Search

Continuous gravitational waves (CWs) emission from neutron stars carries information about their internal structure and equation of state, and it can provide tests of General Relativity. We present a search for CWs from a set of 45 known pulsars in the first part of the fourth LIGO--Virgo--KAGRA observing run, known as O4a. We conducted a targeted search for each pulsar using three independent analysis methods considering the single-harmonic and the dual-harmonic emission models. We find no evidence of a CW signal in O4a data for both models and set upper limits on the signal amplitude and on the ellipticity, which quantifies the asymmetry in the neutron star mass distribution. For the single-harmonic emission model, 29 targets have the upper limit on the amplitude below the theoretical spin-down limit. The lowest upper limit on the amplitude is $6.4\!\times\!10^{-27}$ for the young energetic pulsar J0537-6910, while the lowest constraint on the ellipticity is $8.8\!\times\!10^{-9}$ for the bright nearby millisecond pulsar J0437-4715. Additionally, for a subset of 16 targets we performed a narrowband search that is more robust regarding the emission model, with no evidence of a signal. We also found no evidence of non-standard polarizations as predicted by the Brans-Dicke theory., Comment: main paper: 12 pages, 6 figures, 4 tables

Astrometry of pulsars, particularly their distances, serves as a critical input for various astrophysical experiments using pulsars. Pulsar timing is a primary approach for determining a pulsar's position, parallax, and distance. In this paper, we explore the influence of the solar wind on astrometric measurements obtained through pulsar timing, focusing on its potential to affect the accuracy of these parameters. Using both theoretical calculation and mock-data simulations, we demonstrate a significant correlation between the pulsar position, annual parallax and the solar-wind density parameters. This correlation strongly depends on the pulsar's ecliptic latitude. We show that fixing solar-wind density to an arbitrary value in the timing analysis can introduce significant bias in the estimated pulsar position and parallax, and its significance is highly dependent on the ecliptic latitude of the pulsar and the timing precision of the data. For pulsars with favourable ecliptic latitude and timing precision, the astrometric and solar-wind parameters can be measured jointly with other timing parameters using single-frequency data. The parameter correlation can be mitigated by using multi-frequency data, which also significantly improves the measurement precision of these parameters; this is particularly important for pulsars at a medium or high ecliptic latitude. Additionally, for a selection of pulsars we reprocess their EPTA Data Release 2 data to include modelling of solar-wind effect in the timing analysis. This delivers significant measurements of both parallax and solar-wind density, the latter of which are consistent with those obtained at low-frequency band. In the future, combining pulsar timing data at gigahertz and lower frequencies will probably deliver the most robust and precise measurements of astrometry and solar wind properties in pulsar timing., Comment: 15 pages, 15 figures, 1 table, accepted for publication in MNRAS

Ultra-light axion-like particles (ALPs) can be a viable solution to the dark matter problem. The scalar field associated with ALPs, coupled to the electromagnetic field, acts as an active birefringent medium, altering the polarisation properties of light through which it propagates. In particular, oscillations of the axionic field induce monochromatic variations of the plane of linearly polarised radiation of astrophysical signals. The radio emission of millisecond pulsars provides an excellent tool to search for such manifestations, given their high fractional linear polarisation and negligible fluctuations of their polarisation properties. We have searched for the evidence of ALPs in the polarimetry measurements of pulsars collected and preprocessed for the European Pulsar Timing Array (EPTA) campaign. Focusing on the twelve brightest sources in linear polarisation, we searched for an astrophysical signal from axions using both frequentist and Bayesian statistical frameworks. For the frequentist analysis, which uses Lomb-Scargle periodograms at its core, no statistically significant signal has been found. The model used for the Bayesian analysis has been adjusted to accommodate multiple deterministic systematics that may be present in the data. A statistically significant signal has been found in the dataset of multiple pulsars with common frequency between $10^{-8}$ Hz and $2\times10^{-8}$ Hz, which can most likely be explained by the residual Faraday rotation in the terrestrial ionosphere. Strong bounds on the coupling constant $g_{a\gamma}$, in the same ballpark as other searches, have been obtained in the mass range between $6\times10^{-24}$ eV and $5\times10^{-21}$ eV. We conclude by discussing problems that can limit the sensitivity of our search for ultra-light axions in the polarimetry data of pulsars, and possible ways to resolve them., Comment: 24 pages, 15 figures

Context: Timing of pulsar PSR J0337+1715 provides a unique opportunity to test the strong equivalence principle (SEP) with a strongly self-gravitating object. This is due to its unique situation in a triple stellar system with two white dwarfs. Aims: Our previous study suggested the presence of a strong low-frequency signal in the timing residuals. We set out to model it on a longer dataset in order to determine its nature and improve accuracy. Methods: Three models are considered: chromatic or achromatic red-noise, and a small planet in a hierarchical orbit with the triple stellar system. These models are implemented in our numerical timing model. We perform Bayesian inference of posterior distributions. Best fits are compared using information-theoretic criteria. Results: Chromatic red noise from dispersion-measure variations is ruled out. Achromatic red noise or a planet in keplerian orbit provide the best fits. If it is red noise then it appears exceptionally strong. Assuming the presence of a planet, we obtain a marginal detection of mutual interactions which allows us to constrain its mass to $\sim 0.5 M_{\rm Moon}$ as well as its inclination. The latter is intriguingly coincident with a Kozai resonance. We show that a longer observation span will ultimately lead to a clear signature of the planet model due to its mutual interactions with the triple system. We produce new limits on SEP violation: $|\Delta| < 1.5\cdot 10^{-6}$ or $|\Delta| < 2.3\cdot 10^{-6}$ at 95% confidence level under the planet or red-noise hypothesis, respectively. This model dependence emphasises the need for additional data and model selection. As a by-product, we estimate a rather low supernova kick velocity of $\sim 110-125 \rm km/s$, strengthening the idea that it is a necessary condition for the formation of pulsar triple systems.

