Could the Local Cavity be an Irregularly Shaped Strömgren Sphere?

Extending for 50–200 pc in all directions from the Sun, the Local Cavity has been characterized as an old supernova bubble consisting of low-density million-degree plasma heated by supernova shocks. We summarize the arguments for and against this model and conclude that hydrogen in the Local Cavity is fully ionized, and the plasma near the Galactic plane is mostly warm (10,000–20,000 K) rather than hot (106 K). The brightest extreme-ultraviolet source detected in the EUVE all-sky survey is the star ϵ CMa. Its EUV radiation photoionizes the outer layers of the Local Interstellar Cloud and other nearby warm interstellar clouds despite the star’s 124 pc distance. Pulsar dispersion measures indicate an electron density of 0.012 cm−3 in the Local Cavity itself. At this density the Strömgren sphere of ϵ CMa is as large as the Local Cavity. We propose that the Local Cavity is an irregularly shaped Strömgren sphere containing a small percentage of hot gas likely in many filamentary structures. We also propose that shocks from recent supernovae encountered pre-existing Strömgren sphere gas, and that the partially ionized Local Interstellar Cloud and other nearby clouds could have been formed when supernova shocks encountered regions with relatively weak magnetic fields producing compression, higher density, and recombining hydrogen.


Introduction
Recent three-dimensional models of the interstellar medium (ISM) within 3kpc of the Sun show a cavity region of low absorption and thus low density extending 100-200pc from the Sun, surrounded in most directions by dense clouds identified by absorption in the NaI D and CaII K lines. The shape of this Local Cavity is irregular with a few dense clouds within 70-100pc of the Sun and low-density chimneys extending into the halo toward the North and South Galactic poles. The models presented by Capitanio et al. (2017), Lallement et al. (2019), and Leike et al. (2020) are based on reddening and color excess obtained from a variety of sources, including diffuse interstellar absorption bands with distances to stars from GAIA. These models describe the morphology of the low-density region surrounding the Sun that is now called the Local Cavity. Located within the Local Cavity is the Cluster of Local Interstellar Clouds (CLIC) consisting of warm (5000-10,000 K) partially ionized clouds extending 5-10pc outward from the Sun Frisch et al. 2011). The Sun is located at the edge of and will soon exit one member of the CLIC, the Local Interstellar Cloud (LIC). At least one cold (10-30 K) dense cloud called the Local Leo Cold Cloud (LLCC) is located in the Local Cavity at a distance between 11.3 and 24.3pc from the Sun (Peek et al. 2011). Fuchs et al. (2006) and Benitez et al. (2002) presented a convincing case that the Local Cavity was produced by supernova explosion blast waves that heated and evacuated the surrounding interstellar gas and produced an exterior dense shell of cooler gas. Breitschwerdt et al. (2016) found that a total of 14-20 supernovae over the past 13 Myr in the Scorpius-Centaurus Association created this multiple supernova remnant, with the two most recent supernovae occurring about 2.3 Myr ago at a distance of 90-100pc. The recent age of these two supernovae has been inferred from the presence of the radioactive 60 Fe isotope produced by electron-capture supernovae and found embedded in deep ocean crust samples (e.g., Wallner et al. 2016). The effect of supernova blast waves is to produce a remnant consisting of highly ionized million-degree gas that cools by radiation, expansion, and shock heating of denser material at the edge of expansion. The Local Cavity was likely created by the cumulative heating, expansion, and subsequent cooling of many supernova events. The most recent of these supernovae would have evolved inside of the Local Cavity producing a hot bubble that filled a portion or all of the present volume of the Local Cavity. Shelton (1999) computed the long-term evolution of a supernova explosion expanding into a previously evacuated low-density (0.01 cm −3 ) modest temperature (10 4 K) cavity. These hydrodynamic simulations that include non-equilibrium ionization could provide an approximate model for the present day Local Cavity after the most recent supernova explosions.
After more than 40 yr of intensive studies, the question of what fills the Local Cavity still has no complete answer. The presence of some million-degree gas is universally accepted, but much or most of the Local Cavity could be filled with something else. Until now, what fills the Local Cavity has been studied by modeling the observed diffuse X-ray emission, where it is formed, and whether it is primarily thermal emission from diffuse hot gas or largely local emission produced when the solar wind ions charge exchange with neutral hydrogen in the heliosphere (Cravens et al. 2001). Unfortunately, the identification of the matter filling the Local Cavity is frustrated by two uncertain but critical parameters: the collisional excitation rates for the charge-exchange processes and the electron density in the Local Cavity. We critically review the evidence for hot gas in the Local Cavity and propose that most of the gas in the Local Cavity is at a much lower temperature and that hydrogen is completely ionized. Our proposed model for the Local Cavity consists of an irregularly shaped Strömgren sphere that contains some high-temperature gas.

