Vertical Scale Height Research Articles

Revisiting the Vertical Distribution of H i Absorbing Clouds in the Solar Neighborhood

The vertical distribution of cold neutral hydrogen (H i) clouds is a constraint on models of the structure, dynamics, and hydrostatic balance of the interstellar medium. In 1978, Crovisier pioneered a method to infer the vertical distribution of H i absorbing clouds in the solar neighborhood. Using data from the Nançay 21 cm absorption survey, Crovisier determined the mean vertical displacement of cold H i clouds, 〈∣z∣〉. We revisit that author’s analysis and explore the consequences of truncating the H i absorption sample in Galactic latitude. For any nonzero latitude limit, we find that the quantity inferred by Crovisier is not the mean vertical displacement but rather a ratio involving higher moments of the vertical distribution. The resultant distribution scale heights are thus ∼1.5 to ∼3 times smaller than previously determined. In light of this discovery, we develop a Bayesian Monte Carlo Markov Chain method to infer the vertical distribution of H i absorbing clouds. We fit our model to the original Nançay data and find a vertical distribution moment ratio 〈∣z∣3〉/〈∣z∣2〉 = 97 ± 15 pc, which corresponds to a Gaussian scale height σ z = 61 ± 9 pc, an exponential scale height λ z = 32 ± 5 pc, and a rectangular half-width W z,1/2 = 129 ± 20 pc. Consistent with recent simulations, the vertical scale height of cold H i clouds appears to remain constant between the inner Galaxy and the Galactocentric distance of the solar neighborhood. Local fluctuations might explain the large-scale height observed at the same Galactocentric distance on the far side of the Galaxy.

Into the thick of it: ALMA 0.45 mm observations of HL Tau at a resolution of 2 au

To comprehend the efficiency of dust evolution within protoplanetary disks, it is crucial to conduct studies of these disks using high-resolution observations at multiple wavelengths with the Atacama Large Millimeter/submillimeter Array (ALMA). In this work, we present high-frequency ALMA observations of the HL Tau disk using its Band 9 centered at a wavelength of 0.45 mm. These observations achieve the highest angular resolution in a protoplanetary disk to date, 12 milliarcseconds (mas), allowing the study of the dust emission at scales of 2 au. We used these data to extend the previously published multiwavelength analysis of the HL Tau disk, constraining the dust temperature, dust surface density, and maximum grain size throughout the disk. We performed this modeling for compact solid dust particles as well as for porous particles. Our new 0.45 mm data mainly trace optically thick emission, providing a tight constraint to the dust temperature profile. We derive maximum particle sizes of $ cm from the inner disk to $ au. Beyond this radius, we find particles between 300 mu m and 1 mm. The total dust mass of the disk is 2.1 J $ with compact grains, and it increases to 6.3 M$_ J $ assuming porous particles. Moreover, an intriguing asymmetry is observed at 32 au in the northeast inner part of the HL Tau disk at 0.45 mm. We propose that this asymmetry is the outcome of a combination of factors, including the optically thick nature of the emission, the orientation of the disk, and a relatively large dust scale height of the grains that is preferentially traced at 0.45 mm. To validate this, we conducted a series of radiative transfer models using the software RADMC-3D. Our models varying dust masses and scale heights successfully replicate the observed asymmetry in the HL Tau disk. If this scenario is correct, our measured dust mass within 32 au would suggest a dust scale height H/R$>0.08$ for the inner disk. Finally, the unprecedented resolution allowed us to probe the dust emission down to scales of a few au for the first time. We observed an increase in brightness temperature inside the estimated water snowline, and we speculate whether this might indicate a traffic-jam effect in the inner disk. Our results show that 0.45 mm observations of protoplanetary disks can be used to robustly constrain the radial profile of their dust temperature. Additionally, the higher optical depths at this wavelength can be used to constrain the vertical scale height of the dust. Finally, these higher frequencies allow us to reach higher spatial resolutions, which have the potential to resolve the region within the water snowline in disks.