The recent detection of extended $\gamma$-ray emission around middle-aged pulsars is interpreted as inverse-Compton scattering of ambient photons by electron-positron pairs escaping the pulsar wind nebula, which are confined near the system by unclear mechanisms. This emerging population of $\gamma$-ray sources was first discovered at TeV energies and remains underexplored in the GeV range. To address this, we conducted a systematic search for extended sources along the Galactic plane using 14 years of Fermi-LAT data above 10 GeV, aiming to identify a number of pulsar halo candidates and extend our view to lower energies. The search covered the inner Galactic plane ($\lvert l\rvert\leq$ 100$^{\circ}$, $\lvert b\rvert\leq$ 1$^{\circ}$) and the positions of known TeV sources and bright pulsars, yielding broader astrophysical interest. We found 40 such sources, forming the Second Fermi Galactic Extended Sources Catalog (2FGES), most with 68% containment radii smaller than 1.0$^{\circ}$ and relatively hard spectra with photon indices below 2.5. We assessed detection robustness using field-specific alternative interstellar emission models and by inspecting significance maps. Noting 13 sources previously known as extended in the 4FGL-DR3 catalog and five dubious sources from complex regions, we report 22 newly detected extended sources above 10 GeV. Of these, 13 coincide with H.E.S.S., HAWC, or LHAASO sources; six coincide with bright pulsars (including four also coincident with TeV sources); six are associated with 4FGL point sources only; and one has no association in the scanned catalogs. Notably, six to eight sources may be related to pulsars as classical pulsar wind nebulae or pulsar halos., Comment: 43 pages, 17 figures, 11 tables

We present high precision measurements of the radiative heat transfer of a glass microsphere immersed in a thermal bath in vacuum facing three different planar substrates (SiO2, SiC and Au), which exhibit very different optical behaviors in the infrared region. Using a thermoresistive probe on a cantilever, we show the non-monotonic behavior of the radiative flux between the microsphere and its environment when the microsphere is brought closer to the substrate in the far-field to near-field transition regime. We demonstrate that this unexpected behavior is related to the singularities of dressed emission mechanisms in this three-body system sphere-substrate-bath with respect to the separation distance., Comment: 5 pages, 3 figures + Supplementary

Pulsar Timing Array (PTA) collaborations gather high-precision timing measurements of pulsars with the aim of detecting gravitational wave (GW) signals. A major challenge lies in the identification and characterization of the different sources of noise that may hamper their sensitivity to GWs. The presence of time-correlated noise that resembles the target signal might give rise to degeneracies that can directly impact the detection statistics. In this work, we focus on the covariance that exists between a "chromatic" dispersion measure (DM) noise and an "achromatic" stochastic gravitational wave background (GWB). "Chromatic" associated to the DM noise means that its amplitude depends on the frequency of the incoming pulsar photons measured by the radio-telescope. Several frequency channels are then required to accurately characterise its chromatic features and when the coverage of incoming frequency is poor, it becomes impossible to disentangle chromatic and achromatic noise contributions. In this paper, we explore this situation by injecting realistic GWB into 100 realizations of two mock versions of the second data release (DR2) of the European PTA (EPTA), characterized by different frequency coverage. The first dataset is a faithful copy of DR2, in which the first half of the data is dominated by only one frequency channel of observation; the second one is identical except for a more homogeneous frequency coverage across the full dataset. We show that for 91% of the injections, a better frequency coverage leads to an improved statistical significance (~1.3dex higher log Bayes factor on average) of the GWB and a better characterization of its properties. We propose a metric to quantify the degeneracy between DM and GWB parameters and show that it is correlated with a loss of significance for the recovered GWB and an increase in the GWB bias towards a higher and flatter spectral shape.

We present the localization and host galaxy of FRB 20190208A, a repeating source of fast radio bursts (FRBs) discovered using CHIME/FRB. As part of the PRECISE repeater localization program on the EVN, we monitored FRB 20190208A for 65.6 hours at $\sim1.4$ GHz and detected a single burst, which led to its VLBI localization with 260 mas uncertainty (2$\sigma$). Follow-up optical observations with the MMT Observatory ($i\gtrsim 25.7$ mag (AB)) found no visible host at the FRB position. Subsequent deeper observations with the GTC, however, revealed an extremely faint galaxy ($r=27.32 \pm0.16$ mag), very likely ($99.95 \%$) associated with FRB 20190208A. Given the dispersion measure of the FRB ($\sim580$ pc cm$^{-3}$), even the most conservative redshift estimate ($z_{\mathrm{max}}\sim0.83$) implies that this is the lowest-luminosity FRB host to date ($\lesssim10^8L_{\odot}$), even less luminous than the dwarf host of FRB 20121102A. We investigate how localization precision and the depth of optical imaging affect host association, and discuss the implications of such a low-luminosity dwarf galaxy. Unlike the other repeaters with low-luminosity hosts, FRB 20190208A has a modest Faraday rotation measure of a few tens of rad m$^{-2}$, and EVN plus VLA observations reveal no associated compact persistent radio source. We also monitored FRB 20190208A for 40.4 hours over 2 years as part of the \'ECLAT repeating FRB monitoring campaign on the Nan\c{c}ay Radio Telescope, and detected one burst. Our results demonstrate that, in some cases, the robust association of an FRB with a host galaxy will require both high localization precision, as well as deep optical follow-up., Comment: submitted to ApJL

Recent constraints on neutron star mass and radius have advanced our understanding of the equation of state (EOS) of cold dense matter. Some of them have been obtained by modeling the pulses of three millisecond X-ray pulsars observed by the Neutron Star Interior Composition Explorer (NICER). Here, we present a Bayesian parameter inference for a fourth pulsar, PSR J1231$-$1411, using the same technique with NICER and XMM-Newton data. When applying a broad mass-inclination prior from radio timing measurements and the emission region geometry model that can best explain the data, we find likely converged results only when using a limited radius prior. If limiting the radius to be consistent with the previous observational constraints and EOS analyses, we infer the radius to be $12.6 \pm 0.3$ km and the mass to be $1.04_{-0.03}^{+0.05}$ $M_\odot$, each reported as the posterior credible interval bounded by the $16\,\%$ and $84\,\%$ quantiles. If using an uninformative prior but limited between $10$ and $14$ km, we find otherwise similar results, but $R_{\mathrm{eq}} = 13.5_{-0.5}^{+0.3}$ km for the radius. In both cases, we find a nonantipodal hot region geometry where one emitting spot is at the equator or slightly above, surrounded by a large colder region, and where a noncircular hot region lies close to southern rotational pole. If using a wider radius prior, we only find solutions that fit the data significantly worse. We discuss the challenges in finding the better fitting solutions, possibly related to the weak interpulse feature in the pulse profile., Comment: 23 pages, 13 figures (2 of which are figure sets), 3 tables, published in ApJ

