1 Introduction

The heliosphere plows through the local interstellar medium (ISM) at a velocity of about \(26\mbox{ km}\,\mbox{s}^{-1}\) (Witte et al. 1993; Lallement and Bertaux 2.1 Grain Charging

The grain charge is determined by various charging currents that result from exposure of the dust to the ambient plasma and ionizing ultraviolet UV radiation (Horanyi 1996). The electric charge on dust grains directly determines the charge-to-mass ratio of dust grains (\(q/m\)) and thus the influence of electromagnetic forces on their dynamical evolution. To first order,Footnote 1 dust grains are charged to the same electric potential determined by the ambient plasma/radiation conditions.

For dust grains with radius \(a\), the amount of electric charge (\(Q_{ \mathrm{d}}\)) is proportional to the grain size and the surface electric potential (\(\phi \) in Volt) and can be written as:

$$ Q_{\mathrm{d}} = 4\pi \epsilon _{0}\, a\, \phi \;, $$
(1)

where \(\epsilon _{0} = 8.8541\cdot 10^{-12}\) A2 s4 kg−1 m−3 is the vacuum permittivity. Furthermore, the grain charge-to-mass ratio increases with decreasing grain radii as \(q/m \propto \phi \, a^{-2}\), indicating that grain charging and the effects of the Lorentz force are more important for smaller grains.

The temporal evolution of grain charge can be calculated by including charging currents from electron and ion collection (\(J_{\mathrm{e}}\) and \(J_{\mathrm{i}}\)), photoemission (\(J_{\mathrm{ph}}\)), and secondary electron emission (\(J_{\mathrm{sec}}\)), and be written as:

$$ \frac{\mathrm{d}Q_{\mathrm{d}}}{\mathrm{d}t} = J_{\mathrm{e}}+J_{ \mathrm{i}}+J_{\mathrm{ph}}+J_{\mathrm{sec}}\;. $$
(2)

Under normal solar system conditions, the most important charging current is due to ambient plasma electrons (\(J_{\mathrm{e}}\)). Assuming ion and electron temperatures are the same, the lighter electrons, because of their higher mobility, constitute a negative current with an amplitude higher than that of the positive ion current (\(J_{\mathrm{i}}\)) by a factor of \(\sqrt{m_{\mathrm{i}}/m_{\mathrm{e}}} > 43\), where \(m_{\mathrm{i}}\) and \(m_{\mathrm{e}}\) are the ion and electron mass, respectively (Horanyi 1996; Spitzer 1941). If only plasma ion and electron collection are considered, there is a negative grain potential at equilibrium. For a Maxwellian proton-electron plasma, the equilibrium grain potential (\(\phi _{\mathrm{eq}}\)) can be solved analytically as \(\phi _{\mathrm{eq}} \approx -2.5\, k\,T_{\mathrm{e}}/e\) (Spitzer 1941), where \(k\,T_{\mathrm{e}}\) is the plasma electron temperature in eV and \(e\) is the elementary charge.

Ionizing radiation, such as solar and stellar UV and energetic particles, produces photoelectrons (\(J_{\mathrm{ph}}\)) and secondary electrons (\(J_{ \mathrm{sec}}\)) and results in charging currents that counterbalance the electron collection current, leading to a more positive grain potential. A significant solar UV flux comes from the Lyman-\(\alpha \) emission at a wavelength of 121.6 nm, at an energy of 10.2 eV that exceeds the typical work functionFootnote 2 (approximately 6–8 eV) of candidate ISD materials (see Fig. 1 of Draine 1978), allowing photoelectron production. Similarly, plasma electrons with sufficient energy will create secondary electrons, leading to similar charging effects (Meyer-Vernet 1982). In addition, the photoelectric yields for grains with sizes comparable to or smaller than the photon penetration depth (of order 10-50 nm) can be enhanced (Watson 1973; Draine 1978), leading to a more positive potential. Secondary electron yields can be similarly enhanced for grain sizes smaller than or comparable to the electron penetration length (of order 10s of nm for ∼ 100 eV electrons), also leading to more positive grain potential (Draine and Salpeter 1979b; Chow et al. 1993; Ma et al. 2013; Slavin et al. 2012). This effect also leads to higher charges for dust aggregates consisting of small particles (Ma et al. 2013). The secondary electron yield from energetic ions is generally much lower and thus less relevant for ISD charging.

