Hydrostatic Equilibrium Models Research Articles

Spatially resolved properties of extraplanar diffuse ionized gas in NGC 3511 and NGC 3513

Abstract Gaseous, disk-halo interfaces are shaped by processes that are critical to galaxy evolution, including gas accretion and outflows. Extraplanar diffuse ionized gas (eDIG) layers are characterized by scale heights that largely exceed those predicted by their temperature, suggesting the presence of turbulent energy injection from star formation feedback. However, the origin of this large scale height remains uncertain. To explore the connection between eDIG and star-forming disks, we present a spatially-resolved case study of a nearby pair of sub-L*, intermediately inclined disk galaxies NGC 3511/3513. We decompose optical nebular lines observed using long-slit spectroscopy into narrow and broad velocity components. In NGC 3511, the broad component has three distinctive characteristics in comparison to the narrow component: (1) significantly higher velocity dispersions (a median 〈σ〉Broad = 24 km s−1compared to 〈σ〉Narrow = 13 km s−1), (2) elevated [N ii]λ6583/Hα and [S ii]λ6716/Hα line ratios, and (3) a rotational velocity lag. These characteristics support the origin of the broad component in an extraplanar, gaseous disk. In NGC 3513, the broad component reveals disk-halo circulation via localized outflows at radius ≲ 1 kpc. For NGC 3511, we test a vertical hydrostatic equilibrium model with pressure support supplied by thermal and turbulent motions. Under this assumption, the eDIG velocity dispersion corresponds to a scale height hz ≳ 0.2 − 0.4 kpc at R = 3 − 5 kpc, a factor of a few above the thermal scale height (hz ≲ 0.1 kpc). This highlights the importance of turbulent motions to the vertical structure of the gaseous, disk-halo interface.

Spectrum synthesis for radially pulsating stars with shocked atmospheres

ABSTRACT spec_puls describes a suite of computer programs to simulate the emergent spectrum from a radially pulsating star. It combines a Christy-type non-linear pulsation code with classical stellar atmosphere codes. The principal aim is to interpret the dynamical spectrum of the radially pulsating extreme helium star V652 Herculis (V652 Her), which shows a strong shock at minimum radius. The components are general enough to treat other classes of radial pulsation. The theoretical spectrum from a shocked pulsation model shows line doubling, with the blue component emerging at standstill velocity and accelerating blueward. The doubling phase depends on line depth and parent ion. The behaviour of line cores post-shock points to a drop in the ionization temperature, although the gas temperature in the model remains high. Shock compression leads to phase-dependent strengthening of Stark-broadened line wings, with the far wings responding first. With velocity-, temperature-, and pressure-sensitive diagnostics, detailed tomography of the pulsation-driven shock in V652 Her seems possible. Even when no shock is present, the dynamical spectrum is significantly different from a model in hydrostatic equilibrium. Using the quasi-static approximation (e.g. at maximum radius) may lead to a considerable underestimate of the star’s mean effective temperature and surface gravity.

Anisotropic compact objects with Finch–Skea geometry in EGB gravity

We present a new class of relativistic anisotropic stellar models with spherically symmetric matter distribution in Einstein Gauss–Bonnet (EGB) gravity. A higher dimensional Finch–Skea geometry in the theory is taken up here to construct stellar models in hydrostatic equilibrium. The Gauss–Bonnet term is playing an important role in accommodating neutron stars. We study the physical features namely, the energy density, the radial and tangential pressures and the suitability of the models. It is found that the equation of state of such stars are non-linear which is determined for a given mass and radius of known stars. The stability of the stellar models are also explored for a wide range of values of the model parameters.

