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Robert A. Main

Publications and source records attributed to Robert A. Main.

At least 19 recordsLinked to original sources

Debiasing the Observed Fast Radio Burst Population with the CHIME/FRB Selection Function

The recent release of CHIME/FRB Catalog~2 provides the largest sample to date with which to investigate the intrinsic distributions of fast radio bursts (FRBs). Leveraging an expanded campaign of 587,367 synethetic bursts injected into the live CHIME/FRB search pipeline, we perform a population analysis of the fluence, scattering timescale, pulse width, and dispersion measure distributions of Catalog~2 FRBs. We first infer the intrinsic population using a resampling-based framework that accounts for instrumental selection effects following previous CHIME/FRB population studies. A central goal of this work is to constrain the intrinsic distribution of scattering timescales, that remained weakly constrained in Catalog~1 owing to limited statistics at moderate and large scattering times ($\tau \gtrsim 10\,\mathrm{ms}$ at 600~MHz) and sparse injection coverage in this regime. Second, we construct an explicit multidimensional selection function by training a logistic regression model on the injected events. This model estimates the detection probability as a function of FRB observable properties, including higher-order interaction terms. We incorporate this selection function into a simulation-based inference framework to refine the inferred intrinsic scattering-timescale distribution. We find evidence for a slight downturn in the intrinsic FRB scattering timescale distribution, though a flat or slightly rising distribution cannot be ruled out, that is further supported through a comparison with the higher-frequency scattering timescale distribution observed by Commensal Real-time ASKAP Fast Transients (CRAFT) survey.

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Imaging without visibilities: FAST-Effelsberg scintillometry of PSR B1508+55

Context. The spatially coherent multipath propagation of pulsar radiation leads to a temporal and spectral interference patterns called scintillation. It is caused by density variations in the ionized interstellar medium, which often take the form of thin scattering screens filled with multiple subimages of the pulsar. PSR B1508+55 is known to be scattered by one or two such screens. Aims. We investigate appropriate methods to achieve precise astrometry for a scattering screen from simultaneous observations of only two telescopes on a very long baseline without forming visibilities. Methods. Two simultaneous observations of PSR B1508+55 were performed with the 100-m telescope at Effelsberg and the Five-hundred-meter Aperture Spherical Telescope (FAST). Using and improving existing scintillometry techniques, we leveraged the evolving, very long baseline to precisely measure the screen orientation, effective velocity, and scintillation arc curvature. We inferred the one-screen and two-screen model parameters and we imaged the closer screen. Results. Each single epoch leads to much tighter angular constraints than long-term monitoring of scintillation arcs, revealing an ongoing evolution of the orientation of the closer screen. Images of the scattered pulsar were obtained with a resolution on the order of 0.1 mas. These results confirm the highly anisotropic alignment of the scattered images, while also revealing small-scale deviations from a large-scale straight line. Conclusions. We demonstrate that simultaneous observations of scintillation can be used as a powerful substitute for very long baseline inferometry.

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No Measurable Changes in Radio and X-ray Emission Surrounding Glitches in the Young Pulsar PSR J2229+6114

We present our first result from an ongoing pulsar glitch monitoring campaign at the Canadian Hydrogen Intensity Mapping Experiment (CHIME), in which we analyzed the radio and X-ray emission surrounding four glitches in PSR~J2229+6114. Using daily CHIME observations, we detected a glitch in PSR~J2229+6114 in near-real time and triggered an X-ray follow-up with the Nuclear Spectroscopic Telescope Array (NuSTAR) two days after the glitch. We identified three additional glitch events in archival CHIME/Pulsar observations that coincided with an independent X-ray observing campaign with the Neutron star Interior Composition Explorer (NICER).. Our data show there is no measurable change in the source's X-ray and radio emission during the four glitch events, in stark contrast to the post-glitch activity in high-magnetic-field, rotation-powered pulsars (RPPs), which have been observed to exhibit magnetar-like X-ray outbursts immediately after large glitches. Those high-magnetic-field (high-$B$) RPPs are considered transitional objects between ordinary RPPs and magnetars, thereby leading to a unifying neutron star model in which the inferred dipolar surface magnetic field strength serves as a unifying parameter. However, such a model remains challenged, in part, by the lack of constraints near the low-$B$ end of the high-$B$ regime, and our result provides additional evidence that magnetar-like post-glitch activity is likely more common among high-$B$ RPPs.

