Fermi-LAT Research Articles

K2 Optical Emission from OJ 287 and Other γ-Ray Blazars on Hours-to-weeks Timescales from 2014 to 2018

We present second observations by K2 of OJ 287 and seven other γ-ray active galactic nuclei (AGNs) obtained in 2017–2018, second and third observations of the lobe-dominated, steep-spectrum quasar 3C 207, and observations of nine additional blazars not previously observed with K2. The AGNs were observed simultaneously with K2 and the Fermi Large Area Telescope for 51–81 days. Our full sample, observed in 2014–2018, contained 16 BL Lacertae objects (BL Lacs), nine flat-spectrum radio quasars (FSRQs), and four other γ-ray AGNs. Twelve BL Lacs and seven FSRQs exhibited fast, jagged light curves, while four BL Lacs and two FSRQs had slow, smooth light curves. Some objects changed their red-noise character significantly between repeated K2 observations. The optical characteristics of OJ 287 derived from the short-cadence K2 light curves changed between observations made before and after the predicted passage of the suspected secondary supermassive black hole through the accretion disk of the primary supermassive black hole. The average slopes of the periodogram power spectral densities of the BL Lacs’ and FSRQs’ light curves differed significantly, by ≈12%, with the BL Lac slopes being steeper, and a Kolmogorov–Smirnov test with a p-value of 0.039 indicates that these samples probably come from different populations; however, this result is not as strongly supported by power spectral response (PSRESP) analyses. Differences in the origin of the jets from the ergosphere or accretion disk in these two classes could produce such a disparity, as could different sizes or locations of emission regions within the jets.

Investigating the Multiband Nonthermal Radiative Properties of HESS J1420−607

HESS J1420−607 is a γ-ray emitting source associated with the pulsar wind nebula (PWN) powered by the energetic pulsar PSR J1420−6048. Based on 14 yr of data obtained with the Fermi Large Area Telescope, we re-analyzed its GeV γ-ray radiative properties, resulting in detailed spectra obtained within the band 10–200 GeV. Moreover, we use a one-zone time-dependent model for the multiband nonthermal emission from pulsar wind nebulae to investigate the radiative properties of the nebula associated with HESS J1420−607. Assuming that the electrons/positrons are injected into the PWN with a broken power law spectrum with indexes of ∼1.6 and ∼2.7, as well as a break Lorentz factor of ∼5 × 106, the results indicate that the multi-wavelength spectral energy distribution is consistent with the detected fluxes in both X-rays and γ-rays. The results support that the γ-rays detected can be produced via inverse Compton scattering of the energetic electrons/positrons within the PWN.

Investigating the gamma-ray burst from decaying MeV-scale axion-like particles produced in supernova explosions

We investigate the characteristics of the gamma-ray signal following the decay of MeV-scale Axion-Like Particles (ALPs) coupled to photons which are produced in a Supernova (SN) explosion. This analysis is the first to include the production of heavier ALPs through the photon coalescence process, enlarging the mass range of ALPs that could be observed in this way and giving a stronger bound from the observation of SN 1987A. Furthermore, we present a new analytical method for calculating the predicted gamma-ray signal from ALP decays. With this method we can rigorously prove the validity of an approximation that has been used in some of the previous literature, which we show here to be valid only if all gamma rays arrive under extremely small observation angles (i.e. very close to the line of sight to the SN). However, it also shows where the approximation is not valid, and offers an efficient alternative to calculate the ALP-induced gamma-ray flux in a general setting when the observation angles are not guaranteed to be small. We also estimate the sensitivity of the Fermi Large Area Telescope (Fermi-LAT) to this gamma-ray signal from a future nearby SN and show that in the case of a non-observation the current bounds on the ALP-photon coupling gaγ are strengthened by about an order of magnitude. In the case of an observation, we show that it may be possible to reconstruct the product gaγ 2 ma , with ma the mass of the ALP.

