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Ralf-Jürgen Dettmar

Publications and source records attributed to Ralf-Jürgen Dettmar.

At least 19 recordsLinked to original sources

Probing the magnetic field of a coronal mass ejection with PSR J1022+1001

We investigate whether low-frequency pulsar observations can provide LoS magnetic field estimates and whether these are consistent with synthetic LoS signatures extracted from a three-dimensional CME reconstruction constrained by Solar Orbiter data. We analyze a CME occultation of the LoS to PSR J1022+1001 on 20 August 2021 at a projected heliocentric distance of 24.6 R_sun, observed simultaneously with LOFAR and NenuFAR. From LOFAR, we derive time-resolved dispersion measure (DM) and rotation measure (RM) and isolate the CME contributions using background estimates for interstellar, solar wind and ionospheric components. We then infer the density-weighted LoS-averaged magnetic field component _PSR from the ratio delta-RM/delta-DM. In parallel, we reconstruct the CME using a semi-empirical 3DCORE model fitted to Solar Orbiter in-situ magnetic field observations at 0.65 au. We sample the modeled magnetic field along the pulsar LoS using fixed spatial sampling points and compute synthetic LoS-averaged signatures _3D for different flux rope configurations. The derived _PSR increases from approximately -9 nT to a peak near 63 nT during the observed interval. Comparison with synthetic signatures shows that the polarity and temporal evolution of the LoS signal are strongly dependent on the flux rope configuration and only a South-West-North (SWN) configuration (confirmed by Solar Orbiter in-situ data) reproduces the observed sign and overall evolution, whereas alternative configurations are incompatible. The modeled amplitudes, however, are systematically larger than the pulsar-derived values by roughly a factor of five. We show that simultaneous low-frequency pulsar DM and RM measurements can provide LoS magnetic field estimates for a CME and can be used to test CME magnetic structure against data-constrained three-dimensional reconstructions.

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Probing Variations in Earth's Ionosphere Using Pulsars

We present high cadence 10-minute rotation measure (RM) monitoring of PSR~J0814+7429 using the LOw-Frequency ARray, aiming to probe ionospheric variability along the pulsar line of sight (LoS). By separating the ionospheric contribution from the observed RM, we quantitatively reconstruct the diurnal variation of the ionospheric electron density along the pulsar LoS based on the World Magnetic Model. The derived variations exhibit clear solar-driven modulation, including the ionospheric noontime bite-out phenomenon, and show good agreement with the LoS total electron content reconstructed from independent global vertical total electron content maps. These results demonstrate the feasibility of using pulsars as probes of temporal variations in the electron density of the Earth's ionosphere.

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Probing Magnetic Fields In and Around Galaxies Near and Far

In order to understand the magnetization of galaxies and the role of magnetic fields in feedback processes that govern star formation and galaxy evolution, it is essential to have a comprehensive census of magnetic fields in and around galaxies from the nearby Universe to high redshifts. In this chapter, we outline the science goals, strategies, techniques, and observational requirements with SKA AA4 for (1) a homogeneous polarimetric survey of nearby galaxies - mapping both the diffuse polarized emission as well as producing a dense RM grid within the virial radius; (2) a survey of the interstellar magnetic fields in distant galaxies targeting strong lensing systems with polarized lensed quasars, as well as a general statistical back-illumination survey to probe the redshift evolution of magnetic fields in the CGM. These proposed observations will serve as a major step towards understanding the co-evolution of galaxies and their magnetic fields over cosmic time and provide constraints on galactic dynamo theories.