While the steady-state grain potential is determined by plasma temperature, the charging time (i.e., the time for grains to reach \(\phi _{\mathrm{eq}}\)) largely depends on plasma density. For grains in low-density plasmas, the charging time could be long compared to their traverse time, meaning that the grain potential could deviate significantly from the local equilibrium potential. The same applies to very small grains (nanodust), since charging time increases with decreasing grain cross-section. In addition, considering the quantized nature of electric charges, the charging currents can no longer be treated as “continuous” under these conditions. Various numerical methods have been developed to model discrete grain charging (Draine and Sutin 1987; Cui and Goree 1994), which are overall more computationally expensive than the continuous current calculations.

2.2 Surface Charges in and Near the Heliosphere

The charging environment in the inner heliosphere is dominated by the Sun, i.e., the solar wind and solar UV radiation. Since the solar wind electron density and solar UV flux decrease outward with the inverse square of heliocentric distance, the grain equilibrium potential remains roughly constant over the inner heliosphere, at around \(\phi _{eq} \cong +5\) to +15 V, depending on the secondary electron yield (Slavin et al. 2012) and plasma temperature. The potential also depends on the composition of the dust (e.g. Kimura and Mann 1998) and the morphology (Ma et al. 2013). In the heliosheath the plasma density is lower than in the VLISM and the temperatures are higher (see Fig. 1, leftFootnote 3), which leads to a higher grain potential for particles that are larger than 100 nm (Fig. 1, right, from Slavin et al. 2012). Dust grains outside of the heliosphere have a small electric potential of about −0.2 to +1 V depending on their size and composition, due to the low temperatures and weak UV field. Nanodust outside the heliosphere may pile up near the heliopause (Slavin et al. 2012) and can undergo acceleration effects due to stochastic charging (Hoang et al. 2012). Charging timescales are in the range of several hours for dust grains with radius of about 0.1 μm in the heliosheath, and on the order of minutes to hours in the ISM (see Fig. 2). The charging times are shorter for larger particles (Draine and Sutin 1987; Horanyi 1996). The charging times are short in comparison with the time for the dust particles to reach different plasma regions in the heliosphere.

Fig. 1
figure 1

The heliosphere properties from MHD+kinetic modeling (left), including heating of the plasma by pickup ions and the corresponding (calculated) dust particle surface charge (right), with distance from the Sun through the different regions of the heliosphere, including the small particle effect, from Slavin et al. (2012), p. 2 \(\copyright \) AAS. Reproduced with permission

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Fig. 2
figure 2

The charging time for dust grains with radius of 0.1 μm versus the distance to the Sun for the currents from photoionization, electrons, and ions from the plasma

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2.3 Sputtering

Another effect of ambient plasma is sputtering, an erosion process driven by incident ions. In the first order, the grain sputtering lifetime is proportional to grain size, i.e., the sputtering lifetime is shorter for smaller grains. However, considering the sputtering yield caused by solar wind protons of the order of 10−2 (Schmidt and Arends 1985), the sputtering lifetime of ISDs is of the order of 105 years, much longer than their traversal time in the heliosphere. During the long residence times of ISD particles in the interstellar medium, particles that are overtaken by supernova blastwaves can undergo substantial erosion and even total destruction. The resulting grain lifetimes are uncertain, but recent estimates suggest ∼350 Myr as a reasonable estimate (Draine and Salpeter 1979a; Jones et al. 1994; Bocchio et al. 2014), implying that most solid material in the ISD population must have been grown in the interstellar medium (Draine 2009a). One recent grain model concludes that the bulk of the interstellar grain population consists of grains that individually contain multiple materials, including approximately equal volumes of amorphous silicates and hydrocarbons (Hensley and Draine 2022).

2.4 Collisions

Grain-grain collisions are not a significant process for ISDs in the heliosphere. Assuming a homogenous interplanetary dust density of 50 km−3 with a characteristic grain size of 2 μm, the collisional probability of ISDs passing through the heliosphere is negligibly low at around 10−5. However, large zodiacal dust particles and meteoroids will have \(\sim 10^{7}\) impacts of submicron ISD particles per cm2 per Myr of exposure.Footnote 4 With ISD impact speeds of \(\sim 30\) km/s, this will result in microcratering. The ISD particles will be vaporized, and the larger zodiacal dust particles will undergo gradual erosion of the surface. If the mass of material excavated from one microcrater is \(\sim 10^{2}\) times the mass of the ISD impactor, this will result in an erosion rate of \(\sim 0.3\) μm/Myr.

