through experimental databases.
Quick reminder of the FIFRELIN model Pre-neutron fission fragment mass A and kinetic energy KE distributions are experimental data used as input data in the code. Data from  [1]  are used in this work for the study of 252 Cf(sf). Recent available data have been published  [2]  and will be used in a near future for comparison but this is out of the scope of this paper. Details related to the FIFRELIN "calculation route" can be found in  [3]  and  [4]. The main steps are reminded hereafter. Nuclear charge Z is sampled from the so-called Wahl Z p model. When the light fragment A L , Z L , KE L characteristics are sampled, the complementary heavy fragment of a binary fission is selected by mass, charge and linear momentum conservation. Before starting the de-excitation process, the excitation and spin-parity of both fragments have to be known.
Accurate determination of the masses of K2-3 c and K2-3 d evidently requires a larger dataset and denser sampling to trace out the activity signal. Here we present the results of an intense RV follow-up of K2-3 conducted over three seasons with the HARPS-N and HARPS spectrographs. Despite having data from several independent teams, and having precise transit ephemeris from highprecision photometry  (Beichman et al. 2016) , measuring the mass of K2-3 c and K2-3 d has been challenging. The paper is organized as follows. We first introduce the RV datasets and discuss the significant signals present in the data through a frequency analysis (Sect. 2). In Sect. 3 we present updated stellar parameters and analyse the photometric light curves of K2-3 and the Hα line activity indicator time series.
Description and first look on the HARPS(-N) radial velocity datasets Northern and Southern spectroscopic observations of K2-3 were carried out between January 22, 2015 and July 7, 2017, producing a total of 211 HARPS-N and 138 HARPS spectra. Of the 349 spectra, 283 are unpublished observations while 66 HARPS observations were previously published by  Almenara et al. (2015). The HARPS-N spectra come from two independent programs: the HARPS-N Collaboration Guaranteed Time Observations (GTO) 2 and the Global Architecture of Planetary Sys-tems programs (GAPS,  Benatti et al. 2016). The two collaborations shared observing time on this target to maximize the number of RV measurements and to optimise the observing strategy. The spectra were reduced with the version 3. 7 of the HARPS-N Data Reduction Software (DRS)  (Cosentino et al.
Definition of the final dataset We excluded some observations from our analysis for two reasons. We did not consider spectra with a signal-to-noise ratio S/N ≤11 as measured at λ=550 nm (echelle orders 46 and 49 for HARPS-N and HARPS, respectively). We then identified RV measurements potentially contaminated by scattered moonlight. This is particularly important for faint targets like K2-3 which lie close to the Ecliptic plane. By using the procedure described in Section 2. 1 of  Malavolta et al. (2017) , we identified 5 HARPS-N spectra that are probably contaminated by scattered moonlight, and we discarded them from the dataset 3. We could not perform the same analysis on the full HARPS dataset because nearly half of those spectra were acquired with simultaneous Fabry-Perot and not with fibre B on sky.
Radial velocity extraction In this study we primarily use RVs extracted with the TERRA pipeline (Anglada-Escudé & Butler 2012). TERRA is commonly used to extract radial velocities of M-dwarfs because it typically provides measurements with better precision and lower scatter than those extracted for low-mass stars with the CCF recipe of on-line DRS pipeline  (Perger et al. 2017 ). The HARPS fibre link was upgraded with octagonal fibres on  May 28, 2015 (Lo Curto et al. 2015) , introducing an RV offset between data acquired before and after the upgrade. We accounted for this offset by producing pre-and post-upgrade spectral templates to extract the RVs, and by introducing a velocity zero point offset for each dataset as free parameter when fitting the time series. The TERRA RV time series are listed in the on-line Tables ?? and ?? for HARPS-N and HARPS, respectively.
Preliminary RV frequency analysis We conducted a preliminary analysis of the radial velocity datasets using the Generalized Lomb-Scargle (GLS) algorithm   (Zechmeister & Kürster 2009)  to identify significant signals. We performed the GLS frequency analysis of the Northern and Southern datasets separately as well as the combined RV dataset, removing RV offsets as determined by the analysis described in Sect. 4. We show the resulting periodograms in Figs. 1 2 3. The HARPS-N periodogram is dominated by a signal at 37. 2±0. 1 days 6  , which we identify as the rotation period of the star (see  Sect. 3). This signal has a p-value=0. 01%, as estimated by bootstrapping the data, i. e. by randomly drawing the RV measurements (with replacement) and generating 10 000 mock datasets. Its semi-amplitude is 2.