The First AGILE Solar Flare Catalog

We report the Astro-rivelatore Gamma a Immagini LEggero (AGILE) observations of solar flares, detected by the onboard anticoincidence system in the 80–200 keV energy range, from 2007 May 1 to 2022 August 31. In more than 15 yr, AGILE detected 5003 X-ray, minute-lasting transients, compatible with a solar origin. A cross-correlation of these transients with the Geostationary Operational Environmental Satellites (GOES) official solar flare database allowed us to associate an intensity class (i.e., B, C, M, or X) to 3572 of them, for which we investigated the main temporal and intensity parameters. The AGILE data clearly revealed the solar activity covering the last stages of the 23rd cycle, the whole 24th cycle, and the beginning of the current 25th cycle. In order to compare our results with other space missions operating in the high-energy range, we also analyzed the public lists of solar flares reported by RHESSI and Fermi Gamma-ray Burst Monitor. This catalog reports 1424 events not contained in the GOES official data set, which, after statistical comparisons, are compatible with low-intensity, short-duration solar flares. Besides providing a further data set of solar flares detected in the hard X-ray range, this study allowed to point out two main features: a longer persistence of the decay phase in the high-energy regime, with respect to the soft X-rays, and a tendency of the flare maximum to be reached earlier in the soft X-rays with respect to the hard X-rays. Both these aspects support a two-phase acceleration mechanism of electrons in the solar atmosphere.

Constraints on the Gamma-Ray Emission from Small Solar System Bodies with the Fermi Large Area Telescope Data

All known small solar system bodies have diameters between a few meters and a few thousands of kilometers. Based on the collisional evolution of solar system bodies, a larger number of asteroids with diameters down to ∼2 m is thought to exist. As all solar system bodies, small bodies can be passive sources of high-energy gamma-rays, produced by the interaction of energetic cosmic rays impinging on their surfaces. Since the majority of known asteroids are in orbits between Mars and Jupiter (in a region known as the Main Belt), we expect them to produce a diffuse emission close to the ecliptic plane. In this work, we have studied the gamma-ray emission coming from the ecliptic using the data collected by the Large Area Telescope (LAT) onboard the Fermi satellite. We have fit the results with simulations of the gamma-ray intensity at the source level (calculated with the software FLUKA) to constrain the small solar system bodies population. Finally, we have proposed a model describing the distribution of asteroid sizes and we have used the LAT data to constrain the gamma-ray emission expected from this model and, in turn, on the model itself.

Classification of the Fermi-LAT blazar candidates of uncertain type using extreme gradient boosting

ABSTRACT Machine learning based approaches are emerging as very powerful tools for many applications including source classification in astrophysics research due to the availability of huge high quality data from different surveys in observational astronomy. The Large Area Telescope on board Fermi satellite (Fermi-LAT) has discovered more than 6500 high energy gamma-ray sources in the sky from its survey over a decade. A significant fraction of sources observed by the Fermi-LAT either remains unassociated or has been identified as Blazar Candidates of Uncertain type (BCUs). We explore the potential of eXtreme Gradient Boosting – a supervised machine learning algorithm to identify the blazar subclasses among a sample of 112 BCUs of the 4FGL catalogue whose X-ray counterparts are available within 95 per cent uncertainty regions of the Fermi-LAT observations. We have used information from the multiwavelength observations in IR, optical, UV, X-ray, and γ-ray wavebands along with the redshift measurements reported in the literature for classification. Among the 112 uncertain type blazars, 62 are classified as BL Lacertae objects and six have been classified as flat spectrum radio quasars. This indicates a significant improvement with respect to the multiperceptron neural network based classification reported in the literature. Our study suggests that the gamma-ray spectral index, and IR colour indices are the most important features for identifying the blazar subclasses using the XGBoost classifier. We also explore the importance of redshift in the classification BCU candidates.

Fermi Blazars in the Zwicky Transient Facility Survey: A Correlation Study

We report on our correlation analysis for the γ-ray blazars detected with the Large Area Telescope (LAT) onboard the Fermi Gamma-ray Space Telescope (Fermi), for which we use the Fermi-LAT data and the optical zr and zg band data from the Zwicky Transient Facility survey in the time period approximately from 2018 July to 2022 February. We start from the full sample of the Fermi-LAT blazars and find ∼38% of them as significant variables in both γ-ray and optical bands. Among the variables, which are 705 blazars, 95 are selected as our targets based on the requirement for the γ-ray brightnesses. Then 15 out of the 95 blazars are found to show the γ-ray–optical correlations in the ∼3.7 yr time period. Most of the 15 blazars are classified as low synchrotron peaked (LSP) ones with the time lags between the γ-ray and optical bands in a range from −19 to +25 days. The results generally fit the often-considered emission scenario for the LSP blazars. Two cases of showing ∼−100 days time lags are discussed, which require further studies for confirmation. Our analysis results suggest that among the detected significant variables, ∼23% LSPs can show γ-ray and optical correlations, while their average γ-ray fluxes are above ∼4 × 10−8 photon cm−2 s−1.

