Lyα Absorption in a “Croissant-like” Heliosphere

Lyα absorption profiles have been used to detect astrospheres and heliospheric absorption from the hydrogen wall and heliotail. Using magnetohydrodynamic models of the heliosphere, we can compare simulated to observed Lyα profiles to probe the neutral hydrogen within and near the heliosphere. There is an ongoing controversy whether the heliosphere has a long “comet-like” tail or a short “croissant-like” tail. Here we present the first Lyα absorption investigation using a croissant-like heliosphere. With identical boundary conditions we compare the BU model, which presents a croissant-like tail, and the Moscow model, which presents a comet-like tail. The BU and Moscow models present nearly identical Lyα profiles toward nose targets (α Cen and 36 Oph). Differences in Lyα profiles are shown toward the tail target (HD 35296). Despite the shortened heliotail of the croissant model, significant downwind heliosheath absorption is seen, just 5% shallower and shifted by 4 km s−1. This implies that an extended tail model is not required to reproduce the heliosheath Lyα absorption observations. Finer observation gratings may be able to resolve this shift. Additionally, when using higher interstellar medium (ISM) neutral and plasma densities and lower magnetic field (∣B LISM∣ = 3.2 μG, α BV ≈ 40°) than in the Moscow model, we find better agreement with observed Lyα profiles. None of the models presented show agreement in all directions simultaneously. Furthermore, we show that for the ISM conditions with the least certainty (n p,LISM, n H,LISM, T LISM, B LISM), B LISM has the most significant effect on the structure of the hydrogen wall and Lyα profiles.