Evidence for Hot Gas inside the Local Cavity
The Local Cavity was originally called the Local Bubble or Local Hot Bubble (LHB) on the basis of observed presumably thermal X-ray emission and theoretical models that predicted hot plasma in supernova remnants. Diffuse soft X-ray emission was first observed by sounding rocket experiments (e.g., McCammon et al. 1983) and subsequently with satellites. McCammon & Sanders (1990) reviewed the early observations and their interpretations. Prior to the unexpected discovery of X-ray emission from Comet Hyakutake (Lisse et al. 1996), the 70-284eV emission, usually called the 1/4 keV emission, was shown to be emitted from all directions within a few hundred parsecs of the Sun with enhanced emission near the Galactic poles. The 0.5-1keV emission was also thought to be partially from the Local Cavity and partially from the Galactic halo rather than extragalactic. The emission in both bands could be explained by thermal emission from a million-degree gas inside of the Local Cavity, but there was uncertainty concerning this interpretation (McCammon & Sanders 1990). The sensitive ROSAT sky maps in the 1/4, 3/4, and 1.5keV bands (obtained by Snowden et al. 1995) confirmed the source of diffuse X-ray emission from all directions. The 1/4keV maps, but not the 3/ 4keV maps, showed emission enhanced by a factor of three near the Galactic poles relative to the Galactic plane. Evidence that the diffuse soft X-ray emission originates primarily within the Galaxy rather than in the halo or beyond came from shadowing experiments in which the emission in the direction of dense hydrogen and molecular clouds was compared to the X-ray flux just outside of the clouds. Shadowing experiments of dense H I clouds showed that essentially all of the 1/4keV emission originates from in front of these clouds that are opaque to X-rays, whereas a substantial portion of the 3/4keV emission is partially obscured by the clouds and, therefore, comes from behind the clouds (Snowden 1993;Snowden et al. 2000). The absence of shadows from clouds within 150pc of the Sun, in particular MBM12 at 65pc (Snowden 1993) and the LLCC within 25pc (Peek et al. 2011), requires that nearly all of the 1/ 4keV emission must originate within the Local Cavity, but where in the Local Cavity and whether the hot gas fills all or only a portion of the Local Cavity is a debated topic.
The initial theoretical models of the interstellar gas (e.g., Field et al. 1969) assumed a two-component medium consisting of warm and cold gas, but the discovery of diffuse X-ray emission led to the incorporation of a third hotter component. The theoretical models of McKee & Ostriker (1977) and Wolfire et al. (1995) describe interstellar gas consisting of three components: cold (  T 50 K) neutral and molecular gas, warm (T = 5000-8000 K) neutral or partially ionized gas, and million-degree low-density ionized plasma. The warm partially ionized gas clouds within a few parsecs of the Sun  have properties roughly consistent with the warm component predicted by the classical models, and dense cold molecular clouds are observed typically by CO and H I 21 cm emission. The nearest cold gas with a temperature of 15-30K is the LLCC, located at a distance between 11.3 and 24.3pc from the Sun (Peek et al. 2011).
While these classical models provide a rough explanation for many observations, the models make a number of assumptions that are unlikely to be valid in the dynamic ISM. For example, the individual components are each assumed to be in steadystate equilibrium, each component is in pressure equilibrium with adjacent components, and the ionization and excitation of important ions are in steady-state equilibrium with the local temperature. However, numerical simulations by Berghöfer & Breitschwerdt (2002), which include supernova explosions and realistic thermal and dynamic processes, predict a very wide range of densities and temperatures in the ISM but no pressure equilibrium and no stable thermal phases.
Nevertheless, the rough agreement between the available observations and the theoretical models provided evidence that the heliosphere, together with the adjacent warm CLIC clouds, and the LLCC are all embedded in a region containing hot gas. The evidence for some 16 supernova explosions within the last 13 Myr in the nearby Scorpio-Centaurus Association that have provided heat and shocks in the solar neighborhood supported the idea that hot gas is present the Local Cavity.

Problems with the Local Hot Bubble Model
Several authors have called attention to problems with assuming that the Local Cavity is entirely filled with milliondegree gas or even that hot gas is present in the solar neighborhood. Welsh & Shelton (2009), in particular, provided a comprehensive listing of the observations that question the presence and amount of nearby hot gas.
Solar wind charge exchange (SWCX) emission: The unexpected detection of X-ray emission from Comet Hyakutake (Lisse et al. 1996) led to the recognition that chargeexchange reactions between solar wind ions and neutral gas in the heliosphere can produce X-ray emission (Cravens 1997;Cravens et al. 2001) that is indistinguishable from the emission produced by a million-degree plasma without unavailable high-resolution spectroscopy. This result led to two different scenarios: (1) that roughly half of the observed diffuse X-ray emission in the Galactic plane is produced by SWCX reactions inside of the heliosphere, with the other half produced by hot plasma in the Local Cavity (Robertson & Cravens 2003;Galeazzi et al. 2014), or (2) essentially all of the 0.75 keV emission in the Galactic plane is SWCX emission and there is no need for emission from a hot plasma except near the Galactic poles (Snowden et al. 1994;Cox 1998;Koutroumpa et al. 2009;Koutroumpa 2012). Essentially all of the observed X-ray emission from in front of the LLCC (11.3-24.3 pc) and the MBM12 cloud (about 90 pc) can be explained by SWCX emission without the need for hot gas in these sight lines (Peek et al. 2011). Estimates of the relative amounts of SWCX and hot gas emission depend critically on the incompletely known collisional excitation rates of the charge-exchange reactions. Using the then available rates, Koutroumpa et al. (2009) found that the SWCX emission in front of the shadowing clouds is 212-460 Snowdens 3 with a mean value of 333 Snowdens. With this range of SWCX emission rates, most of the observed 1/4 keV emission in the Galactic plane can be accounted for by SWCX emission. Subsequently, Galeazzi et al. (2014) compared 1/4 keV measurements in the Sun's helium focusing cone with ROSAT measurements in the same direction to infer a much smaller SWCX emission rate of about 140 Snowdens, which indicates that the SWCX accounts for only 40% of the emission near the Galactic plane and that hot gas must produce the remaining 60%.