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Pulsar scintillation studies with LOFAR III. Annual variations in PSR~J0814$+$7429

The interstellar scintillation observed in radio pulsars arises from interference between electromagnetic waves scattered by electron density fluctuations in the turbulent interstellar plasma, providing a critical tool for probing the small-scale structure of the ionized interstellar medium and the pulsar system itself. The primary aim of this work is to study long-term scintillation variations for a bright and nearby pulsar, PSR J0814$+$7429, carried out from 2013 September to 2023 September with the LOw-Frequency ARray (LOFAR) High Band Antennae in the frequency range of 120 - 170 MHz. We derive the basic scintillation parameters, scintillation bandwidth ($Δν_{\rm d}$) and scintillation timescale ($Δτ_{\rm d}$), from the two-dimensional (2D) auto-covariance function of the dynamic spectra that are a 2D matrix of pulse intensity as a function of time and frequency. We present the long-term monitoring of $Δν_{\rm d}$ and $Δτ_{\rm d}$ for PSR J0814$+7429$, which shows a strong annual variation in the time series of the $Δτ_{\rm d}$. From our modeling of the annual variations of scintillation velocities, the scattering screen is anisotropic and located at $0.23\pm0.02$ kpc from the Earth, likely corresponding to the boundary of the Local Bubble.

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CHANG-ES. XXXVIII. A Thin Radio Halo Shaped by Slow Cosmic-Ray Transport in the Quiescent Galaxy NGC 4565

We present the VLA C-array S-band (2--4 GHz) radio continuum observations of the nearby edge-on spiral galaxy NGC 4565, a target from the Continuum Halos in Nearby Galaxies - an EVLA (CHANG-ES) Survey. We conduct rotation measure synthesis to probe the magnetic field structure and analyze the vertical radio continuum intensity profiles using the 1-D cosmic ray transportation models. The radio continuum emission of NGC 4565 is vertically compact, with a vertical-to-radial extent ratio of $\sim 1/6$. Its vertical profile is optimally described by a two-component Gaussian distribution, yielding a mean Gaussian halo scale height of $\sim 3.0$ kpc. The magnetic field is weak, predominantly disk-parallel, with an equipartition strength of $\lesssim 5\ μ$G and a rotation measure profile indicative of an axisymmetric spiral structure. Nevertheless, we identify a localized, faint vertical magnetic field component in the northeastern region, hinting at an X-shaped structure that spatially coincides with extraplanar structures detected in H I and soft X-ray emission. The CR transport modeling favors a flux-tube advection scenario, with a slow initial velocity of $v_0 \approx 60$ km s$^{-1}$, consistent with a limited energy input from star formation. Therefore, the absence of an extended radio halo can be explained by the low star formation rate, the weak magnetic field, and the inefficient CR transport. The localized X-shaped field may trace a weak, magnetically guided outflow or a tidal perturbation induced by the nearby companion. NGC 4565 is thus a key quiescent benchmark for understanding the physical conditions required to drive large-scale outflows and generate extended radio halos.

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MEDUSA I. Tracing magnetic field structures in tidal arms of the dwarf-dwarf merger NGC 1487

Dwarf galaxies are important laboratories for studying cosmic magnetism because they can maintain strong magnetic fields via the action of turbulent dynamo despite their low mass and weak gravitational potential. The Magnetic-field Evolution in Dwarf galaxies from Ultra-deep SKA Analysis (MEDUSA) survey is the first SKA-pathfinder programme designed to obtain deep continuum, polarisation, and HI data for dwarf galaxies, enabling a comprehensive study of their radio spectra, magnetic fields, and gas kinematics across a representative population. By analysing the radio continuum spectra and polarisation of the dwarf-dwarf galaxy merger NGC 1487 from the MEDUSA sample, we aim to determine its magnetic field strength and to characterise the large-scale and turbulent components of its magnetic field. We utilise highly sensitive multi-band radio continuum data from MeerKAT L-band (1.28 GHz) and Australia Telescope Compact Array (ATCA) L/S (2.1 GHz), C (5.5 GHz), and X-bands (9 GHz). We analysed the magnetic field configuration using polarisation and rotation measure (RM) synthesis. The integrated spectral energy distribution has a non-thermal spectral index of $α_{\rm nth} = -0.678\pm0.085$. Synchrotron and inverse Compton losses cause a spectral break at $ν_{\rm b} = 6.2\pm1.3$ GHz. In star-forming regions, the magnetic field exhibits strong small-scale fluctuations in RM, suggesting the action of a small-scale dynamo. Conversely, the field becomes more ordered, aligning with the tidal arms toward the galaxy's outskirts, showing a large-scale magnetic field over $\approx3$ kpc. Observations of the dwarf-dwarf merger NGC 1487 show that even low-mass galaxy mergers, likely the building blocks of larger galaxies in the early Universe, can rapidly amplify and produce coherent large-scale magnetic field structures, highlighting their key contribution in the early magnetisation of galaxies.

