arXiv subjects

M. Brüggen

Publications and source records attributed to M. Brüggen.

At least 127 records · Page 7Linked to original sources

arXiv2021

A LOFAR-uGMRT spectral index study of distant radio halos

Context. Radio halos are megaparsec-scale diffuse radio sources{ mostly} located at the centres of merging galaxy clusters. The common mechanism invoked to explain their origin is the re-acceleration of relativistic particles caused by large-scale turbulence. Aims. Current re-acceleration models predict that a significant number of halos at high redshift should be characterised by very steep spectra ($α<-1.5$) because of increasing inverse Compton energy losses. In this paper, we investigate the spectral index properties of a sample of nine clusters selected from the second Planck Sunyaev-Zel'dovich catalogue showing diffuse radio emission with the Low Frequency Array (LOFAR) in the 120-168 MHz band. This is the first time that radio halos discovered at low frequencies are followed up at higher frequencies. Methods. We analysed upgraded Giant Metrewave Radio Telescope (uGMRT) observations in Bands 3 and 4, that is, 250-500 and 550-900 MHz respectively. These observations were combined with existing LOFAR data to obtain information on the spectral properties of the diffuse radio emission. Results. We find diffuse radio emission in the uGMRT observations for five of the nine high-$z$ radio halos previously discovered with LOFAR. For those, we measure spectral indices in the range of $-1$ to $-1.4$. For the uGMRT non-detections, we estimated that the halos should have a spectral index steeper than $-1.5$. We also confirm the presence of one candidate relic. Conclusions. Despite the small number of clusters, we find evidence that about half of the massive and merging clusters at high redshift host radio halos with a very steep spectrum. This is in line with theoretical predictions, although larger statistical samples are necessary to test models.

astro-ph.CO↗

arXiv2021

Dissecting nonthermal emission in the complex multiple-merger galaxy cluster Abell 2744: Radio and X-ray analysis

We present the first deep low frequency radio observations of the massive and highly disturbed galaxy cluster Abell 2744 using the upgraded Giant Metrewave Radio Telescope (uGMRT). The cluster is experiencing a very complex multiple merger and hosts a giant halo and four radio relics. The uGMRT observations, together with existing VLA and Chandra observations, allow us to study the complexity of the physical mechanisms active in this system. Our new images reveal that the central halo emission is more extended toward low frequencies. We find that the integrated spectrum of the halo follows a power-law between 150 MHz and 3 GHz, while its subregions show significantly different spectra, also featuring high frequency spectral steepening. The halo also shows local regions in which the spectral index is significantly different from the average value. Our results highlight that an overall power-law spectrum, as observed in many radio halos, may also arise from the superposition of different subcomponents. The comparison of the radio surface brightness and spectral index with the X-ray brightness and temperature reveals for the first time different trends, indicating that the halo consists of two main components. All four relics in this system follow a power-law radio spectrum, compatible with shocks with Mach numbers in the range $3.0-4.5$. All relics are also highly polarized from 1-4 GHz and show low Faraday dispersion measures, suggesting that they are located in the outermost regions of the cluster. The complexity in the distribution and properties of nonthermal components in Abell 2744 supports a multiple merger scenario, as also highlighted by previous X-ray and lensing studies. Our unique results demonstrate the importance of sensitive and high-resolution, multi-frequency radio observations for understanding the interplay between the thermal and non-thermal components of the ICM.

astro-ph.CO↗

arXiv2021

Sub-arcsecond imaging with the International LOFAR Telescope: II. Completion of the LOFAR Long-Baseline Calibrator Survey

The Low-Frequency Array (LOFAR) Long-Baseline Calibrator Survey (LBCS) was conducted between 2014 and 2019 in order to obtain a set of suitable calibrators for the LOFAR array. In this paper we present the complete survey, building on the preliminary analysis published in 2016 which covered approximately half the survey area. The final catalogue consists of 30006 observations of 24713 sources in the northern sky, selected for a combination of high low-frequency radio flux density and flat spectral index using existing surveys (WENSS, NVSS, VLSS, and MSSS). Approximately one calibrator per square degree, suitable for calibration of $\geq$ 200 km baselines is identified by the detection of compact flux density, for declinations north of 30 degrees and away from the Galactic plane, with a considerably lower density south of this point due to relative difficulty in selecting flat-spectrum candidate sources in this area of the sky. Use of the VLBA calibrator list, together with statistical arguments by comparison with flux densities from lower-resolution catalogues, allow us to establish a rough flux density scale for the LBCS observations, so that LBCS statistics can be used to estimate compact flux densities on scales between 300 mas and 2 arcsec, for sources observed in the survey. The LBCS can be used to assess the structures of point sources in lower-resolution surveys, with significant reductions in the degree of coherence in these sources on scales between 2 arcsec and 300 mas. The LBCS survey sources show a greater incidence of compact flux density in quasars than in radio galaxies, consistent with unified schemes of radio sources. Comparison with samples of sources from interplanetary scintillation (IPS) studies with the Murchison Widefield Array (MWA) shows consistent patterns of detection of compact structure in sources observed both interferometrically with LOFAR and using IPS.