Introduction
The properties of the heliosphere have been debated extensively since its theoretical foundations were developed in the 1950s (Davis 1955;Parker 1961;Axford 1973).The long-standing paradigm of a comet-shaped long-tailed heliosphere (Baranov & Malama 1993) has been challenged recently with theory and modeling (Drake et al. 2015;Opher et al. 2015;Dialynas et al. 2017).Opher et al. (2015) argued that the solar magnetic field plays an active role in confining the heliosheath (the region between the heliospheric termination shock (TS) and the heliopause (HP)) plasma rather than the previously assumed passive role.This result agreed with Yu (1974), who suggested that magnetic tension was important in shaping the heliosphere.This confinement creates a two-lobe structure, referred to as a "croissant-like" heliosphere.Such confinement can be seen in models such as Izmodenov & Alexashov's (2015) and Pogorelov et al.'s (2015), although they argue for a long-tailed heliosphere.In Opher et al. (2021), a neutral-driven instability in the tail was discovered along the axis of the solar magnetic field and was suggested to be the cause of the tail splitting.In the Moscow model the flows within the heliosheath seem to be laminar; the underlying cause of this difference is still unknown and motivates future investigation.
The interstellar medium (ISM) is the material in the region of space between stars.In the vicinity of the Sun, this region is full of mostly partially ionized hydrogen."The ISM" is a broad term that is used inconsistently throughout the literature and as such we will be referring to the parsec-scale region of space between stars as the ISM.The region of space just in front of the heliosphere but "pristine" in the sense that the presence of the heliosphere has not influenced it will be referred to as the local interstellar medium (LISM).Finally, the region of the ISM that is slowed and heated by the presence of the heliosphere will be called the very local interstellar medium (VLISM).
Magnetohydrodynamic (MHD) simulations of the heliosphere are sensitive to the LISM conditions.It has been shown that the strength and direction of the interstellar magnetic field (B LISM ) affects the size and structure of the heliosphere.This is especially true for the hydrogen wall (Zank et al. 2013), a buildup of neutral hydrogen in the nose direction of the heliosphere in the VLISM.The hydrogen wall is formed by neutral hydrogen charge-exchanging with the slowed down and heated plasma in front of the heliosphere, creating a similarly slow and hot population of neutral hydrogen.The nature of the plasma slowdown is heavily influenced by the magnetic field of the LISM, as the velocity of the LISM is close to the superfast magnetosonic velocity, and as such minor changes to the interstellar magnetic field can make the flow superslow or superfast (Zieger et al. 2013).
The LISM conditions have not been precisely constrained yet.The conditions with the least certainty are the plasma density (n p,LISM ), neutral hydrogen density (n H,LISM ), and the strength and direction of B LISM .To constrain the strength and direction of B LISM , studies have used various techniques to determine these parameters with varying success.Lallement et al. (2005Lallement et al. ( , 2010) ) used the deflection of the flow of neutral hydrogen (λ = 252.5°±0.7°, β = 8.9°± 0.5°, where λ and β are the ecliptic J2000 longitude and latitude, respectively) through the heliosphere relative to the flow of pristine neutral helium (λ = 255.4°±0.5°, β = 5.2°± 0.2°; Witte 2004) to determine a plane that B LISM should lie within.This plane is known as the hydrogen deflection plane (HDP).Izmodenov et al. (2005) showed that the deviation between interstellar neutral hydrogen and pristine helium flow could be reproduced using simulations that treated the neutrals kinetically while using MHD for the ions by offsetting B LISM from V LISM within the HDP.Pogorelov et al. (2008) also showed that the hydrogen flow deviates into the plane defined by V LISM and B LISM .Opher et al. (2006) showed that a B LISM within the HDP could reproduce the TS asymmetries observed by Voyager 1 and 2.
While these previous investigations showed that B LISM should be within the HDP, there is an ongoing debate on the specific direction and strength of B LISM .The angle between V LISM and B LISM is known as α BV , and when B LISM is assumed to be within the HDP, it fully describes the direction.Izmodenov et al. (2005) determined that the B LISM that best reproduces the deflection of neutrals had a strength of ∼2.5 μG with an α BV = 45°.Pogorelov et al. (2008) found that the best B LISM to reproduce the neutral deflection had a strength of 3 μG with an α BV = 30°.Opher et al. (2007) found the B LISM most consistent with Voyager radio observations had a strength of ∼1.8 μG with an α BV = 30°.By looking at the Voyager TS crossings, Izmodenov (2009) found that a B LISM with a strength of 2.5-3.5 μG and an α BV = 15°-30°was the best configuration to reproduce the crossings.Still, they neglected the effect of the solar magnetic field.When considering the impact of the solar magnetic field, Opher et al. (2009) found a B LISM with a strength of 3.7-5.5 μG and an α BV = 20°-30°was needed.Also, Pogorelov et al. (2007) found that a B LISM with a strength >3 μG was required to account for the ISM velocity vector tilt when considering the solar magnetic field.
More recently, Zirnstein et al. (2016) used the Interstellar Boundary Explorer (IBEX) ribbon, a circular arc of enhanced energetic neutral atom flux as seen by IBEX centered at (λ, β) ∼(221°, 39°) (McComas et al. 2009a(McComas et al. , 2009b)), to determine the B LISM to have a strength of 2.93 μG and an α BV ≈ 40°.However, this relies on the assumption of which mechanisms produce the IBEX ribbon.The direction of the B LISM determined from the IBEX ribbon observations is in the HDP within the uncertainties associated with the ribbon location.Opher et al. (2020) used a multi-fluid MHD model of the heliosphere and found that Voyager magnetic field observations outside the heliosphere could be reasonably reproduced with a B LISM with a strength of 3.2 μG and an α BV = 40°.Izmodenov & Alexashov (2020) used the same observed magnetic field measurements outside the heliosphere to constrain a strength of 3.75 μG and α BV = 60°.They also considered other factors, such as TS and HP distances, to narrow the field of approximately 50 models considered.Recently, Frisch et al. (2022) used starlight polarization from dust grains to constrain the direction of B LISM close to that of Zirnstein et al. (2016).However, starlight polarization is sensitive to parsec scales rather than scales closer to the heliosphere.These constraints have a B LISM -V LISM angle between 15°and 60°and a strength between 1.8 and 5.5 μG.
A few techniques have been employed to constrain the LISM neutral hydrogen and plasma densities (n H,LISM and n p,LISM , respectively).Direct measurements of the H + and He 2+ distribution from the SWICS instrument from the Ulysses spacecraft allowed Gloeckler et al. (1997) and Izmodenov et al. (2003) to estimate a neutral hydrogen and proton density.This estimate is determined by finding the neutral hydrogen density at the TS that best reproduce Ulysses observations and then assuming a filtration from the hydrogen wall and heliosheath to derive n H,LISM and n p,LISM at large distances from the heliosphere.Swaczyna et al. (2020) used observations from the SWAP instrument on board the New Horizons spacecraft to determine a local neutral hydrogen density at the TS from pickup ion (PUI) observations from 11 to 38 au.They then similarly extrapolated the density at the TS to the ISM using an assumed filtration.Izmodenov (2009) constrained interstellar neutral and plasma densities along with magnetic field strength and direction with 2D MHD models using inferred TS neutral densities, TS crossing time and locations, and the deflection of interstellar neutral hydrogen.The value of n H,LISM from these investigations ranged from 0.14 to 0.195 cm −3 .
One indirect measurement used to investigate the heliosphere's structure is the Lyα absorption profile for nearby stars (Izmodenov et al. 2002;Zank et al. 2013;Wood et al. 2014).One prominent feature of a star's spectra is the Lyα emission line (with a wavelength at the center λ 0 = 121.567nm).The observed emission line comprises various emission and absorption sources from the observed star to the observer close to the Earth.These sources, starting nearest to the observed star, are intrinsic stellar emission, astrospheric absorption, ISM absorption, LISM absorption, and geocoronal emission.
For solar-like stars, the Lyα emission is very strong relative to the background blackbody emission.Neutral hydrogen along the line of sight (LOS) attenuates this intrinsic profile, with the precise profile shape being determined by the distribution of the neutral hydrogen encountered.The neutral hydrogen within the star's astrosphere, in the ISM, and within the heliosphere have distinct characteristic velocities and temperatures and, as such, show up distinctly in the blue, center, and red sides of the absorption profile, respectively.The geocoronal emission is simple to correct as it is usually fully contained within the saturated absorption.
To compare to these observations, simulated Lyα absorption profiles can be constructed from three parts: the assumed intrinsic Lyα profile of the observed star, the derived properties of the ISM along the LOS, and the distribution of neutral hydrogen from a heliosphere model.In principle, the distribution of neutral hydrogen within the astrosphere of the observed star is also needed to calculate the astrospheric absorption.However, the astrospheric component of the absorption is isolated to the blue side of the observed spectra so the heliospheric component, which is the focus of this study, is well differentiated.Differences between observations and simulated Lyα profiles have been used to argue for Lyα absorption caused by the hydrogen wall just upwind of the heliosphere (Linsky & Wood 1996;Zank et al. 2013), in the heliosheath (Wood et al. 2014), and within astrospheres (Wood et al. 2005).These comparisons were made by combining modeled stellar emission profiles, ISM conditions derived from absorption-line fitting, and neutral hydrogen profiles along the LOS from MHD models.
Previous works have found varying degrees of success with matching simulated profiles to observations.Izmodenov et al. (2002) examined the effect of changing n p,LISM and n H,LISM , while ignoring the impact of the interstellar magnetic field, B LISM .They found agreement with observations for upwind targets (36 Oph, α Cen), where hydrogen wall absorption is required.For the flank targets (31 Com, β Cas), the absorption can be entirely explained by ISM absorption.As such, the models with realistic interstellar neutral densities (with respect to current observational uncertainties) gave good agreement, but the models with unrealistically high plasma and neutral densities had too much absorption from the heliosheath.
Although the downwind targets, Sirius and ò Eri, are nearly at the same angle from the upwind direction, they have very different behaviors.Sirius required significant heliosheath absorption to match the observations, while ò Eri could be explained with just ISM absorption.For Sirius, some of the LISM conditions could reproduce the observed emission, but most did not show enough heliosheath absorption.More recent studies have included interstellar and solar magnetic fields.These studies have found significant heliosheath absorption and agreement with observations by extending the simulation domain further downwind for the target stars HD 35296 and χ 1 Ori (Wood et al. 2014).Even with improvement to heliosphere models, such as a kinetic treatement of neutrals and inclusion of magnetic fields, differences between observed and simulated profiles persist in the downwind directions.
Furthermore, there are issues in Lyα absorption modeling that have not been sufficiently resolved.Models of a given LISM condition are unable to simultaneously match profiles from all LOS.Some studies show that the model conditions that best reproduce upwind LOS with significant hydrogen wall absorption are not the model conditions that best reproduce downwind LOS with significant heliosheath absorptions.Another issue to be addressed is that there is difficulty reproducing multiple upwind directions, such as 36 Oph and α Cen, with the same model.This suggests that the models used so far are still missing something fundamental to reproduce the observations.Kornbleuth et al. (2021) compared a long-tailed (Moscow) and short-tailed (BU) model of the heliosphere and found differences manifested for distances beyond 400 au.Longtailed heliosphere models have a heliosheath that extends for thousands of au.Using a domain that does not extend far enough downwind can underpredict the column density of neutral hydrogen from the heliosheath along the LOS and therefore underpredict the amount of absorption that the heliosheath neutrals contribute.In contrast, the heliosheath of a croissant-like heliosphere extends to approximately 400 au near a heliolatitude of 0°, with a longer extent in the lobes.In a croissant-like heliosphere, there is disturbed ISM downwind that is heated by the turbulence of the heliospheric jets and mixing with heliosheath plasma (Opher et al. 2015;Michael et al. 2021).Due to this structure, the entire heliosheath is well within the domain used in these computational models.However, the neutrals created in a given region are not confined to the region they are created in and, as such, can be seen in regions outside of their designated region.
None of the studies on Lyα absorption have produced profiles using a croissant-like heliosphere model.As such, it is important to investigate whether profiles produced using this type of model are consistent with observational data and if differences between "comet-like" and croissant-like models can be distinguished in Lyα observations.This paper is organized as follows.Section 2 describes the details of the models.Specifically, the BU MHD model will be discussed in Section 2.1.The description of Lyα absorption modeling is broken down into heliospheric and interstellar absorption, described in Sections 2.2 and 2.3, respectively.In Section 3, Lyα absorption profiles from the short-tailed BU and long-tailed Moscow models are compared to determine if differences between these models are observable in Lyα.Then, in Section 4, Lyα absorption profiles from the BU model using different LISM conditions are compared to observations and the results from Wood et al. (2014) to validate the BU model against extended tail models using LISM conditions derived from observations.Finally, Section 5 presents a parameter study to determine the relative importance of the four main LISM parameters on Lyα absorption profiles.Section 6 presents a summary and conclusion.