How the dynamical properties of globular clusters impact their γ-ray and X-ray emission

ABSTRACT The X-ray and γ-ray emission of globular clusters (GCs) is attributed to their large fraction of compact binary systems, especially those with millisecond pulsars (MSPs). We analyse a population of 124 Galactic GCs to investigate how their dynamical properties affect the formation and evolution of compact binary systems and how this can be translated into the clusters’ observed X-ray and γ-ray emission. We use mainly Chandra X-ray Observatory and Fermi Large Area Telescope observations to achieve our goals and start by detecting 39 GCs in γ rays, seven of which are not listed in previous Fermi-LAT catalogs. Additionally, we find that the total number of X-ray sources within a GC and its γ-ray luminosity are linearly correlated with the stellar encounter rate, indicating that compact binary systems are mainly formed via close stellar encounters. We also find an unexpected rise in the number of X-ray sources for GCs with low rates of stellar encounters, suggesting that there is a dynamical threshold where the formation of X-ray sources is dominated by stellar encounters. Furthermore, we use the Heggie-Hills law to find that subsequent stellar encounters in these compact binaries will, on average, make the binaries even harder, with basically no possibility of binary ionization. Finally, we find that all GCs are point-like sources in γ rays, indicating that the MSPs are concentrated in the clusters’ cores, likely due to dynamical friction.

Multimessenger Characterization of Markarian 501 during Historically Low X-Ray and γ-Ray Activity

We study the broadband emission of Mrk 501 using multiwavelength observations from 2017 to 2020 performed with a multitude of instruments, involving, among others, MAGIC, Fermi's Large Area Telescope (LAT), NuSTAR, Swift, GASP-WEBT, and the Owens Valley Radio Observatory. Mrk 501 showed an extremely low broadband activity, which may help to unravel its baseline emission. Nonetheless, significant flux variations are detected at all wave bands, with the highest occurring at X-rays and very-high-energy (VHE) γ-rays. A significant correlation (>3σ) between X-rays and VHE γ-rays is measured, supporting leptonic scenarios to explain the variable parts of the emission, also during low activity. This is further supported when we extend our data from 2008 to 2020, and identify, for the first time, significant correlations between the Swift X-Ray Telescope and Fermi-LAT. We additionally find correlations between high-energy γ-rays and radio, with the radio lagging by more than 100 days, placing the γ-ray emission zone upstream of the radio-bright regions in the jet. Furthermore, Mrk 501 showed a historically low activity in X-rays and VHE γ-rays from mid-2017 to mid-2019 with a stable VHE flux (>0.2 TeV) of 5% the emission of the Crab Nebula. The broadband spectral energy distribution (SED) of this 2 yr long low state, the potential baseline emission of Mrk 501, can be characterized with one-zone leptonic models, and with (lepto)-hadronic models fulfilling neutrino flux constraints from IceCube. We explore the time evolution of the SED toward the low state, revealing that the stable baseline emission may be ascribed to a standing shock, and the variable emission to an additional expanding or traveling shock.

Temporal and Spectral Evolution of Gamma-Ray Burst Broad Pulses: Identification of High-latitude Emission in the Prompt Emission

We perform a detailed analysis of broad pulses in bright gamma-ray bursts (GRBs) to understand the evolution of GRB broad pulses. Using the temporal and spectral properties, we test the high-latitude emission (HLE) scenario in the decaying phase of broad pulses. The HLE originates from the curvature effect of a relativistic spherical jet, where higher-latitude photons are delayed and softer than the observer’s line-of-sight emission. The signature of HLE has not yet been identified undisputedly during the prompt emission of GRBs. The HLE theory predicts a specific relation, ∝ , between the peak energy E p in ν F ν spectra and the spectral flux F ν measured at E p , . We search for evidence of this relation in 2157 GRBs detected by the Gamma-ray Burst Monitor on board the Fermi Gamma-ray Space Telescope from 2008 to 2017. After imposing unbiased selection criteria in order to minimize contamination in a signal by background and overlaps of pulses, we build a sample of 32 broad pulses in 32 GRBs. We perform a time-resolved spectral analysis on each of these 32 broad pulses and find that the evolution of 18 pulses (56%) is clearly consistent with the HLE relation. For the 18 broad pulses, the exponent δ in the relation of ∝ E p δ is distributed as a Gaussian function with a median and width of 1.99 and 0.34, respectively. This result provides a constraint on the emission radius of GRBs with the HLE signature.