2.5 Sublimation

Solar heating will only produce sublimation of refractory grain materials (e.g., silicates, metal oxides, hydrocarbons) if the grains approach very close (within \(\sim 0.01\) AU) to the Sun. Ices, if present, could be sublimed at distances of \(\sim 5\) AU, but the ISD population entering from the local diffuse ISM is thought to be ice-free, as H2O ice absorption features are absent in the diffuse ISM (e.g., Whittet et al. 1997). Sublimation therefore appears to be unimportant for ISD grains in the heliosphere except very close to the Sun.

2.6 Centrifugal Disruption

Radiative torques on grains resulting from scattering and absorption of anisotropic starlight are understood to produce spin-up of grains in the diffuse ISM to appreciable rotational speeds (e.g., Draine and Weingartner 1996, 1997). Within the heliosphere, the much higher intensity of solar radiation will spin grains up to higher rotational velocities. ISD particles entering the Solar system may be disrupted if they approach within a few AU of the Sun (Silsbee and Draine 2016). If ISDs have low tensile strengths, this effect can be important at even larger distances (Hoang 2019).

3 Dynamics of Dust in and Around the Heliosphere

This section briefly describes the dynamics of interstellar dust moving in and through the heliosphere. We start by describing the dynamics of the dust in the supersonic solar wind, followed by a discussion on the filtering effect this has on the dust flow, and finally, we discuss the filtering in the heliospheric boundary regions. An in-depth description of the ISD dynamics in the supersonic solar wind is given in Landgraf (2000), Sterken et al. (2012). The filtering effect is described in Landgraf et al. (2000), Sterken et al. (2013) and the filtering in the boundary regions of the heliosphere is discussed in detail in Kimura and Mann (1998, 1999), Linde and Gombosi (2000), Czechowski and Mann (2003b,a), Slavin et al. (2012), Alexashov et al. (2016).

Three forces dominate the dynamics of ISD in the heliosphere: solar gravity, solar radiation pressure, and Lorentz force. Their dominance depends on the size, charge and optical properties of a particle and on its location in the solar system (e.g., Fig. 1 in Sterken et al. 2012 from Landgraf 1998). Other forces may also be important for interplanetary dust particles (IDP), in particular the Poynting–Robertson drag and planetary perturbations, due to the longer residence times while being on elliptical (Keplerian) orbits. However, planetary perturbations, Poynting–Robertson drag, the Yarkowsky effect,Footnote 5 and solar wind corpuscular drag can be neglected for ISD in our heliosphere (Altobelli 2004). Although IDPs and nanodust from the inner solar system may play an important (but so far not yet well explored) role in heliosphere physics, this paper focuses mainly on ISD.

The equation of motion for ISD particles can be formulated as follows:

$$ {\mathbf{\ddot{r}}} = - \frac{(1-\beta )GM_{\odot}}{|{\mathbf{r}}^{3}|}{\mathbf{r}} + \frac{Q}{m} \left ( {\dot{\mathbf{r}}}_{\mathrm{p},\mathrm{sw}} \times \mathbf{B_{sw} }\right ) $$
(3)

with r the position vector of the particle, \(\beta \) the ratio of solar radiation pressure force and gravity, \(G\) the gravitational constant, \(M_{\odot}\) the mass of the Sun, \(\frac{Q}{m}\) the charge to mass ratio of the dust particle, \({\dot{\mathbf{{r}}}}_{\mathrm{p},\mathrm{sw}}\) the velocity of the dust particle with respect to the solar wind, and \({\mathbf{B}}_{\mathrm{SW}}\) the solar wind magnetic field. The following sections describe the motion of ISD in the heliosphere, sorted by particle size.

3.1 Dynamics of Micron-Sized ISD Moving Through the Heliosphere

Micron-sized ISD that moves into the heliosphere is mainly affected by solar gravity. Particles larger than a micrometer have higher number densities downstream from the Sun, due to gravitational focusing (e.g., Fig. 3, left). While interplanetary dust revolves around the Sun for a thousand to a million years and the Poynting–Robertson drag and collisions dominate its long-term evolution,Footnote 6 the ISD passes through the solar system in only about 50 years (about 5.5 AU per year on average).