Modeling
For this investigation, target stars were chosen to probe the structure of the heliosphere in the upwind (nose) and downwind (tail) directions.Flank targets are not of interest, as they do not have significant hydrogen wall or heliosheath absorption in their profiles.The specific stars chosen were 36 Oph, α Cen, and HD 35296.Figure 1 shows a schematic view of the direction toward these stars.These stars have detected hydrogen wall absorption (36 Oph, α Cen) or heliosheath absorption (HD 35296) and have been modeled using earlier long-tailed heliosphere models.In particular, HD 35296 presents a great opportunity to probe the heliotail as it is nearly directly downwind, just 3°off downwind.Using these stars, we can directly compare a short-tail to a comet-tail heliosphere model as well as to observations.These observations are taken with two instruments from the Hubble Space Telescope with various gratings and therefore observation resolutions.The observations of α Cen were taken with the GHRS instrument with the echelle-A grating, which has a resolving power R = λ/δλ ≈ 100,000.This instrument has since been replaced by the Space Telescope Imaging Spectrograph, where the observations of the other two targets come from.The observations of 36 Oph used the E140H grating, which has a resolving power R ≈ 100,000, and the observations of HD 35296 used the E140M grating, which has a resolving power R ≈ 40,000.These observations are taken from Wood et al. (2014).
The Lyα absorption profiles in our modeling are generated from three components.These components are the intrinsic Lyα emission of each target star, the absorption of Lyα from the heliospheric neutral hydrogen, and the absorption from ISM neutral hydrogen outside the model's domain.The contribution by the ISM absorption was determined in Wood et al. (2014) by simultaneously fitting multiple absorption lines of the target star.We use the results of this study to isolate just the differences in heliosphere models by avoiding differences introduced from absorption-line fitting.The values used can be seen in Table 1.

BU Model
The BU model is a self-consistent kinetic-MHD code that couples multiple components within the space-weather modeling framework (SWMF; Tóth et al. 2005).The MHD model represents the outer heliosphere (OH) domain and the kinetic neutral model is the particle tracker (PT) domain of SWMF.The OH component is a 3D multi-fluid MHD model adapted from the Block-Adaptive Tree Solar wind Roe-type Upwind Scheme (BATS-R-US) code (Opher et al. 2003(Opher et al. , 2009(Opher et al. , 2020;;Tóth et al. 2012).The PT component is the Adaptive Mesh Particle Simulator (AMPS), which is a global kinetic 3D particle code using the direct simulation Monte Carlo (DSMC) method (Tenishev et al. 2021).
For this project the OH component is initially configured to solve for a single ion population and multiple neutral populations, although OH can solve multiple ion populations (Opher et al. 2020).This multi-fluid neutral, single-fluid plasma treatment is run to a steady-state plasma solution.From this steady-state solution, the OH component is configured to only solve ideal MHD equations for a single plasma fluid, and the neutrals are solved kinetically using the PT component.The OH and PT components are coupled via source terms calculated within the PT component from tracked chargeexchange events.
The PT component of SWMF calculates the source terms due to charge exchange by solving the Boltzmann equation for neutral hydrogen streaming through the heliosphere and letting it interact with the ion fluid obtained by the MHD model.These source terms are found statistically via DSMC.This statistical estimation is determined by following the trajectory of test particles streaming through the heliosphere charge-exchanging with the plasma until a sufficient number of charge-exchange events occur throughout the domain to have acceptable statistics (Michael et al. 2021).To achieve these statistics, we use a subcycling scheme, meaning that AMPS is run for many time steps to accrue charge-exchange events before evolving our plasma solution.Since these simulations are run to steady state, using a subcycling scheme (Tóth et al. 2012) is appropriate.The charge-exchange events are accrued over 5000 time steps, with over 140 million particles modeled.The source terms calculated are passed from the PT component to the OH component where the plasma solution is evolved.These steps are repeated until a quasi-steady-state solution is reached.
The OH and PT use the same domain extent but different grid resolutions.The boundary of the model extends ±1500 au in the X direction, and ±2000 au in the Y and Z directions.This coordinate system is defined with X being 5°above the interstellar flow direction, Z being parallel to the solar rotation axis, and the Y direction the right-hand complement to these directions.
The specific BU models used in Sections 3 and 4 come from Kornbleuth et al. (2020) and Kornbleuth et al. (2021), respectively.These models will be referred to as "model BU1" and "model BU2," respectively.Both model BU1 and model BU2 use the same domain extent, but there are slight differences in the grid cell size between the models.For both models the PT component uses a resolution of 4.7 au in the interior (−280 au x 560 au, −500 au y 500 au, −380 au z 380 au) and then gradually increases to as large as 18 au near the outer boundary.For the model BU1, used in Section 3, the OH component utilizes a refined grid with a resolution of 1 and 2 au near the nose (−190 au x −100, −100 au y 100 au, −85 au z 85 au and −190 au x 110 au, −300 au y 300 au, −200 au z 200 au, respectively) and a resolution of 4 au for the heliosheath (from −300 au x 1000 au, −410 au y 410 au,−450 au z 450 au).The model BU2, used in Section 4, is slightly less refined with 3 au resolution for −120 au x 120 au and 6 au resolution for −240 au x 560 au.
The LISM outer boundary condition for each model is also described in Table 2.The Moscow model we will be using for the direct comparison to BU1 is labeled "IA1" in this table.Model BU1 and model IA1, which is used in Section 3, use LISM conditions that give heliopause and termination shock distances and magnetic field strengths outside of the heliopause in best agreement with Voyager observations based on Izmodenov & Alexashov (2020).While the Moscow model can model helium in the heliosphere, here IA1 does not include this effect to allow a direct comparison to the BU1 model.The LISM consists of n H,LISM = 0.14 cm −3 and n p,LISM = 0.04 cm −3 , with both the neutral and ionized components moving at the same velocity of V LISM = 26.4km s −1 and with the same temperature of T LISM = 6530 K.The interstellar magnetic field has a magnitude of 3.75 μG, 60°from V LISM (the so-called α BV ) within the HDP.The inner boundary conditions are 22 yr averaged solar wind conditions from 1995 to 2017, as described in Izmodenov & Alexashov (2020) and Kornbleuth et al. (2021).The magnetic field is described with a Parker spiral with a strength of 37.5 μG at 1 au.The solar magnetic field is modeled as unipolar in both the BU and Moscow models (Izmodenov & Alexashov 2015;Opher et al. 2015).As noted by Izmodenov & Alexashov (2015), magnetic forces in ideal MHD do not depend on the polarity or direction of the solar wind magnetic field; therefore, this approach allows the model to capture the magnetic field strength in the heliosphere as well as its effects while avoiding spurious numerical dissipation in regions where the solar magnetic field reverses polarity, such as the heliospheric current sheet (Michael et al. 2018).The IA1 model implements the inner boundary conditions at 1 au and the BU1 model implements them at 10 au by extracting the values of the Moscow model at 10 au.
One of the significant differences between the BU and Moscow models is how the heliopauses of each model are treated.In the BU model, reconnection is suppressed in the nose but allowed across the heliopause in the flanks based on diamagnetic arguments (Opher et al. 2017).In contrast, the Moscow model does not allow it.This lack of "communication" across the heliopause in the Moscow model creates a difference in magnetic topology.In the Moscow model there is a jump in thermal pressure just inside the heliopause and a jump in magnetic pressure just on the outside of the heliopause that is not seen in the BU model (Kornbleuth et al. 2021).
The heliopauses of these models can be seen in Figure 2. The shape of the heliopause is affected by the interstellar flow and the solar wind conditions (Korolkov & Izmodenov 2021, 2023).The BU heliopause is defined using a temperature isosurface that best separates the plasma that is unambiguously of solar origin from plasma that lie on magnetic field lines connected to the LISM.This definition has been used in previous studies and was explicitly explored in Michael et al. (2021).In future works (C.Onubogu 2023, in preparation), we will be revisiting this definition by implementing a level-set function.The heliopause in the Moscow model is determined by fitting a moving grid to discontinuities using a soft-fitting technique, proposed by Godunov et al. (1979), allowing for high resolution near each of the major discontinuities.Three conditions are applied to the grid surfaces determined to be the HP: (i) no mass flux through the surface, (ii) B n = 0, and (iii) the balance of total pressure on the two sides of the surface.The second BU model investigated, model BU2, is case 2 from Kornbleuth et al. (2020).The LISM conditions used are taken from Opher et al. (2020) and give good agreement with Voyager 1 and 2 outside of the heliopause.The LISM conditions differ from the previous conditions.They are as follows: n H,LISM = 0.18 cm −3 , n p,LISM = 0.06 cm −3 , with both the neutral and ionized components moving at the same velocity of V LISM = 26.4km s −1 and with the same temperature of T LISM = 6519 K.The interstellar magnetic field has a magnitude of 3.2 μG and is oriented toward the IBEX ribbon.This direction is within the HDP within the uncertainty of the measurement, with an α BV = 39.5°.The inner boundary condition is implemented at 10 au and is a fast-slow solarminimum-like configuration.The solar magnetic field is also treated as unipolar.