High-resolution X-ray spectroscopy provides a new tool for separating the contributions of SWCX and hot gas thermal emission from within the Local Cavity, although incomplete SWCX collisional rates and the dependence of such rates on the solar wind speed limit the accuracy of the separation. Analysis of four high-spectral-resolution rocket observations led Wulf et al. (2019) to conclude that thermal emission from hot gas dominates the emission from within the Local Cavity at high Galactic latitudes but that SWCX is an important contributor to the emission at low latitudes. LHB gas is clearly present within the Local Cavity, but the extent to which hot gas fills the Local Cavity is uncertain. where the hot gas comes in contact with warm gas at the edge of the partially ionized warm gas clouds in the CLIC either in a conduction front or a turbulent mixing layer. O VI absorption lines are detected in the circumstellar environment of hot stars and at high Galactic latitudes, but O VI absorption has not been detected in lines of sight toward any stars within 58pc of the Sun (Barstow et al. 2010). The Local Cavity gas, at least in the environment of the local warm clouds, must therefore be cooler than 300,000K yet still be mostly ionized so as to not show neutral hydrogen absorption.
There have also been searches for other ions formed at temperatures near 10 5 K that would be indicative of interfaces with hot gas. Most of these searches, as summarized by Jenkins & Gry (2020), found only upper limits for the C IV absorption except in three sight lines. Jenkins & Gry (2020) then searched for absorption lines of Si IV, C IV, and N V at or near the velocities associated with warm clouds in the lines of sight. For this search they selected the star HD32309 located at 60pc, which is inside of the Local Cavity but well beyond the warm clouds in the CLIC. This star was considered optimal for the search because the interstellar magnetic field is predicted to be perpendicular to the cloud surface and thus not able to suppress heat transfer from surrounding hot gas. Upper limits to the absorption in these three ions for this and most other lines of sight provides a strong argument against the presence of hot gas near the local warm clouds. Jenkins & Gry (2020) considered several possible explanations for the absence of detected C IV absorption and thus the compelling case against a conduction or turbulent interface between the warm gas clouds and hot gas. They suggested that the warm clouds could be surrounded by 10 4 K ionized gas with a possible interface with hot gas located beyond the sight lines to the nearby stars, that is beyond 60pc. This suggestion is consistent with our Strömgren sphere model of the Local Cavity presented in Section 6.
Upper limits on EUV line emission: Upper limits for diffuse high-temperature emission obtained by the Espectrógrafo Ultra-violeta extremo para la Radiación Difusa satellite (Edelstein et al. 2001) exclude significant emission from both 10 6 K and intermediate-temperature (10 5 K) gas in the Local Cavity. Upper limits obtained with the Cosmic Hot Interstellar Plasma Spectrometer satellite by Hurwitz et al. (2005) for diffuse emission of Fe lines, in particular the Fe IX 171.1Å line, are also inconsistent with the predicted emission from putative 10 6 K thermal plasma in the Local Cavity.
While there are possible explanations for each of these observational discrepancies, one should consider other models of the Local Cavity that could explain low-density gas that is much cooler than 10 6 K with H fully ionized. Two reasons for the conclusion that little or no atomic hydrogen is present between the CLIC and the edge of the Local Cavity are (1) the very low upper limit to N(H I) in the 124pc line of sight to òCMa (Gry et al. 1995) and (2) the absence of a significant increase in N(H I) for lines of sight longer than 10pc (Wood et al. 2005). Lyu & Bruhweiler (1996) and Breitschwerdt & Schmutzler (1999) proposed that the Local Cavity gas is a recombining remnant of a past ionization event such as a supernova shock wave. In this non-equilibrium plasma, the degree of ionization can be far higher than the electron temperature of the gas (Shelton 1999). This model is supported by the presence of young massive stars in the nearby Scopius-Centaurus OB Association and the likely presence of a previous group of massive stars that produced many supernova explosions.
Welsh & Shelton (2009) proposed a "Hot-Top model" in which there is no hot gas except near the Galactic poles, but elsewhere the Local Cavity gas is highly ionized with an electron temperature of about 20,000K in rough pressure equilibrium with the partially ionized warm clouds. However, they provide no physical explanation for this model. A third possible model is an old supernova remnant in which most of the hot gas has cooled and is now photoionized by stellar EUV radiation sources inside the Local Cavity. We describe this Strömgren sphere model in Section 6.

What Fraction of the Local Cavity is Filled with LHB
Gas and What is its Structure? Liu et al. (2017) proposed a three-dimensional model for the structure of the LHB that fills most of the Local Cavity. The physical parameters of this LHB model are based on the results of Galeazzi et al. (2014) who found that SWCX is responsible for only 40%±5% of the X-ray emission in the Galactic plane with the remaining 60%±5% being diffuse X-ray emission from the LHB. With this estimate for the foreground SWXC, the Galactic plane X-ray emission from the LHB is 203±24 RU and the emission measure of this hot gas is EM= = n n L e p ( ) ´-1.55 0.018 10 3 cm −6 pc. Snowden et al. (2014) assumed that the LHB gas completely fills the path length L through the Local Cavity to a dense cloud, with L≈85 pc after a 5pc correction for the CLIC clouds. For this value of L, the emission measure predicts that ( ) = ´n 4.68 0.47 10 e 3 cm −3 . With this value for the electron density and the emission measures inferred from the ROSAT All Sky survey (RAST) measurements of hot gas in all directions, Liu et al. (2017) proposed a three-dimensional model of the LHB that neatly fits into the contours of the Local Cavity within 100-200pc of the Sun. This model predicts that essentially all of the Local Cavity is filled with the LHB.
It is important to recognize the circular logic of this analysis. The assumption that the entire path L≈85 pc from the Sun to a close dense cloud is filled with LHB gas led to an inferred electron density ( ) = ´n 4.67 0.47 10 e 3 cm −3 . With this assumed electron density, the hot gas in the LHB completely fills the 85pc path length. If instead, we use the only available measurement of the electron density in the Local Cavity, n e =0.012 cm −3 , which is based on pulsar dispersion measurements (see Section 6), then the EM of hot gas in the Galactic plane predicts that L≈10.7 pc rather than 85pc. Thus, only 20% of the path length through the Local Cavity is LHB gas and the filling factor for hot gas in the Local Cavity is likely a similar fraction. Thus most of the Local Cavity is filled with something that is not hot gas. Since the partially ionized gas in the CLIC extends only 5-10pc, the Local Cavity is filled mostly with gas that contains fully ionized hydrogen. What is the source of this ionization?