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Radio Monitoring Campaign of Active Repeater FRB 20220912A with CHIME

FRB 20220912A is a highly active repeating fast radio burst (FRB) source, discovered by the Canadian Hydrogen Intensity Mapping Experiment (CHIME) using its real-time FRB detection system (CHIME/FRB). Here, we present results from a radio monitoring campaign of FRB 20220912A using CHIME, including ~200 hours of data collected by CHIME/Pulsar, spanning 1.5 years following the source's discovery. We present an analysis of a sample of 828 CHIME-detected bursts from FRB 20220912A, in the 400-800 MHz radio frequency band. The source remains highly active for ~10 weeks and has a bimodal wait-time distribution with peaks at $160^{+120}_{-70}$ ms and $306^{+14}_{-13}$ s. Assuming a radio efficiency factor of $10^{-4}$ and a beaming angle of 0.1, we estimate the total emitted energy from the source over the entire observing campaign to be $2 \times 10^{43}$ ergs. We report a 2.3$\sigma$ detection of a linear increase in the DM of $1.4 \pm 0.6$ pc cm$^{-3}$ yr$^{-1}$, with no significant trend in rotation measure (with a 3$\sigma$ upper limit of 13.4 rad m$^{-2}$ yr$^{-1}$). We contrast our findings with other active repeaters, which exhibit different DM and RM evolution to indicate that FRB 20220912A may reside in a unique local environment.

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Constraining the mass of the M31 ionized baryon Halo using CHIME/FRB Catalog 2

The circumgalactic medium (CGM) surrounding galaxies is believed to be a significant reservoir of baryons, yet its total mass remains poorly constrained. We present a novel approach to probe the CGM of the Andromeda galaxy (M31) using fast radio bursts (FRBs) from the CHIME/FRB Catalog 2. By comparing the dispersion measures (DMs) of 171 FRBs whose sightlines intersect M31's halo (within $r_{\rm vir}= 302\,\mathrm{kpc}$) to a control sample of 684 FRBs, we estimate the DM contribution from M31's CGM. We find evidence for an excess DM of $\delta\mathrm{DM} = 5.9$--$59.6\,\mathrm{pc\,cm^{-3}}$ in the inner halo ($\approx 0$--$151\,\mathrm{kpc}$) and $\delta\mathrm{DM} = 25.7$--$64.6\,\mathrm{pc\,cm^{-3}}$ in the outer halo ($\approx 151$--$302\,\mathrm{kpc}$). Using a generalized halo model parameterized by a closure radius $r_{\mathrm{close}}$, we constrain the baryon distribution and infer a best-fit value for $r_{\mathrm{close}}$ to be $9.2^{+9.9}_{-4.9}\,r_{\rm vir}$ ($1\sigma$), corresponding to a total CGM mass of $M_{b,\mathrm{halo}} = 18.6^{+7.9}_{-8.4} \times 10^{10}\,M_\odot$. Our results suggest that M31 may harbor a substantial fraction of its cosmic baryon budget in diffuse, ionized gas. This work demonstrates the potential of FRBs as a powerful tool for studying the CGM of nearby galaxies, with future larger samples expected to provide tighter constraints on the baryon content of galactic halos.

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A Spatial Gap in the Sky Distribution of Fast Radio Burst Detections Coinciding with Galactic Plasma Overdensities