Binary asteroid (31) Euphrosyne: ice-rich and nearly spherical

Aims. Asteroid (31) Euphrosyne is one of the biggest objects in the asteroid main belt and it is also the largest member of its namesake family. The Euphrosyne family occupies a highly inclined region in the outer main belt and contains a remarkably large number of members, which is interpreted as an outcome of a disruptive cratering event. Methods. The goals of this adaptive-optics imaging study are threefold: to characterize the shape of Euphrosyne, to constrain its density, and to search for the large craters that may be associated with the family formation event. Results. We obtained disk-resolved images of Euphrosyne using SPHERE/ZIMPOL at the ESO 8.2 m VLT as part of our large program (ID: 199.C-0074, PI: Vernazza). We reconstructed its 3D shape via the ADAM shape modeling algorithm based on the SPHERE images and the available light curves of this asteroid. We analyzed the dynamics of the satellite with the Genoid meta-heuristic algorithm. Finally, we studied the shape of Euphrosyne using hydrostatic equilibrium models. Conclusions. Our SPHERE observations show that Euphrosyne has a nearly spherical shape with the sphericity index of 0.9888 and its surface lacks large impact craters. Euphrosyne’s diameter is 268 ± 6 km, making it one of the top ten largest main belt asteroids. We detected a satellite of Euphrosyne – S/2019 (31) 1 – that is about 4 km across, on a circular orbit. The mass determined from the orbit of the satellite together with the volume computed from the shape model imply a density of 1665 ± 242 kg m−3, suggesting that Euphrosyne probably contains a large fraction of water ice in its interior. We find that the spherical shape of Euphrosyne is a result of the reaccumulation process following the impact, as in the case of (10) Hygiea. However, our shape analysis reveals that, contrary to Hygiea, the axis ratios of Euphrosyne significantly differ from those suggested by fluid hydrostatic equilibrium following reaccumulation.

Snapshot: connections between internal and surface properties of massive stars

ABSTRACT We introduce snapshot, a technique to systematically compute stellar structure models in hydrostatic and thermal equilibrium based on three structural properties – core mass Mcore, envelope mass Menv, and core composition. This approach allows us to connect these properties of stellar interiors to the luminosity and effective temperature Teff in a more systematic way than with stellar evolution models. We compute core-H burning models with total masses of Mtotal = 8–60 M⊙ and central H mass fractions from 0.70 to 0.05. Using these, we derive an analytical relationship between Mcore, Mtotal, and central H abundance that can be readily used in rapid stellar evolution algorithms. In contrast, core-He burning stars can have a wide range of combinations of Mcore, Menv, and core compositions. We compute core-He burning models with Mcore = 2–9 M⊙, Menv = 0–50 M⊙, and central He mass fractions of 0.50 and 0.01. Models with Mcore/Mtotal from 0.2 to 0.8 have convective envelopes, low Teff and will appear as red supergiants (RSGs). For a given Mcore, they exhibit a small variation in luminosity (0.02 dex) and Teff ($\sim 400\, \mathrm{K}$) over a wide range of Menv ($\sim$2–20 M⊙). This means that it is not possible to derive RSG masses from luminosities and Teff alone. We derive the following relationship between Mcore and the total luminosity of an RSG during core He burning: log Mcore ≃ 0.44log L/L⊙ − 1.38. At Mcore/Mtotal ≈ 0.2, our models exhibit a bistability and jump from an RSG to a BSG structure. Our models with Mcore/Mtotal > 0.8, which correspond to stripped stars produced by mass-loss or binary interaction, show that Teff has a strong dependence on Menv, Mcore, and the core composition. We constrain the mass of one of these stripped stars in a binary system, HD 45166, and find it to be less than its estimated dynamical mass. When a large observational sample of stripped stars becomes available, our results can be used to constrain their Mcore, Menv, mass-loss rates, and the physics of binary interaction.

Carbon and Oxygen Isotopic Ratios. II. Semiregular Variable M Giants

Abstract Carbon and oxygen isotopic ratios are reported for a sample of 51 SRb- and Lb-type variable asymptotic giant branch stars. Vibration-rotation first- and second-overtone CO lines in 1.5–2.5 μm spectra were measured to derive isotopic ratios for 12C/13C, 16O/17O, and 16O/18O. Comparisons with previous measurements for individual stars and with various samples of evolved stars, as available in the extant literature, are discussed. Using the oxygen isotopic ratios, the masses of the SRb stars can be derived. Combining the masses with Gaia luminosities, the SRb stars are shown to be antecedents of the Mira variables. The limiting parameters where plane-parallel, hydrostatic equilibrium model atmospheres can be used for abundance analysis of M giants are explored.