By fitting the 42-82Å spectrum of diffuse X-ray emission observed with the DXS spectrometer with a combination of SWCX and hot thermal gas emission, Smith et al. (2014) found that thermal emission from million-degree gas could explain only 26%±4% of the observed X-ray flux, with the remainder a combination of fast and solar wind SWCX flux. This result would reduce the hot gas component of the X-ray emission by a factor of 2.3 compared to that assumed by Liu et al. (2017) and the volume of the LHB by a factor of 12. Given the constraint of the pulsar-derived electron density, the results of both Galeazzi et al. (2014) and Smith et al. (2014) support our conclusion that the LHB gas fills only a small fraction of the Local Cavity volume. What then fills most of the Local Cavity volume and what are the properties of this gas?

Sources of EUV Radiation
Aside from the Sun, the brightest observed source of extreme-UV (EUV) radiation detected by the EUVE satellite is the B2II star òCMa (d=124 pc) with an intrinsic ionizing flux of about 2.7×10 46 s −1 (Vallerga & Welsh 1995). This flux estimate includes a correction for absorption by a hydrogen column density, N(H I)=9×10 17 cm −2 , along the line of sight to the star. Gry et al. (1995), however, argued that N(H I) 5×10 17 cm −2 on the basis of HST spectra, in which case the intrinsic ionizing flux from òCMa would be smaller than that estimated by Vallerga & Welsh (1995). In their reanalysis of the òCMa sightline based on higher resolution far-UV spectra, Gry & Jenkins (2001) used measured column densities of O I to infer column densities of neutral hydrogen through each of the three clouds in the line of sight and the total N(H I) toward the star. With the assumption that oxygen is undepleted in the three clouds, they inferred N(H I)=6.0± 1.2×10 17 cm −2 . With the alternative assumption that the depletion of oxygen in the three clouds is the same as average values in the ISM, they inferred that N(H I)=9.0±2.0×10 17 cm −2 .
Since these values are consistent with the original estimate of N(H I)=9×10 17 cm −2 , we will use intrinsic ionizing flux value proposed by Vallerga & Welsh (1995).
In their study of the òCMa line of sight with the echelle gratings on HST/GHRS, Gry & Jenkins (2001) measured absorption in many interstellar lines at the predicted radial velocities of the LIC and Blue clouds (their components 1 and 2). For the LIC component, the temperature T=7000±1200 K and electron density n e =0.12±0.05 cm −3 measured from the C II line ratio and the Mg II/Mg I line ratio are consistent with the values obtained by . For component 2, the Blue cloud originally seen toward Sirius, Gry & Jenkins (2001) obtained a high temperature T=8200-30,000 K and low electron density n e =0.016-0.088 cm −3 . However, Redfield & Linsky (2004) found for the αCMa A and B sight lines that = -+ T 3000 1000 2000 K at the Blue cloud velocity. Analysis of other stars observed through the Blue cloud are needed to understand the difference in temperature. The results obtained by Gry & Jenkins (2001) for the third component are very interesting because the inferred ionization of hydrogen is very high (0.955%-0.985%). They argued that the third component lies beyond the LIC and Blue clouds and is very highly ionized by the unabsorbed EUV radiation from òCMa. Since S II is generally undepleted and is the dominate ionization stage in warm interstellar gas, they could estimate from N(S II) the total hydrogen column density N(H tot)=9.4±1.45×10 17 cm -2 in the òCMa sightline. From the difference between N(H I) and N(H tot), they concluded that at least 96% of the sightline to òCMa is either empty or filled with highly ionized hydrogen.
The second brightest EUV source is βCMa (B1 II-III; d=151 pc), followed by many hot white dwarfs located inside of the Local Bubble (Vallerga & Welsh 1995;Vallerga 1998). The total ionization rate of 33 hot white dwarfs measured by EUVE is ∼1.6×10 45 photons s −1 (Welsh et al. 2013), which is more than a factor of 10 times smaller than the ionizing flux in the 500-912Å band from òCMa. Interstellar absorption along the line of sight to βCMa was studied by Dupin & Gry (1998) using UV spectra from HST/GHRS and by Jenkins et al. (2000) using UV spectra from the IMAPS instrument. Jenkins et al. (2000) identified a velocity component at the predicted radial velocity of the Blue cloud. There is also absorption at the predicted radial velocity of the LIC.

Constraints on the Wind of òCMa
The referee pointed out that the decline in EUV flux from òCMa shortward of the He I photoionization edge at 504Å is too small to be explained only by interstellar He I absorption.
To test this statement, we used the interstellar He I column densities obtained by Dupuis et al. (1995) from EUVE spectra of six white dwarfs at distances (42-90 pc) consistent with their lines of sight being entirely within the Local Cavity. Since N (He I) increases linearly with distance except for the most distant of these stars, we scaled the measured N(He I) toward the closest star GD71 to the distance of òCMa obtaining N(He I)=(1.54±0.24)×10 17 cm −2 , which produces an optical depth of 1.15±0.18 at 504Å corresponding to a flux decrease by a factor of -3.0 0.36 0.78 at the bound-free edge. The observed flux decrease, however, is a factor of 5-15 (Cassinelli et al. 1995), which requires an optical depth of 1.6-2.7. Two factors that complicate this analysis are the confluence of interstellar He I absorption lines, which reduces the observed flux longward of 504Å, and the uncertain emission in stellar models used to predict the flux shortward of 504Å.