We analyze the positional and morphological properties of about 3600 unique fast radio burst (FRB) sources reported in the second FRB catalog generated by the Canadian Hydrogen Intensity Mapping Experiment (CHIME) telescope. We find a two-dimensional dependence of FRB detections on sky position, and identify a significant absence of detections in a roughly circular region centered at Galactic coordinates (77.7$^\circ$, 0.9$^\circ$), spanning an area of 213.6 deg$^2$. This detection gap spatially coincides with the Cygnus X region $--$ a plasma-rich star-forming region in the Milky Way. This feature is most likely the result of increased sky temperature and strong multi-path scattering by turbulent ionized plasma, which broadens the FRB signals beyond detectability in the CHIME band. Our simulations yield a mean of 6 expected FRB detections within the gap when accounting for the elevated sky temperature in the direction of the detection gap. We infer that a lower limit of the maximum scattering timescale $\tau_{\rm sc,\, 1\,GHz} \geq 5.59$ ms, obtained without assuming a model of the Galactic electron distribution, is sufficient to suppress the brightness of all coincident FRBs. A similar suppression is seen in Catalog 2 along other high-emission measure (EM) sightlines (i.e., EM$\geq$2900 pc cm$^{-6}$), further supporting a broader trend of suppression due to Galactic scattering. Future very long baseline interferometry (VLBI) measurements of scattering disks with CHIME Outriggers could help confirm our interpretation. Our work highlights the notion that FRBs can serve as new, model-independent tracers of the warm ionized medium within our Milky Way Galaxy.

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CHIME/FRB Discovery of an Unusual Circularly Polarized Long-Period Radio Transient with an Accelerating Spin Period

We report the discovery of CHIME J1634+44, a Long Period Radio Transient (LPT) unique for two aspects: it is the first known LPT to emit fully circularly polarized radio bursts, and it is the first LPT with a significant spin-up. Given that high circular polarization ($>90$\%) has been observed in FRB~20201124A and in some giant pulses of PSR~B1937+21, we discuss the implications of the high circular polarization of CHIME J1634+44 and conclude its emission mechanism is likely to be ``pulsar-like''. While CHIME J1634+44 has a pulse period of 841 s, its burst arrival patterns are indicative of a secondary 4206 s period, probably associated with binary activity. The timing properties suggest it has a significantly negative period derivative of $\dot{P}=-9.03(0.11)\times 10^{-12}$ s s$^{-1}$. Few systems have been known to spin-up, most notably transitional millisecond pulsars and cataclysmic binaries, both of which seem unlikely progenitors for CHIME J1634+44. If the period was only associated with the spin of the object, then the spin up is likely generated by accretion of material from a companion. If, however, the radio pulse period and the orbital period are locked, as appears to be the case for two other LPTs, the spin up of CHIME J1634+44 could be driven by gravitational wave radiation.

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Scintillometry of Fast Radio Bursts: Resolution effects in two-screen models

Fast Radio Bursts (FRBs) exhibit scintillation and scattering, often attributed to interactions with plasma screens in the Milky Way and the host galaxy. When these two screens appear "point-like" to each other, two scales of scintillation can be observed with sufficient frequency resolution. A screen perceives a second screen as extended or resolved when the angular size of the latter is smaller than the angular resolution of the former. We define the ratio of these two as the Resolution Power (RP). Previous observational studies have argued that, in the resolving regime, scintillations disappear, assuming that a screen resolving another screen is equivalent to a screen resolving an incoherent emission region. In this theoretical and simulation-based study of resolving effects in two-screen scenarios, we argue that resolving quenches only the relatively broad-scale scintillation and that this quenching is a gradual process. We present qualitative and quantitative predictions for dynamic spectra, spectral autocorrelation functions (ACF), and modulation indices in resolved and unresolved regimes of two-screen systems. We show that the spectral ACF of a two-screen system has a product term in addition to the sum of individual screen contributions, causing the total modulation index to rise to \sqrt(3) in the unresolved regime. To aid in discovering resolving systems, we also present observable trends in multi-frequency observations of a screen resolving another screen or incoherent emission. Additionally we introduce a new formula to estimate the distance between the FRB and the screen in its host galaxy. We also show that this formula, like previous ones in the literature, is only applicable to screens that are two-dimensional in the plane of the sky.