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Magnetic fields in planetary nebulae detected through non-thermal radio continuum emission

Context. Planetary nebulae are shells ejected by low- and intermediate-mass stars. The slow wind ejected by the asymptotic giant branch star is compressed by a fast stellar wind to produce an expanding gaseous shell surrounding a hot bubble. The shell is a source of thermal radio emission which shows a spectral index between -0.1 and 2. Only two planetary nebulae are known to show non-thermal radio emission indicating magnetic fields and non-thermal electrons. Aims. The aim of this paper is verification of presence of magnetic fields of planetary nebulae. Magnetic fields can have a significant influence on shaping planetary nebulae. Methods. We observed a sample of northern planetary nebulae in radio continuum at 144 MHz with the Low Frequency Array. We combined our observations with archival observations at higher frequencies. Results. The spectral indices in 30 planetary nebulae were below -0.1, indicating non-thermal radio emission. The majority of this sample consists of bipolar planetary nebulae, which are known to originate from binary central stars. Most of the nebulae have sizes larger than 20 arcsec. Magnetic fields and nonthermal emission may be common in smaller planetary nebulae, but can be suppressed by thermal emission. Our results suggest that different mechanisms can be responsible for the origin of magnetic fields and non-thermal emission in planetary nebulae.

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CHILLING: Continuum Halos in LVHIS Local Irregular Nearby Galaxies - Radio continuum spectral behavior of dwarf galaxies

Dwarf galaxies, due to their shallow gravitational potentials, provide critical environments for studying feedback mechanisms from star formation and its impacts on dwarf galaxy evolution. In particular, radio continuum (RC) observations offer valuable insights into cosmic ray dynamics, which play a significant role in shaping these processes. This study investigates the detectability and spectral characteristics of RC emission in a sample of 15 dwarf galaxies (11 gas-rich, star forming dwarfs and 4 blue compact dwarfs) spanning a broad range of stellar masses and star formation histories. Using multi-band RC data (L/S-, C-, and X-band) from the Australia Telescope Compact Array, we analyse the physical conditions responsible for RC emission and explore the dominant emission mechanisms within these systems. RC emission is detected in 11 out of the 15 galaxies. Our results indicate that RC emission correlates strongly with star formation rate, far-infrared, and stellar mass, while dynamic parameters such as HI and rotational velocity exhibit no significant correlation with RC detectability. Spectral analysis reveals that the RC spectral energy distribution in these galaxies frequently deviate from a simple power-law behavior, instead displaying curvature that suggests more complex underlying physical processes. Statistical model comparison confirms that a single power-law model is inadequate to capture the observed spectral shapes, emphasising the necessity of more sophisticated approaches. Additionally, the observed radio-far-infrared correlation indicates that cosmic ray electrons in lower-mass dwarf galaxies cool more rapidly than they can escape (e.g. via galactic winds), resulting in a measurable RC deficit.