Dust growth and pebble formation in the initial stages of protoplanetary disk evolution

Aims. The initial stages of planet formation may start concurrently with the formation of a gas-dust protoplanetary disk. This makes the study of the earliest stages of protoplanetary disk formation crucially important. Here we focus on dust growth and pebble formation in a protoplanetary disk that is still accreting from a parental cloud core. Methods. We have developed an original three-dimensional numerical hydrodynamics code, which computes the collapse of rotating clouds and disk formation on nested meshes using a novel hybrid Coarray Fortran-OpenMP approach for distributed and shared memory parallelization. Dust dynamics and growth are also included in the simulations. Results. We found that the dust growth from ~1 µm to 1–10 mm already occurs in the initial few thousand years of disk evolution but the Stokes number hardly exceeds 0.1 because of higher disk densities and temperatures compared to the minimum mass Solar nebular. The ratio of the dust-to-gas vertical scale heights remains rather modest, 0.2–0.5, which may be explained by the perturbing action of spiral arms that develop in the disk soon after its formation. The dust-to-gas mass ratio in the disk midplane is highly nonhomogeneous throughout the disk extent and is in general enhanced by a factor of several compared to the fiducial 1:100 value. Low St hinders strong dust accumulation in the spiral arms compared to the rest of the disk and the nonsteady nature of the spirals is also an obstacle. The spatial distribution of pebbles in the disk midplane exhibits a highly nonhomogeneous and patchy character. The total mass of pebbles in the disk increases with time and reaches a few tens of Earth masses after a few tens of thousand years of disk evolution. Conclusions. We found that protoplanetary disks with an age ≤20 kyr can possess notable amounts of pebbles and feature dust-togas density enhancements in the disk midplane. Hence, these young disks can already be ripe for the planet formation process to start. Multidimensional numerical models of disk formation that consider the coevolution of gas and dust including dust growth are important to improve our understanding of planet formation.

RZ Piscium Hosts a Compact and Highly Perturbed Debris Disk

RZ Piscium (RZ Psc) is well known in the variable star field because of its numerous irregular optical dips in the past 5 decades, but the nature of the system is heavily debated in the literature. We present multiyear infrared monitoring data from Spitzer and WISE to track the activities of the inner debris production, revealing stochastic infrared variability as short as weekly timescales that is consistent with destroying a 90 km sized asteroid every year. ALMA 1.3 mm data combined with spectral energy distribution modeling show that the disk is compact (∼0.1–13 au radially) and lacks cold gas. The disk is found to be highly inclined and has a significant vertical scale height. These observations confirm that RZ Psc hosts a close to edge-on, highly perturbed debris disk possibly due to migration of recently formed giant planets that might be triggered by the low-mass companion RZ Psc B if the planets formed well beyond the snowlines.

Constraining turbulence in protoplanetary discs using the gap contrast: an application to the DSHARP sample

ABSTRACT Constraining the strength of gas turbulence in protoplanetary discs is an open problem that has relevant implications for the physics of gas accretion and planet formation. In this work, we gauge the amount of turbulence in six of the discs observed in the DSHARP programme by indirectly measuring the vertical distribution of their dust component. We employ the differences in the gap contrasts observed along the major and the minor axes due to projection effects, and build a radiative transfer model to reproduce these features for different values of the dust scale heights. We find that (a) the scale heights that yield a better agreement with data are generally low ($\lesssim 4\, \mathrm{AU}$ at a radial distance of $100\, \mathrm{AU}$), and in almost all cases we are only able to place upper limits on their exact values; these conclusions imply (assuming an average Stokes number of ≈10−2) low turbulence levels of αSS ≲ 10−3 − 10−4; (b) for the 9 other systems we considered out of the DSHARP sample, our method yields no significant constraints on the disc vertical structure; we conclude that this is because these discs have either a low inclination or gaps that are not deep enough. Based on our analysis we provide an empirical criterion to assess whether a given disc is suitable to measure the vertical scale height.

Bars and boxy/peanut bulges in thin and thick discs

The Milky Way and a majority of external galaxies possess a thick disc. However, the dynamical role of the (geometrically) thick disc in the bar formation and evolution is not fully understood. Here, we investigate the effect of thick discs in the formation and evolution of bars by means of a suite of N-body models of (kinematically cold) thin and (kinematically hot) thick discs. We systematically varied the mass fraction of the thick disc, the thin-to-thick disc scale length ratio, and the thick disc scale height to examine the bar formation under diverse dynamical scenarios. Bars form almost always in our models, even in the presence of a massive thick disc. The part of the bar that consists of the thick disc closely follows the overall growth and temporal evolution of the part of the bar that consists of the thin disc, but the part of the bar in the thick disc is weaker than the part of the bar in the thin disc. The formation of stronger bars is associated with a simultaneous greater loss of angular momentum and a more intense radial heating. In addition, we demonstrate a preferential loss of angular momentum and a preferential radial heating of disc stars in the azimuthal direction within the extent of the bar in both thin and thick disc stars. For purely thick-disc models (without any thin disc), the bar formation critically depends on the disc scale length and scale height. A larger scale length and/or a larger vertical scale height delays the bar formation time and/or suppresses the bar formation almost completely in thick-disc-only models. We find that the Ostriker-Peeble criterion predicts the bar instability scenarios in our models better than the Efstathiou-Lake-Negroponte criterion.