astro-ph.GA↗

arXiv2021

Origin of the ring structures in Hercules A -- Sub-arcsecond 144 MHz to 7 GHz observations

The prominent radio source Hercules A features complex structures in its radio lobes. Although it is one of the most comprehensively studied sources in the radio sky, the origin of the ring structures in the Hercules A radio lobes remains an open question. We present the first sub-arcsecond angular resolution images at low frequencies (<300 MHz) of Hercules A, made with the International LOFAR Telescope. With the addition of data from the Karl G. Jansky Very Large Array, we mapped the structure of the lobes from 144 MHz to 7 GHz. We explore the origin of the rings within the lobes of Hercules A, and test whether their properties are best described by a shock model, where shock waves are produced by the jet propagating in the radio lobe, or by an inner-lobe model, where the rings are formed by decelerated jetted plasma. From spectral index mapping our large frequency coverage reveals that the curvature of the different ring spectra increases with distance away from the central active galactic nucleus. We demonstrate that the spectral shape of the rings is consistent with synchrotron aging, which speaks in favor of an inner-lobe model where the rings are formed from the deposition of material from past periods of intermittent core activity.

astro-ph.GA↗

arXiv2021

Morphology of radio relics II: Properties of polarised emission

Radio relics are diffuse radio sources in galaxy clusters that are associated with merger shock waves. Detailed observations of radio relics in total intensity and in polarisation show complex structures on kiloparsec scales. The relation between the observed features and the underlying morphology of the magnetic field is not clear. Using three-dimensional magneto-hydrodynamical simulations, we study the polarised emission produced by a shock wave that propagates through a turbulent medium that resembles the intracluster medium. We model the polarised synchrotron emission on the basis of diffusive shock acceleration of cosmic-ray electrons. We find that the synchrotron emission produced in a shocked turbulent medium can reproduce some of the observed features in radio relics. Shock compression can give rise to a high polarisation fraction at the shock front and a partial alignment of the polarisation $E$-vectors with the shock normal. Our work confirms that radio relics can also be formed in an environment with a tangled magnetic field. We also discuss the effect of Faraday Rotation intrinsic to the source, and how our results depend on the angular resolution of observations.

astro-ph.HE↗

arXiv2021

The eROSITA Final Equatorial-Depth Survey (eFEDS): LOFAR view of brightest cluster galaxies and AGN feedback

During the performance verification phase of the SRG/eROSITA telescope, the eROSITA Final Equatorial-Depth Survey (eFEDS) has been carried out. It covers a 140 deg$^2$ field located at 126$^\circ <$ R.A. $< 146^\circ$ and -3$^\circ <$ Dec. $< +6^\circ$ with a nominal exposure over the field of 2.2 ks. 542 candidate clusters were detected in this field, down to a flux limit $F_X \sim 10^{-14}$ erg s$^{-1}$ cm$^{-2}$ in the 0.5-2 keV band. In order to understand radio-mode feedback in galaxy clusters, we study the radio emission of brightest cluster galaxies of eFEDS clusters, and we relate it to the X-ray properties of the host cluster. Using LOFAR we identify 227 radio galaxies hosted in the BCGs of the 542 galaxy clusters and groups detected in eFEDS. We treat non-detections as radio upper limits. We analyse the properties of radio galaxies, such as redshift and luminosity distribution, offset from the cluster centre, largest linear size and radio power. We study their relation to the intracluster medium of the host cluster. We perform statistical tests to deal with upper limits on the radio luminosities. BCGs with radio-loud AGN are more likely to lie close to the cluster centre than radio-quiet BCGs. There is a clear relation between the cluster's X-ray luminosity and the radio power of the BCG. Statistical tests indicate that this correlation is not produced by selection effects in the radio band. We see no apparent link between largest linear size of the radio galaxy and central density of the host cluster. Converting the radio luminosity to kinetic luminosity, we find that radiative losses of the intracluster medium are in an overall balance with the heating provided by the central AGN. Finally, we tentatively classify our objects into disturbed and relaxed, and we show that the link between the AGN and the ICM apparently holds regardless of the dynamical state of the cluster.