Constraints on the Intergalactic Magnetic Field Using Fermi-LAT and H.E.S.S. Blazar Observations

Magnetic fields in galaxies and galaxy clusters are believed to be the result of the amplification of intergalactic seed fields during the formation of large-scale structures in the universe. However, the origin, strength, and morphology of this intergalactic magnetic field (IGMF) remain unknown. Lower limits on (or indirect detection of) the IGMF can be obtained from observations of high-energy gamma rays from distant blazars. Gamma rays interact with the extragalactic background light to produce electron−positron pairs, which can subsequently initiate electromagnetic cascades. The gamma-ray signature of the cascade depends on the IGMF since it deflects the pairs. Here we report on a new search for this cascade emission using a combined data set from the Fermi Large Area Telescope and the High Energy Stereoscopic System. Using state-of-the-art Monte Carlo predictions for the cascade signal, our results place a lower limit on the IGMF of B > 7.1 × 10−16 G for a coherence length of 1 Mpc even when blazar duty cycles as short as 10 yr are assumed. This improves on previous lower limits by a factor of 2. For longer duty cycles of 104 (107) yr, IGMF strengths below 1.8 × 10−14 G (3.9 × 10−14 G) are excluded, which rules out specific models for IGMF generation in the early universe.

The Detection of Possible γ-Ray Quasi-periodic Modulation with ∼600 days from the Blazar S2 0109+22

In this work, we analyzed the long-term γ-ray data by a Fermi Large Area Telescope of blazar S2 0109+22, ranging from 2008 to 2023. The quasi-periodic oscillations (QPOs) of blazars aided in investigating the physical properties of internal supermassive black holes, the nature of variability, and the underlying radiation mechanism. We employed four different methods—Weighted Wavelet Z-transform, Lomb–Scargle periodogram, REDFIT and phase folded light curve analysis, for searching QPO signals. Our analysis identified a possible QPO behavior with a periodicity of ∼600 days in 2013 November–2023 January at a significance level of ∼3.5σ. This QPO signal sustained ∼9 yr, corresponding to 5.6 cycles, which was in good agreement with the previously observed periodicity of ∼657 days in radio. We explained this phenomenon based on the accretion model and the lighthouse effect, in a binary black hole system.

Multicollision Internal Shock Lepto-hadronic Models for Energetic Gamma-Ray Bursts (GRBs)

For a subpopulation of energetic gamma-ray bursts (GRBs), a moderate baryonic loading may suffice to power ultra-high-energy cosmic rays (UHECRs). Motivated by this, we study the radiative signatures of cosmic-ray protons in the prompt phase of energetic GRBs. Our framework is the internal shock model with multicollision descriptions of the relativistic ejecta (with different emission regions along the jet), plus time-dependent calculations of photon and neutrino spectra. Our GRB prototypes are motivated by Fermi-Large Area Telescope-detected GRBs (including GRB 221009A) for which further, owing to the large energy flux, neutrino nonobservation of single events may pose a strong limit on the baryonic loading. We study the feedback of protons on electromagnetic spectra in synchrotron- and inverse Compton-dominated scenarios to identify the multiwavelength signatures, to constrain the maximally allowed baryonic loading, and to point out the differences between hadronic and inverse Compton signatures. We find that hadronic signatures appear as correlated flux increases in the optical-UV to soft X-ray and GeV–TeV gamma-ray ranges in the synchrotron scenarios, whereas they are difficult to identify in inverse Compton-dominated scenarios. We demonstrate that baryonic loadings around 10, which satisfy the UHECR energetic requirements, do not distort the predicted photon spectra in the Fermi Gamma-Ray Burst Monitor range and are consistent with constraints from neutrino data if the collision radii are large enough (i.e., the time variability is not too short). It therefore seems plausible that under the condition of large dissipation radii a population of energetic GRBs can be the origin of the UHECRs.