On the distribution of the cold neutral medium in galaxy discs

ABSTRACT The cold neutral medium (CNM) is an important part of the galactic gas cycle and a precondition for the formation of molecular and star-forming gas, yet its distribution is still not fully understood. In this work, we present extremely high resolution simulations of spiral galaxies with time-dependent chemistry such that we can track the formation of the CNM, its distribution within the galaxy, and its correlation with star formation. We find no strong radial dependence between the CNM fraction and total neutral atomic hydrogen (H i) due to the decreasing interstellar radiation field counterbalancing the decreasing gas column density at larger galactic radii. However, the CNM fraction does increase in spiral arms where the CNM distribution is clumpy, rather than continuous, overlapping more closely with H2. The CNM does not extend out radially as far as H i, and the vertical scale height is smaller in the outer galaxy compared to H i with no flaring. The CNM column density scales with total mid-plane pressure and disappears from the gas phase below values of PT/kB = 1000 K cm−3. We find that the star formation rate density follows a similar scaling law with CNM column density to the total gas Kennicutt–Schmidt law. In the outer galaxy, we produce realistic vertical velocity dispersions in the H i purely from galactic dynamics, but our models do not predict CNM at the extremely large radii observed in H i absorption studies of the Milky Way. We suggest that extended spiral arms might produce isolated clumps of CNM at these radii.

A Simplified Ocean Physics? Revisiting Abyssal Recipes

Abstract Simplified descriptions of the ocean are useful both for formulating explanatory theories and for conveying meaningful global attributes. Here, using a 26-yr average of a global state estimate from ECCO, the basis for Munk’s “abyssal recipes” is evaluated on a global scale between 1000- and 3000-m depth. The two specific hydrographic stations he used prove untypical, with potential temperature and salinity more generally displaying different vertical scale heights, and thus differing in one-dimensional (in the vertical) values of mixing coefficients and/or vertical velocities. The simplest explanation is that the circulation is fully three-dimensional with temperature and salinity fields not describable with a one-dimensional steady balance. In contrast, the potential density and buoyancy are quantitatively describable through a one-dimensional exponential balance, and which calls for an explanation in terms of turbulent mixing processes.

Stirred but not shaken: a multiwavelength view of HD 16743’s debris disc

ABSTRACT Planetesimals – asteroids and comets – are the building blocks of planets in protoplanetary discs and the source of dust, ice, and gas in debris discs. Along with planets they comprise the left-over material after star formation that constitutes a planetary system. Planets influence the dynamics of planetesimals, sculpting the orbits of debris belts to produce asymmetries or gaps. We can constrain the architecture of planetary systems, and infer the presence of unseen planetary companions, by high spatial resolution imaging of debris discs. HD 16743 is a relatively young F-type star that hosts a bright edge-on debris disc. Based on far-infrared Herschel observations its disc was thought to be stirred by a planetary companion. Here, we present the first spatially resolved observations at near-infrared and millimetre wavelengths with HST and ALMA, revealing the disc to be highly inclined at $87{_{.}^{\circ}} 3~^{+1{_{.}^{\circ}} 9}_{-2{_{.}^{\circ}} 5}$ with a radial extent of 157.7$^{+2.6}_{-1.5}$ au and an full width at half maximum of 79.4$^{+8.1}_{-7.8}$ au (ΔR/R = 0.5). The vertical scale height of the disc is 0.13 ± 0.02, significantly greater than typically assumed unstirred value of 0.05, and could be indicative of stirring of the dust-producing planetesimals within the disc by bodies at least a few times the mass of Pluto up to 18.3 M⊕ in the single object limit.