For example, a one-month alias of the 37-day signal occurs at 0. 061 c/d (=1/37+f s. m. c/d), while a one-month alias of P b occurs at 0. 065 c/d. Both aliases are visible in Fig. 2. The signals that most clearly emerge in the periodogram of the combined dataset are those of the planet K2-3 b and the stellar rotation period, which are highly significant and have almost the same power (Fig. 3 ). The signal of planet K2-3 c is more weakly present, with a p-value∼1%. We have applied an offset to each separate dataset, as derived from our analysis described in Sect. 4.
A bootstrap (with replacement) Monte Carlo analysis based on 10 000 mock datasets reveals that these peaks are statistically significant, with false alarm probabilities lower than 0. 1%. We are, however, unable to ascertain whether the 211 day period or its alias at 450 days is the true underlying period. The origin of this long-period signal is unclear. If the signal is astrophysical, one possible explanation is an intermediate-duration activity cycle. Some tentative evidence exists for such cycles in low-mass stars  (Savanov 2012; Robertson et al. 2013) , and they could represent sub-cycles superimposed on longer duration activity cycles, as observed for the Sun (so called 'Rieger cycles'). We note that the 211 day period is close to the 230 day signal observed in the MEarth photometry. The second highest peak in the periodogram of the Hα indicator is close to the expected stellar rotation period and is highly significant (P=40.
Gaussian Process regression analysis of radial velocities We used the stellar activity information derived in Section 3 to perform a detailed analysis of the combined HARPS-N and HARPS RV datasets within a Bayesian framework based on Gaussian process (GP) regression. It has now become standard in RV analysis to use GPs to model the stellar contribution to the RV variations, jointly with a number of Keplerian functions describing the planetary orbital motion (see  Haywood et al. 2014  for the first application of this technique). This approach has proven to be a powerful way of retrieving planetary masses from high-precision RV measurements when a signal closely related to the stellar rotation period, or its harmonics, is present in the RV time series  (Dumusque et al. 2017). For a general description of the GP method, and its performances when applied to RV time series, we refer, amongst others, to the recent works by  López-Morales et al.
This functional form is suitable for modelling a recurrent signal linked to stellar rotation, and takes into account the finite-lifetime of the active regions. Eq. 1 contains four covariance matrix hyperparameters: h represents the amplitude of the correlations; θ represents the rotation period of the star; w is the length scale of the periodic component, linked to the size evolution of the active regions; and λ is the correlation decay time scale, that can be physically related to the active regions lifetime. The remaining parameters in Eq. 1 are: σ RV,instr (t), which is the RV internal error at time t for each spectrograph (or independent dataset); σ jit,instr , which are additional uncorrelated 'jitter' terms, one for each instrument (or independent dataset), that we add in quadrature to the internal errors to account for additional instrumental effects and noise sources neither included in σ RV,instr (t) nor modelled by the q-p kernel; and δ t,t , which is the Kronecker delta function.
5•P rot. This choice is first motivated by the marginal posterior obtained with the trial MCMC analysis of the dataset for the first and second seasons, which is symmetric around λ=36 days (σ ∼ 8 days). An evolutionary time scale of the order of the stellar rotation period can also be guessed directly by looking at the K2 light curve, which shows changes in its pattern from one rotation to the next  11. We also used the results of  Giles et al. (2017) (Eq. 8)  to get a loose estimate of the time scale based on the RMS of the K2 data and the stellar effective temperature. The equation for determining the time scale was derived by  Giles et al. (2017)  using a calibration sample not biased by spectral type and, though faster rotators than K2-3 are analysed in  Giles et al. work , it could be tentatively used for a star with P rot =40 days.