Fig. 3
figure 3

Trajectories of dust grains with \(\beta =0.5\) (corresponding to 0.8 μm radius) and with \(\beta = 1.6\) (corresponding to ca. 0.2 μm radius). A so-called \(\beta \)-cone is visible for \(\beta \) larger than 1. Credit: Sterken et al. (2012), p. \(3 - 4\), reproduced with permission \(\copyright \) ESO

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The solar radiation pressure plays a significant role for particles smaller than one micrometer. The ratio of the solar radiation pressure and solar gravity (\(\beta \)) depends mainly on the particle size, composition, density, and surface morphology. For each particle with a fixed set of these properties (hence, not changing in time due to processes like sublimation, collision, etc.), a so-called \(\beta \)-curve relates the \(\beta \)-value of the particles to their size. \(\beta \)-curves can either be retrieved through experiments in the laboratory (e.g., Gustafson 1994) or by Mie calculations (e.g., Draine and Lee 1984). Each particle size has one \(\beta \)-value, but some \(\beta \)-values can have two corresponding particle sizes. The \(\beta \)-curve has a maximum value typically ranging from below one for certain silicates to five for darker materials like carbon or graphite (e.g., Kimura and Mann 1999). Examples of \(\beta \)-curves are given in a.o. Schwehm (1976), Gustafson (1994), Kimura and Mann (1999), Kimura et al. (2003), Silsbee and Draine (2022). Interstellar nanodust can be probed in situ with an Interstellar Probe (Brandt et al. 2022; McNutt et al. 2022) outside of the heliosphere; see also Sect. 5.2, Fig. 10 for an illustration of the ISD size distribution. The biggest difference to the physics of submicrometer-sized dust is the charging mechanism that includes the small particle effect, and stochastic charging (see Sect. 2). Its importance for astrophysics cannot be underestimated, in particular in the range from macromolecules to nanodust sizes (see also Sect. 6.4).

3.4 Filtering Effect of the Heliosphere

The ISD gets filtered in the solar system due to (1) the forces discussed above inside the solar system and, (2) in particular, at the outer boundary regions of the heliosphere (the termination shock, heliosheath and heliopause) where the dust grain charges are higher than in the solar system. Currently, the time-dependence of the ISD filtering in the boundary regions is not understood.

Linde and Gombosi (2000) simulated the filtering of the ISD in the heliosphere boundary regions for the defocusing phase of the solar cycle (1996). Although these authors found a cut-off at \(0.1\text{--}0.2\) μm (\(10^{-16} - 10^{-17}\) kg), Ulysses and Cassini have measured ISD particles with masses down to about 10−18 kg (Krüger et al. 11 is derived from a 3D extinction density map reconstructed by inversion of about 40 million individual extinction estimates (Vergely et al. 2022). The local and global patterns and what may influence the nearby magnetic field orientation in the local clouds is unclear. The weakness of the polarization fraction is also a possible sign of weak alignment of the grains.

Fortunately, due to the growing interest in the nearby interstellar medium magnetic configuration, which is important for Cosmic Microwave Background (CMB) polarized foreground removal, there are ongoing efforts to improve polarization measurements. It may expected that such efforts will benefit to the local cloud studies.

6.4 Dust Composition

Sophisticated dust models have been built to explain the bulk of remote multi-wavelength observations of the ISD (see e.g., Fig. 10). However, the actual number of grain types, their size distribution, and their composition still differ among models, and in situ data are crucially needed to complement remote sensing.

In this respect, a very interesting finding is the absence of convincing evidence of carbon in the interstellar grains detected in situ with the Cassini spacecraft (Altobelli et al. 2016). The Stardust sample return also found no convincing evidence for carbon (these samples were larger than the Cassini dust particles), except for one sample that was partially destroyed upon impact and plausibly may have been carbon-dominated (Westphal et al. 2014). According to a recent model (Jones 2021), carbon is contained in a population of small grains and is mostly absent from the large silicate and graphite grains. The non-detection of carbon may be due to the high charge-to-mass ratio (and/or high \(\beta \)-values) of the small carbonaceous grains and their subsequent exclusion from the inner heliosphere (see previous sections) or due to exothermic chemical reactions on their pathway into the solar system (Kimura et al. 2020). On the other hand, the remote observations are not inconsistent with a total absence of such grains in the local clouds (Slavin and Frisch 2006), as could happen if the small grains are fully destroyed by shocks or intense radiation. Measurements from an interstellar probe would be of considerable interest in this respect.

The remaining questions also include the role and sites of production and destruction of the many carbonaceous macromolecules that correspond to the intermediate state between grains and gaseous species, and produce the hundreds of irregular absorption bands observed in spectra of objects behind dense clouds, the so-called Diffuse Interstellar Bands (DIBs). Detecting DIBs associated with local clouds would be a step forward in understanding where these particles reside and how they participate in the ISD lifecycle. Unfortunately, DIBs are weak, and up to now their unambiguous detection has been made only in the spectra of distant stars. In the same way that extinction due to the local clouds could be detected by accumulating a large number of individual measurements, it is hoped that an accumulation of spectra of nearby stars could reveal the weak DIBs potentially associated with local clouds. Vast amounts of data recorded with the Radial Velocity Spectrometer (RVS) on board Gaia are being analyzed. The RVS wavelength range contains the 860 nm DIB already detected in many ground-based spectra. Optimistically, results about the local clouds may occur in the near future.