Three-dimensional structure of the central molecular zone

ABSTRACT A detailed comparison of H i and CO line cube data of the Galactic Centre (GC) region from the archives is obtained. The central molecular zone (CMZ) is shown to be embedded in the H i disc (central H i zone, CHZ) of radius ∼320 pc and vertical scale height ∼70 pc. A radio continuum belt is shown to run parallel to molecular Arms I and II. The belt draws a double infinity (∞∞) on the sky, connecting Sgr E (l ∼ −1${_{.}^{\circ}}$2), C, B1, B2, and Sgr D (+1${_{.}^{\circ}}$2), and is interpreted as a warping star-forming ring. The molecular Arms are closely associated with the H i arms on the longitude-velocity diagram (LVD), showing coherent rigid-body ridges. Due to the close relationship between H i and CO, the H i line absorption can be used to determine the Arms’ position relative to Sgr A, B1, B2, and C. Combining the trigonometric data of proper motions of Sgr A* and maser sources of Sgr B2 as well as radial velocities, the 3D velocity vector of Sgr B2 is determined. From these analyses, the molecular Arm I with Sgr B2 is shown to be located in the near side of Sgr A*, and Arm II with Sgr C in the other side, both composing a pair of symmetrical Arms around the GC. We present a possible 3D view of Sgr A through E and Arms I and II along with a parameter list.

Beyond the Local Volume. II. Population Scaleheights and Ages of Ultracool Dwarfs in Deep HST/WFC3 Parallel Fields

Ultracool dwarfs (UCDs) represent a significant proportion of stars in the Milky Way, and deep samples of these sources have the potential to constrain the formation history and evolution of low-mass objects in the Galaxy. Until recently, spectral samples have been limited to the local volume (d < 100 pc). Here, we analyze a sample of 164 spectroscopically characterized UCDs identified by Aganze et al. in the Hubble Space Telescope (HST) WFC3 Infrared Spectroscopic Parallel Survey (WISPS) and 3D-HST. We model the observed luminosity function using population simulations to place constraints on scaleheights, vertical velocity dispersions, and population ages as a function of spectral type. Our star counts are consistent with a power-law mass function and constant star formation history for UCDs, with vertical scaleheights of 249 pc for late-M dwarfs, 153 pc for L dwarfs, and 175 pc for T dwarfs. Using spatial and velocity dispersion relations, these scaleheights correspond to disk population ages of 3.6 Gyr for late-M dwarfs, 2.1 Gyr for L dwarfs, and 2.4 Gyr for T dwarfs, which are consistent with prior simulations that predict that L-type dwarfs are on average a younger and less dispersed population. There is an additional 1–2 Gyr systematic uncertainty on these ages due to variances in age-velocity relations. We use our population simulations to predict the UCD yield in the James Webb Space Telescope PASSAGES survey, a similar and deeper survey to WISPS and 3D-HST, and find that it will produce a comparably sized UCD sample, albeit dominated by thick disk and halo sources.

Bubbles and OB associations

Abstract Supernovae explosions (SNe) in a stratified interstellar disc can create large scale structures and outflows perpendicular to the disc. Their morphology and emission characteristics depend on interrelations between the number of exploded SNe, the ISM vertical scale height, the height above the ISM disc at which SNe are located, and the mid-plane density of ambient gas. When observed such out-of-plane gas structures do characterize properties of the driving SNe and reveal the presence of underlying stellar clusters. Even though the morphology and emission properties of such structures are sensitive to characteristics of ambient gas they might be used for rough estimates of the clusters’ mass.

Hydrodynamics of warps in the local model of astrophysical discs

ABSTRACT We show how the local approximation of astrophysical discs, which is the basis for the well-known model of the shearing box, can be used to study many aspects of the dynamics of warped discs. In the local model, inclination of the orbit of a test particle, with respect to the reference orbit, corresponds to a vertical oscillation of the particle at the orbital frequency. Warping of a disc corresponds to a locally axisymmetric corrugation of the mid-plane of the disc that oscillates vertically at the orbital frequency, while evolution of the warp corresponds to a modulation of the complex amplitude of the vertical oscillation. We derive a conservation law for this amplitude that is the local equivalent of the conservation of angular momentum and therefore governs the evolution of the warp. For length scales that are long compared to the vertical scale height of the disc, the known non-resonant and resonant regimes of warp dynamics, including the diffusive and wave-like regimes of Keplerian discs, occur in the local model in the same way as in a global view of warped discs.