Analysis of the combined radial velocity dataset We analysed the full RV dataset without binning the data when more than one observation is available during the same night. To guarantee a wide exploration of the parameter space, we adopted 150 independent chains properly initialized to start from well separated locations. We discarded the first 3 000 steps of each chain by resetting the sampler. The MCMC chains reached the convergence according to the Gelman-Rubin statistics after 18 000 steps, and a further burn-in (0. 75% of the total steps) was applied to calculate the best-fit values of the parameters (see  Eastman et al. 2013 and references therein). We show the best-fit results for all the free parameters and derived quantities in Table  3. The mass of the super-Earth K2-3 b is robustly determined with a signal-to-noise ratio of ∼7σ, while the mass of K2-3 c is detected with a lower significance of 2.
6σ. The mass of K2-3 d remains undetermined, with a 1σ upper limit of about ∼ 2M ⊕. This suggestes that the mass of K2-3 d is too low to be detected, but it is also plausible that the low-amplitude of the Doppler signal, compared to that of the stellar activity component, and its proximity to the stellar rotation period allow the signal to be absorbed into our GP activity model  (Vanderburg et al. 2016). We investigate the robustness of this upper limit in Sections 5. 1 and 5. 2. We show the RV curves in Fig. 8 , with the stellar activity contribution subtracted, and folded at the best-fit orbital periods. The stellar contribution to the RV time series resulting from our fit is shown in Fig. 9. The stellar activity component of the model is reliably described by our best-fit results. The stellar rotation period and the evolutionary time scale of the active regions appear to be well characterized for both datasets.
As we have found from the analysis of the RV datasets of other targets, the GP quasi-periodic regression tends to suppress low frequencies in the residuals. This means that if an additional long-term modulation is actually present in the original data, and it is not explicitly included in the fitted model, it would be absorbed by the stellar activity component and disappear in the residuals, after removing the planetary solutions. However, we note that the data in Fig. 9  do not show any long-term trend residual suggestive of an activity cycle or a longer period companion to K2-3 not included in our global model. We also note that the stellar rotation period, as retrieved by the GP regression, differs from that derived with GLS by ∼3 days. This difference is because the functional form of the quasi-periodic kernel used to model the stellar contribution is different from the simple sinusoid used γ HARPS-N [m s -1 ] U (-10, +10) γ HARPS-pre [m s -1 ] U (-10, +10) γ HARPS-post [m s -1 ] U (-10, +10) σ jit,HARPS-N [m s -1 ] U (0.
05, 5) σ jit,HARPS-pre [m s -1 ] U (0. 05, 5) σ jit,HARPS-post [m s -1 ] U (0. 05, 5) Notes. ( a) Ephemeris from  Beichman et al. (2016) , derived from transit observations with K2 and Spitzer. T 0 is the time of inferior conjunction. by the GLS periodogram. We calculated the GLS periodogram of the GP quasi-periodic stellar activity timeseries and found the strongest peak at P=37 days, reproducing the period found in our GLS analysis of the RV dataset. The RMS of the residuals is 2. 6 m s -1 , only slightly higher than the median of the internal errors.
Cross-check with the alternative RV extraction method In order to test the robustness of the results using RVs obtained with the TERRA dataset, we also extracted the RVs using an independent pipeline described by  Astudillo-Defru et al. (2015 , 2017). In brief, this pipeline works by aligning all the spectra to a common reference frame by removing the Earth's barycentric radial velocity and the RVs of K2-3 measured by the DRS as an initial guess. Then a median template is computed from the aligned spectra and regions of the spectra contaminated by tellurics are rejected. The template is used to calculate a chi-square profile as a function of RVs for each individual spectrum, whose minimum corresponds to the stellar RV. The radial velocities from this alternative pipeline are listed in Tab.
1 +1. 3 -1. 2 3. 2 +1. 2 -1. 1 M p,d (M ⊕ ) 1. 2 +1. 4 -0. 7 [<1. 8 (68. 3 th perc. )] 1. 3 +1. 5 -0. 8 [<1. 9 (68. 3 th perc. )] 2. 7 +1. 2 -0. 8 (see Sect. 5. 1) ρ p,b [g cm -3 ] 3. 0 +1. 3 -0. 9 3. 2 +1. 3 -0. 9 ρ p,c [g cm -3 ] 3. 1 +1. 9 -1. 3 3. 2 +1. 8 -1. 3 ρ p,d [g cm -3 ] 1. 6 +2. 1 -1. 0 [<2. 4 (68. 3 th perc. )] 1. 6 +2. 1 -1. 0 3. 1 m p sin i (K p • M 2 3 s • √ 1 -e 2 • P 1 3 p )/(2πG) 1 3 ; a [(M s • G) 1 3 • P 2 3 p ]/(2π) 2 3 , where G is the gravitational constant. 3 ). The blue line is the best-fit curve, while the shaded grey area represents the ±1σ confidence interval. present dataset and the adopted model, we cannot determine a bulk density of K2-3 c accurately enough to put reliable constraints on its possible composition, and we can only place an Fig. 10. TERRA RV residuals, after removing the planetary and stellar activity signals, as fitted within a GP quasi-periodic framework (Table  3 ).