Heliospheric Lyα Absorption
As light from an emitting star transits to our solar system it can be absorbed by neutral hydrogen along the LOS and attenuate the observed emission at a given wavelength.This absorption is given via where I 0 (λ) is the intrinsic intensity, τ(λ) is the optical depth, and I(λ) is the final intensity.For convenience, a conversion from wavelength λ to heliocentric radial velocity v will be used, v = c(1 − λ 0 /λ), turning all functions of wavelength into functions of heliocentric radial velocity.
Within our model, the neutral hydrogen is treated kinetically, but to characterize the distribution of each cell we take moments of the kinetic phase-space distribution.It is convenient to assume the neutral hydrogen distribution can be constructed of multiple populations, with their own moments, depending on the location of charge exchange.We use four distinct populations to capture neutrals created within the pristine LISM, heated LISM, heliosheath, and supersonic solar wind.We only consider the absorption from the heliosheath population and the hydrogen wall.The supersonic solar wind population is negligible and the pristine LISM population is wrapped up into the ISM absorption.While the neutral distributions are not Maxwellian, using the moments of the velocity distribution as our density, velocity, and temperature has been performed in previous studies and is used here (Izmodenov et al. 2002;Wood et al. 2014).
The column density distribution toward a LOS, N(v), is constructed by using the moments of the distributions for each cell.These moments approximate the density, bulk velocity, and temperature of a Maxwellian as where b kT m 2 p = is the thermal velocity, and n, u, and T are the neutral hydrogen's density, bulk velocity, and temperature, respectively.m p is the mass of a proton, k is the Boltzmann constant, and e is Euler's number.Δl is the path length through the cell.
The distribution function in each cell is combined to find the total column density for each LOS.Optical depth as a function of velocity is related to the column density distribution as v Nv . The final function for the absorption in the heliocentric rest frame is then where m e is the mass of an electron, q e is the charge of an electron, λ 0 is the central wavelength of the Lyα transition, f is the oscillator strength, which is 0.416, and c is the speed of light.

Interstellar Medium Lyα absorption
Doppler broadening is not a valid assumption for the interstellar absorption outside the simulations' boundary due to the large column density toward each target.The absorption from the quantum-mechanical Lorentzian damping wings of the natural line profile is essential for these column densities and, as such, must be considered.A Voigt profile convolves a Maxwellian and a Lorenzian profile to account for this effect and is used here.The optical depth from a Voigt-profiledominated absorption is where In these equations, the constants are C p .m e is the electron mass, and Γ is the damping constant of the Lyα transition, which is 6.25 × 10 8 s.This absorption has three free parameters (T, V, N) that are fit using other absorption lines along the LOS.For this study, these values are taken from Wood et al. (2014), as extensive work has already been done to find the best values for the LOS in question (Table 1).

