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P. M. W. Kalberla

Publications and source records attributed to P. M. W. Kalberla.

At least 19 recordsLinked to original sources

Molecular hydrogen in filaments at high Galactic latitudes

Context. Neutral atomic hydrogen (HI) absorption lines can be used to probe the cold neutral medium (CNM) at high Galactic latitudes. Cold HI with a significant optical depth from the GASKAP-HI survey is found to be located predominantly if not exclusively within filamentary structures that can be identified as caustics with the Hessian operator. Most of these HI filaments (57%) are also observable in the far-infrared (FIR) and trace the orientation of magnetic field lines. Aims. We considered whether molecular hydrogen (H2) might also be preferentially associated with CNM filaments. Methods. We analyzed 241 H2 absorption lines against stars and determined whether the lines of sight intersected HI or FIR filaments. Using Far Ultraviolet Spectroscopic Explorer (FUSE) H2 data in the velocity range -50 < vLSR < 50 km/s, we traced 65 additional H2 lines for filamentary HI and FIR structures in velocity and probed the H2 absorption for coincidences in position and velocity. Results. For 305 out of 306 positions, the lines of sight with H2 absorption intersect HI filaments. In 120 cases, there is also evidence for a correlation with dusty FIR filaments. All of the 65 available sight lines with known velocities intersect HI filaments. In 64 cases, the H2 velocities are consistent with HI filament velocities. For FIR filaments, an agreement is found for only 13 out of 14 H2 absorption lines. Conclusions. For the majority of H2 absorption lines, there is evidence that H2 is associated with cold HI filaments. Evidence of an association with FIR filaments is less compelling. Confusion along the line of sight limits the detectability of FIR filaments. For a comparable degree of UV excitation in the disk and lower Galactic halo, the formation rate of H2 appears to be enhanced in HI filaments with increased CNM densities.

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The cold neutral medium in filaments at high Galactic latitudes

Context. The HI distribution at high Galactic latitudes is found to be filamentary and closely related to the far infrared (FIR) in caustics with coherent velocity structures. These structures trace the orientation of the magnetic field lines. Aims. Recent absorption observations with the Australian SKA Pathfinder Telescope have led to major improvements in our understanding of the physical properties of the cold neutral medium (CNM) at high Galactic latitudes. We use these results to explore how far the physical state of the CNM may be related with caustics in HI and FIR. Methods. We trace filamentary FIR and HI structures and probe the absorption data for coincidences in position and velocity. Results. 57 percent of the absorption positions are associated with known FIR/HI caustics, filamentary dusty structures with a coherent velocity field. The remaining part of the absorption sample is coincident in position and velocity with genuine HI filaments that are closely related to the FIR counterparts. Thus, within the current sensitivity limitations, all of the positions with HI absorption lines are associated with filamentary structures in FIR and/or HI. We summarize physical parameters for then CNM along filaments in the framework of filament velocities that have been determined from a Hessian analysis of FIR and HI emission data. Velocity deviations between absorption components and filament velocities are due to local turbulence and we determine for the observed CNM an average turbulent velocity dispersion of 2.48 < delta_vturb < 3.9 km/s. The CNM has a mean turbulent Mach number of Mt = 3.4 +/- 1.6 km/s. Conclusions. Most, if not all, of the CNM in the diffuse ISM at high Galactic latitudes is located in filaments, identified as caustics with the Hessian operator.

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Caustics and velocity caustics in the diffuse interstellar medium at high Galactic latitudes

The FIR distribution at high Galactic latitudes, observed with Planck, is filamentary with coherent structures in polarization. These structures are also closely related to HI filaments with coherent velocity structures. There is a long-standing debate about the physical nature of these structures. They are considered either as velocity caustics, fluctuations engraved by the turbulent velocity field or as cold three-dimensional density structures in the interstellar medium (ISM). We discuss different approaches to data analysis and interpretation in order to work out the differences. We considered mathematical preliminaries for the derivation of caustics that characterize filamentary structures in the ISM. Using the Hessian operator, we traced individual FIR filamentary structures in HI from channel maps as observed and alternatively from data that are provided by the velocity decomposition algorithm (VDA). VDA is claimed to separate velocity caustics from density effects. Based on the strict mathematical definition, the so-called velocity caustics are not actually caustics. These VDA data products may contain caustics in the same way as the original HI observations. Caustics derived by a Hessian analysis of both databases are nearly identical with a correlation coefficient of 98%. However, the VDA algorithm leads to a 30% increase in the alignment uncertainties when fitting FIR/HI orientation angles. We used HI absorption data to constrain the physical nature of FIR/HI filaments and determine spin temperatures and volume densities of FIR/HI filaments. HI filaments exist as CNM structures; outside the filaments no CNM absorption is detectable. The CNM in the diffuse ISM is exclusively located in filaments with FIR counterparts. These filaments at high Galactic latitudes exist as cold density structures; velocity crowding effects are negligible.