An important source of additional He I opacity could be absorption in the stellar wind. Cohen et al. (1996) found that wind absorption is required to explain both the X-ray flux observed by ROSAT and the EUV flux observed by EUVE. In their wind model, which is similar to that generally accepted for O-type stars, the embedded hot (T>10 5.5 K) gas produced by shocks fills less than about 10% of the volume and gas at temperatures below 10 5 K fills the remainder.
The additional He I attenuation at the 504Å bound-free edge can be estimated from the attenuation of iron complex emission lines at 175Å to 0.13-0.21 of their predicted flux level in the wind model. Since the He I opacity at 504Å is about a factor of 6.0 larger at 504Å than at 175Å, the estimated wind opacity has an optical depth of 11-15 at 504Å, which is far too large to explain the observed decrease in the flux shortward of 504Å. However, X-rays and EUV emission from embedded shocks in the wind can photoionize neutral helium throughout the wind, and the absorption cross-sections for neutral and singly ionized helium are about the same at 175Å. Attenuation of the 175Å feature could be due primarily to singly ionized helium rather than neutral helium. Therefore, helium in the wind could be highly ionized, reducing the He I optical depth in the wind at 504Å by a large factor. We can estimate this factor from the increase in optical depth needed to produce a flux decrease shortward of 504Å by the observed factor of 5-15. Since the interstellar optical depth is 1.15±0.18, the additional optical depth from He I absorption in the wind is 0.45-1.6 rather than 11-15. This reduced optical depth requires that the wind be highly ionized with N(He I)/N(He)=0.046-0.16.

Effects of EUV Radiation
The hydrogen column density through the three clouds in the direction of òCMa is N(H I)=9 10 17 cm -2 . As a result the remaining 124pc sightline to the star has extremely little neutral hydrogen, N(H I)<2×10 17 cm -2 or n(H I)<0.00052 cm −3 . This supports the assumption that beyond the CLIC, hydrogen in the Local Cavity is essentially fully ionized.
The region within Galactic longitude 225°l290°and Galactic latitude −60°b+10°shows very low H I column densities corresponding to a skin depth of <0.35 pc from the geometric center of the LIC in the direction of òCMa. Linsky et al. (2019) called this region the "hydrogen hole." The lines of sight to òCMa, βCMa, and Sirius as seen from the center of the LIC all traverse the hydrogen hole and all three stars lie inside of the Local Cavity. These three strong sources of ionizing radiation shape the morphology of the LIC as measured from N(H I). Welsh et al. (1999) referred to the low hydrogen column density along the lines of sight to òCMa and βCMa as an interstellar tunnel or local chimney that extends beyond these stars to the Galactic halo.

The Strömgren Sphere Model of the Local Cavity
In a classic paper, Strömgren (1939) showed that the EUV radiation (λ<912 Å) from a hot star completely ionizes hydrogen in its surrounding volume (called a Strömgren sphere) out to a distance, now called the Strömgren radius.
Here the build up of neutral hydrogen opacity absorbs the photoionizing radiation, producing a narrow partially ionized shell surrounded by neutral hydrogen gas. Strömgren developed a simple model assuming that the hot star is located in a constant density environment in which flows are ignored and photoionization of hydrogen is balanced by recombination in a steady state. In this case, the radius of the classical Strömgren sphere is where dN dt i is the number of ionizing photons per second, n i and n e are the number densities of ions and electrons inside of the Strömgren sphere, and α≈4×10 −13 cm 3 s −1 is the recombination factor (Harwit 1988). For the 504-912Å radiation, where most of the ionizing radiation from òCMa is located, hydrogen will be fully ionized and helium mostly neutral inside of the Strömgren sphere. For a harder radiation field with significant radiation at wavelengths shortward of the 504Å photoionization edge of He 0 or the 228Å photoionization edge of He + , as is the case for very hot white dwarfs such as G191-B2B and HZ43, then helium will be either singly or doubly ionized. Tat & Terzian (1999) estimated the sizes of Strömgren spheres around hot white dwarfs in the Local Cavity using the classical Strömgren sphere model. This model has been extended to include dust opacity, clumpiness, diffuse radiative transfer, and dynamics (e.g., Yorke 1986).
McCullough (2000) computed irregularly shaped models for the case of a hot star embedded in a larger ionized cavity. Depending on the location of the hot star in the cavity, the H II region around the star is no longer a sphere. Rather, the H II region produced by the hot star is larger than for the classic case because the surrounding gas is not neutral and the two H II regions can merge.
SiriusB could also be an important local ionization source given its short 2.6pc distance from the heliosphere. Fitting the HST spectrum of SiriusB with a non-LTE model atmosphere, Barstow et al. (2005) obtained the stellar parameters T eff =25,193 K, log g=8.556, and radius 0.0081 solar. M. Barstow (2021, private communication) kindly computed the flux shortward of 912Å for this model as 9.4×10 39 photonss −1 . The radius of a classical Strömgren sphere for this photon flux is 0.25pc for an assumed n e =0.1 cm −3 (Redfield & Falcon 2008) or 1.14pc for an assumed n e =0.01 cm −3 . These calculations are for an isolated Strömgren sphere surrounded by neutral hydrogen, but SiriusB is embedded in the large H II region ionized by òCMa.