upper limit on the bulk density of K2-3 d. This impacts our understanding of the formation and evolutionary scenarios which led to the observed system architecture, and makes inferences about the habitability of K2-3 d especially challenging. Why is the characterization of this system so challenging, despite the large dataset we have collected with two world-class spectrographs? Can we rule out a rocky composition for K2-3 d? To provide answers to these questions we have performed simulations to investigate the impact of the observing sampling, stellar activity, and internal RV uncertainties on our ability to retrieve masses for the K2-3 planets.
Simulations using real epochs We ran a first set of simulations based on the real epochs of our observations with the objective of improving the estimate of K2-3 d's mass, for which we could provide only an upper limit, and for assessing the robustness of our result for K2-3 c's mass, despite its low significance. First, we adopted our best-fit values of the GP hyperparameters (TERRA dataset) to generate the stellar activity RV signal. We then injected planetary signals (circular orbits) with semi-amplitudes K b =2. 7 m s -1 , K c =0. 95 m s -1 , and K d =1 m s -1 , and the known periods and times of transit (Table  3 ) into the simulated activity signal. We refer to the dataset built in this way as the exact solution. While the simulated Doppler semi-amplitudes for K2-3 b and K2-3 c are those we have derived from real data, for K2-3 d we have assumed a value corresponding approximately to a purely rocky composition, given the measured radius 12.
We then created N=156 mock RV time series 13. Each dataset was obtained by randomly drawing RV values normally distributed around the exact solution, where σ 2 RV (t) + σ 2 jit,instr was used as the variance of the normal distributions at each epoch. We analysed each synthetic dataset following the same procedure as for the real data (Section 4. 2) and recorded the best-fit values of the free parameters once the MCMC chains reached convergence. Results from these simulations depend on the actual properties of the stellar activity observed during our campaign. More complex simulations to explore in detail the effects of the stellar activity could also be carried out, where each hyperparameter is randomly drawn within the uncertainties while keeping the others fixed. However, such simulations, which would require a large number of mock datasets (i.
e. thousands) and a correspondingly huge amount of computational time, are beyond the scope of this paper. Thus, our simulations do not explore the possibility that the non-detection is due to the proximity of the stellar rotation period θ to the orbital period of K2-3 d, which could be a limiting factor  (Vanderburg et al. 2016). We note that the amplitude h of the stellar activity term is precisely known (∼ 10σ, Tab. 3), so we expect that drawing values from the posterior distribution of this hyperparameter would not significantly change the results of our simulations. Analysis framework. For each i th simulated dataset we derive a posterior distribution for the Doppler semi-amplitudes of planets c and d that we call K p,i , where p=(c, d). Each semiamplitude is characterized by a median value K med p,i and upper and lower uncertainties σ + p,i and σ - p,i (as derived from the 16 th and 84 th percentiles).
We then calculate the median recovered semi-amplitude K med p,N of all the K med p,i. We compare the median recovered semi-amplitude K med p,N with the injected value K p,inj in 12 K=1 m s -1 corresponds to M p =4 M ⊕. 13 The number of simulations is as large as possible given the computational expense of a GP analysis on each simulated dataset (up to∼10 hours each). order to draw conclusions about the results obtained for the real RV dataset. For K2-3 d, we define the ratio r d,i =(K d,inj -K med d,i )/σ + d,i to measure the discrepancy between the best-fit estimate and the injected value in units of σ + d,i. The term (K d,inj -K med d,i ) is weighted by σ + d,i in order to take the skewness of each posterior distribution into account. By averaging r d,i over the number, N, of simulated datasets we get the metric r d , that we propose as a way to correct the measured semi-amplitude K d,meas using the equation K d,real = K d,meas + r d • σ + d,meas , (2) where K d,meas and σ + d,meas come from our best-fit solution (Tab.