Correspondence analysis, multiple correspondence analysis and their discriminant counterparts (i.e., discriminant simple correspondence analysis and discriminant multiple correspondence analysis) are methods of choice for analyzing multivariate categorical data. In these methods, variables are integrated into optimal components computed as linear combinations whose weights are obtained from a generalized singular value decomposition (GSVD) that integrates specific metric constraints on the rows and columns of the original data matrix. The weights of the linear combinations are, in turn, used to interpret the components, and this interpretation is facilitated when components are 1) pairwise orthogonal and 2) when the values of the weights are either large or small but not intermediate-a pattern called a simple or a sparse structure. To obtain such simple configurations, the optimization problem solved by the GSVD is extended to include new constraints that implement component orthogonality and sparse weights. Because multiple correspondence analysis represents qualitative variables by a set of binary variables, an additional group constraint is added to the optimization problem in order to sparsify the whole set representing one qualitative variable. This new algorithm-called group-sparse GSVD (gsGSVD)-integrates these constraints via an iterative projection scheme onto the intersection of subspaces where each subspace implements a specific constraint. In this paper, we expose this new algorithm and show how it can be adapted to the sparsification of simple and multiple correspondence analysis, and illustrate its applications with the analysis of four different data sets-each illustrating the sparsification of a particular CA-based analysis.

PSR J1618-3921 is one of five known millisecond pulsars (MSPs) in eccentric orbits (eMPSs) located in the Galactic plane, whose formation is poorly understood. Earlier studies of these objects revealed significant discrepancies between observation and predictions from standard binary evolution scenarios of pulsar-Helium white dwarf binaries. We conducted observations with the L-band receiver of the MeerKAT radio telescope and the UWL receiver of the Parkes Murriyang radio telescope between 2019 and 2021. These data were added to archival observations. We perform an analysis of this joint 23-year-dataset. We use the recent observations to give a brief account of the emission properties of J1618-3921, including a Rotating Vector model fit of the linear polarisation position angle of the pulsar. The long timing baseline allowed for a highly significant measurement of the rate of advance of periastron of $\dot{\omega}$. We can only report a low significance detection of the orthometric Shapiro delay parameters $h_3$ and $\varsigma$, leading to mass estimates of the total and individual binary masses. We detect an unexpected change in the orbital period of, which is an order of magnitude larger and carries an opposite sign to what is expected from Galactic acceleration and the Shklovskii effect. We also detect a significant second derivative of the spin frequency. Furthermore, we report an unexpected, abrupt change of the mean pulse profile in June 2021 with unknown origin. We propose that the anomalous $\dot{P_b}$ and $\ddot{f}$ indicate an additional varying acceleration due to a nearby mass, i.e., the J1618-3921 binary system is likely part of a hierarchical triple. This finding suggests that at least some eMSPs might have formed in triple star systems. Although the uncertainties are large, the binary companion mass is consistent with the $P_b$ - $M_{WD}$ relation., Comment: 17 pages, 11 figures, 3 tables

In this work, we investigated the presence of strictly periodic, as well as quasi-periodic signals, in the timing of the 25 millisecond pulsars from the EPTA DR2 dataset. This is especially interesting in the context of the recent hints of a gravitational wave background in these data, and the necessary further study of red-noise timing processes, which are known to behave quasi-periodically in some normal pulsars. We used Bayesian timing models developed through the run_enterprise pipeline: a strict periodicity was modelled as the influence of a planetary companion on the pulsar, while a quasi-periodicity was represented as a Fourier-domain Gaussian process. We found that neither model would clearly improve the timing models of the 25 millisecond pulsars in this dataset. This implies that noise and parameter estimates are unlikely to be biased by the presence of a (quasi-)periodicity in the timing data. Nevertheless, the results for PSRs J1744--1134 and J1012+5307 suggest that the standard noise models for these pulsars may not be sufficient. We also measure upper limits for the projected masses of planetary companions around each of the 25 pulsars. The data of PSR J1909--3744 yielded the best mass limits, such that we constrained the 95-percentile to 2*10^{-4} Earth-masses (roughly the mass of the dwarf planet Ceres) for orbital periods between 5 d--17 yr. These are the best pulsar planet mass limits to date., Comment: Submitted for publication in MNRAS

Pulsars are detected over the whole electromagnetic spectrum, from radio wavelengths up to very high energies, in the GeV-TeV range. Whereas the radio emission site for young pulsars is well constrained to occur at altitudes about several percent of the light-cylinder radius and $\gamma$-ray emission is believed to be produced in the striped wind, outside the light-cylinder, their non-thermal X-ray production site remains unknown. The aim of this letter is to localize the non-thermal X-ray emission region based on multi-wavelength pulse profile fitting for PSR J2229+6114, a particularly good candidate due to its high X-ray brightness. Based on the geometry deduced from the joint radio and $\gamma$-ray pulse profiles, we fix the magnetic axis inclination angle and the line of sight inclination angle but we leave the region of X-ray emission unlocalised, somewhere between the surface and the light-cylinder. We localize this region and its extension by fitting the X-ray pulse profile as observed by the NICER, NuSTAR and RXTE telescopes in the ranges 2-7 keV, 3-10 keV and 9.4-22.4 keV, respectively. We constrain the non-thermal X-ray emission to arise from altitudes between $0.2\,r_L$ and $0.55\,r_L$ where $r_L$ is the light cylinder radius. The magnetic obliquity is approximately $\alpha \approx 45\deg-50\deg$ and the line of sight inclination angle $\zeta \approx 32\deg-48\deg$. This letter is among the first works to tightly constrain the location of the non-thermal X-ray emission from pulsars. We plan to apply this procedure to several other good candidates to confirm this new result., Comment: Accepted for publication in A&A

Pulsar timing arrays (PTAs) are designed to detect low-frequency gravitational waves (GWs). GWs induce achromatic signals in PTA data, meaning that the timing delays do not depend on radio-frequency. However, pulse arrival times are also affected by radio-frequency dependent "chromatic" noise from sources such as dispersion measure (DM) and scattering delay variations. Furthermore, the characterization of GW signals may be influenced by the choice of chromatic noise model for each pulsar. To better understand this effect, we assess if and how different chromatic noise models affect achromatic noise properties in each pulsar. The models we compare include existing DM models used by NANOGrav and noise models used for the European PTA Data Release 2 (EPTA DR2). We perform this comparison using a subsample of six pulsars from the NANOGrav 15 yr data set, selecting the same six pulsars as from the EPTA DR2 six-pulsar dataset. We find that the choice of chromatic noise model noticeably affects the achromatic noise properties of several pulsars. This is most dramatic for PSR J1713+0747, where the amplitude of its achromatic red noise lowers from $\log_{10}A_{\text{RN}} = -14.1^{+0.1}_{-0.1}$ to $-14.7^{+0.3}_{-0.5}$, and the spectral index broadens from $\gamma_{\text{RN}} = 2.6^{+0.5}_{-0.4}$ to $\gamma_{\text{RN}} = 3.5^{+1.2}_{-0.9}$. We also compare each pulsar's noise properties with those inferred from the EPTA DR2, using the same models. From the discrepancies, we identify potential areas where the noise models could be improved. These results highlight the potential for custom chromatic noise models to improve PTA sensitivity to GWs.