BU-Moscow Direct Comparison
The LOS chosen for direct comparison between the BU1 and IA1 models are shown in Figure 1.Both 36 Oph and α Cen are reliable targets to probe the hydrogen wall, while HD 35296 has detected heliotail absorption.These are the directions most sensitive to model differences.
Figure 3 shows that both models using identical boundary conditions produce nearly identical neutral and plasma density for distances less than 400 au down the tail.The plasma and neutral solutions become less similar at heliotail distances greater than 400 au from the Sun.The neutral solutions are more similar for longer distances tailward.As the neutral hydrogen has a large mean-free path, on the order of the size of the heliosphere, and the plasma solutions are similar, the neutrals travel further down before the differences become significant.
To quantify the differences between the solutions, cuts directly upwind are shown in Figure 4. Due to the lack of communication between the ISM and solar wind in the model IA1, there is a sharp drop in the magnetic field strength at the heliopause where the plasma pressure replaces the magnetic field pressure so that the total pressure is conserved.Model BU1 shows a higher plasma density, magnetic field strength, and neutral density throughout this domain from −400 to −100 au, approximately spanning the hydrogen wall.The maximum difference is 10% in the plasma density.Magnetic field strength and neutral density differences peak at about 5%.However, in most line cuts the differences are less than 5% for each parameter.This higher peak value of the magnetic field contributes to a greater slowdown in the plasma in front of the heliopause.From this greater slowdown, the plasma density increases, and the increased plasma density in turn creates a larger buildup of neutral hydrogen density.
To determine if this difference in hydrogen density is observable, we must evaluate the differences in the neutral conditions on LOS toward target stars.Figure 5 shows line cuts of density, radial velocity, and temperature of the neutral solution, specifically the hydrogen wall population, of both models toward the stars 36 Oph and α Cen.We see similar differences in these cuts as in Figure 4.
Figure 6 shows the modeled Lyα profiles generated from the LOS profiles presented in Figure 5.The modeled Lyα profiles are compared to observations normalized to the ISM absorption for the LOS.The differences between these models and observations are large with respect to other recent investigations into Lyα absorption (Zank et al. 2013;Wood et al. 2014).The LISM conditions used in those studies were specifically chosen to match the observations.As mentioned prior, the LISM conditions used in the solutions presented in this section were chosen to match Voyager 1 and 2 observations from just outside the heliopause (Izmodenov & Alexashov 2020).In this section, we are primarily interested in the differences between these models under identical conditions.
The region of the absorption profile in which the normalized flux is near zero intensity will be referred to as the saturated absorption region.The velocity corresponding to 0.5 normalized flux will be called the half flux velocity.Finally, the region to the right of the half flux velocity will be called the partial absorption region.These points and regions are explicitly shown in Figure 7.We chose to show these on a downwind target as the upwind targets do not have significant heliosheath absorption, which makes the partial absorption region less distinct.
The Lyα profiles of model BU1 and model IA1, seen in Figure 6, are nearly identical.The difference between the half flux velocity of the model BU1 and model IA1 profiles is less than 0.3 km s −1 for 36 Oph and 0.2 km s −1 for α Cen.As the observations were taken with different gratings, the spectral resolutions toward 36 Oph and α Cen are approximately 1.3 and 0.8 km s −1 , respectively.Therefore, the difference we see here would be undifferentiable with current observations.The differences in hydrogen density, velocity, and temperature seen in the line cuts are not observable, and therefore the shape of the heliosphere is undifferentiated in upwind Lyα observations.
We would expect any differences to be more prominent in the downwind direction, as this is where the most significant differences between the models appear.Figure 8 shows the neutral profiles toward the target star HD 35296.For this target, the neutral conditions are split into two parts: the neutrals created in the hydrogen wall that have streamed into the heliotail, and the neutrals created in the heliosheath.These two populations show up as the saturated and the partial absorption regions in the final absorption profile, respectively.
Outside of the neutral hydrogen depletion region near the Sun, the neutral hydrogen population created in the hydrogen wall in model BU1 peaks at a higher value than in model IA1 and starts to increase in density after approximately 400 au downwind.For the neutrals created in the heliosheath, a similar divergence between the models can also be seen at about 400 au, but IA1 provides higher heliosheath hydrogen number density than BU1.
This difference in behavior beyond 400 au can be explained due to the differences in the heliotail configuration of the two models  approximately 3.2 km s −1 since they were taken with a slightly coarser grating.The shift between these models is large enough that the observations of the object technically have enough resolution to distinguish the two profiles.However, in practice the uncertainties associated with these observations would make this infeasible.Also, the depth of the partial absorption at 70 km s −1 is deeper in model IA1.The maximum difference between the curves is 5% near 85 km s −1 .These effects can be explained with a closer look at the profile components.
Figure 9 shows how the neutral populations influence the differences presented in Figure 7.The neutrals created in the hydrogen wall, solid lines, show a broader absorption profile for model BU1, which has a higher neutral density along the LOS and therefore a wider saturated absorption.The extent of the profile rightward can be seen shifting the half flux velocity to the right in model BU1.Neutrals created in the heliosheath, dashed lines, in model IA1 have a larger density throughout the extent of the cut.This creates a deeper absorption in the region dominated by helisheath neutrals.Even though there is a maximum difference between the heliosheath absorptions of approximately 11% at about 40 km s −1 , the maximum difference between the simulated profiles is less than half of this value because most of the absorption difference is well within the saturated absorption from the hydrogen wall neutrals.
The differences in profiles downwind can be attributed to neutral hydrogen velocity distribution differences due to heliotail configurations.The neutral hydrogen velocity distributions are primarily affected due to the shorter heliotail in model BU1.Downwind of 400 au, when the LOS is outside of the heliopause in model BU1, neutral hydrogen chargeexchanges with plasma that is disturbed ISM plasma in model BU1 but heliosheath plasma in model IA1.
There is a significant lack of absorption in all three directions explored using these boundary conditions.The LISM parameters used as boundary conditions for models BU1 and IA1 were inferred from a comparison of the IA1 model and various Voyager observations.Section 4 shows that using a different set of LISM conditions allows for better agreement between models and Lyα observations.This implies that there is a tension between the LISM parameters that best match Lyα observations and the LISM parameters that best match voyager observations.This tension will need to be resolved in future work.It is worth noting that the LISM parameters inferred using the IA1 boundary conditions were found using timedependent solar wind conditions, while we used 22 yr solar cycle average conditions.However, the time-dependent effect would probably not resolve the lack of absorption; hence, this tension remains.