Ratio Between Over‐Satellite Electron Content and Plasma Density Measured by Swarm: A Proxy for Topside Scale Height

AbstractIn‐situ plasma density (Ne) and Over‐Satellite Electron Content (OSEC) measured at Low‐Earth‐Orbit (LEO) are basic parameters for analyzing ionospheric plasma. In this study, we calculate the ratio of OSEC to Ne (OSEC‐to‐Ne ratio; α) measured by Swarm in the daytime topside, which is analogous to the traditional slab thickness of the ionosphere. Dependence of the α on latitude, local time, season, and solar activity generally agrees with the known climatology of vertical scale height (VSH) of the topside ionosphere. Hence, the α can be deemed a proxy for the VSH. Calibrated Swarm‐A and Swarm‐B data at two different altitudes further demonstrate that lower‐altitude Ne and α can reasonably estimate higher‐altitude Ne. In addition, a new method is proposed to estimate effective ion mass from the α and electron/ion temperature measured by Swarm. The estimates are broadly consistent with recent reports on topside ion composition. All these results demonstrate the usefulness of the α in constraining vertical profiles and composition of the topside ionosphere. Caveats for using the α are given, and possible directions of future improvement are discussed.

Challenging the Disk Instability Model. I. The Case of YZ LMi

Abstract Observations of YZ LMi show enhanced emission along the stream trajectory beyond impact at the disk rim during outbursts as well as when the quiescent disk is large. We investigated whether these features can be explained in terms of either gas stream overflow or penetration within the frameworks of the disk instability model (DIM) and the mass-transfer instability model (MTIM) of outbursting disks. Gas stream overflow is not possible because the vertical scale height of the stream is significantly lower than that of the outer disk and because there is no combination of parameters which enables stream overflow on a larger disk while preventing it on a smaller disk. Stream penetration requires the gas stream to be denser than the outer disk regions. This requirement cannot be met by a low-viscosity DIM disk because its density is significantly larger than that of the gas stream over the whole range of mass-transfer rates where the thermal-viscous instability occurs. On the other hand, the high-viscosity MTIM disk has much lower densities which decrease with increasing radius, easily allowing for gas stream penetration during outbursts (when mass-transfer rate and stream density increase) as well as in large quiescent disks. The observed features are not consistent with DIM, but can be plausibly explained by MTIM. These results suggest that the outbursts of YZ LMi are the response of a high-viscosity disk to bursts of enhanced mass-transfer rate. In this case, the outburst decline timescale of (2–3) days implies a viscosity parameter in the range α = 3–4.

Formation of ring-like structures in flared α-discs with X-ray/FUV photoevaporation

ABSTRACT Protoplanetary discs are complex dynamical systems where several processes may lead to the formation of ring-like structures and planets. These discs are flared following a profile where the vertical scale height increases with radius. In this work, we investigate the role of this disc flaring geometry on the formation of rings and holes. We combine a flattening law change with X-ray and FUV photoevaporative winds. We have used a semi-analytical 1D viscous α approach, presenting the evolution of the disc mass and mass rate in a grid of representative systems. Our results show that changing the profile of the flared disc may favour the formation of ring-like features resembling those observed in real systems at the proper evolutionary times, with proper disc masses and accretion rate values. However, these features seem to be short-lived and further enhancements are still needed for better matching all the features seen in real systems.

Estimation of the Radial Scale Length and Vertical Scale Height of the Galactic Thin Disk from Cepheids

Up-to-date data on 2214 classical Cepheids have been used. The model of an exponential matter density distribution in the Galactic thin disk has been applied. New estimates of the radial disk scale length $h_R,$ the distance of the Sun from the symmetry plane $z_\odot$, and the vertical disk scale height $h_z$ have been obtained. Based on samples of 1087 Cepheids younger than 120 Myr and 1127 Cepheids older than 120 Myr, we have found $h_R=2.30\pm0.09$ kpc and $h_R=1.96\pm0.12$ kpc, respectively. It has turned out that an unambiguous estimate of $h_R$ cannot be obtained from their overall radial distribution. However, we have constructed the radial distribution of 806 Cepheids of different ages at the time of their birth from which we have found $h_R=2.36\pm0.24$ kpc. We show that $h_z$ depends strongly on the age of stars. For example, from 705 Cepheids younger than 120 Myr with heliocentric distances $r<6$ kpc we have found $z_\odot=-17\pm4$ pc and $h_z=75\pm5$ pc. From 393 Cepheids older than 120 Myr at $r<6$ kpc, we have found $z_\odot=-39\pm11$ pc and $h_z=131\pm10$ pc.