The measurement of pulsar pulse times-of-arrival (ToAs) is a crucial step in detecting low-frequency gravitational waves. To determine ToAs, we can use template-matching to compare each observed pulse profile with a standard template. However, using different combinations of templates and template-matching methods (TMMs) without careful consideration may lead to inconsistent results. In pulsar timing array (PTA) experiments, distinct ToAs from the same observations can be obtained, due to the use of diverse templates and TMMs. In other words, employing diverse approaches can yield different timing results and would thus have a significant impact on subsequent gravitational wave searches. In this paper, we examine several commonly used combinations to analyze their effect on pulse ToAs. we evaluate the potential impact of template and TMM selection on thirteen typical millisecond pulsars within the European PTA. We employ pulsar timing methods, specifically the root mean square and reduced chi-square $\chi_r^2$ of the residuals of the best timing solution to assess the outcomes. Additionally, we evaluate the system-limited noise floor (SLNF) for each pulsar at various telescopes operating around 1.4~GHz using frequency-resolved templates. Our findings suggest that utilizing data-derived and smoothed templates in conjunction with the Fourier-domain with Markov-chain Monte Carlo (FDM) TMM is generally the most effective approach, though there may be exceptions that require further attention. Furthermore, we determine that pulse phase jitter noise does not significantly limit the current precision of the European PTA's timing, as jitter levels derived from other studies are much smaller than the SLNF., Comment: Accepted by A&A

Pulsar Timing Array (PTA) collaborations recently reported evidence for the presence of a gravitational wave background (GWB) in their datasets. The main candidate that is expected to produce such a GWB is the population of supermassive black hole binaries (SMBHB). Some analyses showed that the recovered signal may exhibit time-dependent properties, i.e. non-stationarity. In this paper, we propose an approximated non-stationary Gaussian process (GP) model obtained from the perturbation of stationary processes. The presented method is applied to the second data release of the European pulsar timing array to search for non-stationary features in the GWB. We analyzed the data in different time slices and showed that the inferred properties of the GWB evolve with time. We find no evidence for such non-stationary behavior and the Bayes factor in favor of the latter is $\mathcal{B}^{NS}_{S} = 1.5$. We argue that the evolution of the GWB properties most likely comes from the \mf{improvement of the observation cadence} with time and \mf{better} characterization of the noise of individual pulsars. Such non-stationary GWB could also be produced by the leakage of non-stationary features in the noise of individual pulsars or by the presence of an eccentric single source., Comment: 14 pages, 14 figures

Millisecond pulsars are extremely precise celestial clocks: as they rotate, the beamed radio waves emitted along the axis of their magnetic field can be detected with radio telescopes, which allows for tracking subtle changes in the pulsars' rotation periods. A possible effect on the period of a pulsar is given by a potential coupling to dark matter, in cases where it is modeled with an "ultralight" scalar field. In this paper, we consider a universal conformal coupling of the dark matter scalar to gravity, which in turn mediates an effective coupling between pulsars and dark matter. If the dark matter scalar field is changing in time, as expected in the Milky Way, this effective coupling produces a periodic modulation of the pulsar rotational frequency. By studying the time series of observed radio pulses collected by the European Pulsar Timing Array experiment, we present constraints on the coupling of dark matter, improving on existing bounds. These bounds can also be regarded as constraints on the parameters of scalar-tensor theories of the Fierz-Jordan-Brans-Dicke and Damour-Esposito-Far\`{e}se types in the presence of a (light) mass potential term., Comment: 17 pages, 5 figures, Updated plots, matching published version

Similarity analyses between multiple correlation or covariance tables constitute the cornerstone of network neuroscience. Here, we introduce covSTATIS, a versatile, linear, unsupervised multi-table method designed to identify structured patterns in multi-table data, and allow for the simultaneous extraction and interpretation of both individual and group-level features. With covSTATIS, multiple similarity tables can now be easily integrated, without requiring a priori data simplification, complex black-box implementations, user-dependent specifications, or supervised frameworks. Applications of covSTATIS, a tutorial with Open Data and source code are provided. CovSTATIS offers a promising avenue for advancing the theoretical and analytic landscape of network neuroscience., Comment: The first two authors contributed equally to this work

We have searched for radio pulsations towards 49 Fermi Large Area Telescope (LAT) 1FGL Catalog $\gamma$-ray sources using the Green Bank Telescope at 350 MHz. We detected 18 millisecond pulsars (MSPs) in blind searches of the data; 10 of these were discoveries unique to our survey. Sixteen are binaries, with eight having short orbital periods $P_B < 1$ day. No radio pulsations from young pulsars were detected, although three targets are coincident with apparently radio-quiet $\gamma$-ray pulsars discovered in LAT data. Here, we give an overview of the survey and present radio and $\gamma$-ray timing results for the 10 MSPs discovered. These include the only isolated MSP discovered in our survey and six short-$P_B$ binary MSPs. Of these, three have very low-mass companions ($M_c$ $\ll$ 0.1M$_{\odot}$) and hence belong to the class of black widow pulsars. Two have more massive, non-degenerate companions with extensive radio eclipses and orbitally modulated X-ray emission consistent with the redback class. Significant $\gamma$-ray pulsations have been detected from nine of the discoveries. This survey and similar efforts suggest that the majority of Galactic $\gamma$-ray sources at high Galactic latitudes are either MSPs or relatively nearby non-recycled pulsars, with the latter having on average a much smaller radio/$\gamma$-ray beaming ratio as compared to MSPs. It also confirms that past surveys suffered from an observational bias against finding short-$P_B$ MSP systems., Comment: Accepted for publication in ApJ (25 pages, 15 figues, 4 tables)