HALOGAS: the properties of extraplanar HI in disc galaxies

We present a systematic study of the extraplanar gas (EPG) in a sample of 15 nearby late-type galaxies at intermediate inclinations using publicly available, deep interferometric H I data from the Hydrogen Accretion in LOcal GAlaxieS (HALOGAS) survey. For each system we masked the H I emission coming from the regularly rotating disc and used synthetic datacubes to model the leftover “anomalous” H I flux. Our model consists of a smooth, axisymmetric thick component described by three structural and four kinematical parameters, which are fit to the data via a Markov chain Monte Carlo (MCMC) based Bayesian method. We find that extraplanar H I is nearly ubiquitous in disc galaxies as we fail to detect it in only two of the systems with the poorest spatial resolution. The EPG component encloses ∼5−25% of the total H I mass with a mean value of 14%, and has a typical thickness of a few kpc which is incompatible with expectations based on hydrostatic equilibrium models. The EPG kinematics is remarkably similar throughout the sample, and consists of a lagging rotation with typical vertical gradients of ∼ − 10 km s−1 kpc−1, a velocity dispersion of 15−30 km s−1, and, for most galaxies, a global inflow in both the vertical and radial directions with speeds of 20−30 km s−1. The EPG H I masses are in excellent agreement with predictions from simple models of the galactic fountain that are powered by stellar feedback. The combined effect of photo-ionisation and interaction of the fountain material with the circumgalactic medium can qualitatively explain the kinematics of the EPG, but dynamical models of the galactic fountain are required to fully test this framework.

Cosmic Snow Clouds: Self-gravitating Gas Spheres Manifesting Hydrogen Condensation

Abstract We present hydrostatic equilibrium models of spherical, self-gravitating clouds of helium and molecular hydrogen, focusing on the cold, high-density regime where solid- or liquid-hydrogen can form. The resulting structures have masses from 0.1 M ⊙ down to several ×10−8 M ⊙, and span a broad range of radii: 10−4 ≲ R(au) ≲ 107. Our models are fully convective, but all have a two-zone character with the majority of the mass in a small, condensate-free core, surrounded by a colder envelope where phase equilibrium obtains. Convection in the envelope is unusual in that it is driven by a mean-molecular-weight inversion, rather than by an entropy gradient. In fact, the entropy gradient is itself inverted, leading to the surprising result that envelope convection transports heat inward. In turn, that permits the outer layers to maintain steady-state temperatures below the cosmic microwave background. Among our hydrostatic equilibria we identify thermal equilibria appropriate to the Galaxy, in which radiative cooling from H2 is balanced by cosmic-ray heating. These equilibria are all thermally unstable, albeit with very long thermal timescales in some cases. The specific luminosities of all our models are very low, and they therefore describe a type of baryonic dark matter. Consequently such clouds are thermally fragile: when placed in a harsh radiation field, they will be unable to cool effectively and disruption will ensue as heat input drives a secular expansion. Disrupting clouds should leave trails of gas and H2 dust in their wake, which might make them easier to detect. Our models may be relevant to the cometary globules in the Helix Nebula and the G2 cloud orbiting Sgr A*.

Modeling of Solar Atmosphere Parameters Above Sunspots Using RATAN-600 Microwave Observations

Models of the upper transition region of sunspots have been derived based on the observed radio spectrum between 3 and 18 GHz from Radio Astronomical Telescope of the Academy of Sciences 600 (RATAN-600) observations. Our objective is to match the spectrum to show that, within the limits of the one-dimensional observations and modeling, we have obtained a reasonable description of the upper transition-region structure of sunspots. We have developed a diagnostic method, based on iterative correction of the temperature–height profile in the transition region and lower corona, and applied it to three selected active regions with unipolar gyroresonance sources. Good agreement is achieved between observed and modeled microwave spectra using one-dimensional, time-independent models in hydrostatic equilibrium characterized by a given temperature as a function of height. We found that above sunspots the upper height of a transition region is located at 2 – 2.3 Mm, and the temperature of the low corona is about 1.5 – 2.5 MK.

Stellar structure model in hydrostatic equilibrium in the context of -gravity

In this work we present a stellar structure model from the -gravity point of view capable of describing some classes of stars (white dwarfs, brown dwarfs, neutron stars, red giants and the Sun). This model is based on -gravity field equations for , hydrostatic equilibrium equation and a polytropic equation of state. We compare the results obtained with those found by Newtonian theory. It has been observed that in these systems, where high curvature regimes emerge, stellar structure equations undergo modifications. Despite the simplicity of this model, the results are satisfactory. The estimated values of pressure, density and temperature of the stars are within those determined by observations. This -gravity model has proved to be necessary to describe stars with strong fields such as white dwarfs, neutron stars and brown dwarfs, while stars with weaker fields, such as red giants and the Sun, are best described by Newtonian theory.