astro-ph.CO↗

arXiv2021

Abell 1430: A merging cluster with exceptional diffuse radio emission

Diffuse radio emission has been found in many galaxy clusters, predominantly in massive systems which are in the state of merging. The radio emission can usually be classified as relic or halo emission, which are believed to be related to merger shocks or volume-filling turbulence, respectively. Recent observations have revealed radio bridges for some pairs of very closeby galaxy clusters. The mechanisms that may allow to explain the high specific density of relativistic electrons, necessary to explain the radio luminosity of these bridge regions, are poorly explored. We analyse the galaxy cluster Abell 1430 with LoTSS data in detail and complement it with recent JVLA L-band observations, XMM-Newton, Chandra, and SDSS data. Moreover, we compare our results to clusters extracted from the "The Three Hundred Project" cosmological simulation. We find that Abell 1430 consists of two components, namely A1430-A and A1430-B. We speculate that the two components undergo an off-axis merger. The more massive component shows diffuse radio emission which can be classified as radio halo showing a low radio power given the mass of the cluster. Most interestingly, there is extended diffuse radio emission, dubbed as the `Pillow', which is apparently related to A1430-B and thus related to low density intracluster or intergalactic medium. To date, a only few examples for emission originating from such regions are known. These discoveries are crucial to constrain possible acceleration mechanisms, which may allow to explain the presence of relativistic electrons in these regions. Our results indicate a spectral index of $α_{144\,\text{MHz}}^{1.5\,\text{GHz}}=-1.4\pm0.5$ for the Pillow. If future observations confirm a slope as flat as the central value of -1.4 or even flatter, this would pose a severe challenge for the electron acceleration scenarios.

astro-ph.CO↗

arXiv2021

Simulating the transport of relativistic electrons and magnetic fields injected by radio galaxies in the intracluster medium

Radio galaxies play an important role in the seeding of cosmic rays and magnetic fields in galaxy clusters. Here, we simulate the evolution of relativistic electrons injected into the intracluster medium by radio galaxies. Using passive tracer particles added to magnetohydrodynamical adaptive-mesh simulations, we calculate the evolution of the spectrum of relativistic electrons taking into account energy losses and re-acceleration mechanisms associated with the dynamics of the intracluster medium. Re-acceleration can occur at shocks via diffusive shock acceleration, and in turbulent flows via second-order Fermi re-acceleration. This study confirms that relativistic electrons from radio galaxies can efficiently fill the intracluster medium over scales of several $100 \rm ~Myr$, and that they create a stable reservoir of fossil electrons that remains available for further re-acceleration by shock waves and turbulent gas motions. Our results also show that late evolution of radio lobes and remnant radio galaxies is significantly affected by the dynamics of the surrounding intracluster medium. Here the diffusive re-acceleration couples the evolution of relativistic particles to the gas perturbations. In the near future, deep radio observations, especially at low frequencies, can probe such mechanisms in galaxy clusters.

astro-ph.HE↗

arXiv2021

Discovery of a radio halo (and relic) in a $M_{500} < 2 \times 10^{14}$ M$_\odot$ cluster

Radio halos are diffuse synchrotron sources observed in dynamically unrelaxed galaxy clusters. Current observations and models suggest that halos trace turbulent regions in the intra-cluster medium where mildly relativistic particles are re-accelerated during cluster mergers. Due to the higher luminosities and detection rates with increasing cluster mass, radio halos have been mainly observed in massive systems ($M_{500} \gtrsim 5 \times10^{14}$ M$_\odot$). Here, we report the discovery of a radio halo with a largest linear scale of $\simeq$750 kpc in PSZ2G145.92-12.53 ($z=0.03$) using LOFAR observations at 120$-$168 MHz. With a mass of $M_{500} = (1.9\pm0.2) \times 10^{14}$ M$_\odot$ and a radio power at 150 MHz of $P_{150} = (3.5 \pm 0.7) \times 10^{23}$ W/Hz, this is the least powerful radio halo in the least massive cluster discovered to date. Additionally, we discover a radio relic with a mildly convex morphology at $\sim$1.7 Mpc from the cluster center. Our results demonstrate that LOFAR has the potential to detect radio halos even in low-mass clusters, where the expectation to form them is very low ($\sim$5%) based on turbulent re-acceleration models. Together with the observation of large samples of clusters, this opens the possibility to constrain the low end of the power-mass relation of radio halos.