The volumetric representation of human interactions is one of the fundamental domains in the development of immersive media productions and telecommunication applications. Particularly in the context of the rapid advancement of Extended Reality (XR) applications, this volumetric data has proven to be an essential technology for future XR elaboration. In this work, we present a new multimodal database to help advance the development of immersive technologies. Our proposed database provides ethically compliant and diverse volumetric data, in particular 27 participants displaying posed facial expressions and subtle body movements while speaking, plus 11 participants wearing head-mounted displays (HMDs). The recording system consists of a volumetric capture (VoCap) studio, including 31 synchronized modules with 62 RGB cameras and 31 depth cameras. In addition to textured meshes, point clouds, and multi-view RGB-D data, we use one Lytro Illum camera for providing light field (LF) data simultaneously. Finally, we also provide an evaluation of our dataset employment with regard to the tasks of facial expression classification, HMDs removal, and point cloud reconstruction. The dataset can be helpful in the evaluation and performance testing of various XR algorithms, including but not limited to facial expression recognition and reconstruction, facial reenactment, and volumetric video. HEADSET and its all associated raw data and license agreement will be publicly available for research purposes., Comment: Accepted in ISMAR 2023 and published in IEEE Transactions on Visualization and Computer Graphics Dataset: https://webpages.tuni.fi/headset

Using validated numerical methods, interval arithmetic and Taylor models, we propose a certified predictor-corrector loop for tracking zeros of polynomial systems with a parameter. We provide a Rust implementation which shows tremendous improvement over existing software for certified path tracking., Comment: final version

We analyzed the globular cluster M5 (NGC 5904) using 15 years of gamma-ray data from the Fermi Large Area Telescope (LAT). Using rotation ephemerides generated from Arecibo and FAST radio telescope observations, we searched for gamma-ray pulsations from the seven millisecond pulsars (MSPs) identified in M5. We detected no significant pulsations from any of the individual pulsars. Also, we searched for possible variations of the gamma-ray emission as a function of orbital phase for all the six MSPs in binary systems, but did not detect any significant modulations. The gamma-ray emission from the direction of M5 is well described by an exponentially cutoff power-law spectral model, although other models cannot be excluded. The phase-averaged emission is consistent with being steady on a time scale of a few months. We estimate the number of MSPs in M5 to be between 1 and 10, using the gamma-ray conversion efficiencies for well-characterized gamma-ray MSPs in the Third Fermi Large Area Telescope Catalog of Gamma-ray Pulsars, suggesting that the sample of known MSPs in M5 is (nearly) complete, even if it is not currently possible to rule out a diffuse component of the observed gamma rays from the cluster., Comment: 14 pages, 5 figures, 3 tables, published in ApJ

The promising improvement in compression efficiency of Versatile Video Coding (VVC) compared to High Efficiency Video Coding (HEVC) comes at the cost of a non-negligible encoder side complexity. The largely increased complexity overhead is a possible obstacle towards its industrial implementation. Many papers have proposed acceleration methods for VVC. Still, a better understanding of VVC complexity, especially related to new partitions and coding tools, is desirable to help the design of new and better acceleration methods. For this purpose, statistical analyses have been conducted, with a focus on Coding Unit (CU) sizes and inter coding modes., Comment: Accepted by ICIP 2022

The Versatile Video Coding (VVC) standard has been finalized by Joint Video Exploration Team (JVET) in 2020. Compared to the High Efficiency Video Coding (HEVC) standard, VVC offers about 50% compression efficiency gain, in terms of Bjontegaard Delta-Rate (BD-rate), at the cost of about 10x more encoder complexity. In this paper, we propose a Convolutional Neural Network (CNN)-based method to speed up inter partitioning in VVC. Our method operates at the Coding Tree Unit (CTU) level, by splitting each CTU into a fixed grid of 8x8 blocks. Then each cell in this grid is associated with information about the partitioning depth within that area. A lightweight network for predicting this grid is employed during the rate-distortion optimization to limit the Quaternary Tree (QT)-split search and avoid partitions that are unlikely to be selected. Experiments show that the proposed method can achieve acceleration ranging from 17% to 30% in the RandomAccess Group Of Picture 32 (RAGOP32) mode of VVC Test Model (VTM)10 with a reasonable efficiency drop ranging from 0.37% to 1.18% in terms of BD-rate increase., Comment: Accepted by IVMSP

The 5n-vector ensemble method is a multiple test for the targeted search of continuous gravitational waves from an ensemble of known pulsars. This method can improve the detection probability combining the results from individually undetectable pulsars if few signals are near the detection threshold. In this paper, we apply the 5n-vector ensemble method to the O3 data set from the LIGO and Virgo detectors considering an ensemble of 201 known pulsars. We find no evidence for a signal from the ensemble and set a 95% credible upper limit on the mean ellipticity assuming a common exponential distribution for the pulsars' ellipticities. Using two independent hierarchical Bayesian procedures, we find upper limits of $1.2 \times 10^{-9}$ and $2.5 \times 10^{-9}$ on the mean ellipticity for the 201 analyzed pulsars.

In this article, we study the parameterized complexity of the Set Cover problem restricted to semi-ladder-free hypergraphs, a class defined by Fabianski et al. [Proceedings of STACS 2019]. We observe that two algorithms introduced by Langerman and Morin [Discrete & Computational Geometry 2005] in the context of geometric covering problems can be adapted to this setting, yielding simple FPT and kernelization algorithms for Set Cover in semi-ladder-free hypergraphs. We complement our algorithmic results with a compression lower bound for the problem, which proves the tightness of our kernelization under standard complexity-theoretic assumptions.

The Versatile Video Coding (VVC) standard has been recently finalized by the Joint Video Exploration Team (JVET). Compared to the High Efficiency Video Coding (HEVC) standard, VVC offers about 50% compression efficiency gain, in terms of Bjontegaard Delta-Rate (BD-rate), at the cost of a 10-fold increase in encoding complexity. In this paper, we propose a method based on Convolutional Neural Network (CNN) to speed up the inter partitioning process in VVC. Firstly, a novel representation for the quadtree with nested multi-type tree (QTMT) partition is introduced, derived from the partition path. Secondly, we develop a U-Net-based CNN taking a multi-scale motion vector field as input at the Coding Tree Unit (CTU) level. The purpose of CNN inference is to predict the optimal partition path during the Rate-Distortion Optimization (RDO) process. To achieve this, we divide CTU into grids and predict the Quaternary Tree (QT) depth and Multi-type Tree (MT) split decisions for each cell of the grid. Thirdly, an efficient partition pruning algorithm is introduced to employ the CNN predictions at each partitioning level to skip RDO evaluations of unnecessary partition paths. Finally, an adaptive threshold selection scheme is designed, making the trade-off between complexity and efficiency scalable. Experiments show that the proposed method can achieve acceleration ranging from 16.5% to 60.2% under the RandomAccess Group Of Picture 32 (RAGOP32) configuration with a reasonable efficiency drop ranging from 0.44% to 4.59% in terms of BD-rate, which surpasses other state-of-the-art solutions. Additionally, our method stands out as one of the lightest approaches in the field, which ensures its applicability to other encoders.