3). As an alternative approach, for each marginal distribution K d,i we calculate the percentile corresponding to the position of K d,inj. We use the median over N of these percentiles to derive an estimate for K d,real from the posterior distribution obtained for the real dataset. Results for K2-3 c. The distribution of the median values K med c,i is shown in Fig. 11. The median of this distribution is K med c,N =0. 96 +0. 27 -0. 22 m s -1 , where the uncertainties represent the 16 th and 84 th percentiles. Looking at the values for σ + c,i and σ - c,i over all the marginal posteriors K c,i , we note that <( σ + c,i -σ - c,i )> = 0. 01 m s -1 , indicating that the distributions are normal-shaped, and their average is <σ + c,i > = < σ - c,i > = 0. 33 m s -1. These results show that the injected signal K c,inj =0.
95 m s -1 is well recovered, and indicate that our estimate of K c from the real dataset is reliable, despite our detection having a significance < 3-σ. Results for K2-3 d. A sample of the N posterior distributions K d,i is shown in Fig. 12. The distribution of K med d,i is shown in Fig. 13. The median of this distribution is K med d,N =0. 54 +0. 18 -0. 14 m s -1 , while we get <σ + d,i >=0. 47 m s -1 and <σ - d,i >=0. 35 m s -1 for the 68. 3% confidence interval of each distribution. Therefore, the semi-amplitude K d is generally underestimated with respect to K d,inj. This result is suggestive when compared to what we get for K c. As shown in Fig. 8 , the phase coverage of our data is uniform for planet K2-3 c, and fairly uniform for planet K2-3 d. Then, we would expect two signals with an equal semi-amplitude (here K c,inj K d,inj ) to be recovered with similar significance in absence of other hampering factors.
√ N. We use this result and our best-fit value for K d,meas =0. 29 +0. 34  -0. 18 to draw N=10 000 random values for r d and K d,meas , obtaining a distribution of N samples for K d,real from Eq. 2. By taking the median of this distribution and the 68. 3% confidence interval we get K d,real =0. 63 +0. 32  -0. 18 m s -1. This corresponds to M d,real =2. 7 +1. 2 -0. 8 M ⊕ and ρ d,real =3. 1 +2. 0 -1. 2 g cm -3 for the planet mass and density. By using the second approach mentioned above, we find that K d,real corresponds on average at the 83 th percentile of the K d posterior distribution for the real dataset, that is K d,real =0. 62 m s -1 , which is a result equal to that obtained with the first method. Our statistical analysis shows that K d,real is <1 m s -1 with 1σ confidence. This in turn suggests that the planets in the K2-3 system may have very similar bulk densities and thus share a similar composition, although this outcome should be taken with caution due to the large uncertainties in the masses and densities for K2-3 c and K2-3 d.
The role of the observing sampling The mock datasets have been created as described in Section 5. 1. We have generated all the epochs suitable for observations during the 2017 observing season in addition to the real ones. We have simulated only one measurement per night avoiding super- position with the epochs corresponding to the real observations. Every random epoch has been selected by placing constraints on the Moon phase illumination and distance from the target (they have to be <90% and >45 • , respectively), and on the altitude of the star above the horizon (airmass<1. 7). Using these criteria we got 112 and 100 additional new epochs for HARPS-N and HARPS, respectively. We randomly removed 10% of them at each simulation run to account for bad weather, thus simulating an optimistic scenario for a feasible follow-up 14.
The uncertainties σ RV (t) of the mock RV data have been randomly drawn from normal distributions, with mean and σ equal to the average and RMS values of the HARPS-N and HARPS post-upgrade internal errors derived with TERRA. The final mock dataset is obtained by randomly shifting each data point of the exact solution within the error bars by a quantity ∆RV(t) drawn from a normal distribution with mean zero and σ equal to σ 2 RV (t) + σ 2 jit. An example mock dataset is show in Fig. 14. Our final sample is composed of N=97 mock datasets. Also in this case, we have analysed each simulated dataset within the same GP quasi-periodic framework applied to the real dataset, except for the σ jit terms that were not included as free parameters, and we have analysed the outcomes as described in Sect.