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Exploring magnetised galactic outflows in starburst dwarf galaxies NGC 3125 and IC 4662

The study of radio emission in starburst dwarf galaxies provides a unique opportunity to investigate the mechanisms responsible for the amplification and transport of magnetic fields. Local dwarfs are often considered proxies for early-Universe galaxies, so this study may provide insights into the role of non-thermal components in the formation and evolution of larger galaxies. By investigating the radio continuum spectra and maps of the starburst dwarf galaxies, we aim to draw conclusions on their magnetic field strengths and configurations, as well as the dynamics of cosmic ray (CR) transport. We perform a radio continuum polarimetry study of two of the brightest starburst IRAS Revised Bright Galaxy Sample (RBGS) dwarf galaxies, NGC 3125 and IC 4662. By combining data of the Australian Telescope Compact Array (2.1 GHz) and MeerKAT (1.28 GHz), we analyse the underlying emission mechanism and the CR transport in these systems. We find flat spectra in those dwarf galaxies over the entire investigated frequency range, which sharply contrasts with observations of massive spiral galaxies. Because the expected cooling time of CR electrons is much shorter than their escape time, we would expect a steepened steady-state CR electron spectrum. The flat observed spectra suggest a substantial contribution from free-free emission at high frequencies and absorption at low frequencies, which may solve this puzzle. For NGC 3125, we measure a degree of polarisation between 0.75% and 2.6%, implying a turbulent field and supporting the picture of a comparably large thermal emission component that could be sourced by stellar radiation feedback and supernovae.

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Uncovering Extraplanar Gas in UGCA 250 with the Ultra-deep MHONGOOSE Survey

We use the neutral atomic hydrogen (HI) observations of the edge-on galaxy UGCA 250, taken as part of the MeerKAT HI Observations of Nearby Galactic Objects - Observing Southern Emitters (MHONGOOSE) survey to investigate the amount, morphology, and kinematics of extraplanar gas. The combination of high column density sensitivity and high spatial resolution of the survey over a large field of view is ideal for studying the underlying physics governing the extraplanar gas. These data reveal 9 additional detections within the field of view along with UGCA 250, with 8 of them being within $\sim$ 200 km s$^{-1}$ of the galaxy's systemic velocity. The galaxy seems to have a tail-like feature extending away from it in the southern direction up to $\sim$ 41 kpc (in projection). We also detect a cloud at anomalous velocities, but we did not find any optical counterpart. We construct a detailed tilted ring model for this edge-on galaxy to gain a deeper understanding of the vertical structure of its neutral hydrogen. The model that best matches the data features a thick disc with a scale height of $\sim$ 3$\pm$1 kpc and an HI mass of about 15$\%$ of the total HI mass. This extraplanar gas is detected for the first time in UGCA 250. Our analysis favours a mixed origin for the extraplanar gas in UGCA 250, likely arising from a combination of internal stellar feedback and external tidal interactions.

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Two 100 TeV neutrinos coincident with the Seyfert galaxy NGC 7469

In 2013, the IceCube collaboration announced the detection of a diffuse high-energy astrophysical neutrino flux. The origin of this flux is still largely unknown. The most significant individual source is the close-by Seyfert galaxy NGC 1068 at 4.2-sigma level with a soft spectral index. To identify sources based on their counterpart, IceCube releases realtime alerts corresponding to neutrinos with a high probability of astrophysical origin. We report here the spatial coincidence of two neutrino alerts, IC220424A and IC230416A, with the Seyfert galaxy NGC 7469 at a distance of 70 Mpc. We evaluate, a-posteriori, the chance probability of such a coincidence and discuss this source as a potential neutrino emitter based on its multi-wavelength properties and in comparison to NGC 1068 by performing a Goodness-of-Fit test. The test statistic is derived from a likelihood ratio that includes the neutrino angular uncertainty and the source distance. We apply this test first to a catalog of AGN sources and second to a catalog of Seyfert galaxies only. Our a-posteriori evaluation excludes the possibility of an accidental spatial coincidence of both neutrinos with the Seyfert galaxy NGC 7469 at 3.2-sigma level, leaving open the possibility that either one or both neutrinos originated from the source. To be compatible with non-detections of TeV neutrinos, the source would need to have a hard spectral index.