With the advent of multi-wavelength electromagnetic observations of neutron stars, spanning many decades in photon energies, from radio wavelengths up to X-rays and $\gamma$-rays, it becomes possible to significantly constrain the geometry and the location of the associated emission regions. In this work, we use results from the modelling of thermal X-ray observations of PSR~J0030+0451 from the NICER mission and phase-aligned radio and $\gamma$-ray pulse profiles to constrain the geometry of an off-centred dipole able to reproduce the light-curves in these respective bands simultaneously. To this aim, we deduce a configuration with a simple dipole off-centred from the location of the centre of the thermal X-ray hot spots and show that the geometry is compatible with independent constraints from radio and $\gamma$-ray pulsations only, leading to a fixed magnetic obliquity of $\alpha \approx 75\deg$ and a line of sight inclination angle of $\zeta \approx 54\deg$. We demonstrate that an off-centred dipole cannot be rejected by accounting for the thermal X-ray pulse profiles. Moreover, the crescent shape of one spot is interpreted as the consequence of a small scale surface dipole on top of the large scale off-centred dipole., Comment: Accepted for publication in A&A

The Australian, Chinese, European, Indian, and North American pulsar timing array (PTA) collaborations recently reported, at varying levels, evidence for the presence of a nanohertz gravitational wave background (GWB). Given that each PTA made different choices in modeling their data, we perform a comparison of the GWB and individual pulsar noise parameters across the results reported from the PTAs that constitute the International Pulsar Timing Array (IPTA). We show that despite making different modeling choices, there is no significant difference in the GWB parameters that are measured by the different PTAs, agreeing within $1\sigma$. The pulsar noise parameters are also consistent between different PTAs for the majority of the pulsars included in these analyses. We bridge the differences in modeling choices by adopting a standardized noise model for all pulsars and PTAs, finding that under this model there is a reduction in the tension in the pulsar noise parameters. As part of this reanalysis, we "extended" each PTA's data set by adding extra pulsars that were not timed by that PTA. Under these extensions, we find better constraints on the GWB amplitude and a higher signal-to-noise ratio for the Hellings and Downs correlations. These extensions serve as a prelude to the benefits offered by a full combination of data across all pulsars in the IPTA, i.e., the IPTA's Data Release 3, which will involve not just adding in additional pulsars, but also including data from all three PTAs where any given pulsar is timed by more than as single PTA., Comment: 21 pages, 9 figures, submitted to ApJ

We report on exceptionally bright bursts (>400 Jy ms) detected from the repeating fast radio burst source FRB 20220912A using the Nan\c{c}ay Radio Telescope (NRT), as part of the ECLAT (Extragalactic Coherent Light from Astrophysical Transients) monitoring campaign. These bursts exhibit extremely luminous, broadband, short-duration structures (~ 16 microseconds), which we term 'microshots' and which can be especially well studied in the NRT data given the excellent signal-to-noise and dynamic range (32-bit samples). The estimated peak flux density of the brightest microshot is 450 Jy. We show that the microshots are clustered into dense 'forests', by modelling them as Weibull distributions and obtaining Weibull shape parameters of approximately 0.5. Our polarimetric analysis reveals that the bursts are nearly 100% linearly polarised; have < 10% circular polarisation fractions; a near-zero average rotation measure of 0.10(6) rad/m^2; and varying polarisation position angles over the burst duration. For one of the bursts, we analyse raw voltage data from simultaneous observations with the Westerbork RT-1 single 25-m dish. These data allow us to measure the scintillation bandwidth, 0.30(3) MHz, and to probe the bursts on (sub-)microsecond timescales. Some important nuances related to dedispersion are also discussed. We propose that the emission mechanism for the broadband microshots is potentially different from the emission mechanism of the broader burst components which still show a residual drift of a few hundred MHz/ms after correcting for dispersion using the microshots. We discuss how the observed emission is phenomenologically analogous to different types of radio bursts from the Sun., Comment: submitted to MNRAS, 19 pages, 13 figures

Accurate polarimetric calibration of the radio pulse profiles from pulsars is crucial for studying their radiation properties at these wavelengths. Inaccurate calibration can also distort recorded pulse profiles, introducing noise in time of arrival (TOA) data and thus degrading pulsar timing analyses. One method for determining the full polarimetric response of a given telescope is to conduct observations of bright polarized pulsars over wide ranges of parallactic angles, to sample different orientations of their polarization angle and determine the cross-couplings between polarization feeds. The Nan\c{c}ay decimetric Radio Telescope (NRT) is a 94m equivalent meridian telescope, capable of tracking a given pulsar for approximately one hour around transit. In November 2019, we began conducting regular observations of the bright and highly linearly polarized pulsar PSR~J0742$-$2822, in a special mode where the feed horn rotates by $\sim 180^\circ$ over the course of the one hour observation, mimicking wide parallactic angle variations and enabling us to determine the polarimetric response of the NRT at 1.4~GHz. The improved polarimetric response of the NRT as determined from these observations was applied to observations of a selection of MSPs with published polarimetric properties. We find that the new polarimetric profiles and polarization position angles are consistent with previous findings, unlike NRT polarimetric results obtained with the previously used method of calibration. The analysis of timing data on J1730$-$2304, J1744$-$1134, and J1857+0953 shows that the new calibration method improves the quality of the timing, and the Matrix Template Matching (MTM) method proves very effective at reducing noise from imperfect calibration. For pulsars with sufficient degrees of polarization, the MTM method appears to be the preferred method for extracting TOAs from NRT observations., Comment: Accepted to Astronomy & Astrophysics. 20 pages, 16 figures, 2 tables, abstract significantly shortened to match astro-ph limit