The missing parameters needed to estimate Strömgren sphere radii are the electron and proton densities in the line of sight to the star. There are no direct measurements of n e or n p for the òCMa line of sight or the Local Cavity in general, but dispersion measures of radio signal time delays from pulsars provide a good estimate. The mean electron density in the lines of sight to the nearest five pulsars at distances of 156-372pc is 0.0120±0.0029 cm −3 (see Table 1). For comparison, the mean electron density in the thick disk of the Galaxy is 0.01132±0.00043 cm −3 (Yao et al. 2017a), or 0.015±0.001cm −3 (Ocker et al. 2020). However, the electron density in the VLISM beyond the heliopause at 138-148au from the Sun is about 0.11cm −3 (Ocker et al. 2021), and the electron density in the VLISM inferred from IBEX measurements and ionization of He is 0.063cm −3 (Bzowski et al. 2019). For the electron density in the Local Cavity of n e =0.012 cm −3 and assuming that n p =n e , the radius of the Strömgren sphere of òCMa is R≈160 pc. EUV radiation from βCMa, other hot stars, and white dwarfs will increase the size of the Strömgren sphere. Since òCMa is only 124pc away, the LIC and other warm clouds in the CLIC are surrounded by ionized Strömgren sphere gas, which likely has a temperature of 10,000-20,000K.
This simple calculation leading to R≈ 160 pc has a number of important consequences.  , the cloud thicknesses are 0.25pc. The cloud thicknesses in these directions are, therefore, consistent with their being Strömgren shells. It is likely that the outer edges of all clouds and, in particular, the filamentary clouds like Mic facing the EUV radiation from òCMa are Strömgren shells.
A second consequence of R≈160 pc is that the entire Local Cavity could be an irregularly shaped Strömgren sphere ionized by òCMa and other hot stars and white dwarfs. Welsh et al. (2013) computed the sizes of isolated Strömgren spheres surrounding 33 hot white dwarfs inside the Local Cavity based on EUVE measurements of their EUV radiation. Since these white dwarfs lie inside of the Strömgren sphere of òCMa, the combined EUV radiation from all of these stars is sufficient to ionize a region larger than 160pc and likely the entire Local Cavity.
The likely time of the most recent supernova explosion in the Local Cavity is obtained from measurements of the isotope 60 Fe with a half-life of 2.6 Myr that is formed during supernova explosions. This isotope has been discovered in deep ocean ferromanganese crusts that are dated by other isotopes to an age of 1.5-3.2 Myr (Wallner et al. 2016). Supernova shocks at that time would have heated the existing low-density gas that subsequently cooled by radiation and expansion. The EUV radiation of òCMa and other hot stars would have maintained the hydrogen ionization of the Local Cavity that had cooled or never was heated. As shown by observations of the much younger Cygnus Loop supernova remnant (Raymond et al. 2020), hot and photoionized warm gas could both exist in the present day Local Cavity.

Is there a Pressure Balance Problem with the Strömgren
Sphere Model?
The total pressure of interstellar gas P total includes thermal pressure = P n T th total , magnetic pressure p = P B 8 mag 2 , cosmic ray pressure P cr , and turbulent pressure P turb . There may also be other terms resulting from suprathermal or nonthermal ions. In the absence of systematic vertical flows, the total pressure of gas is balanced by the weight of the overlying matter perpendicular to the Galactic plane. In the Galactic plane, this mass loading corresponds to a gravitational pressure P grav =3.0×10 −12 dyn cm −2 or P grav /k B =22,000 K cm −3 (Cox 2005), where k B is Boltzmann's constant (1.38046×10 −16 erg deg −1 ). In the following, we divide all pressures by k B to facilitate intercomparisons. Since the Sun lies only a short distance above the plane, 13.4±4.4 pc (Yao et al. 2017b), the mass loading is about the same as in the Galactic plane. Table 2 summarizes the individual pressure terms and the total pressures for the Strömgren Sphere and LHB models. Galactic cosmic rays are routinely measured at 1 au with a typical pressure P cr =3260 K cm −3 (Parker 1969), but this is a lower limit to the Galactic cosmic ray pressure in the ISM because magnetic fields in the heliosphere deflect lower energy cosmic ray particles. Beyond the heliopause, Voyager1 measured Galactic cosmic rays at energies above 3Mev per nucleon with a broad maximum in the energy spectrum at 10-50 MeV per nucleon (Cummings et al. 2016). The energy density E/V=0.83-1.02 eV cm −3 corresponds to a pressure = =  P E V 2 3 7150 730 cr K cm −3 , because the cosmic rays are mostly nonrelativistic. Since Voyager1 and Voyager2 detected no radial gradient in the cosmic ray pressure (Stone et al. 2019), we assume that P cr has the same value in the Local Cavity.
There are only indirect estimates of the magnetic field strength in the Local Cavity. The de Avillez & Breitschwerdt (2005) simulations show a mean magnetic pressure P mag =5580 K cm −3 corresponding to an average total magnetic field B=4.4 μG, but the local magnetic field strengths in this simulation have a wide range. The analysis of dispersion measures and rotation measures   of four pulsars within 300 pc of the Sun in the third Galactic quadrant yields m » B 3.3 G with a large reduced χ 2 =40 (Salvati 2010). For longer path lengths through the Galactic plane, Sobey et al. (2019) derived a mean longitudinal magnetic field of m  4.0 0.3 G from pulsar data. Analysis of the IBEX ribbon data by Zirnstein et al. (2016) resulted in a magnetic field strength in the VLISM of 3 μG corresponding to P mag =2600 K cm −3 . Measurements of the magnetic field by Voyager 1 after passage through the heliopause show a very slow linear decrease in the magnetic field strength with distance reaching B=4.0 μG at the end of 2020 (149.2 au from the Sun). This result is an extension and re-calibration (L. Burlaga 2021, private communication) of the results published by Burlaga et al. (2021). Considering all of these values, we estimate the Local Cavity mean magnetic field strength to be m =  B 3.5 0.5 G, corresponding to = P mag -+ 3530 940 1080 K cm −3 . Cox (2005) called attention to P th providing only about 10% of P grav in the ISM with nonthermal pressure terms (P mag and P cr ) both much larger than P th unless the gas is hot. Typically the sum of P mag and P cr equals about half of P grav with the remainder from P turb and other terms. For the Local Cavity, we have found that + = + P P 7150 3530 mag cr =10,680 K cm −3 , approximately half of P grav .
