The separates the solar and interstellar domains

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Are the Heliosphere, Very Local Interstellar Medium, and Local Cavity in Pressure Balance with Galactic Gravity?∗

Corresponding author: Jeffrey L. Linsky

∗ Based on observations made with the NASA/ESA Hubble Space Telescope obtained from the Data Archive at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS AR-09525.01A. These observations are associated with programs #12475, 12596.

al. (1995, 2003), assume time independent pressure balance among several thermal components and use this assumption to compute values of steady-state temperature and density phases that are either cold, warm (neutral or ionized) or hot. Recent detailed simulations by Gurvich et al. (2020) describe the dynamic equilibrium and approximate balance with gravity of different thermal regimes in the disks of Milky Way-mass galaxies.

A different model emerges from the simulations by de Avillez & Breitschwerdt (2005) in which the energy produced by exploding supernovae produces a very active interstellar medium in which there are no stable phases but rather large variations in density, temperature, magnetic fields, and flows both spatially and temporally. The Local Bubble, also called the Local Cavity, in which the Local Interstellar Cloud (LIC) and other partially ionized warm clouds reside, was created by multiple supernova events (Ma´ız-Apell´aniz 2001; Breitschwardt & de Avillez 2006) and could be such an active region. However, the last nearby supernova exploded about 2.2 million years ago (Breitschwerdt et al. 2016; Wallner et al. 2016), and the interstellar gas in the initially Hot Local Bubble (HLB) could have cooled and settled down to a nearly quiescent state since then.

Pressure balance in the LISM 3

(Outer Heliosheath) VLISM

Figure 1. Fig. 1: Schematic cut through heliosphere and the VLISM in the meridional plane that contains the interstellar magnetic field (BISM) and the Sun. The undisturbed VLISM lies outside the Bow Wave or Bow Shock on the right, where the interstellar flow is unaffected by the presence of the heliosphere. In the pristine VLISM neutral atoms (solid arrows) and plasma (dashed arrows) have the same velocity VISNinfinity relative to the Sun. Between the heliopause and Bow Wave is the disturbed VLISM (or Outer Heliosheath), where the interstellar plasma flow is slowed down and diverted around the HP. Here, the interstellar magnetic field (BISM) is compressed and draped around the HP. The maximum compression occurs where BISM is parallel to the HP. Between the HP and the TS is the Heliosheath or Inner Heliosheath, which contains the subsonic solar wind, along with pickup ions and supra-thermal particles. The HP separates the solar and interstellar domains. Also indicated are the trajectories of Voyagers 1 and 2, projected into this meridional plane.

The size of the heliosphere and its three dimensional shape are controlled by the balance of total pressures between the disturbed VLISM and pristine VLISM and the total pressure balance at the HP between the HS and the disturbed VLISM. The ionization of inflowing interstellar gas also plays an important role in these pressure balances. The heliosphere is now embedded in low density interstellar gas with n(H I)≈ 0.2 cm−3(Slavin & Frisch 2008), but it has traversed both inter-cloud and supernova remnant regions containing fully ionized hydrogen. The heliosphere may also have traversed high-density cold clouds such as the Local Leo Cold Cloud (Peek et al. 2011) with densities in excess of 104cm−3and pressures orders of magnitude larger than at present. In the latter case, the size of the HP would have shrunk to the orbits of Jupiter or even the Earth (Zank & Frisch 1999; M¨uller et al. 2006). Linsky et al. (2022) showed that the mean density in the LIC and nearby partially ionized clouds is about n(H I)=0.10 cm−3, and Swaczyna et al. (2022a) proposed that the density in the immediate environment of the heliosphere is twice this density, n(H I)=0.20 cm−3, because the LIC and G clouds overlap in this region.

As the Sun journeys through the LIC, other partially ionized clouds, and fully ionized hydrogen gas in the Local Severe Cavity, the size of the heliosphere must respond to changes in the external pressure (M¨uller et al. 2006).