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CHIME All-sky Multiday Pulsar Stacking Search (CHAMPSS): System Overview and First Discoveries

We describe the CHIME All-sky Multiday Pulsar Stacking Search (CHAMPSS) project. This novel radio pulsar survey revisits the full Northern Sky daily, offering unprecedented opportunity to detect highly intermittent pulsars, as well as faint sources via long-term data stacking. CHAMPSS uses the CHIME/FRB datastream, which consists of 1024 stationary beams streaming intensity data at $0.983$\,ms resolution, 16384 frequency channels across 400--800\,MHz, continuously being searched for single, dispersed bursts/pulses. In CHAMPSS, data from adjacent east-west beams are combined to form a grid of tracking beams, allowing longer exposures at fixed positions. These tracking beams are dedispersed to many trial dispersion measures (DM) to a maximum DM beyond the Milky Way's expected contribution, and Fourier transformed in time to form power spectra. Repeated observations are searched daily to find intermittent sources, and power spectra of the same sky positions are incoherently stacked, increasing sensitivity to faint persistent sources. The $0.983$\,ms time resolution limits our sensitivity to millisecond pulsars; we have full sensitivity to pulsars with $P > 60\,$ms, with sensitivity gradually decreasing from $60$ ms to $2$\,ms as higher harmonics are beyond the Nyquist limit. In a commissioning survey, data covering $\sim 1/16$ of the CHIME sky was processed and searched in quasi-realtime over two months, leading to the discovery of eleven new pulsars, each with $S_{600} > 0.1$\,mJy. When operating at scale, CHAMPSS will stack $>$1\,year of data along each sightline, reaching a sensitivity of $\lesssim 30\, μ$Jy for all sightlines above a declination of $10^{\circ}$, and off of the Galactic plane.

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CHIME/FRB Outriggers: Design Overview

The Canadian Hydrogen Intensity Mapping Experiment (CHIME) has emerged as the world's premier facility for studying fast radio bursts (FRBs) through its fast transient search backend CHIME/FRB\@. The CHIME/FRB Outriggers project will augment this high detection rate of 2--3 FRBs per day with the ability to precisely localize them using very long baseline interferometry (VLBI). Using three strategically located stations in North America and deploying recently developed synoptic VLBI observing techniques, the Outriggers will provide $\sim 50$~milliarcsecond localization precision for the majority of detected FRBs. This paper presents an overview of the design and implementation of the Outriggers, covering their geographic distribution, structural design, and observational capabilities. We detail the scientific objectives driving the project, including the characterization of FRB populations, host galaxy demographics, and the use of FRBs as cosmological probes. We also discuss the calibration strategies available to mitigate ionospheric and instrumental effects, ensuring high-precision localization. With two stations currently in science operations, and the third in commissioning, the CHIME/FRB Outriggers project is poised to become a cornerstone of the FRB field, offering unprecedented insights into this enigmatic cosmic phenomenon.

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Investigating the sightline of a highly scattered FRB through a filamentary structure in the local Universe

Fast radio bursts (FRBs) are unique probes of extragalactic ionized baryonic structure as each signal, through its burst properties, holds information about the ionized matter it encounters along its sightline. FRB 20200723B is a burst with a scattering timescale of $τ_\mathrm{400\,MHz} >$1 second at 400 MHz and a dispersion measure of DM $\sim$ 244 pc cm$^{-3}$. Observed across the entire CHIME/FRB frequency band, it is the single-component burst with the largest scattering timescale yet observed by CHIME/FRB. The combination of its high scattering timescale and relatively low dispersion measure present an uncommon opportunity to use FRB 20200723B to explore the properties of the cosmic web it traversed. With an $\sim$arcminute-scale localization region, we find the most likely host galaxy is NGC 4602 (with PATH probability $P(O|x)=0.985$), which resides $\sim$30 Mpc away within a sheet filamentary structure on the outskirts of the Virgo Cluster. We place an upper limit on the average free electron density of this filamentary structure of $\langle n_e \rangle < 4.6^{+9.6}_{-2.0} \times 10^{-5}$ cm$^{-3}$, broadly consistent with expectations from cosmological simulations. We investigate whether the source of scattering lies within the same galaxy as the FRB, or at a farther distance from an intervening structure along the line of sight. Comparing with Milky Way pulsar observations, we suggest the scattering may originate from within the host galaxy of FRB 20200723B.