We present 294 pulsars found in GeV data from the Large Area Telescope (LAT) on the Fermi Gamma-ray Space Telescope. Another 33 millisecond pulsars (MSPs) discovered in deep radio searches of LAT sources will likely reveal pulsations once phase-connected rotation ephemerides are achieved. A further dozen optical and/or X-ray binary systems co-located with LAT sources also likely harbor gamma-ray MSPs. This catalog thus reports roughly 340 gamma-ray pulsars and candidates, 10% of all known pulsars, compared to $\leq 11$ known before Fermi. Half of the gamma-ray pulsars are young. Of these, the half that are undetected in radio have a broader Galactic latitude distribution than the young radio-loud pulsars. The others are MSPs, with 6 undetected in radio. Overall, >235 are bright enough above 50 MeV to fit the pulse profile, the energy spectrum, or both. For the common two-peaked profiles, the gamma-ray peak closest to the magnetic pole crossing generally has a softer spectrum. The spectral energy distributions tend to narrow as the spindown power $\dot E$ decreases to its observed minimum near $10^{33}$ erg s$^{-1}$, approaching the shape for synchrotron radiation from monoenergetic electrons. We calculate gamma-ray luminosities when distances are available. Our all-sky gamma-ray sensitivity map is useful for population syntheses. The electronic catalog version provides gamma-ray pulsar ephemerides, properties and fit results to guide and be compared with modeling results., Comment: 142 pages. Accepted by the Astrophysical Journal Supplement

Annual variations of interstellar scintillation can be modelled to constrain parameters of the ionized interstellar medium. If a pulsar is in a binary system, then investigating the orbital parameters is possible through analysis of the orbital variation of scintillation. In observations carried out from 2011 January to 2020 August by the European Pulsar Timing Array radio telescopes, PSRs~J0613$-$0200 and J0636+5128 show strong annual variations in their scintillation velocity, while the former additionally exhibits an orbital fluctuation. Bayesian theory and Markov-chain-Monte-Carlo methods are used to interpret these periodic variations. We assume a thin and anisotropic scattering screen model, and discuss the mildly and extremely anisotropic scattering cases. PSR~J0613$-$0200 is best described by mildly anisotropic scattering, while PSR~J0636+5128 exhibits extremely anisotropic scattering. We measure the distance, velocity and degree of anisotropy of the scattering screen for our two pulsars, finding that scattering screen distances from Earth for PSRs~J0613$-$0200 and J0636+5128 are 316$^{+28}_{-20}$\,pc and 262$^{+96}_{-38}$\,pc, respectively. The positions of these scattering screens are coincident with the shell of the Local Bubble towards both pulsars. These associations add to the growing evidence of the Local Bubble shell as a dominant region of scattering along many sightlines., Comment: Accepted by SCIENCE CHINA Physics, Mechanics & Astronomy ( SCPMA)

Light field is a type of image data that captures the 3D scene information by recording light rays emitted from a scene at various orientations. It offers a more immersive perception than classic 2D images but at the cost of huge data volume. In this paper, we draw inspiration from the visual characteristics of Sub-Aperture Images (SAIs) of light field and design a compact neural network representation for the light field compression task. The network backbone takes randomly initialized noise as input and is supervised on the SAIs of the target light field. It is composed of two types of complementary kernels: descriptive kernels (descriptors) that store scene description information learned during training, and modulatory kernels (modulators) that control the rendering of different SAIs from the queried perspectives. To further enhance compactness of the network meanwhile retain high quality of the decoded light field, we accordingly introduce modulator allocation and kernel tensor decomposition mechanisms, followed by non-uniform quantization and lossless entropy coding techniques, to finally form an efficient compression pipeline. Extensive experiments demonstrate that our method outperforms other state-of-the-art (SOTA) methods by a significant margin in the light field compression task. Moreover, after aligning descriptors, the modulators learned from one light field can be transferred to new light fields for rendering dense views, indicating a potential solution for view synthesis task.

Pulsar Timing Array experiments probe the presence of possible scalar or pseudoscalar ultralight dark matter particles through decade-long timing of an ensemble of galactic millisecond radio pulsars. With the second data release of the European Pulsar Timing Array, we focus on the most robust scenario, in which dark matter interacts only gravitationally with ordinary baryonic matter. Our results show that ultralight particles with masses $10^{-24.0}~\text{eV} \lesssim m \lesssim 10^{-23.3}~\text{eV}$ cannot constitute $100\%$ of the measured local dark matter density, but can have at most local density $\rho\lesssim 0.3$ GeV/cm$^3$., Comment: 5 pages + acknowledgements + refs, 2 figures. Text and figures match the version published in PRL

The European Pulsar Timing Array (EPTA) and Indian Pulsar Timing Array (InPTA) collaborations have measured a low-frequency common signal in the combination of their second and first data releases respectively, with the correlation properties of a gravitational wave background (GWB). Such signal may have its origin in a number of physical processes including a cosmic population of inspiralling supermassive black hole binaries (SMBHBs); inflation, phase transitions, cosmic strings and tensor mode generation by non-linear evolution of scalar perturbations in the early Universe; oscillations of the Galactic potential in the presence of ultra-light dark matter (ULDM). At the current stage of emerging evidence, it is impossible to discriminate among the different origins. Therefore, in this paper, we consider each process separately, and investigate the implications of the signal under the hypothesis that it is generated by that specific process. We find that the signal is consistent with a cosmic population of inspiralling SMBHBs, and its relatively high amplitude can be used to place constraints on binary merger timescales and the SMBH-host galaxy scaling relations. If this origin is confirmed, this is the first direct evidence that SMBHBs merge in nature, adding an important observational piece to the puzzle of structure formation and galaxy evolution. As for early Universe processes, the measurement would place tight constraints on the cosmic string tension and on the level of turbulence developed by first-order phase transitions. Other processes would require non-standard scenarios, such as a blue-tilted inflationary spectrum or an excess in the primordial spectrum of scalar perturbations at large wavenumbers. Finally, a ULDM origin of the detected signal is disfavoured, which leads to direct constraints on the abundance of ULDM in our Galaxy., Comment: 30 pages, 23 figures, replaced to match the version published in Astronomy & Astrophysics, note the change in the numbering order in the series (now paper IV)