Turbulence in supernova remnants is produced at large scales by supernova shocks and then converted to smaller scales by interactions with density and magnetic field inhomogeneities. On intermediate scales turbulence can be generated by many processes including thermal instabilities, thermal shell instabilities, density inhomogeneities, and magnetic instabilities as described by Raymond et al. (2020). Given this complexity and the range of scales involved, there is no simple way of quantifying the turbulent pressure. We propose that the random motions of nearby warm interstellar clouds relative to the common velocity vector of the CLIC provides a rough estimate of the macroscopic turbulent pressure in the Local Cavity. The mean value of these random motions is v=17.9 km s −1 Frisch et al. 2011). This velocity is consistent with the 15-21 km s −1 rms velocities for moderate temperature gas in the de Avillez & Breitschwerdt (2005) simulation (see below). Assuming that these random motions are typical of random motions within the Local Cavity, we compute r = = = P v n m v 1.1 8510 turb 2 H H 2 K cm −3 . The sum of + P P cr mag + P turb =19,590 K cm −3 , leaving only 2410 cm −3 K available for P th and other possible terms if there is approximate balance with P grav . We assume that P turb is the same in both warm and hot gas regions, but P turb could be larger in the hot gas regions.
The gas temperature in Strömgren spheres is typically 10,000-20,000 K, and the pulsar dispersion measured electron density in the Local Cavity is n e =0.012 cm −3 . If we assume a temperature T=15,000±5000 K, then = = P nT 2.2 e th  400 130 K cm −3 . If, on the other hand, the Local Cavity contains a hot bubble that has not cooled significantly, then we assume a temperature of (1.0±0.3)×10 6 K and electron density of 0.012 cm −3 resulting in a thermal pressure P th =26,400± 7920 K cm −3 . The sum of the four pressure terms for the Local Hot Bubble model is then P total =45,590 -+ 8.010 8.030 K cm −3 , and P total far exceeds P grav by 23,590 -+ 8.030 8010 K cm −3 . The pressure terms summarized in Table 2 are estimates and the nonthermal terms may differ somewhat between the Strömgren Sphere and LHB models. Nevertheless, we find that the total pressure in the Strömgren Sphere model is in rough balance with P grav , whereas the total pressure for the Local Hot Bubble model far exceeds P grav . This excess pressure in the LHB model predicts rapid expansion perpendicular to the Galactic plane. Indeed, X-ray emission indicating significant 10 6 K gas emission is observed in the Galactic pole directions, and expansion of hot gas would be consistent with its overpressure. We conclude that the Strömgren Sphere model does not have a pressure balance problem, but the LHB model is likely over-pressured compared to P grav . In a future paper, we will extend this study to a comparison of the total pressures in the outer heliosphere, LIC, and warm and hot gas in the Local Cavity, and consider whether the local ISM is close to or far from total pressure equilibrium.
We next consider whether a heterogeneous model of the Local Cavity gas is consistent with detailed simulations of the ISM. de Avillez & Breitschwerdt (2005) computed a threedimensional simulation of the ISM including magnetic fields with a grid scale of 1.25 pc. Their model includes supernovae explosions at the mean Galactic rate, shock heating, radiative cooling, mass flows (ram pressure) that produce turbulence (turbulent pressure) and expansion into the halo when there is overpressure leading to a Galactic fountain flow pattern. Inclusion of these processes leads to a wide range of local densities, temperatures, and magnetic field strengths. For example, the initially uniform input magnetic field strength of 3 μG is distorted by the ram pressure such that local field strengths range from 0.1 to 15 μG and the spatially averaged field strength becomes 4.45 μG. Magnetic pressure controls the dynamics for the cold (T<200 K) gas, ram pressure controls the < < + T 200 10 5.5 K gas, and thermal pressure controls the hotter gas. Unlike earlier theoretical models, this simulation shows that there are no thermally stable temperature phases, because the supernova driven turbulence mixes the gas faster than it can cool. As a result, most of the interstellar gas is at temperatures that would be thermally unstable in the absence of such rapid flows. In this simulation, the million-degree gas is over-pressured and cannot be confined to the Galactic disk by magnetic fields. This produces fountain outflow and a circulation pattern. While these simulations do not include cosmic ray generation and pressure, EUV photoionization, and some other essential physical processes, they indicate that lowdensity regions like the Local Cavity could contain a range of temperatures with outflows perpendicular to the Galactic plane.

Morphology of the Local Cavity
In Section 4, we argued that the Local Cavity is filled mostly by warm gas with a smaller amount of 10 6 K gas. We now consider the likely distribution of hot and warm gas in the Local Cavity given the constraints that the most recent supernova occurred about 2.3 million years ago and that the mean electron density in the Local Cavity is now 0.012 cm −3 .
While many models of the LHB implicitly assume that the hot gas homogeneously fills a compact structure within the Local Cavity, spectroscopic imaging of supernova remnants provides a very different picture. For example, images of the 10,000 yr old Cygnus Loop supernova remnant in emission lines of [O III], [O II], and Hα reveal that hot gas has a filamentary structure, likely shocks, in which thermal pressure dominates, whereas the warm gas has a more diffuse structure in which magnetic pressure likely dominates over thermal pressure (Raymond et al. 2020). In HST/WFC images of the Cygnus Loop, they measured shock propagation speeds of 130 km s −1 . Since the time for such shocks to traverse 100 pc is 800,000 yr, strong shocks should no longer be present in the Local Cavity. Instead, the shock-heated gas should still be present because the hot gas cooling time for an electron density of 0.012 cm −3 is about 10 million years. These arguments support a Local Cavity model in which the hot gas is located in many filamentary structures similar to what is observed in the Cygnus Loop.