BU Model Comparison to Observations and Other Models
Previous studies have found good agreement with the Lyα observations using LISM conditions quite different from those used in our direct comparison (Section 3).Here we present results from model BU2 that employs LISM conditions, which produce Lyα profiles that better match the Lyα observations.The LISM conditions are listed in Table 2 and are as follows: n p,LISM = 0.06 cm −3 , n H,LISM = 0.18 cm −3 , V LISM = 26.4km s −1 , T LISM = 6530 K, and a B LISM with a strength of 3.2 μG in the direction of the IBEX ribbon (47.3°a nd −34.6°in ecliptic longitude and latitude, respectively).
Figure 10 shows that the LISM conditions used in model BU2 create a larger hydrogen wall and more depleted neutrals downwind than the LISM conditions used in model BU1.
Simulated Lyα profiles are generated for model BU2 using the same LOS as before.We compare model BU2 to two models from Wood et al. (2014), the most recent investigation to use the Moscow MHD model to simulate Lyα absorption.The LISM parameters used in these models is described in Table 2 and referred to as model W1 and model W2, accordingly.The LISM neutral and plasma densities for model BU2 match the densities used in model W1 and model W2.The B LISM used for model BU2 does not match the strength or direction of model W1 or model W2.We have already presented the differences between models using identical conditions in the previous section and, as such, are using models W1 and W2 to place model BU2 in context with the ongoing work to match Lyα profiles.These models use uniform solar wind conditions, as does the BU model.Model W1 has a magnetic field strength of 3.5 μG and is oriented 45°f rom V LISM in the HDP (46.1°and −42.4°in ecliptic longitude and latitude, respectively).W2 has a field strength of 4.4 μG and is oriented 20°from V LISM in the HDP (62.5°and −20.8°i n ecliptic longitude and latitude, respectively).Figure 11 shows how model BU2 Lyα profiles compare to observations and the results from model W1 and model W2.
Model BU2 and models W1 and W2 match upwind observations similarly.Both models W1 and W2 match the observations in the 36 Oph direction slightly better than model BU2, while model BU2 matches somewhat better than models W1 and W2 in the α Cen direction.For 36 Oph, the model BU2 half flux velocity is at 26.0 km s −1 , whereas models W1 and W2 have half flux velocities of 27.8 and 26.6 km s −1 , respectively.As mentioned earlier, the observations of 36 Oph have a velocity bin width of approximately 1.3 km s −1 .The difference between model BU2 and model W1 of 1.8 km s −1 would fall in adjacent observation bins, but the difference between model BU2 and model W2 of 0.6 km s −1 would be indistinguishable.The largest differences between the models can be seen near 30 km s −1 , where model BU2 disagrees with observations more than W1 and W2.
For α Cen the half flux velocity for models BU2 is at 32.1 km s −1 , whereas models W1 and W2 are at 32.1 and 33.8 km s −1 , respectively.The observations for α Cen have a narrower velocity bin width of approximately 0.8 km s −1 .Similarly to 36 Oph, the half flux velocity is indistinguishable between BU2 and W2 but slightly different between BU2 and W1.At 40 km s −1 , model BU2 better agrees with the observations, whereas models W1 and W2 overpredict the absorption.None of these models can match both of these targets simultaneously, so matching both upwind directions simultaneously should be a goal of future Lyα investigation.This might shed light on understanding our VLISM.Left: neutral hydrogen density showing the hydrogen wall neutral population (solid), heliosheath population (dashed), and total neutral density (dotted-dashed).Center: neutral hydrogen bulk velocity along the line of sight (LOS) for the hydrogen wall neutral population (solid) and heliosheath neutrals (dashed).Right: neutral density temperature along the LOS for hydrogen wall neutrals (solid) and heliosheath neutrals (dashed).Downwind, model BU2 shows a slightly different profile than models W1 and W2.Model BU2 has a saturated absorption that closely matches the model W2 profile, while the partial absorption of model BU2 matches the model W1 profile closer.The heliosheath being much smaller in extent in model BU2 can explain the difference between the models.The partial absorption from the heliosheath neutrals is not as strong in model BU2 since the column density of heliosheath neutrals is smaller.However, the half intensity velocity of model BU2 lands nearly halfway between W1 and W2.For model BU2 the half intensity velocity is 89.9 km s −1 as compared to 87.2 and 94.3 km s −1 for W1 and W2, respectively.Although these differences between these half flux velocities are large compared to velocity differences for α Cen and 36 Oph, the observations toward HD 35296 have a velocity bin width of approximately 3.2 km s −1 .Similar to the last two objects, the difference between model BU2 and model W1 is undifferentiable, while the larger difference would fall in separate observation bins.Higher-resolution observations would allow for an easier differentiation, and potentially reveal the tail structure if the LISM conditions are strongly constrained.
Overall, model BU2 can match observations as well as the Moscow models used in Wood et al. (2014) for upwind and downwind targets.The differences between the models that  appear are nearly unobservable, with only the most extreme of model differences being even plausibly differentiable with current observations.An improvement to the spectral resolution of the observations would be needed to differentiate these models.Also, a larger difference between observations and simulated profiles exists downwind compared to upwind.Determining precise LISM conditions will improve our match to observations in the future.
For the downwind target, the treatment of the plasma distribution function within the heliosheath should be improved by using a non-Maxwellian plasma distribution.Treating the solar wind ions as a single fluid does not adequately capture the effect of the PUIs within the heliosphere.These ions will fill the heliosheath and affect the global and specifically neutral properties through charge exchange.As described in Malama et al. (2006) and Opher et al. (2020), a separate treatment of the cold solar wind and hot PUIs shrinks the heliosphere.This is because the PUIs charge-exchange and leave the system.In particular, Opher et al. (2020) showed that in 3D the heliosphere becomes more symmetrical in the nose region, with the PUIs charge-exchanging and leaving the system.The difference in the shape of the heliosphere would change the conditions upstream of the heliosphere, and, consequently, the flow of neutral hydrogen through the heliosphere.This, in turn, will change the neutral solution, which could present as a difference in the Lyα absorption.This should be explored in future works.