The 2021 Activity of the Fast-radio-burst-emitting Galactic Magnetar SGR 1935+2154 as Observed by NASA’s Fermi Gamma-Ray Burst Monitor

The galactic, fast-radio-burst-emitting magnetar SGR 1935+2154 entered an active X-ray burst episode in 2021 September, nearly a year after emitting a fast radio burst with an X-ray counterpart. We report on the temporal and spectral properties of the activity, which included bright intermediate flares, and present a burst catalog of the Fermi Gamma-Ray Burst Monitor observations. We compare this activity to the previous 6 yr history of the source since its discovery in 2014. The bursts show a mean log-Gaussian duration T 100 ∼ 77.34 ms, a cutoff power-law peak energy E peak ∼ 26.62 keV, and a photon index ΓCPL ∼ 0.49, and blackbody soft and hard temperatures kT BBs ∼ 5.23 keV and kT BBh ∼ 9.24 keV, respectively. The burst fluence spans 3 orders of magnitude (10−8–10−5 erg cm−2) and follows . The anticorrelation between the blackbody temperature and the emission area is weaker in the hard component at but is improved in the soft component at , compared to previous activities, with an overall correlation. The 2021 bursts have higher average and integrated fluence than the 2014–2020 episodes and are relatively shorter than the 2019–2020 activities yet comparable to the earlier episodes. During 2014–2021, the burst mean peak energy (E peak) shows a slight softening and is generally softer than other magnetars. We discuss our results in terms of magnetar physics and emission mechanisms.

Search for dark matter lines at the Galactic Center with 14 years of Fermi data

Dark matter (DM) in the Milky Way halo may annihilate or decay to photons, producing monochromatic gamma rays. We search for DM-induced spectral lines using 14 years of data from the Large Area Telescope onboard the Fermi Gamma-ray Space Telescope ($\textit{Fermi}$-LAT) between $10\,\mathrm{GeV}$ and $2\,\mathrm{TeV}$ in the inner Milky Way leveraging both the spatial and spectral morphology of an expected signal. We present new constraints as strong as $\langle \sigma v \rangle \lesssim 6\times 10^{-30}\, \mathrm{cm}^3/\mathrm{s}$ for the two-to-two annihilations and $\tau \gtrsim 10^{30}\,\mathrm{s}$ for one-to-two decays, representing leading sensitivity between $10\,\mathrm{GeV}$ and $\sim$$500\,\mathrm{GeV}$. We consider the implications of our line-constraints on the Galactic Center Excess (GCE), which is a previously-observed excess of continuum $\sim$GeV gamma-rays that may be explained by DM annihilation. The Higgs portal and neutralino-like DM scenarios, which have been extensively discussed as possible origins of the GCE, are constrained by our work because of the lack of observed one-loop decays to two photons. More generally, we interpret our null results in a variety of annihilating and decaying DM models, such as neutralinos, gravitinos, and glueballs, showing that in many cases the line search is more powerful than the continuum, despite the continuum annihilation being at tree level.

Two Transient Quasi-periodic Oscillations in γ-Ray Emission from the Blazar S4 0954+658

In this work, we report periodicity search analyses in the gamma-ray light curve of the blazar S4 0954+658 in monitoring undertaken by the Fermi Large Area Telescope. Four analytical methods and a tool are adopted to detect any periodic flux modulation and corresponding significance level, revealing: (i) a quasi-periodic oscillation (QPO) of 66 days with a significance level of >5σ spanning over 600 days from 2015 to 2016 (MJD 57,145–57,745), resulting in continuous observation of nine cycles, which is one of the longest cycles discerned in blazar gamma-ray light curves; (ii) a possible QPO of 210 days at a moderate significance of ∼3.5σ, which lasted for over 880 days from 2020 to 2022 (MJD 59,035–59,915) and for four cycles. In addition, we discuss several physical models to explain the origin of the two transient QPOs and conclude that a geometrical scenario involving a plasma blob moving helically inside the jet can explain the timescale of the QPO.

Higgsino Dark Matter Confronts 14Years of Fermi γ-Ray Data.