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CHANG-ES XXXV: Cosmic Ray Transport and Magnetic Field Structure of NGC 3556 at 3 GHz

Radio halos of edge-on galaxies are crucial for investigating cosmic ray propagation and magnetic field structures in galactic environments. We present VLA C-configuration S-band (2--4 GHz) observations of the spiral galaxy NGC 3556, a target from the Continuum Halos in Nearby Galaxies - an EVLA Survey (CHANG-ES). We estimate the thermal contribution to the radio emission from a combination of the H$α$ and mid-IR data, and employ Rotation Measure Synthesis to reveal the magnetic field structures. In our data, NGC 3556 exhibits a box-like radio halo extending nearly 7 kpc from the galactic plane. The scale height of the total S-band intensity in the halo is $1.68\pm 0.29$ kpc, while that of the non-thermal intensity is $1.93\pm 0.28$ kpc. Fitting the data to a 1-D cosmic-ray transport model, we find advection to describe the cosmic-ray propagation within the halo better than diffusion, with advection speeds of $245 \pm 15$ km s$^{-1}$ and $205 \pm 25$ km s$^{-1}$ above and below the disk, respectively. The magnetic field is detected patchily across the galaxy, displaying a toroidal configuration in the rotation measure map. The mean equipartition magnetic field strength is approximately $8.3\ μ$G in the disk and $4.5\ μ$G in the halo. In addition, a bubble-like structure extends nearly 3~kpc into the southern halo, aligned with the polarized intensity and H$α$ image, suggestive of superwinds generated by recent star formation feedback in the nuclear region.

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eDIG-CHANGES III: the lagging eDIG revealed by multi-slit spectroscopy of NGC 891

The kinematic information of the extraplanar diffuse ionized gas (eDIG) around galaxies provides clues to the origin of the gas. The eDIG-CHANGES project studies the physical and kinematic properties of the eDIG around the CHANG-ES sample of nearby edge-on disk galaxies. We use a novel multi-slit narrow-band spectroscopy technique to obtain the spatial distribution of spectral properties of the ionized gas around NGC 891, which is often regarded as an analog of the Milky Way. We developed specific data reduction procedures for the multi-slit narrow-band spectroscopy data taken with the MDM 2.4m telescope. The data presented in this paper covers the H$α$ and [N II]$λλ$6548,6583Åemission lines. The eDIG traced by the H$α$ and [N II] lines shows an obvious asymmetric morphology, being brighter in the northeastern part of the galactic disk and extending a few kpc above and below the disk. Global variations in the [N II]/H$α$ line ratio suggest additional heating mechanisms for the eDIG at large heights beyond photoionization. We also construct position-velocity (PV) diagrams of the eDIG based on our optical multi-slit spectroscopy data and compare them to similar PV diagrams constructed with the H I data. The dynamics of the two gas phases are generally consistent with each other. Modeling the rotation curves at different heights from the galactic mid-plane suggests a vertical negative gradient in turnover radius and maximum rotation velocity, with magnitudes of approximately $3$ kpc kpc$^{-1}$ and $22-25$ km s$^{-1}$ kpc$^{-1}$, respectively. Measured vertical gradients of the rotation curve parameters suggest significant differential rotation of the ionized gas in the halo, or often referred to as the lagging eDIG. Systematic study of the lagging eDIG in our eDIG-CHANGES project, will help us to better understand the dynamics of the ionized gas in the halo.