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Aspect ratios of far-infrared and H i filaments in the diffuse interstellar medium at high Galactic latitudes

Dusty magnetized structures observable in the far-infrared (FIR) at high Galactic latitudes are ubiquitous and found to be closely related to HI filaments with coherent velocity structures. Considering dimensionless morphological characteristics based on Minkowski functionals, we determine the distribution of filamentarities $F$ and aspect ratios $A$ for these structures. Our data are based on Planck FIR and HI4PI HI observations. Filaments have previously been extracted by applying the Hessian operator. We trace individual filamentary structures along the plane of the sky and determine $A$ and $F$. Filaments in the diffuse interstellar medium (ISM) are seldom isolated structures, but are rather part of a network of filaments with a well-defined, continuous distribution in $A$ and $F$. This distribution is self-replicating, and the merger or disruption of individual filamentary structures leads only to a repositioning of the filament in $A$ and $F$ without changing the course of the distribution. FIR and HI filaments identified at high Galactic latitudes are a close match to model expectations for narrow filaments with approximately constant widths. This distribution is continuous without clear upper limits on the observed aspect ratios. Filaments are associated with enhanced column densities of CO-dark $H_2$. Radial velocities along the filaments are coherent and mostly linear with typical dispersions of $Δv_{\mathrm{LSR}} = 5.24 $ km/s. The magnetic field strength in the diffuse turbulent ISM scales with hydrogen volume density as $B \propto n_{\mathrm{H}}^{0.58} $. At high Galactic latitudes, we determine an average turbulent magnetic field strength of $\langle δB \rangle = 5.3 ~μ$G and an average mean strength of the magnetic field in the plane of the sky of $\langle B_{\mathrm{POS}} \rangle = 4.4 ~μ$G.

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Local HI filaments driven by a small-scale dynamo. Update on the velocity decomposition algorithm

Context. HI filaments are closely related to dusty magnetized structures that are observable in the far infrared (FIR). Recently it was proposed that the coherence of oriented HI structures in velocity traces the line of sight magnetic field tangling. Aims. We study the velocity-dependent coherence between FIR emission at 857 GHz and HI on angular scales of 18 arcmin. Methods. We use HI4PI HI data and Planck FIR data and apply the Hessian operator to extract filaments. For coherence, we require that local orientation angles θ in the FIR at 857 GHz along the filaments be correlated with the HI. Results. We find some correlation for HI column densities at |v_LSR | < 50 km/, but a tight agreement between FIR and HI orientation angles θ exists only in narrow velocity intervals of 1 km/s. Accordingly, we assign velocities to FIR filaments. Along the line of sight these HI structures show a high degree of the local alignment with θ, as well as in velocity space. Interpreting these aligned structures in analogy to the polarization of dust emission defines an HI polarization. We observe polarization fractions of up to 80%, with averages of 30%. Orientation angles θ along the filaments, projected perpendicular to the line of sight, are fluctuating systematically and allow a characteristic distribution of filament curvatures to be determined. Conclusions. Local HI and FIR filaments identified by the Hessian analysis are coherent structures with well-defined radial velocities. HI structures are also organized along the line of sight with a high degree of coherence. The observed bending of these structures in the plane of the sky is consistent with models for magnetic field curvatures induced by a Galactic small-scale turbulent dynamo.