Spectroscopic Evidence of Alfvén Wave Damping in the Off-limb Solar Corona

Abstract We investigate the off-limb active-region and quiet-Sun corona using spectroscopic data. The active region is clearly visible in several spectral lines formed in the temperature range of 1.1–2.8 MK. We derive the electron number density using the line ratio method, and the nonthermal velocity in the off-limb region up to the distance of 140 Mm. We compare density scale heights derived from several spectral line pairs with expected scale heights per the hydrostatic equilibrium model. Using several isolated and unblended spectral line profiles, we estimate nonthermal velocities in the active region and quiet Sun. Nonthermal velocities obtained from warm lines in the active region first show an increase and then later either a decrease or remain almost constant with height in the far off-limb region, whereas nonthermal velocities obtained from hot lines show consistent decrease. However, in the quiet-Sun region, nonthermal velocities obtained from various spectral lines show either a gradual decrease or remain almost constant with height. Using these obtained parameters, we further calculate Alfvén wave energy flux in both active and quiet-Sun regions. We find a significant decrease in wave energy fluxes with height, and hence provide evidence of Alfvén wave damping. Furthermore, we derive damping lengths of Alfvén waves in the both regions and find them to be in the range of 25–170 Mm. Different damping lengths obtained at different temperatures may be explained as either possible temperature-dependent damping or by measurements obtained in different coronal structures formed at different temperatures along the line of sight. Temperature-dependent damping may suggest some role of thermal conduction in the damping of Alfvén waves in the lower corona.

THE UNUSUALLY HIGH HALO CONCENTRATION OF THE FOSSIL GROUP NGC 6482: EVIDENCE FOR WEAK ADIABATIC CONTRACTION

ABSTRACT Although fossil galaxy systems are thought to be very old, and thus should possess above-average halo concentrations, typically fossils have unexceptional concentrations of their masses. We revisit the massive isolated elliptical galaxy/fossil group NGC 6482 for which previous X-ray studies of a modest Chandra observation obtained a very uncertain, but also possibly very high, halo concentration. We present new measurements of the hot gas surface brightness, temperature, and iron abundance using the modest Chandra observation and a previously unpublished Suzaku observation, the latter of which allows the measurements of the gas properties to be extended out to . By constructing hydrostatic equilibrium models of the gas with separate components for the gas, the stellar mass of the large central galaxy (BCG), and the dark matter (DM), we measure and using a Navarro-Frenk-White (NFW) DM profile. For a halo of this mass, the measured concentration c 200 exceeds the mean value (7.1) expected for relaxed ΛCDM halos by in terms of the observational error, and by considering the intrinsic scatter in the ΛCDM c–M relation, which situates NGC 6482 as the most extreme outlier known for a fossil system. We explored several variants of adiabatic contraction (AC) models and, while the AC models provide fits of the same quality as the uncontracted models, they do have the following advantages: (1) lower c 200 that is less of an outlier in the ΛCDM c–M relation, and (2) baryon fractions that agree better with the mean cosmic value. While the standard AC prescriptions yield a BCG stellar mass that is uncomfortably low compared to results from stellar population synthesis (SPS) models, a weaker AC variant that artificially shuts off cooling and star formation at z = 2 yields the same stellar mass as the uncontracted models. These are probably the reasons why our X-ray analysis prefers this weaker AC variant applied to either an NFW or Einasto DM halo. Finally, the stellar mass we measure for the BCG from the hydrostatic analysis strongly favors results from SPS models with a Chabrier or Kroupa initial mass function (IMF) over a Salpeter IMF.

On the model structure of the gravity field of Mars

A discussion is presented about the constraints used in constructing a model for the internal structure of Mars. The most important fact is that the Martian chemical model proposed by Wanke and Dreibus (WD) has stood the test of time. This means that the chondritic ratio Fe/Si = 1.71 can be used as a constraint in constructing an interior structure model of the planet. Consideration is given to the constructing of the reference surface of Mars. It is concluded that the effectively hydrostatic-equilibrium model of Mars is well suited for this purpose. The areoid heights and gravity anomalies in the model of Mars are calculated. The results are shown in the figures (maps) and comments made. The results are compared with the similar data for the Earth. Mars deviates much more strongly from the hydrostatic equilibrium than the Earth. It is suggested that the average thickness of the Martian elastic lithosphere should exceed that of the Earth’s continental lithosphere.