astro-ph.CO↗

arXiv2021

Radio relics in PSZ2 G096.88+24.18: A connection with pre-existing plasma

Giant radio relics are arc-like structures of diffuse, non-thermal synchrotron radiation that trace shock waves induced by galaxy cluster mergers. The particle (re-)acceleration mechanism producing such radio relics is unclear. One major open question is whether relics can be formed directly from a population of thermal seed electrons, or if pre-existing relativistic seed electrons are required. In some cases AGN can provide such a population of sub-GeV electrons. However, it is unclear how common this connection is. In this paper we present LOFAR 140 MHz and VLA L-band radio observations, as well as Chandra data of PSZ2 G096.88+24.18, a merging galaxy cluster system hosting a pair of radio relics. A large patch of diffuse emission connects a bright radio galaxy with one of the relics, likely affecting the properties of the relic. We find that the most plausible explanation for the connection is that the merger shock wave has passed over an AGN lobe. The shock passing over this seed population of electrons has led to an increased brightness in the relic only in the region filled with seed electrons.

astro-ph.HE↗

arXiv2021

Radio galaxies in galaxy groups: kinematics, scaling relations and AGN feedback

We investigate the kinematic properties of a large (N=998) sample of COSMOS spectroscopic galaxy members distributed among 79 groups. We identify the Brightest Group Galaxies (BGGs) and cross-match our data with the VLA-COSMOS Deep survey at 1.4 GHz, classifying our parent sample into radio/non-radio BGGs and radio/non-radio satellites. The radio luminosity distribution spans from $L_R\sim2\times10^{21}$ W Hz$^{-1}$ to $L_R\sim3\times$10$^{25}$ W Hz$^{-1}$. A phase-space analysis, performed by comparing the velocity ratio (line-of-sight velocity divided by the group velocity dispersion) with the galaxy-group centre offset, reveals that BGGs (radio and non-radio) are mostly ($\sim$80\%) ancient infallers. Furthermore, the strongest ($L_R>10^{23}$ W Hz$^{-1}$) radio galaxies are always found within 0.2$R_{\rm vir}$ from the group centre. Comparing our samples with HORIZON-AGN, we find that the velocities and offsets of simulated galaxies are more similar to radio BGGs than to non-radio BGGs, albeit statistical tests still highlight significant differences between simulated and real objects. We find that radio BGGs are more likely to be hosted in high-mass groups. Finally, we observe correlations between the powers of BGG radio galaxies and the X-ray temperatures, $T_{\rm x}$, and X-ray luminosities, $L_{\rm x}$, of the host groups. This supports the existence of a link between the intragroup medium and the central radio source. The occurrence of powerful radio galaxies at group centres can be explained by Chaotic Cold Accretion, as the AGN can feed from both the galactic and intragroup condensation, leading to the observed positive $L_{\rm R}-T_{\rm x}$ correlation.

astro-ph.GA↗

arXiv2021

Nonthermal phenomena in the center of Abell 1775: An 800 kpc head-tail, revived fossil plasma and slingshot radio halo

Thermal gas in the center of galaxy clusters can show substantial motions that generate surface-brightness and temperature discontinuities known as cold fronts. The motions may be triggered by minor or off-axis mergers that preserve the cool core of the system. The dynamics of the thermal gas can also generate radio emission from the intra-cluster medium (ICM) and impact the evolution of clusters' radio sources. We aim to study the central region of Abell 1775, a system in an ambiguous dynamical state at $z=0.072$ which is known to host an extended head-tail radio galaxy, with the goal of investigating the connection between thermal and nonthermal components in its center. We made use of a deep (100 ks) Chandra observation accompanied by LOFAR 144 MHz, GMRT 235 MHz and 610 MHz, and VLA 1.4 GHz radio data. We find a spiral-like pattern in the X-ray surface brightness that is mirrored in the temperature and pseudo-entropy maps. Additionally, we characterize an arc-shaped cold front in the ICM. We interpret these features in the context of a slingshot gas tail scenario. The structure of the head-tail radio galaxy "breaks" at the position of the cold front, showing an extension that is detected only at low frequencies, likely due to its steep and curved spectrum. We speculate that particle reacceleration is occurring in the outer region of this tail, which in total covers a projected size of $\sim800$ kpc. We also report the discovery of revived fossil plasma with ultra-steep spectrum radio emission in the cluster core together with a central diffuse radio source that is bounded by the arc-shaped cold front. The results reported in this work demonstrate the interplay between thermal and nonthermal components in the cluster center and the presence of ongoing particle reacceleration in the ICM on different scales.