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Optical alignment of contamination-sensitive Far-Ultraviolet spectrographs for Aspera SmallSat mission

Aspera is a NASA Astrophysics Pioneers SmallSat mission designed to study diffuse OVI emission from the warm-hot phase gas in the halos of nearby galaxies. Its payload consists of two identical Rowland Circle-type long-slit spectrographs, sharing a single MicroChannel plate detector. Each spectrograph channel consists of an off-axis parabola primary mirror and a toroidal diffraction grating optimized for the 1013-1057 Angstroms bandpass. Despite the simple configuration, the optical alignment/integration process for Aspera is challenging due to tight optical alignment tolerances, driven by the compact form factor, and the contamination sensitivity of the Far-Ultraviolet optics and detectors. In this paper, we discuss implementing a novel multi-phase approach to meet these requirements using state-of-the-art optical metrology tools. For coarsely positioning the optics we use a blue-laser 3D scanner while the fine alignment is done with a Zygo interferometer and a custom computer-generated hologram. The detector focus requires iterative in-vacuum alignment using a Vacuum UV collimator. The alignment is done in a controlled cleanroom facility at the University of Arizona.

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MeerKAT discovery of a double radio relic and odd radio circle: connecting cluster and galaxy merger shocks

We present the serendipitous discovery of (1) a large double radio relic associated with the galaxy cluster PSZ2 G277.93+12.34 and (2) a new odd radio circle, ORC J1027-4422, both found in the same deep MeerKAT 1.3 GHz wide-band radio continuum image. The angular separation of the two arc-shaped cluster relics is ~16 arcmin or ~2.6 Mpc for a cluster redshift of z ~ 0.158. The thin southern relic, which shows several ridges/shocks including one possibly moving inwards, has a linear extent of ~1.64 Mpc. In contrast, the northern relic is about twice as wide, twice as bright, but only has a largest linear size of ~0.66 Mpc. Complementary SRG/eROSITA X-ray images reveal extended emission from hot intracluster gas between the two relics and around the narrow-angle tail (NAT) radio galaxy PMN J1033-4335 (z ~ 0.153) located just east of the northern relic. The radio morphologies of the NAT galaxy and the northern relic, which are also detected with the Australian Square Kilometer Array Pathfinder (ASKAP) at 888 MHz, suggest both are moving in the same outward direction. The discovery of ORC J1027-4422 in a different part of the same MeerKAT image makes it the 4th known single ORC. It has a diameter of ~90 arcsec corresponding to 400 kpc at a tentative redshift of z ~ 0.3 and remains undetected in X-ray emission. Supported by simulations, we discuss similarities between outward moving galaxy and cluster merger shocks as the formation mechanisms for ORCs and radio relics, respectively.

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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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Evidence for a large off-centered galactic outflow and its connection to the extraplanar diffuse ionized gas in IC 1553

Aims. We analyze a MUSE optical integral field spectrum of the star-forming edge-on galaxy IC 1553 in order to study its extraplanar diffuse ionized gas (eDIG) and the processes shaping its disk-halo interface. Methods. We extracted the optical emission line properties from the integral field spectrum and generated the commonly used emission line diagnostic diagrams in order to analyze the ionization conditions and the distribution of the eDIG. Furthermore, we performed gravitational potential fitting to investigate the kinematics of a suspected galactic outflow. Results. We find that the eDIG scale height has a maximum value of approximately 1.0 kpc and decreases roughly linearly with the radial distance from the galactic center in projection. The ionization state of the eDIG is not consistent with a pure photoionization scenario and instead requires a significant contribution from shock ionization. This, in addition to the gas kinematics, strongly suggests the presence of a galactic scale outflow, the origin of which lies at least 1.4 kpc away from the galactic center. The inferred shock velocity in the eDIG of approximately 225 km s-1 is comparable to the escape velocity estimated from our potential modelling. The asymmetric distribution of currently star-forming clusters produces a range of different ionization conditions in the eDIG. As a result, the vertical emission line profiles vary quantitatively and qualitatively along the major axis of the galaxy. This analysis illustrates that it is crucial in studies of the eDIG to use observations that take the spatial and kinematical distributions into account, such as those done with integral field units, to form an accurate picture of the relevant physical properties.

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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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