The total pressure in each region of the heliosphere and VLISM consists of several components: cosmic-ray pressure P(cr), magnetic pressure P(mag)=B2/8π ,where B is the magnetic field strength, turbulent pressure P(turb)=ρv2, where ρ is the density and v is the turbulent velocity, thermal pressure P(th) =nkT, where T is the temperature and n is the density of all contributing particle populations, the pressure of hot (pick-up) ions P(hot-ions), the pressure of supra-thermal ions P(supra-th), and the ram pressure P(ram). Not all of these components contribute significantly in each region. Pressure has units of dynes cm−2or picoPascals (pPa), where 1pPa=10−11dynes cm−2. It is convenient to divide the pressure by Boltzmann’s constant k = 1.38×10−16erg deg−1, in which case P/k = 72, 400 pPa has units of Kcm−3, and is proportional to temperature (in kelvins) times density.

We consider the pressure components on either side of the heliopause, the heliosheath inside of the HP and the disturbed VLISM outside. The interstellar plasma flow stagnates at the HP close to the upwind direction due to the combined action of the plasmas and the magnetic fields. The maximum pressure identified with IBEX ENAs (McComas & Schwadron 2014) is offset from the stagnation region, which is close to the nose. In the maximum pressure region, there is no flow perpendicular to B, but still considerable flow along B. The Voyager missions have provided considerable pressure data inside and outside of the HP. Estimates of the pressure terms in the pristine VLISM immediately outside of the heliosphere are obtained from measurements of neutral hydrogen and to a lesser

The High Energy Telescope 2 on Voyager 1 monitors Galactic Cosmic Rays (GCRs) primarily from protons with energy E > 70 MeV/nucleon and electrons (and positrons) with E > 15 MeV. Cummings et al. (2016) found that protons account for about 70% of the count rate and electrons (and positrons) account for about 25%. They measured a count rate of 2.82/second outside of the HP and about 2.25/second inside of the HP. The corresponding energy density is 0.925 ± 0.095 eV/cm3outside of the HP and 0.74 ± 0.076 eV/cm3immediately inside the HP. Since the GCRs are mostly non-relativistic, P(GCRs)/k = 5, 720 ± 590 Kcm−3inside the HP.

Anomalous cosmic rays (ACRs) are thought to be interstellar neutral atoms that become ionized in the heliosheath and are picked up by the solar wind and accelerated by shocks. Both Voyagers detected ACRs beyond the termina-tion shock (Cummings et al. 2013), but where ACRs are accelerated in the HS is uncertain. The ACR pressure is P(ACRs)/k = 1, 780 ± 180 Kcm−3. Both cosmic ray components provide 36.6% of the total pressure.

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Table 2. Heliosheath pressure components in the solar and HP rest frame (Kcm−3)

4. PRESSURES IN THE PRISTINE VLISM

As stated in the Introduction, the pristine VLISM outside the heliosphere may not feature exactly the average conditions of the LIC, which has long been thought to be the interstellar cloud that surrounds the solar system. In particular, the flow vector of interstellar material relative to Sun, as observed inside the heliosphere, appears to be noticeably different from the mean flow vector of the LIC (Linsky & Redfield 2021). Similarly, the density immediately outside of the heliosphere appears to be substantially higher than the mean density of the LIC (Linsky et al. 2022), perhaps due to the pristine VLISM immediately outside of the heliosphere being a mixture of the LIC and G clouds (Swaczyna et al. 2022a).