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Correlations between turbulent velocity and density fields in the local interstellar medium

Kalberla et al. used HI4PI data to analyze velocity and density fluctuations in the interstellar medium (ISM). They applied the Yuen et al. (2021) velocity decomposition algorithm (VDA) for separating such fluctuations in the position-position-velocity (PPV) space. In the first version of this manuscript they came to the conclusion that velocity and density fields are statistically correlated. Yuen et al. (2021) tried to reproduce these results and pointed to a likely mistake in the VDA expression that was used. We confirm that there was such a software problem. The statement that VDA derived density and velocity fields from HI4PI are anti-correlated needs to be withdrawn. Correct is that these density and velocity fields are uncorrelated. In turn major parts of the conclusions in the first version of this manuscript, based on an erroneous correlation, are invalid. The submission to A&A was withdrawn on 24 February 2022.

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Are observed H i filaments turbulent illusions or density structures? Velocity caustics, facts and fakes

Context. The interstellar medium is affected by turbulence and observed H i structures in channel maps are shaped by turbulent motions. It is taken for granted by a few theoreticians that observed H i structures do not represent real density enhancement but velocity caustics, caused by velocity crowding. This interpretation was questioned and objections by Clark et al. led to violent debates. Aims. To settle the discussion we verify theoretical key parameters by using Effelsberg Bonn H i Survey (EBHIS) observations. Methods. We apply unsharp masking to determine filamentary H i structures at high spatial frequencies. In addition we use Gaussian parameters to distinguish the cold neutral medium (CNM) from observed H i column densities. We compare power spectra and spatial distributions of dust and H i column densities, distinguishing CNM and multiphase column densities at various velocity widths. Results. Observations contradict the Velocity Channel Analysis (VCA) postulate that the spectral index should steepen with the width of the velocity window. We rather find that the thin slice spectral index depends strongly on the H i phase composition. Multiphase power spectra are steeper for regions with cold gas. VCA denies such H i phase dependencies on the power distribution. Separating the CNM we find that the power spectra are significantly flatter than those for the multiphase H i composite. We observe excess CNM power for small scale structures originating from cold dust bearing filaments that are embedded in the CNM. Spectral indices for narrow channel widths depend on the Doppler temperature of the H i gas. In presence of enhanced small scale H i structure the far infrared emission from dust is also enhanced. Conclusions. Small scale cold filamentary H i structures are predominantly caused by density enhancements due to phase transitions rather than by velocity caustics.

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HI filaments are cold and associated with dark molecular gas. HI4PI based estimates of the local diffuse CO-dark H2 distribution

Context. There are significant amounts of H2 in the Milky Way. Due to its symmetry H2 does not radiate at radio frequencies. CO is thought to be a tracer for H2, however CO is formed at significantly higher opacities than H2. Thus, toward high Galactic latitudes significant amounts of H2 are hidden and called CO-dark. Aims. We demonstrate that the dust-to-gas ratio is a tool to identify locations and column densities of CO-dark H2. Methods. We adopt the hypothesis of a constant E(B-V)/NH ratio, independent of phase transitions from HI to H2. We investigate the Doppler temperatures TD, from a Gaussian decomposition of HI4PI data, to study temperature dependencies of E(B-V)/NHI. Results. The E(B-V)/NHI ratio in the cold HI gas phase is high in comparison to the warmer one. We consider this as evidence that cold HI gas toward high Galactic latitudes is associated with H2. Beyond CO-bright regions we find for TD < 1165 K a correlation (NHI + 2NH2 )/NHI prop -log T_D. In combination with a factor XCO = 4.0 10 20 cm^-2 (K km s^-1 )-1 this yields for the full-sky NH /E(B-V) sim 5.1 to 6.7 10^21 cm^-2 mag^-1, compatible with X-ray scattering and UV absorption line observations. Conclusions. Cold HI with T_D < 1165 K contains on average 46% CO-dark H2. Prominent filaments have TD < 220 K and typical excitation temperatures Tex sim 50 K. With a molecular gas fraction of > 61% they are dominated dynamically by H2.

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Turbulent power distribution in the local interstellar medium