THREE-DIMENSIONAL RADIATION TRANSFER IN YOUNG STELLAR OBJECTS

We have updated our publicly available dust radiative transfer code (HOCHUNK3D) to include new emission processes and various 3-D geometries appropriate for forming stars. The 3-D geometries include warps and spirals in disks, accretion hotspots on the central star, fractal clumping density enhancements, and misaligned inner disks. Additional axisymmetric (2-D) features include gaps in disks and envelopes, "puffed-up inner rims" in disks, multiple bipolar cavity walls, and iteration of disk vertical structure assuming hydrostatic equilibrium. We include the option for simple power-law envelope geometry, which combined with fractal clumping, and bipolar cavities, can be used to model evolved stars as well as protostars. We include non-thermal emission from PAHs and very small grains, and external illumination from the interstellar radiation field. The grid structure was modified to allow multiple dust species in each cell; based on this, a simple prescription is implemented to model dust stratification. We describe these features in detail, and show example calculations of each. Some of the more interesting results include the following: 1) Outflow cavities may be more clumpy than infalling envelopes. 2) PAH emission in high-mass stars may be a better indicator of evolutionary stage than the broadband SED slope; and related to this, 3) externally illuminated clumps and high-mass stars in optically thin clouds can masquerade as YSOs. 4) Our hydrostatic equilibrium models suggest that dust settling is likely ubiquitous in T Tauri disks, in agreement with previous observations.

SUNYAEV-ZEL'DOVICH-MEASURED PRESSURE PROFILES FROM THE BOLOCAM X-RAY/SZ GALAXY CLUSTER SAMPLE

We describe Sunyaev-Zel'dovich (SZ) effect measurements and analysis of the intracluster medium (ICM) pressure profiles of a set of 45 massive galaxy clusters imaged using Bolocam at the Caltech Submillimeter Observatory. We have used masses determined from Chandra X-ray observations to scale each cluster's profile by the overdensity radius R500 and the mass-and-redshift-dependent normalization factor P500. We deproject the average pressure profile of our sample into 13 logarithmically spaced radial bins between 0.07R500 and 3.5R500. We find that a generalized Navarro, Frenk, and White (gNFW) profile describes our data with sufficient goodness-of-fit and best-fit parameters (C500, alpha, beta, gamma, P0 = 1.18, 0.86, 3.67, 0.67, 4.29). We also use the X-ray data to define cool-core and disturbed subsamples of clusters, and we constrain the average pressure profiles of each of these subsamples. We find that given the precision of our data the average pressure profiles of disturbed and cool-core clusters are consistent with one another at R>~0.15R500, with cool-core systems showing indications of higher pressure at R<~0.15R500. In addition, for the first time, we place simultaneous constraints on the mass scaling of cluster pressure profiles, their ensemble mean profile, and their radius-dependent intrinsic scatter between 0.1R500 and 2.0R500. The scatter among profiles is minimized at radii between ~0.2R500 and ~0.5R500, with a value of ~20%. The best-fit mass scaling has a power-law slope of 0.49, which is shallower than the nominal prediction of 2/3 from self-similar hydrostatic equilibrium models. These results for the intrinsic scatter and mass scaling are largely consistent with previous analyses, most of which have relied heavily on X-ray derived pressures of clusters at significantly lower masses and redshifts compared to our sample.

Properties of multistranded, impulsively heated hydrodynamic loop models

Aims. We investigate the capability of multistranded loop models subject to nanoflare heating to reproduce the properties recently observed in coronal loops at extreme ultraviolet (EUV) wavelengths. Methods. One-dimensional hydrodynamic simulations of magnetic loop strands were performed with an impulsive, footpointlocalised heating, with a moderate asymmetry between the two loop halves that was produced either by a sequence of identical nanoflares with a given cadence time tC or by a single energy pulse. The temporal evolution of the emission of a multistranded loop was modelled by simply combining the results of independent single-strand simulations, neglecting any spatial interaction among the strands, and was compared with TRACE and SDO/AIA light curves. The density excess with respect to hydrostatic equilibrium (the ψ factor) was evaluated with the filter-ratio technique. Results. Both loop models exhibit a density excess compared with hydrostatic equilibrium models, which agrees well with the observed values (1 ψ 12). However, in the single-pulse model the light curve and density excess maxima do not match. On the other hand, the models with a sequence of nanoflares predict strong emission at lower temperatures that cannot be reconciled with the available observations.