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Constraining Near-Simultaneous Radio Emission from Short Gamma-ray Bursts using CHIME/FRB

We use the Canadian Hydrogen Intensity Mapping Experiment (CHIME) Fast Radio Burst (FRB) Project to search for FRBs that are temporally and spatially coincident with gamma-ray bursts (GRBs) occurring between 2018 July 7 and 2023 August 3. We do not find any temporal (within 1 week) and spatial (within overlapping 3 sigma localization regions) coincidences between any CHIME/FRB candidates and all GRBs with 1 sigma localization uncertainties <1 deg. As such, we use CHIME/FRB to constrain the possible FRB-like radio emission for 27 short gamma-ray bursts (SGRBs) that were within 17 deg. of CHIME/FRB's meridian at a point either 6 hrs prior up to 12 hrs after the high-energy emission. Two SGRBs, GRB 210909A and GRB 230208A, were above the horizon at CHIME at the time of their high-energy emission and we place some of the first constraints on simultaneous FRB-like radio emission from SGRBs. While neither of these two SGRBs have known redshifts, we construct a redshift range for each GRB based on their high-energy fluence and a derived SGRB energy distribution. For GRB 210909A, this redshift range corresponds to z = [0.009, 1.64] with a mean of z=0.13. Thus, for GRB 210909A, we constrain the radio luminosity at the time of the high-energy emission to L <2 x 10e46 erg s-1, L < 5 x 10e44 erg s-1, and L < 3 x 10e42 erg s-1 assuming redshifts of z=0.85, z=0.16, and z=0.013, respectively. We compare these constraints with the predicted simultaneous radio luminosities from different compact object merger models.

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A Gaussian-processes approach to fitting for time-variable spherical solar wind in pulsar timing data

Propagation effects are one of the main sources of noise in high-precision pulsar timing. For pulsars below an ecliptic latitude of $5^\circ$, the ionised plasma in the solar wind can introduce dispersive delays of order 100 microseconds around solar conjunction at an observing frequency of 300 MHz. A common approach to mitigate this assumes a spherical solar wind with a time-constant amplitude. However, this has been shown to be insufficient to describe the solar wind. We present a linear, Gaussian-process piecewise Bayesian approach to fit a spherical solar wind of time-variable amplitude, which has been implemented in the pulsar software run_enterprise. Through simulations, we find that the current EPTA+InPTA data combination is not sensitive to such variations; however, solar wind variations will become important in the near future with the addition of new InPTA data and data collected with the low-frequency LOFAR telescope. We also compare our results for different high-precision timing datasets (EPTA+InPTA, PPTA, and LOFAR) of three millisecond pulsars (J0030$+$0451, J1022$+$1001, J2145$-$0450), and find that the solar-wind amplitudes are generally consistent for any individual pulsar, but they can vary from pulsar to pulsar. Finally, we compare our results with those of an independent method on the same LOFAR data of the three millisecond pulsars. We find that differences between the results of the two methods can be mainly attributed to the modelling of dispersion variations in the interstellar medium, rather than the solar wind modelling.

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Morphologies of Bright Complex Fast Radio Bursts with CHIME/FRB Voltage Data

We present the discovery of twelve thus far non-repeating fast radio burst (FRB) sources, detected by the Canadian Hydrogen Intensity Mapping Experiment (CHIME) telescope. These sources were selected from a database comprising of order $10^3$ CHIME/FRB full-array raw voltage data recordings, based on their exceptionally high brightness and complex morphology. Our study examines the time-frequency characteristics of these bursts, including drifting, microstructure, and periodicities. The events in this sample display a variety of unique drifting phenomenologies that deviate from the linear negative drifting phenomenon seen in many repeating FRBs, and motivate a possible new framework for classifying drifting archetypes. Additionally, we detect microstructure features of duration $\lesssim$ 50 $μs$ in seven events, with some as narrow as $\approx$ 7 $μs$. We find no evidence of significant periodicities. Furthermore, we report the polarization characteristics of seven events, including their polarization fractions and Faraday rotation measures (RMs). The observed $|\mathrm{RM}|$ values span a wide range of $17.24(2)$ - $328.06(2) \mathrm{~rad~m}^{-2}$, with linear polarization fractions between $0.340(1)$ - $0.946(3)$. The morphological properties of the bursts in our sample appear broadly consistent with predictions from both relativistic shock and magnetospheric models of FRB emission, as well as propagation through discrete ionized plasma structures. We address these models and discuss how they can be tested using our improved understanding of morphological archetypes.