Co-formation of the thin and thick discs revealed by APOGEE-DR16 andGaia-DR2

ABSTRACTSince thin disc stars are younger than thick disc stars on average, the thin disc is predicted by some models to start forming after the thick disc had formed, around 10 Gyr ago. Accordingly, no significant old thin disc population should exist. Using 6D coordinates from Gaia-DR2 and age estimates from Sanders &amp; Das, we select ∼24 000 old stars (${\tau \gt 10\mbox{$\, \mathrm{Gyr}$}}$, with uncertainties $\lesssim 15{{\ \rm per\ cent}}$) within $2\mbox{$\, \mathrm{kpc}$}$ from the Sun (full sample). A cross-match with APOGEE-DR16 (∼1000 stars) reveals comparable fractions of old chemically defined thin/thick disc stars. We show that the full sample pericentre radius (rper) distribution has three peaks, one associated with the stellar halo and the other two having contributions from the thin/thick discs. Using a high-resolution N-body + SPH simulation, we demonstrate that one peak, at $\mbox{$r_\mathrm{per}$}\approx 7.1\mbox{$\, \mathrm{kpc}$}$, is produced by stars from both discs that were born in the inner Galaxy and migrated to the Solar Neighbourhood. In the Solar Neighbourhood, ∼1/2 (∼1/3) of the old thin (thick) disc stars are classified as migrators. Our results suggest that thin/thick discs are affected differently by radial migration inasmuch as they have different eccentricity distributions, regardless of vertical scale heights. We interpret the existence of a significant old thin disc population as evidence for an early co-formation of thin/thick discs, arguing that clump instabilities in the early disc offer a compelling explanation for the observed trends.

On the link between the topside ionospheric effective scale height and the plasma ambipolar diffusion, theory and preliminary results

Over the years, an amount of models relying on effective parameters were implemented in the challenging issue of the topside ionosphere description. These models are based on different analytical functions, but all of them depend on a parameter called effective scale height, that is deduced from topside electron density measurements. As their names state, they are effective in reproducing the topside electron density profile only when applied to the analytical function used to derive them. Then, in principle, they do not have any physical meaning. It is the goal of this paper to mathematically link the effective scale height modeled through the Epstein layer to the vertical scale height theoretically deduced from the plasma ambipolar diffusion theory. Firstly, effective and theoretical scale heights are linked through a mathematical relation by showing that they tend to each other in the topside ionosphere. Secondly, their connection is preliminarily demonstrated by calculating effective scale height values from the entire COSMIC/FORMOSAT-3 radio occultation dataset. Thirdly, a possible connection between the vertical gradient of the topside scale height (as obtained by COSMIC/FORMOSAT-3 satellites) and the electron temperature (as obtained by ESA Swarm B satellite) is studied by highlighting corresponding similarities in the diurnal, seasonal, solar activity, and latitudinal variability.

H i scale height in spiral galaxies

ABSTRACT We model the galactic discs of seven nearby large spiral galaxies as three-component systems consist of stars, molecular gas, and atomic gas in vertical hydrostatic equilibrium. We set up the corresponding joint Poisson–Boltzmann equation and solve it numerically to estimate the 3D distribution of H i in these galaxies. While solving the Poisson–Boltzmann equation, we do not consider a constant H i velocity dispersion (σHI); rather, we develop an iterative method to self-consistently estimate the σHI profile in a galaxy by using the observed second-moment profile of the H i spectral cube. Using the density solutions, we determine the H i vertical scale height in our galaxies. We find that the H i discs flare in a linear fashion as a function of radius. H i scale height in our galaxies is found to vary between a few hundred parsecs at the centre to ∼1–2 kpc at the outskirts. We estimate the axial ratio of the H i discs in our sample galaxies and find a median ratio of 0.1, which is much lower than what is found for dwarf galaxies, indicating much thinner H i discs in spiral galaxies. Very low axial ratios in three of our sample galaxies (NGC 5055, NGC 6946, and NGC 7331) suggest them to be potential superthin galaxies. Using the H i distribution and the H i hole sizes in NGC 6946, we find that most of the H i holes in this galaxy are broken out into the circumgalactic medium and this breaking out is more effective in the inner radii as compared to the outer radii.