Effect of Local Interstellar Medium Conditions on Lyα Absorption
Here we present a parameter study on LISM conditions and how they affect Lyα absorption within the heliosphere.The four parameters with the most uncertainty in the LISM are n p,LISM , n H,LISM , T LISM , and B LISM .In previous studies, these parameters have either been changed in concert (Zank et al. 2013) and, as such, the precise effect of each parameter on the structure of the hydrogen wall is unclear, or instead the overall impact on the simulated profiles considered rather than looking at how the structure of the hydrogen wall changes (Wood et al. 2007).We will use values for n p,LISM , n H,LISM , T LISM , and B LISM that are motivated by recent attempts to constrain the LISM.
For this investigation, we use pure MHD simulations with a multi-fluid treatment of neutrals.This limits the interpretation slightly.A kinetic treatment of neutrals is essential to have a realistic neutral solution.However, the computational cost of kinetic-MHD models is much higher than a fluid treatment.Also, it has been shown that the difference upwind is minimal (Alexashov & Izmodenov 2005;Michael et al. 2022) and, as such, we should be able to get valuable results from pure MHD with updated LISM conditions compared to two models (yellow, orange) and observations (black dashed) from Wood et al. (2014).Each panel has an inserted orientation diagram with the heliopause surface in yellow, the upwind direction represented as a red line, and the direction to the target star represented as a gray line.models.We will limit the interpretation to the trends of the absorption profiles rather than how the absorption profiles match with observation and only consider the upwind targets.
These models use a grid with a domain that extends to ±1500 au in the X direction and ±2000 au in the Y and Z directions.The grid has a resolution of 0.75 au in a shell around the 10 au inner boundary and a resolution of 3 au for X, Y, Z < 300 au.The default LISM conditions used by all these models will be the magnetic field configuration of BU1, |B LISM | = 3.75 μG and α BV = 60°, and the plasma and neutral densities and temperatures of BU2, 0.06, 0.18 cm −3 , and 6519 K.
The effect of the first parameter, n p,LISM , is presented in Figure 12. n p,LISM takes on values of 0.04, 0.06, and 0.08 cm −3 .As one would expect, as plasma density is increased the charge-exchange rate increases in front of the heliosphere, creating a larger neutral density in the hydrogen wall.The heliopause boundary moves inward with increasing plasma density.Increased plasma density results in a slight shift in the saturated absorption profile toward higher velocities.The half intensity velocity of these cases span from 18.6 to 19.2 km s −1 , which is a smaller difference than the best spectral resolution of our observations.
Figure 13 shows the effect of changing n H,LISM .The density of neutral hydrogen takes on values of 0.18 and 0.21 cm −3 .Similar to n p,LISM , increasing the neutral hydrogen density in the LISM results in a larger hydrogen wall due to increased charge exchange in front of the heliosphere.The velocity profiles are nearly identical for R < 200 au, with a slight difference past this point.The increased density corresponds to an increase in the temperature of the neutrals throughout the wall.Finally, the effect of an increase in hydrogen density is a slight shift in the saturated absorption profile toward higher velocities.The difference between half intensity velocities is 1.4 km s −1 , approximately the same size as the spectral resolution toward 36 Oph.
Figure 14 shows the effect of changing T LISM for the plasma and neutral components of the LISM.The temperature takes on values of 6500, 7000, and 7500 K.These profiles show slight differences in density and temperature and are nearly identical for velocity.For the density profile, the hydrogen wall begins to gain density further upwind for hotter LISM temperatures.This is because the charge-exchange rate depends on the temperature of the plasma and neutral components.The temperature profiles are slightly higher as LISM temperature increases.However, this effect is small compared to some of the other cases looked at.While the increased LISM temperature increases the temperature of the hydrogen wall, each case reaches a peak temperature of approximately 22,000 K. Higher temperatures of the LISM show up in the simulated absorption profile as slight increases in absorption.The half intensity velocities only span a difference of 0.5 km s −1 , much less than the resolution of the observations toward 36 Oph.
The final part of this investigation will look at the effect of changing the LISM magnetic field.It has been seen that the strength and direction of B LISM can affect the Lyα profile (Wood et al. 2007;Zank et al. 2013), but it was not seen how individual parameters could change the structure of the hydrogen wall and, in turn, the absorption profile.We will assume that the B LISM is in the HDP but the strength and α BV are free to change.
The effect of the LISM magnetic field strength is presented in Figure 15.Decreasing the LISM magnetic field strength increases the hydrogen wall's total density and peak density.It has been shown that a strong magnetic field can mediate the hydrogen wall (Zank et al. 2013) and, as such, is unsurprising.The heliopause also moves inward with increasing magnetic field strength as there is higher magnetic pressure in the LISM.The higher magnetic field strongly affects the density, velocity, and temperature of these profiles.The lower magnetic field strength creates a hydrogen wall that has a higher density and temperature.The velocity profile also shifts, corresponding to where the hydrogen wall begins and ends.Lower LISM magnetic field strength corresponds to a hydrogen wall with a higher density and temperature, which creates more absorption, indicated by a shift in the absorption profile to the right.The half intensity velocity of the profiles span from 18.6 to 21.5 km s −1 , which would be resolved over multiple velocity bins for either upwind spectral resolution.
Finally, the effect of changing the direction of B LISM can be seen in Figure 16.The peak column density and width of the hydrogen wall do not significantly change with the inclination of B LISM .Three significant differences between the models are the velocity profile, temperature profile, and the heliopause distance.The heliopause distance is not a factor in the profiles, as the absorption is independent of distance.Still, it can be  explained by the B LISM being more perpendicular to the heliopause surface, creating a larger magnetic pressure.Changing the angle of the B LISM causes the structure of the hydrogen wall to change and, as such, can be seen in the profiles.For the temperature profile, as B LISM becomes closer to parallel with V LISM the temperature of the neutrals becomes hotter throughout the entire wall.This effect is seen in the simulated profile as a deeper absorption.The half intensity velocities of the models span from 18.5 to 25.9 km s −1 .This is the largest effect of any parameter shown.This is large enough that the differences would span multiple velocity bins even with the poorest spectral resolution of the observations shown here.
The strength and direction of B LISM show a substantial effect on the position of the Lyα profile.These trends are qualitatively consistent with what was seen by Wood et al. (2007).The strong dependence on B LISM presents an opportunity to strongly constrain either the strength of B LISM or the direction of B LISM if the other parameter is known confidently.Figures 12-16 show that of n p,LISM , n H,LISM ,  T LISM , and B LISM the parameters with the strongest effect on absorption profile shape are the strength and orientation of B LISM .Since the LISM flow velocity is near the fast magnetosonic speed, small changes in the magnetic field can substantially affect the resultant flow and corresponding absorption profile.

Conclusion
We present in this paper the first comparison between a short-tailed and long-tailed heliosphere model using Lyα absorption.In this direct comparison, model BU1 and model IA1 produce nearly identical upwind neutral hydrogen distributions and, consequently, almost identical Lyα absorption profiles.Upwind Lyα observations cannot distinguish the heliosphere's shape.This is an expected result, following Kornbleuth et al. (2021), showing nearly identical heliosphere models upwind.
Downwind, the absorption profiles were similar but with notable differences.In this direction, the shortened heliosheath in model BU1 appeared in the simulated absorption profiles as a shallower absorption in the range of 75-150 km s −1 in the heliocentric velocity scale.Also, neutrals created in the hydrogen wall show a saturated absorption shifted rightward by 4 km s −1 .Higher-resolution observations could potentially reveal tail structure if the LISM conditions are well constrained.This difference will be significant for future attempts to match Lyα absorption profiles and to distinguish between a long-tailed and short-tailed heliosphere.
It is important to note that better treatment of the ion population in the heliosheath is needed.Allowing the ion's distribution function to be non-Maxwellian is required for a more realistic heliosheath solution.A more sophisticated ion treatment would give more realistic neutral distributions, which would produce a better Lyα absorption profile.
The second set of LISM conditions investigated showed closer agreement to the observations than the LISM conditions used in the direct BU-Moscow comparison.The boundary conditions used for the direct comparison were chosen to match Voyager observations, not necessarily Lyα absorption, and as such showed underabsorption throughout all comparisons.The boundary conditions with better agreement to Lyα observations consisted of n p,LISM = 0.06, n H,LISM = 0.18 cm −3 , and |B LISM | = 3.2 μG oriented in the IBEX ribbon direction.Models BU2, W1, and W2 match observations as well as each other.Downwind, the absorption from model BU2 was slightly steeper but still off from the observed profiles.The half flux velocity of model BU2 (89.9 km s −1 ) is nearly halfway between W1 (87.2 km s −1 ) and W2 (94.3 km s −1 ).As Section 5 discussed, n p,LISM , n H,LISM , and B LISM all affect the absorption profiles, so no single parameter can be said to be the cause of the better match.And, again, it is important to note that each of these models did not consider the effect of a non-Maxwellian plasma distribution or a separate treatment of PUIs, which will likely help to diminish the tailward discrepancies.
Finally, MHD simulations where a single parameter for the LISM condition was varied showed the effect of n p,LISM , n H,LISM , T LISM , and B LISM on Lyα absorption.LISM plasma density and hydrogen density were directly correlated to the amount of hydrogen wall Lyα absorption.We found that the neutral hydrogen density was a stronger predictor of the position of Lyα absorption.T LISM had a very weak effect on the absorption profile.|B LISM | had an inverse relationship with the hydrogen wall density, a weaker |B LISM | having a stronger Lyα absorption.However, the B LISM -V LISM angle was the strongest predictor of Lyα absorption, causing the most significant difference in Lyα absorption profiles.A better constraint on the strength or direction of B LISM would allow the remaining B LISM parameter to be constrained by Lyα absorption.