To compute the particle related pressures, such as thermal, turbulent, and ram pressure, we include the plasma and neutral gas densities for both H and He assuming a He/H abundance of 0.1. In comparative simulations of heliospheric sizes in response to a wide variety of interstellar medium parameters (densities, temperatures, and speeds relative to the Sun), M¨uller et al. (2006) found that only when including plasma and neutral gas as well as thermal and ram pressure did the variation of the radial distance of the HP from the Sun follow a unique relation with the total pressure. This can be seen in Fig. 6 of their paper, which shows a compilation of these results, along with a power law fit to the total pressure of both components. In fact, the distance of the HP scales as R(HP) ∝ P(total)−1/2, i.e., inversely proportional to the square root of the pressure as expected for pressure balance. For the turbulent and ram pressure, we assume equal velocities for all species, and P(He)/P(H) ≈ 0.4 because of the He/H mass ratio of 4. The neutral H density is taken from a recent PUI analysis using NewHorizons SWAP observations (Swaczyna et al. 2020), the neutral He density from He+PUIs using Ulysses SWICS (Gloeckler et al. 2004), and the H+, He+, and electron densities from observations of the secondary neutrals from the disturbed VLISM (Bzowski et al. 2019). These densities are listed in Table 3. It is interesting to note that the recent neutral density and plasma densities combine with the neutral He density to the canonical He/H density ratio of 0.1.

For the temperature in the pristine VLISM, we adopt T(ISN) = 6, 150±150 K, obtained from the interstellar neutral (ISN) He flow observations after correcting for elastic collisions in the disturbed VLISM (Swaczyna et al. 2022b). This temperature refers to the pristine VLISM in immediate contact with the heliosphere, rather than the mean temperature in the LIC (6511±2773 K (Linsky et al. 2022)) or the mixture of LIC and G cloud temperatures proposed by Swaczyna et al. (2022a).

The effective ram pressure or the fraction of P(ram-VLISM) that the pristine VLISM exerts on the disturbed VLISM is the forward momentum per unit area lost by particles from the pristine VLISM that interact with plasma in the disturbed VLISM rather than passing through unimpeded or being deflected around the heliopause with little forward

8 Linsky and Redfield

5. DISTURBED VLISM PRESSURE OUTSIDE OF THE HELIOPAUSE

The disturbed VLISM pressure components just outside of the HP are compiled in Table 4. Some of these pressures have been directly measured by the Voyager spacecraft but others come from models. As noted in Section 4, beyond the HP Voyager-1 measured Galactic cosmic rays (GCRs) above 3 MeV per nucleon with a broad maximum in the energy spectrum at 10–50 MeV per nucleon (Cummings et al. 2016). The total energy density for protons, ions, and electrons, E/V = 0.83-1.02 eV cm−3, and thus the GCR pressure were actually obtained in the disturbed VLISM (Cummings et al. 2016). It is worth mentioning that about 80% of the GCR pressure is also present inside of the HP, so that at most 20% of the CGR pressure may contribute to shaping the HP because Voyager 1 and Voyager 2 detected no radial gradient in the cosmic ray pressure (Cummings et al. 2016; Stone et al. 2019). We therefore assume that P(cr) has the same value in the VLISM and LIC.

6. PRESSURE IN THE LOCAL CAVITY

Recent three dimensional models of the interstellar medium within 3 kpc of the Sun show a region of low absorption and thus low density extending 100–200 pc from the Sun and surrounded in most directions with dense clouds identified

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 radioactive60Fe 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 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 (104K) 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 years of intensive studies, the question of what fills the Local Cavity remains unanswered. 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 is largely local emission produced when the solar wind ions charge exchange with neutral hydrogen in the heliosphere (Cravens, Robertson & Snowden 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 consider here two models: the Local Hot Bubble model in which million degree gas fills the entire bubble, and a moderate temperature Str¨omgren Sphere Model (Linsky & Redfield 2021) in which the plasma has cooled and hydrogen is fully ionized by the EUV radiation of hot stars. The very different total pressures in these two models provides an interesting test of whether the Local Cavity has remained hot or has cooled since the last supernova event.

7. ARE THE TOTAL PRESSURES IN THE HELIOSPHERE, PRISTINE VLISM, AND LOCAL CAVITY IN EQUILIBRIUM WITH EACH OTHER AND WITH THE GALACTIC GRAVITATIONAL PRESSURE?