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Scintillation Arc from FRB 20220912A

We present the interstellar scintillation analysis of fast radio burst (FRB) 20220912A during its extremely active episode in 2022 using data from the Five-hundred-meter Aperture Spherical Radio Telescope (FAST). We detect a scintillation arc in the FRB's secondary spectrum, which describes the power in terms of the scattered FRB signals' time delay and Doppler shift. The arc indicates that the scintillation is caused by a highly localized region of the ionized interstellar medium (IISM). Our analysis favors a Milky Way origin for the localized scattering medium but cannot rule out a host galaxy origin. We present our method for detecting the scintillation arc, which can be applied generally to sources with irregularly spaced bursts or pulses. These methods could help shed light on the complex interstellar environment surrounding the FRBs and in our Galaxy.

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Periodic interstellar scintillation variations of PSRs~J0613$-$0200 and J0636+5128 associated with the Local Bubble shell

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.

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Pulsar Scintillation Studies with LOFAR: II. Dual-frequency scattering study of PSR J0826+2637 with LOFAR and NenuFAR

Interstellar scattering (ISS) of radio pulsar emission can be used as a probe of the ionised interstellar medium (IISM) and causes corruptions in pulsar timing experiments. Two types of ISS phenomena (intensity scintillation and pulse broadening) are caused by electron density fluctuations on small scales (< 0.01 AU). Theory predicts that these are related, and both have been widely employed to study the properties of the IISM. Larger scales ($\sim$1-100\,AU) cause measurable changes in dispersion and these can be correlated with ISS observations to estimate the fluctuation spectrum over a very wide scale range. IISM measurements can often be modeled by a homogeneous power-law spatial spectrum of electron density with the Kolmogorov ($-11/3$) spectral exponent. Here we aim to test the validity of using the Kolmogorov exponent with PSR~J0826+2637. We do so using observations of intensity scintillation, pulse broadening and dispersion variations across a wide fractional bandwidth (20 -- 180\,MHz). We present that the frequency dependence of the intensity scintillation in the high frequency band matches the expectations of a Kolmogorov spectral exponent but the pulse broadening in the low frequency band does not change as rapidly as predicted with this assumption. We show that this behavior is due to an inhomogeneity in the scattering region, specifically that the scattering is dominated by a region of transverse size $\sim$40\,AU. The power spectrum of the electron density, however, maintains the Kolmogorov spectral exponent from spatial scales of 5$\times10^{-6}$\,AU to $\sim$100\,AU.

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Long-term scintillation studies of EPTA pulsars. I. Observations and basic results

Interstellar scintillation analysis of pulsars allows us to probe the small-scale distribution and inhomogeneities of the ionized interstellar medium. Our priority is to present the data set and the basic measurements of scintillation parameters of pulsars employing long-term scintillation observations carried out from 2011 January to 2020 August by the European Pulsar Timing Array radio telescopes in the 21-cm and 11-cm bands. Additionally, we aim to identify future possible lines of study using this long-term scintillation dataset. We present the long-term time series of $ν_{\rm d}$ and $τ_{\rm d}$ for 13 pulsars. Sanity-checks and comparisons indicate that the scintillation parameters of our work and previously published works are mostly consistent. For two pulsars, PSRs~J1857+0943 and J1939+2134, we were able to obtain measurements of the $ν_{\rm d}$ at both bands, which allows us to derive the time series of frequency scaling indices with a mean and a standard deviation of 2.82$\pm$1.95 and 3.18$\pm$0.60, respectively. We found some interesting features which will be studied in more detail in subsequent papers in this series: (i) in the time series of PSR~J1939+2134, where the scintillation bandwidth sharply increases or decreases associated with a sharp change of dispersion measure; (ii) PSR~J0613$-$0200 and PSR~J0636+5126 show a strong annual variation in the time series of the $τ_{\rm d}$; (iii) PSR~J1939+2134 shows a weak anti-correlation between scintillation timescale and dispersion in WSRT data.

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