Development of a new simple hydrostatic equilibrium model for sustainable evaluation in geothermal energy

Geothermal energy is a renewable energy, that is, the energy removed from the geothermal reservoir is continuously replaced on time scales similar to those required for energy removal. Replacement energy to the geothermal reservoir is supplied by fluid of natural recharge and injection. Sustainable geothermal utilization is the ideal condition of the applied production system to sustain the stable production level over long times. It is very important to manage the mass balance between production, injection and natural recharge in the geothermal reservoir to maintain sustainability during exploitation. A new simple hydrostatic equilibrium model is developed by this mass balance model of geothermal reservoir. This paper builds up a new simple hydrostatic equilibrium model to consider hydrostatic connection between recharged reservoir and discharged reservoir. Principle of fluid-pressure transmission states that pressure exerted anywhere in a confined incompressible fluid is transmitted equally in all directions. Hydrostatic equilibrium occurs when compression due to gravity is balanced by a pressure gradient force in the opposite direction. Mass changes data in this hydrostatic equilibrium model is estimated by gravity changes from repeat gravity measurement method. The equation result between production, injection and mass change rate calculates recharge factor from discharged reservoir. This model also assessed a relatively constant of entered mass flow rate from the surface that continues working during the production and injection well activity. This new simple hydrostatic equilibrium model is applied in Kamojang Geothermal Field, the geothermal reservoir with limited natural recharge.

A parametric physical model for the intracluster medium and its use in joint SZ/X-ray analyses of galaxy clusters

We present a parameterized model of the intra-cluster medium that is suitable for jointly analysing pointed observations of the Sunyaev-Zel'dovich (SZ) effect and X-ray emission in galaxy clusters. The model is based on assumptions of hydrostatic equilibrium, the Navarro, Frenk and White (NFW) model for the dark matter, and a softened power law profile for the gas entropy. We test this entropy-based model against high and low signal-to-noise mock observations of a relaxed and recently-merged cluster from N-body/hydrodynamic simulations, using Bayesian hyper-parameters to optimise the relative statistical weighting of the mock SZ and X-ray data. We find that it accurately reproduces both the global values of the cluster temperature, total mass and gas mass fraction (fgas), as well as the radial dependencies of these quantities outside of the core (r > kpc). For reference we also provide a comparison with results from the single isothermal beta model. We confirm previous results that the single isothermal beta model can result in significant biases in derived cluster properties.

Determination of the Cosmic Distance Scale from Sunyaev‐Zel’dovich Effect andChandraX‐Ray Measurements of High‐Redshift Galaxy Clusters

We determine the distance to 38 clusters of galaxies in the redshift range 0.14 less than or equal to z less than or equal to 0.89 using X-ray data from Chandra and Sunyaev-Zeldovich Effect data from the Owens Valley Radio Observatory and the Berkeley-Illinois-Maryland Association interferometric arrays. The cluster plasma and dark matter distributions are analyzed using a hydrostatic equilibrium model that accounts for radial variations in density, temperature and abundance, and, the statistical and systematic errors of this method are quantified. The analysis is performed via a Markov chain Monte Carlo technique that provides simultaneous estimation of all model parameters. W

Rotating Skyrmion stars

In a previous paper, using an equation of state of dense matter representing a fluid of Skyrmions we constructed the corresponding non-rotating compact-star models in hydrostatic equilibrium; these are mostly fluid stars (the Skyrmion fluid) thus naming them Skyrmion Stars. Here we generalize our previous calculations by constructing equilibrium sequences of rotating Skyrmion stars in general relativity using the computer code RNS developed by Stergioulas. We calculated their masses and radii to be 0:4 M=M 3:45, and 13: 0k m R 23:0 km, respectively (R being the circumferential radius of the star). The period of the maximally rotating Skyrmion stars is calculated to be 0: 8m s P 2:0 ms. We nd that a gap (the height between the star surface and the inner stable circular orbit) starts to appear for M 2:0 M. Specically, the Skyrmion star mass range with an existing gap is calculated to be 1:8 <M= M < 3:0 with the corresponding orbital frequency 0: 8k Hz <ISCO < 1:3 kHz. We apply our model to the 4U 1820-30 low mass X-ray binary and suggest a plausible Skyrmion star candidate in the 4U 1636-53 system. We discuss the diculties encountered by our model in the 4U 0614+09 case with the highest known Quasi-Periodic Oscillation frequency of 1329 Hz. A comparative study of Skyrmion stars and models of neutron stars based on recent/modern equations of state is also presented.