Context: The interstellar medium (ISM) on all scales is full of structures that can be used as tracers of processes that feed turbulence. Aims: We used HI survey data to derive global properties of the angular power distribution of the local ISM. Methods: HI4PI observations on an nside = 1024 HEALPix grid and Gaussian components representing three phases, the cold, warm, and unstable lukewarm neutral medium (CNM, WNM, and LNM), were used for velocities $|v_{\mathrm{LSR}}| \leq 25$ \kms. For high latitudes $|b| > 20°$ we generated apodized maps. After beam deconvolution we fitted angular power spectra. Results: Power spectra for observed column densities are exceptionally well defined and straight in log-log presentation with 3D power law indices $γ\geq -3$ for the local gas. For intermediate velocity clouds (IVCs) we derive $γ= -2.6$ and for high velocity clouds (HVCs) $γ= -2.0$. Single-phase power distributions for the CNM, LNM, and WNM are highly correlated and shallow with $ γ\sim -2.5$ for multipoles $l \leq 100$. Excess power from cold filamentary structures is observed at larger multipoles. The steepest single-channel power spectra for the CNM are found at velocities with large CNM and low WNM phase fractions. Conclusions: The phase space distribution in the local ISM is configured by phase transitions and needs to be described with three distinct different phases, being highly correlated but having distributions with different properties. Phase transitions cause locally hierarchical structures in phase space. The CNM is structured on small scales and is restricted in position-velocity space. The LNM as an interface to the WNM envelops the CNM. It extends to larger scales than the CNM and covers a wider range of velocities. Correlations between the phases are self-similar in velocity.

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Radial velocities in the outermost disk toward the anticenter

We measure the mean Galactocentric radial component of the velocity of stars ($v_R$) in the disk at 8 kpc$ 17$ kpc. Negative velocities are also observed in 21 cm HI maps, possibly dominated by local gas emission. Among the possible dynamical causes for these non-zero $v_R$, factors such as the effect of the Galactic bar, streams, or mergers do not seem appropriate to explain our observations. An explanation might be the gravitational attraction of overdensities in a spiral arm. As a matter of fact, we see a change of regime from positive to negative velocities around $R\approx 15$ kpc, in the position where we cross the Outer spiral arm in the anticenter. The mass in spiral arms necessary to produce these velocities would be about 3\% of the mass of the disk, consistent with our knowledge of the spiral arms. Another scenario that we explore is a simple class of out-of-equilibrium systems in which radial motions are generally created by the monolithic collapse of isolated self-gravitating overdensities.

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Properties of cold and warm HI gas phases derived from a Gaussian decomposition of HI4PI data

Context. A large fraction of the interstellar medium can be characterized as a multiphase medium. The neutral hydrogen gas is bistable with a cold and warm neutral medium (CNM and WNM respectively) but there is evidence for an additional phase at intermediate temperatures, a lukewarm neutral medium (LNM) that is thermally unstable. Aims. We use all sky data from the HI4PI survey to separate these neutral HI phases with the aim to determine their distribution and phase fractions in the local interstellar medium. Methods. HI4PI observations, gridded on an nside = 1024 HEALPix grid, were decomposed into Gaussian components. From the frequency distribution of the velocity dispersions we infer three separate linewidth regimes. Accordingly we extract the HI line emission corresponding to the CNM, LNM, and WNM. We generated all-sky maps of these phases in the local HI gas with -8 < v_LSR < 8 km/s. Results. Each of the HI phases shows distinct structures on all scales. The LNM never exists as a single phase but contributes on average 41% of the HI. The CNM is prominent only for 22% of the sky, contributes there on average 34% but locally up to 60% of the HI and is associated with dust at temperatures T_dust ~ 18.6 K. Embedded cold filaments show a clear anti-correlation between CNM and LNM. Also the smoothly distributed WNM is anti-correlated with the CNM. It contributes for the rest of the sky 39% with dust associated at temperatures T_dust ~ 19.4 K. Conclusions. The CNM in filaments exists on small scales. Here the observed anti-correlation between LNM and CNM implies that both, filaments and the surrounding more extended LNM, must have a common origin.

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HI anisotropies associated with radio-polarimetric filaments. Steep power spectra associated with cold gas