Thermal Higgsino dark matter (DM), with mass around 1TeV, is a well-motivated, minimal DM scenario that arises in supersymmetric extensions of the standard model. Higgsinos may naturally be the lightest superpartners in split-supersymmetry models that decouple the scalar superpartners while keeping Higgsinos and gauginos close to the TeV scale. Higgsino DM may annihilate today to give continuum γ-ray emission at energies less than a TeV in addition to a linelike signature at energies equal to the mass. Previous searches for Higgsino DM, for example with the H.E.S.S. γ-ray telescope, have not reached the necessary sensitivity to probe the Higgsino annihilation cross section. In this work we make use of 14years of data from the Fermi Large Area Telescope at energies above ∼10 GeV to search for the continuum emission near the Galactic Center from Higgsino annihilation. We interpret our results using DM profiles from MilkyWay analog galaxies in the FIRE-2 hydrodynamic cosmological simulations. We set the strongest constraints to date on Higgsino-like DM. Our results show a mild, ∼2σ preference for Higgsino DM with a mass near the thermal Higgsino mass and, depending on the DM density profile, the expected cross section.

Pulsar and Magnetar Navigation with Fermi/GBM and GECAM

The determination of the absolute and relative position of a spacecraft is critical for its operation, observations, data analysis, scientific studies, as well as deep-space exploration in general. A spacecraft that can determine its own absolute position autonomously may perform better than those that must rely on transmission solutions. In this work, we report an absolute navigation accuracy of ∼20 km using 16 day Crab pulsar data observed with Fermi’s Gamma-ray Burst Monitor (GBM). In addition, we propose a new method with the inverse process of the triangulation for joint navigation using repeated bursts like those from the magnetar SGR J1935+2154 observed by the Gravitational-wave High-energy Electromagnetic Counterpart All-sky Monitor and GBM.

Correlation between Emission-line Luminosity and Gamma-Ray Dominance in the Blazar 3C 279

Despite numerous studies, the origin of the γ-ray emission from blazars is still debated, in particular whether it is produced by leptonic or hadronic processes. In this study, we are testing the leptonic scenario for the flat-spectrum radio quasar 3C 279, assuming that the γ-ray emission is generated by inverse Compton scattering of external target photons from the broad-line region (IC-BLR scenario). For this purpose we use a 10 yr data set of the source consisting of the optical spectroscopy data from the Steward Observatory blazar monitoring program and Fermi Large Area Telescope γ-ray data. We search for a possible correlation between the Compton dominance and the emission-line luminosity using the discrete correlation function analysis. As a result, we find no significant correlation between these two quantities at any time lag value, while the emission-line luminosity displays a moderate correlation with the γ-ray flux at a zero time lag. We also reveal that the optical synchrotron continuum flux shows a pronounced correlation with the γ-ray flux, and therefore we interpret these results within the leptonic IC-BLR scenario where the variations in Compton dominance are primarily induced by changes in the magnetic field, rather than in the emission-line luminosity.

Exploring the Emission Mechanisms of Mrk 180 with Long-term X-Ray and γ-Ray Data

Markarian (Mrk) 180 is a BL Lacertae object located at a redshift of 0.045 and is a potential candidate for high-energy cosmic-ray acceleration. We have analyzed the Fermi Large Area Telescope (Fermi-LAT) γ-ray data of Mrk 180 collected over a period of 12.8 yr and found no significant enhancement in the flux from the long-term γ-ray light curve. We have also analyzed Swift X-ray, ultraviolet, and optical, and X-ray Multi-Mirror Mission (XMM-Newton) data to construct the multiwavelength spectral energy distribution (SED). The SED has been modeled with one-zone pure leptonic and lepto-hadronic scenarios to explain the underlying physics of multiwavelength emission. The pure leptonic model and the two lepto-hadronic models, viz., (i) line-of-sight interactions of ultrahigh-energy cosmic rays (UHECRs; E ≳ 1017 eV) with the cosmic background radiation and (ii) the interactions of relativistic protons with the cold protons in the jet, have been compared in our work. Moreover, an earlier study has associated Mrk 180 with the Telescope Array (TA) hotspot of UHECRs at E > 57 EeV. This speculation motivates us to check whether ultrahigh-energy protons and iron nuclei can reach the Earth from Mrk 180. After comparing the results of our simulation with the current observational data, we find that Mrk 180 is unlikely to be a source of the UHECR events contributing to the TA hotspot for conservative strengths of extragalactic magnetic fields.