Elsewhere in the Local Cavity, unshocked gas is warm and photoionized primarily by ò CMa but also by other hot stars and white dwarfs. The warm gas could be the mixture of 5000-9000 K gas in post-shock cooling flows and gas that has cooled from shocks produced by supernova events much older than the recent events. Since the age of ò CMa is 22.5±2.6 Myr (Tetzlaff et al. 2011), recent supernovae shock waves in the Local Cavity would have encountered Strömgren sphere gas. The detection of very small Hα knots in the Cygnus Loop led Raymond et al. (2020) to propose that the knots are neutral gas regions produced when shock waves encountered relatively weak magnetic fields leading to compression and hydrogen recombination. The partially ionized Local Interstellar Cloud and other clouds in the CLIC may have been formed by the same process.

Conclusions
The 40 yr old problem of what fills the Local Cavity requires new thinking and a new model. While the presence of X-ray emitting million-degree gas inside the Local Cavity is generally accepted, whether this LHB gas fills the entire volume of the Local Cavity or only a small fraction had not been settled. We have addressed this question in the following steps that lead to a new model.
(1) Although the collision rates for charge-exchange reactions between solar wind ions and neutral hydrogen in the heliosphere are incomplete and their dependence on the relative speeds of the ions and neutral hydrogen are often not properly taken into account, we adopt the estimate of 40%±5% for the SWCX contribution to the X-ray emission from the Local Cavity. This leads to an emission measure ( ) = = ´n n L EM 1.55 0.018 10 e p 3 cm −6 K for the hot gas in the Galactic plane. Another estimate (Smith et al. 2014) that the contribution of thermal emission from hot gas to the total X-ray emission is a factor of 2.3 times smaller would reduce the EM by the same factor.
(2) An important question is how to compute the path length L of hot gas through the LHB. Snowden et al. (2014) assumed that the entire path L≈85 pc to a nearby cloud is filled with hot gas. The emission measure formula then predicts that the electron density along this line of sight is n e =(4.68± 0.47)×10 −3 cm −3 . Using this value of n e and emission measures in all directions obtained by the ROSAT All Sky Survey to infer path lengths through the hot gas, Liu et al.
(2017) obtained a three-dimensional model of the LHB. However, the only electron density measurement in the Local Cavity is n e =0.0120±0.0029 cm −3 obtained from dispersion measures toward five pulsars with lines of sight that cross the Local Cavity in many directions. With this measured value of n e , the path length of hot gas to the same nearby dense cloud is a factor of 5 smaller than 85 pc and the inferred volume of the LHB is likely a factor of 5 smaller than that determined by Liu et al. (2017). Thus only a small portion of the Local Cavity is filled by LHB gas and most of the volume must be filled with something else. The thermal energy of 10 6 K gas filling about 20% of the Local Cavity volume is about 3×10 50 erg. This is about one-third the 10 51 erg energy of typical supernovae with the rest of the energy radiated over the 2.3 million years since the last supernova explosion.
(3) We propose that most of the Local Cavity is filled with lowdensity modest temperature (10,000-20,000 K) gas containing fully ionized hydrogen. The ionizing source is primarily the star ò CMa with additional contributions from hot white dwarfs inside of the Local Cavity. Even though the distance to this star is 124 pc, it is the brightest source of EUV radiation measured by the EUVE satellite. The extremely low neutral hydrogen column density in the line of sight to this star facilitates photoionization of the Local Interstellar Cloud in this direction and the other partially ionized clouds in the CLIC facing this star. These partially ionized clouds could be similar to the knots of Hα emission seen in the Cygnus Loop that may be produced when shocks encounter regions of low magnetic field strength leading to compression and hydrogen recombination. The electron density of 0.012 cm −3 in the Local Cavity indicates that the Strömgren sphere of ionized hydrogen surrounding ò CMa has a radius of about 160 pc, roughly the size of the Local Cavity. Thus the Local Cavity can be viewed as an irregularly shaped Strömgren sphere containing a small volume of hot gas. (4) Estimates of the total pressures for the Strömgren sphere and LHB models involve the sums of the thermal pressure, magnetic pressure, cosmic ray pressure, turbulent pressure, and possibly other terms. The thermal and cosmic ray pressures are based on measurable parameters, but the turbulent and magnetic field pressures are estimates. The total pressures should approximately balance the weight of the overlying mass perpendicular to the Galactic plane, which is a gravitationally induced pressure P grav /k B =22,000 cm −3 K. The total pressure of the Strömgren sphere model gas is similar to this gravitational pressure, but the pressure in the LHB model far exceeds P grav /k B . The additional pressure in the LHB model could drive outflows perpendicular to the Galactic plane. (5) Our model for the Local Cavity is a region largely filled with low-density warm gas with hydrogen fully ionized by the EUV radiation from the star ò CMa and hot white dwarfs. Embedded in this irregularly shaped Strömgren sphere is LHB gas from present or past supernova shocks occupying a relatively small volume. Observations of the Cygnus Loop suggest that the hot gas consists of filamentary post-shock gas rather than a homogeneous structure. A test of this model would be to measure the polar outflows of hot gas driven by the overpressure of the LHB gas. (6) Since the age of ò CMa is 22.5±2.6 million years, the recent supernova explosions in the Local Cavity would have encountered Strömgren sphere gas. Propagation of supernova shock waves into regions of low magnetic fields would lead to gas compression, more rapid cooling, and higher density clouds with recombined hydrogen. This process may have created the partially ionized clouds in the CLIC and likely elsewhere in the Local