LOFAR detected toward 3C 196 linear polarization structures which were found subsequently to be closely correlated with cold filamentary HI structures. The derived direction-dependent HI power spectra revealed marked anisotropies for narrow ranges in velocity, sharing the orientation of the magnetic field as expected for magneto hydrodynamical turbulence. Using the Galactic portion of the Effelsberg-Bonn HI Survey we continue our study of such anisotropies in the HI distribution in direction of two WSRT fields, Horologium and Auriga; both are well known for their prominent radio-polarimetric depolarization canals. At 349 MHz the observed pattern in total intensity is insignificant but polarized intensity and polarization angle show prominent ubiquitous structures with so far unknown origin. Apodizing the HI survey data by applying a rotational symmetric 50 percent Tukey window, we derive average and position angle dependent power spectra. We fit power laws and characterize anisotropies in the power distribution. We use a Gaussian analysis to determine relative abundances for the cold and warm neutral medium. For the analyzed radio-polarimetric targets significant anisotropies are detected in the HI power spectra; their position angles are aligned to the prominent depolarization canals, initially detected by WSRT. HI anisotropies are associated with steep power spectra. Steep power spectra, associated with cold gas, are detected also in other fields. Radio-polarimetric depolarization canals are associated with filamentary HI structures that belong to the cold neutral medium (CNM). Anisotropies in the CNM are in this case linked to a steepening of the power-spectrum spectral index, indicating that phase transitions in a turbulent medium occur on all scales. Filamentary HI structures, driven by thermal instabilities, and radio-polarimetric filaments are associated with each other.

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HI4PI: A full-sky HI survey based on EBHIS and GASS

Measurement of the Galactic neutral atomic hydrogen (HI) column density, NHI, and brightness temperatures, Tb, is of high scientific value for a broad range of astrophysical disciplines. In the past two decades, one of the most-used legacy HI datasets has been the Leiden/Argentine/Bonn Survey (LAB). We release the HI 4$π$ survey (HI4PI), an all-sky database of Galactic HI, which supersedes the LAB survey. The HI4PI survey is based on data from the recently completed first coverage of the Effelsberg-Bonn HI Survey (EBHIS) and from the third revision of the Galactic All-Sky Survey (GASS). EBHIS and GASS share similar angular resolution and match well in sensitivity. Combined, they are ideally suited to be a successor to LAB. The new HI4PI survey outperforms the LAB in angular resolution (16.2', FWHM) and sensitivity (RMS: 43 mK). Moreover, it has full spatial sampling and thus overcomes a major drawback of LAB, which severely undersamples the sky. We publish all-sky column density maps of the neutral atomic hydrogen in the Milky Way, along with full spectroscopic data, in several map projections including HEALPix.

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Anisotropies in the HI gas distribution toward 3C196

The local Galactic HI gas was found to contain cold neutral medium (CNM) filaments that are aligned with polarized dust emission. These filaments appear to be dominated by the magnetic field and in this case turbulence is expected to show distinct anisotropies. We use the Galactic Effelsberg--Bonn HI Survey (EBHIS) to derive 2D turbulence spectra for the HI distribution in direction to 3C196 and two more comparison fields. Prior to Fourier transform we apply a rotational symmetric 50% Tukey window to apodize the data. We derive average as well as position angle dependent power spectra. Anisotropies in the power distribution are defined as the ratio of the spectral power in orthogonal directions. We find strong anisotropies. For a narrow range in position angle, in direction perpendicular to the filaments and the magnetic field, the spectral power is on average more than an order of magnitude larger than parallel. In the most extreme case the anisotropy reaches locally a factor of 130. Anisotropies increase on average with spatial frequency as predicted by Goldreich and Sridhar, at the same time the Kolmogorov spectral index remains almost unchanged. The strongest anisotropies are observable for a narrow range in velocity and decay with a power law index close to --8/3, almost identical to the average isotropic spectral index of $-2.9 < γ< -2.6$. HI filaments, associated with linear polarization structures in LOFAR observations in direction to 3C196, show turbulence spectra with marked anisotropies. Decaying anisotropies appear to indicate that we witness an ongoing shock passing the HI and affecting the observed Faraday depth.

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A survey of HI gas toward the Andromeda Galaxy

The subsequent coalescence of low--mass halos over cosmic time is thought to be the major formation channel of massive spiral galaxies like the Milky Way and the Andromeda Galaxy (M31). The gaseous halo of a massive galaxy is considered to be the reservoir of baryonic matter persistently fueling the star formation in the disk. Because of its proximity, M31 is the ideal object for studying the structure of the halo gas in great detail. Using the latest neutral atomic hydrogen (HI) data of the Effelsberg-Bonn HI Survey (EBHIS) allows comprising a comprehensive inventory of gas associated with M31. The primary aim is to differentiate between physical structures belonging to the Milky Way Galaxy and M31 and accordingly to test the presence of a M31 neutral gaseous halo. Analyzing the spatially fully sampled EBHIS data makes it feasible to trace coherent HI structures in space and radial velocity. To disentangle Milky Way and M31 HI emission we use a new approach, along with the traditional path of setting an upper radial velocity limit, by calculating a difference second moment map. We argue that M31's disk is physically connected to an asymmetric HI halo of tens of kpc size, the M31 cloud. We confirm the presence of a coherent low-velocity HI filament located in between M31 and M33 aligned at the sky with the clouds at systemic velocity. The physical parameters of the HI filament are comparable to those of the HI clouds at systemic velocity. We also detected an irregularly shaped HI cloud that is is positionally located close to but offset from the stellar body of And XIX.