7 Measurements of Dust in and Around Astrospheres

Unlike the heliosphere, for other astrospheres no in situ dust measurements can be made. Instead, all knowledge of astrospheric dust must be inferred from remote observations, most notably from the thermal emission of dust. Indeed, the primary channel for detecting and examining astrospheres is the infrared emission of hot dust, yielding surveys and catalogs of astrospheric bow shocks (see, e.g., van Buren et al. 1995; Peri et al. 2015; Kobulnicky et al. 2017, and references therein). The existing classification scheme for observational images of astrospheres by Cox et al. (2012) is based on the thermal emission of dust in the far-infrared.

Studies of astrospheric dust typically begin with detecting the distinctive infrared arc structures and their morphological classification (cf., e.g., the above references for general surveys); more precise investigations into these arcs can often reveal substructures. Katushkina et al. (2018) have compared observations of dust by the Spitzer Space Telescope with 3D MHD modeling of the blue supergiant \(\kappa\) Cas, finding cirrus-like filaments beyond the arc structure. Similar studies by, e.g., Decin et al. (2012) and Meyer et al. (2021), comparing data from multiple instruments including the Herschel Space Observatory with hydrodynamic (HD) modeling of the red supergiant Betelgeuse, have found a linear bar in front of multiple arcs. Gvaramadze et al. (2018) modeled the X-ray binary Vela X-1 and a wedge-like structure in its perturbed environment (cf., e.g., Baalmann et al. 2021) to reproduce the filamentary structure found by spectroscopic dust observations. Investigations of other infrared-bright objects have, under closer scrutiny, revealed astrospheric structures. One example is the well-studied exoplanetary debris system of HR 4796A, which in addition to the ring-like emission of the debris disk, also features a much larger, optically bright exo-ring structure that is suggestive of an astrospheric bow shock (Schneider et al. 2018).

In order to generate a (magneto-)hydrodynamic ((M)HD) bow shock, the relative speed between the star and its environment, which generally is either the ISM at rest or an oncoming stream (Povich et al. 2008), must be supersonic and super-Alfvénic (e.g., Herbst et al. 2022). The domain between this bow shock and the astropause, referred to as the outer astrosheath, the VLISM, or the bow shock shell (e.g., Kleimann et al. 2022), features a high density of gas or plasma and, in most cases, of dust. The emission from this domain is the origin of the observable arc-like structure, which is generally referred to as the observed bow shock. van Marle et al. (2011) found with multifluid HD simulations that the dust’s grain size considerably affects its location within the astrosphere (cf. Slavin et al. 2012, for simulations of the heliosphere region between the bow shock/wave and heliopause); the HD bow shock can lead to multiple shell-like features or a thicker continuous arc of dust emission in observational images.

According to Henney and Arthur (2019a,c), the interaction regions of stars with their respective environments can be divided into four regimes: wind-supported bow shocks (WBSs), radiation-supported bow shocks (RBS), potential dust waves (DWs), and radiation-supported bow waves (RBWs). A brief summary of the environments is given below.

By introducing the optical depth of the bow shell to UV radiation, \(\tau _{\mathrm{UV}}\), which can be estimated by the fraction of the observed infrared luminosity of the bow shell’s dust grains to the bolometric luminosity of the star, and the shell momentum efficiency, \(\eta _{\mathrm{sh}}\equiv P_{\mathrm{sh}}/P_{\mathrm{rad}}\), which is the ratio of the thermal and magnetic pressure inside the bow shell, \(P_{\mathrm{sh}}\), to the stellar radiation pressure, \(P_{\mathrm{rad}}\) (Henney and Arthur 2019c, Sect. 2), these four regimes can be visualized as distinct domains in a \(\eta _{\mathrm{sh}}\)-\(\tau _{ \mathrm{UV}}\) diagram (see Fig. 12). It is noteworthy that all four regimes lie on or above the diagonal line

$$ \eta _{\mathrm{sh}}\approx 1.25\tau _{\mathrm{UV}} \ ; $$
(4)

the area below it is forbidden. In three of these regimes, gas and dust are tightly coupled to each other (Henney and Arthur 2022).