astro-ph.CO↗

arXiv2021

Storage Rings and Gravitational Waves: Summary and Outlook

We report some highlights from the ARIES APEC workshop on ``Storage Rings and Gravitational Waves'' (SRGW2021), held in virtual space from 2 February to 18 March 2021, and sketch a tentative landscape for using accelerators and associated technologies for the detection or generation of gravitational waves.

physics.acc-ph↗

arXiv2021

The LOFAR and JVLA view of the distant steep spectrum radio halo in MACS J1149.5+2223

Radio halos and relics are Mpc-scale diffuse radio sources in galaxy clusters, with a steep spectral index $α>1$ ($S\propto ν^{-α}$). It has been proposed that they arise from particle acceleration induced by turbulence and weak shocks, injected in the intracluster medium (ICM) during mergers. MACS J1149.5+2223 (MACS J1149) is a high redshift ($z=0.544$) galaxy cluster possibly hosting a radio halo and a relic. We analysed LOFAR, GMRT, and JVLA radio data at 144, 323, 1500 MHz, and Chandra X-ray data to characterise the thermal and non-thermal properties of the cluster. We obtained radio images at different frequencies to investigate the spectral properties of the radio halo. We used Chandra X-ray images to constrain the thermal properties of the cluster. We measured a steep spectrum of the halo, with $α=1.49\pm 0.12$ between 144 and 1500 MHz. The radio surface brightness distribution across the halo is found to correlate with the X-ray brightness of the ICM, with a sub-linear slope in the range 0.4 to 0.6. We also report two possible cold fronts in north-east and north-west, but deeper X-ray observations are required to firmly constrain the properties of the upstream emission. We show that the combination of high redshift, steep radio spectrum, and sub-linear radio-X scaling of the halo rules out hadronic models. An old ($\sim 1 $ Gyr ago) major merger likely induced the formation of the halo through stochastic re-acceleration of relativistic electrons. We suggest that the two possible X-ray discontinuities may actually be part of the same cold front. In this case, the coolest gas pushed towards the north-west might be associated with the cool core of a sub-cluster involved in the major merger. The peculiar orientation of the south-east relic might indicate a different nature of this source and requires further investigation.

astro-ph.CO↗

arXiv2021

Downstream depolarization in the Sausage relic: a 1-4 GHz Very Large Array study

Radio relics are elongated sources related to shocks driven by galaxy cluster merger events. Although these objects are highly polarized at GHz frequencies ($\gtrsim 20\%$), high-resolution studies of their polarization properties are still lacking. We present the first high-resolution and high-sensitivity polarimetry study of the merging galaxy cluster CIZA J2242.8+5301 in the 1-4 GHz frequency band. We use the $QU$-fitting approach to model the Stokes $I$, $Q$ and $U$ emission, obtaining best-fit intrinsic polarization fraction ($p_0$), intrinsic polarization angle ($χ_0$), Rotation Measure (RM) and wavelength-dependent depolarization ($σ_{\rm RM}$) maps of the cluster. Our analysis focuses on the northern relic (RN). For the first time in a radio relic, we observe a decreasing polarization fraction in the downstream region. Our findings are possibly explained by geometrical projections and/or by decreasing of the magnetic field anisotropy towards the cluster center. From the amount of depolarization of the only detected background radio galaxy, we estimate a turbulent magnetic field strength of $B_{\rm turb}\sim5.6~μ$Gauss in the relic. Finally, we observe Rotation Measure fluctuations of about 30 rad m$^{-2}$ around at the median value of 140.8 rad m$^{-2}$ at the relic position.