Figure 1 .
Figure 1.A schematic view in the meridional plane of the directions of the stars of interest overlaid the neutral density solution of the BU model, with the outer black line corresponding to the BU heliopause.The heliopause is defined using the surface corresponding to a temperature of 2.71 × 10 5 K.The Y coordinates of these stars are projected to the Y = 0 plane.

Figure 2 .
Figure 2. Isosurfaces corresponding to the heliopause, the region separating solar-connected magnetic field lines and ISM-connected magnetic field lines, in the BU model (left) and Moscow model (right).The BU model heliopause is defined using the surface corresponding to a temperature of 2.71 × 10 5 K.The heliopause in the Moscow model is determined by fitting a moving grid to the discontinuity.The black lines overlaid on the isosurfaces correspond to the intersection of the isosurface with the meridional slice.

Figure 3 .
Figure 3. Meridional slices of the BU and Moscow heliosphere models with the BU heliopause in white and the Moscow heliopause in black.Panel (A) shows plasma density contours for the BU model and panel (B) shows plasma density contours for the Moscow model.Panel (C) shows neutral hydrogen density contours for the BU model and panel (D) shows neutral density contours for the Moscow model.
. The LOS toward HD 35296 samples a different region of plasma in model BU1 compared to model IA1.In model BU1, the LOS crosses the heliopause near 400 au and enters a region where the LISM plasma turbulently mixes with heliosheath solar wind plasma along reconnected field lines.However, in model IA1 the LOS remains within the heliosheath.Neutrals created in the BU model downwind of the heliopause have a different characteristic velocity and temperature compared to neutrals created in the Moscow heliosheath plasma.Simulated Lyα profiles from these line cuts are shown in Figure 7.The half flux velocity of the model BU1 profile is shifted by 4 km s −1 to the right compared to the model IA1.The observations of HD 35296 have a spectral resolution of

Figure 4 .
Figure 4. Line cuts directly upwind for both the BU model (blue) and Moscow model (red).Panels (A), (B), and (C) show plasma density, magnetic field strength, and neutral density, respectively.

Figure 5 .
Figure 5. Line cuts of neutral hydrogen parameters toward 36 Oph (top) and α Cen (bottom) for both the BU model (blue) and Moscow model (red).Left: neutral hydrogen density showing the neutrals created in the hydrogen wall in solid lines and the total neutral density in dashed lines.Center: neutral hydrogen bulk velocity along the line of sight (LOS).Right: neutral density temperature along the LOS.

Figure 6 .
Figure 6.Simulated absorption profiles generated from the line cuts from Figure 5 compared to observations taken from Wood et al. (2014), along with a 3D isosurface of the BU model with the directions upwind and toward the star of interest labeled for orientation.Top: toward 36 Oph.Bottom: toward α Cen.

Figure 7 .
Figure 7. Left: simulated absorption profiles generated from the line cuts from Figure 8 compared to observations from Wood et al. (2014).Solid horizontal and vertical black lines denote the half flux velocity.Black arrows with "S.A" and "P.A" point to the saturated absorption region and the partial absorption region, respectively.Right: 3D isosurface of the BU model with the directions upwind and toward HD 35296 labeled for orientation.

Figure 8 .
Figure8.Line cuts of neutral hydrogen parameters toward HD 35296 for both the BU model (blue) and Moscow model (red).Left: neutral hydrogen density showing the hydrogen wall neutral population (solid), heliosheath population (dashed), and total neutral density (dotted-dashed).Center: neutral hydrogen bulk velocity along the line of sight (LOS) for the hydrogen wall neutral population (solid) and heliosheath neutrals (dashed).Right: neutral density temperature along the LOS for hydrogen wall neutrals (solid) and heliosheath neutrals (dashed).

Figure 9 .
Figure 9. Left: line cut of the neutral hydrogen density of the heliosheath neutrals (dashed) and hydrogen wall neutrals (solid).The BU and Moscow solutions show significant departure past approximately 400 au downwind due to the heliopause configurations.Right: simulated absorption profiles generated from the heliosheath neutrals (dashed) and heated ISM neutrals (solid) compared to observations for HD 35296 from Wood et al. (2014).

Figure 10 .
Figure 10.Meridional slices of neutral density contour levels of two BU models showing the effect of the LISM conditions on the neutral solution with both heliopauses overlaid.The black line is the heliopause corresponding to the model used in Section 3 whereas the white line is the heliopause corresponding to the model used in Section 4. Left: neutral solution using the LISM conditions used in the direct BU-Moscow comparison.Right: neutral solution using the higher-density neutral LISM density.

Figure 11 .
Figure 11.Simulated normalized Lyα absorption toward the target stars 36 Oph (top left), α Cen (top right), and HD 35296 (bottom) for the BU model (green solid) with updated LISM conditions compared to two models (yellow, orange) and observations (black dashed) from Wood et al. (2014).Each panel has an inserted orientation diagram with the heliopause surface in yellow, the upwind direction represented as a red line, and the direction to the target star represented as a gray line.

Figure 12 .
Figure 12.Top left: neutral density line cut toward 36 Oph for BU MHD models with varied LISM plasma density.The red, purple, and blue lines correspond to a LISM plasma density of 0.04, 0.06, and 0.08 cm −3 , respectively.Top right: same but for neutral hydrogen parallel velocity.Bottom left: same but for neutral hydrogen temperature.Bottom right: simulated normalized Lyα absorption for the MHD models with varied LISM plasma density.

Figure 13 .
Figure 13.Same as Figure 12 but with a varied LISM neutral hydrogen density.The red and blue lines correspond to a LISM neutral hydrogen density of 0.18 and 0.21 cm −3 , respectively.

Figure 14 .
Figure 14.Same as Figure12but with a varied LISM temperature (both plasma and neutral).The red, purple, and blue lines correspond to a LISM neutral hydrogen density of 7500, 7000, and 6500 K, respectively.

Figure 16 .
Figure 16.Same as Figure 12 but with a varied B LISM -V LISM angle.The purple, red, and blue lines correspond to a B LISM -V LISM angle = 60°, 40°, and 20°within the HDP, respectively.
Wood et al. (2014)it column density (N), heliocentric velocity (V 0 ), and temperature (T) of the ISM toward the target stars fromWood et al. (2014).λ, β are the longitude and latitude of the stars in ecliptic (J2000) coordinates.

Table 2 Model
LISM Conditions Model Name n p,LISM n H,LISM