In Table 6 we list pressures in the rest frame (2ndcolumn) of the respective region and where appropriate including ram pressure in the applicable frame of the surroundings (2ndand 3rdcolumn). We compare the total pressures in the heliosheath just inside, just outside of the HP, the pristine VLISM, and the Local Cavity to determine whether there may be significant imbalances that would cause relative flows. Within their uncertainties, the total pressure outside the heliopause (23, 310 ± 4, 100 Kcm−3) is consistent with the pressure inside (20.500 ± 1, 600 Kcm−3) including the effective ram pressure relative to the Sun. However, other presently unknown pressure sources could be present. The total pressure of the pristine VLISM including ram pressure is consistent with the total pressure in the disturbed VLISM within the uncertainties. These conditions indicate pressure balance among these regions and no anticipated flows or motion of the boundaries. To reiterate, the motion of the pristine VLISM relative to the Sun and thus its ram

Is our result that the total pressures in the heliosheath, including appropriate ram pressures in the heliosheath, disturbed VLISM, and surrounding interstellar gas are in approximate balance with the weight of material above the disk in agreement with recent simulations for galactic disks? Gurvich et al. (2020) used the FIRE-2 galaxy simulation code to study the structures and properties of the multiphase ISM in disks of galaxies with mass typical of the Milky Way. Their simulations included thermal, turbulent, and dynamic pressures as a function of radial distance from the center and height above the disk. The resulting calculations for the disk midplane show that total pressures in the dynamic ISM are typically between 80% and 100% of the weight of overlying material, consistent with our results.

The pressure in the Local Cavity could be far from balance with the gravitational pressure for a number of reasons. One is that the internal velocities created by the last supernova explosion about 2 Myr ago may still be present as shocks producing higher pressures at them or shock lower pressures in their wake. A second reason is that hot gas, if present, would have high thermal pressure leading to expansion of the gas toward the Galactic poles as is observed. Finally, the Local Cavity may still be expanding into the surrounding medium in which case there would be a rarefaction inside the cavity with lower pressure, similar to the rarefaction region in the solar wind behind coronal mass ejections and the compressions behind stream interaction regions (Pizzo 1978). Conversely, a ram pressure term that should be included in the total pressure would raise the pressure just outside the Local Cavity.

• In the heliosheath, the region inside of the heliopause and outside of the temination shock, the pressure of 0.7-24 keV ions and electrons dominates the total pressure, although cosmic rays (Galactic and anomalous) also contribute. To balance the total pressure outside of the heliopause, it is essential to include the dynamic pressure that the heliosheath flow exerts on the gas just outside of the heliopause.

• Outside of the heliopause, in the region called the disturbed very local interstellar medium (disturbed VLISM) or the outer heliosheath (OHS), the cosmic ray, magnetic, and plasma pressures contribute equally to the total pressure. The sum of the magnetic and plasma pressures in the stagnation region just outside of the heliopause balance the ram pressure of plasma inflowing from the LIC resulting from the heliosphere’s motion through the interstellar medium. The total pressures in the heliosheath (20, 500±1, 600 Kcm−3) and outside of the heliopause (23, 310 ± 4, 100 Kcm−3) are in agreement within their respective errors.

Overall, it is interesting to note the approximate balance of the total pressures of the warm interstellar clouds in the solar neighborhood (including dynamic pressures of their relative motions), the surrounding Local Cavity, and the gravitational pressure of the gas on the Galactic plane. This balance even extends to the total pressure of the pristine VLISM on the heliosphere. At this point, we can only speculate concerning the reason(s) for this overall approximate balance, which may depend upon the distribution of the gravitational forces among the motion of the stars and the interstellar gas, along with their internal pressures. A discussion of this topic is beyond the scope of this paper and may be taken up in a future investigation.

Facilities: HST(STIS), HST(HRS), EUVE, Voyager I, Voyager II, IBEX, Ulysses, New Horizons

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