We present the results of a search for continuous gravitational wave signals (CGWs) in the second data release (DR2) of the European Pulsar Timing Array (EPTA) collaboration. The most significant candidate event from this search has a gravitational wave frequency of 4-5 nHz. Such a signal could be generated by a supermassive black hole binary (SMBHB) in the local Universe. We present the results of a follow-up analysis of this candidate using both Bayesian and frequentist methods. The Bayesian analysis gives a Bayes factor of 4 in favor of the presence of the CGW over a common uncorrelated noise process, while the frequentist analysis estimates the p-value of the candidate to be 1%, also assuming the presence of common uncorrelated red noise. However, comparing a model that includes both a CGW and a gravitational wave background (GWB) to a GWB only, the Bayes factor in favour of the CGW model is only 0.7. Therefore, we cannot conclusively determine the origin of the observed feature, but we cannot rule it out as a CGW source. We present results of simulations that demonstrate that data containing a weak gravitational wave background can be misinterpreted as data including a CGW and vice versa, providing two plausible explanations of the EPTA DR2 data. Further investigations combining data from all PTA collaborations will be needed to reveal the true origin of this feature., Comment: 13 figures, 15 pages, accepted

The nanohertz gravitational wave background (GWB) is expected to be an aggregate signal of an ensemble of gravitational waves emitted predominantly by a large population of coalescing supermassive black hole binaries in the centres of merging galaxies. Pulsar timing arrays, ensembles of extremely stable pulsars, are the most precise experiments capable of detecting this background. However, the subtle imprints that the GWB induces on pulsar timing data are obscured by many sources of noise. These must be carefully characterized to increase the sensitivity to the GWB. In this paper, we present a novel technique to estimate the optimal number of frequency coefficients for modelling achromatic and chromatic noise and perform model selection. We also incorporate a new model to fit for scattering variations in the pulsar timing package temponest and created realistic simulations of the European Pulsar Timing Array (EPTA) datasets that allowed us to test the efficacy of our noise modelling algorithms. We present an in-depth analysis of the noise properties of 25 millisecond pulsars (MSPs) that form the second data release (DR2) of the EPTA and investigate the effect of incorporating low-frequency data from the Indian PTA collaboration. We use enterprise and temponest packages to compare noise models with those reported with the EPTA DR1. We find that, while in some pulsars we can successfully disentangle chromatic from achromatic noise owing to the wider frequency coverage in DR2, in others the noise models evolve in a more complicated way. We also find evidence of long-term scattering variations in PSR J1600$-$3053. Through our simulations, we identify intrinsic biases in our current noise analysis techniques and discuss their effect on GWB searches. The results presented here directly help improve sensitivity to the GWB and are already being used as part of global PTA efforts., Comment: 20 pages, 6 figures, 9 tables

Pulsar timing arrays offer a probe of the low-frequency gravitational wave spectrum (1 - 100 nanohertz), which is intimately connected to a number of markers that can uniquely trace the formation and evolution of the Universe. We present the dataset and the results of the timing analysis from the second data release of the European Pulsar Timing Array (EPTA). The dataset contains high-precision pulsar timing data from 25 millisecond pulsars collected with the five largest radio telescopes in Europe, as well as the Large European Array for Pulsars. The dataset forms the foundation for the search for gravitational waves by the EPTA, presented in associated papers. We describe the dataset and present the results of the frequentist and Bayesian pulsar timing analysis for individual millisecond pulsars that have been observed over the last ~25 years. We discuss the improvements to the individual pulsar parameter estimates, as well as new measurements of the physical properties of these pulsars and their companions. This data release extends the dataset from EPTA Data Release 1 up to the beginning of 2021, with individual pulsar datasets with timespans ranging from 14 to 25 years. These lead to improved constraints on annual parallaxes, secular variation of the orbital period, and Shapiro delay for a number of sources. Based on these results, we derived astrophysical parameters that include distances, transverse velocities, binary pulsar masses, and annual orbital parallaxes., Comment: 29 pages, 9 figures, 13 tables, Astronomy & Astrophysics in press

We present the results of the search for an isotropic stochastic gravitational wave background (GWB) at nanohertz frequencies using the second data release of the European Pulsar Timing Array (EPTA) for 25 millisecond pulsars and a combination with the first data release of the Indian Pulsar Timing Array (InPTA). We analysed (i) the full 24.7-year EPTA data set, (ii) its 10.3-year subset based on modern observing systems, (iii) the combination of the full data set with the first data release of the InPTA for ten commonly timed millisecond pulsars, and (iv) the combination of the 10.3-year subset with the InPTA data. These combinations allowed us to probe the contributions of instrumental noise and interstellar propagation effects. With the full data set, we find marginal evidence for a GWB, with a Bayes factor of four and a false alarm probability of $4\%$. With the 10.3-year subset, we report evidence for a GWB, with a Bayes factor of $60$ and a false alarm probability of about $0.1\%$ ($\gtrsim 3\sigma$ significance). The addition of the InPTA data yields results that are broadly consistent with the EPTA-only data sets, with the benefit of better noise modelling. Analyses were performed with different data processing pipelines to test the consistency of the results from independent software packages. The inferred spectrum from the latest EPTA data from new generation observing systems is rather uncertain and in mild tension with the common signal measured in the full data set. However, if the spectral index is fixed at 13/3, the two data sets give a similar amplitude of ($2.5\pm0.7)\times10^{-15}$ at a reference frequency of $1\,{\rm yr}^{-1}$. By continuing our detection efforts as part of the International Pulsar Timing Array (IPTA), we expect to be able to improve the measurement of spatial correlations and better characterise this signal in the coming years., Comment: 21 pages, 14 figures, 4 appendix figures, accepted for publication in A&A

We search for a stochastic gravitational wave background (SGWB) generated by a network of cosmic strings using six millisecond pulsars from Data Release 2 (DR2) of the European Pulsar Timing Array (EPTA). We perform a Bayesian analysis considering two models for the network of cosmic string loops, and compare it to a simple power-law model which is expected from the population of supermassive black hole binaries. Our main strong assumption is that the previously reported common red noise process is a SGWB. We find that the one-parameter cosmic string model is slightly favored over a power-law model thanks to its simplicity. If we assume a two-component stochastic signal in the data (supermassive black hole binary population and the signal from cosmic strings), we get a $95\%$ upper limit on the string tension of $\log_{10}(G\mu) < -9.9$ ($-10.5$) for the two cosmic string models we consider. In extended two-parameter string models, we were unable to constrain the number of kinks. We test two approximate and fast Bayesian data analysis methods against the most rigorous analysis and find consistent results. These two fast and efficient methods are applicable to all SGWBs, independent of their source, and will be crucial for analysis of extended data sets., Comment: 14 pages, 6 figures; typo corrected in (5)