astro-ph.GA↗

arXiv2021

The intra-cluster magnetic field in the double relic galaxy cluster Abell 2345

Magnetic fields are ubiquitous in galaxy clusters, yet their radial profile, power spectrum, and connection to host cluster properties are poorly known. Merging galaxy clusters hosting diffuse polarized emission in the form of radio relics offer a unique possibility to study the magnetic fields in these complex systems. In this paper, we investigate the intra-cluster magnetic field in Abell 2345. This cluster hosts two radio relics that we detected in polarization with 1-2 GHz JVLA observations. X-ray XMM-Newton images show a very disturbed morphology. We derived the Rotation Measure (RM) of five polarized sources within $\sim$ 1 Mpc from the cluster center applying the RM synthesis. Both, the average RM and the RM dispersion radial profiles probe the presence of intra-cluster magnetic fields. Using the thermal electron density profile derived from X-ray analysis and simulating a 3D magnetic field with fluctuations following a power spectrum derived from magneto-hydrodynamical cosmological simulations, we build mock RM images of the cluster. We constrained the magnetic field profile in the eastern radio relic sector by comparing simulated and observed RM images. We find that, within the framework of our model, the data require a magnetic field scaling with thermal electron density as $B(r)\propto n_e(r)$. The best model has a central magnetic field (within a 200 kpc radius) of $2.8\pm0.1$ $μ$G. The average magnetic field at the position of the eastern relic is $\sim$0.3 $μ$G, a factor 2.7 lower than the equipartition estimate.

astro-ph.GA↗

arXiv2020

Physical insights from the spectrum of the radio halo in MACS J0717.5+3745

We present new LOFAR observations of the massive merging galaxy cluster MACS J0717.5+3745. The cluster hosts the most powerful radio halo known to date. These new observations, in combination with published uGMRT (300$-$850 MHz) and VLA (1$-$6.5 GHz) data, reveal that the halo is more extended than previously thought, with a largest linear size of $\sim2.2 \rm Mpc$. The halo shows a steep spectrum ($α_{144\,\text{MHz}}^{1.5\,\text{GHz}}\sim-1.4$) and a steepening ($α_{1.5 \text{GHz}}^{5.5 \text{GHz}}\sim-1.9$) above 1.5 GHz. We find a strong scattering in spectral index maps on scales of 50$-$100 kpc. We suggest that such a strong scattering may be a consequence of the regime where inverse Compton dominate the energy losses of electrons. The spectral index becomes steeper and shows an increased curvature in the outermost regions of the halo. We combined the radio data with \textit{Chandra} observations to investigate the connection between the thermal and non-thermal components of the intracluster medium (ICM). Despite a significant substructure in the halo emission, the radio brightness correlates strongly with the X-ray brightness at all observed frequencies. The radio-versus-X-ray brightness correlation slope steepens at a higher radio frequency (from $b_{144 \text{MHz}}=0.67\pm0.05$ to $b_{3.0 \text{GHz}}=0.98\pm0.09$) and the spectral index shows a significant anti correlation with the X-ray brightness. Both pieces of evidence further support a spectral steepening in the external regions. The compelling evidence for a steep spectral index, the existence of a spectral break above 1.5 GHz, and the dependence of radio and X-ray surface brightness correlation on frequency are interpreted in the context of turbulent reacceleration models. Under this scenario, our results allowed us to constrain that the turbulent kinetic pressure of the ICM is up to 10%.

astro-ph.GA↗

arXiv2020

The impact of Solar wind variability on pulsar timing

High-precision pulsar timing requires accurate corrections for dispersive delays of radio waves, parametrized by the dispersion measure (DM), particularly if these delays are variable in time. In a previous paper we studied the Solar-wind (SW) models used in pulsar timing to mitigate the excess of DM annually induced by the SW, and found these to be insufficient for high-precision pulsar timing. Here we analyze additional pulsar datasets to further investigate which aspects of the SW models currently used in pulsar timing can be readily improved, and at what levels of timing precision SW mitigation is possible. Our goals are to verify: a) whether the data are better described by a spherical model of the SW with a time-variable amplitude rather than a time-invariant one as suggested in literature, b) whether a temporal trend of such a model's amplitudes can be detected. We use the pulsar-timing technique on low-frequency pulsar observations to estimate the DM and quantify how this value changes as the Earth moves around the Sun. Specifically, we monitor the DM in weekly to monthly observations of 14 pulsars taken with LOFAR across time spans of up to 6 years. We develop an informed algorithm to separate the interstellar variations in DM from those caused by the SW and demonstrate the functionality of this algorithm with extensive simulations. Assuming a spherically symmetric model for the SW density, we derive the amplitude of this model for each year of observations. We show that a spherical model with time-variable amplitude models the observations better than a spherical model with constant amplitude, but that both approaches leave significant SW induced delays uncorrected in a number of pulsars in the sample. The amplitude of the spherical model is found to be variable in time, as opposed to what has been previously suggested.

astro-ph.HE↗