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Cold Milky Way Hi gas in filaments

We investigate data from the Galactic Effelsberg--Bonn HI Survey (EBHIS), supplemented with data from the third release of the Galactic All Sky Survey (GASS III) observed at Parkes. We explore the all sky distribution of the local Galactic HI gas with $|v_{\rm LSR}| < 25 $ kms$^{-1}$ on angular scales of 11' to 16'. Unsharp masking (USM) is applied to extract small scale features. We find cold filaments that are aligned with polarized dust emission and conclude that the cold neutral medium (CNM) is mostly organized in sheets that are, because of projection effects, observed as filaments. These filaments are associated with dust ridges, aligned with the magnetic field measured on the structures by Planck at 353 GHz. The CNM above latitudes $|b|>20^\circ$ is described by a log-normal distribution, with a median Doppler temperature $T_{\rm D} = 223$ K, derived from observed line widths that include turbulent contributions. The median neutral hydrogen (HI) column density is $N_{\rm HI} \simeq 10^{19.1}\,{\rm cm^{-2}}$. These CNM structures are embedded within a warm neutral medium (WNM) with $N_{\rm HI} \simeq 10^{20} {\rm cm^{-2}}$. Assuming an average distance of 100 pc, we derive for the CNM sheets a thickness of $< 0.3$ pc. Adopting a magnetic field strength of $B_{\rm tot} = (6.0 \pm 1.8)μ$G, proposed by Heiles & Troland 2005, and assuming that the CNM filaments are confined by magnetic pressure, we estimate a thickness of 0.09 pc. Correspondingly the median volume density is in the range $ 14 < n < 47 {\rm cm^{-3}}$.

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The Effelsberg-Bonn HI Survey: Milky Way gas. First data release

The Effelsberg-Bonn HI Survey (EBHIS) is a new 21-cm survey performed with the 100-m telescope at Effelsberg. It covers the whole northern sky out to a redshift of z~0.07 and comprises HI line emission from the Milky Way and the Local Volume. We aim to substitute the northern-hemisphere part of the Leiden/Argentine/Bonn Milky Way HI survey (LAB) with this first EBHIS data release, which presents the HI gas in the Milky Way regime. The use of a seven-beam L-band array made it feasible to perform this all-sky survey with a 100-m class telescope in a reasonable amount of observing time. State-of-the-art fast-Fourier-transform spectrometers provide the necessary data read-out speed, dynamic range, and spectral resolution to apply software radio-frequency interference mitigation. EBHIS is corrected for stray radiation and employs frequency-dependent flux-density calibration and sophisticated baseline-removal techniques to ensure the highest possible data quality. Detailed analyses of the resulting data products show that EBHIS is not only outperforming LAB in terms of sensitivity and angular resolution, but also matches the intensity-scale of LAB extremely well, allowing EBHIS to be used as a drop-in replacement for LAB. Data products are made available to the public in a variety of forms. Most important, we provide a properly gridded Milky Way HI column density map in HEALPix representation. To maximize the usefulness of EBHIS data, we estimate uncertainties in the HI column density and brightness temperature distributions, accounting for systematic effects.

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Does the stellar distribution flare? A comparison of stellar scale heights with LAB HI data

The question, whether the stellar populations in the Milky Way take part in flaring of the scale heights as observed for the HI gas is a matter of debate. Standard mass models for the Milky Way assume a constant scale height for each of the different stellar distributions. However, there is mounting evidence that at least some of the stellar distributions reach at large galactocentric distances high altitudes that are incompatible with a constant scale height. We discuss recent observational evidence for stellar flaring and compare it with HI data from the Leiden/Argentine/Bonn (LAB) survey. Within the systemic and statistical uncertainties we find a good agreement between both.

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