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Interstellar neutral (ISN) hydrogen is the most abundant species in the outer heliosheath and the very local interstellar medium (VLISM). Charge exchange collisions in the outer heliosheath result in filtration, reducing the ISN hydrogen density inside the heliosphere. Additionally, these atoms are intensively ionized close to the Sun, resulting in a substantial reduction of their density within a few au from the Sun. The products of this ionization - pickup ions (PUIs) - are detected by charged particle detectors. The Solar Wind Around Pluto (SWAP) instrument on New Horizons provides, for the first time, PUI observations from the distant heliosphere. We analyze the observations collected between 22 and 52 au from the Sun to find the ISN hydrogen density profile and compare the results with predictions from global heliosphere models. We conclude that the density profile derived from the observations is inconsistent with steady-state model predictions. This discrepancy is not explained by time variations close to the Sun and thus may be related to the temporal evolution of the outer boundaries or VLISM conditions. Furthermore, we show that the cold and hot models of ISN hydrogen distribution are not a good approximation closer to the termination shock. Therefore, we recommend a new fiduciary point based on the available New Horizons observations at 40 au from the Sun, at ecliptic direction (285.62{\deg}, 1.94{\deg}), where the ISN hydrogen density is 0.11 cm$^{-3}$. The continued operation of New Horizons should give better insight into the source of the discussed discrepancy., Comment: Author Accepted Manuscript. Accepted for publication in The Astrophysical Journal Letters. 11 pages, 4 figures, 1 table

The Rado Graph, sometimes also known as the (countable) Random Graph, can be generated almost surely by putting an edge between any pair of vertices with some fixed probability $p \in (0, 1)$, independently of other pairs. In this article, we study the influence of allowing different probabilities for each pair of vertices. More specifically, we characterize for which sequences $(p_n)_{n\in \mathbb{N}}$ of values in $[0, 1]$ there exists a bijection f from pairs of vertices in $\mathbb{N}$ to $\mathbb{N}$ such that if we put an edge between $v$ and $w$ with probability $p_{f(\{v,w\})}$, independently of other pairs, then the Random Graph arises almost surely.

Direct-sampling observations of interstellar neutral (ISN) species and their secondary populations give information about the physical state of the local interstellar medium and processes occuring in the outer heliosheath. Such observations are performed from Earth's orbit by the IBEX-Lo experiment on board the Interstellar Boundary Explorer (IBEX) mission. IBEX ISN viewing is restricted to directions close to perpendicular to the Earth-Sun line, which limits the observations of interstellar species to several months during the year. A greatly improved data set will be possible for the upcoming Interstellar Mapping and Acceleration Probe (IMAP) mission due to a novel concept of putting the IMAP ISN detector, IMAP-Lo, on a pivot platform that varies the angle of observation relative to the Sun-Earth line and the detector boresight. Here we suggest a 2 yr scenario for varying the viewing angle in such a way that all the necessary atom components can be observed sufficiently well to achieve the science goals of the nominal IMAP mission. This scenario facilitates, among others, removal of the correlation of the inflow parameters of interstellar gas, unambiguous analysis of the primary and secondary populations of interstellar helium (He), neon (Ne) and oxygen (O), and determination of the ionization rates of He and Ne free of possible calibration bias. The scheme is operationally simple, provides a good counting statistics, and synergizes observations of interstellar species and heliospheric energetic neutral atoms., Comment: Approved for ApjS

In situ observations of interstellar neutral (ISN) helium atoms by the IBEX-Lo instrument onboard the Interstellar Boundary Explorer (IBEX) mission are used to determine the velocity and temperature of the pristine very local interstellar medium (VLISM). Most ISN helium atoms penetrating the heliosphere, known as the primary population, originate in the pristine VLISM. As the primary atoms travel through the outer heliosheath, they charge exchange with He$^+$ ions in slowed and compressed plasma creating the secondary population. With more than 2.4 million ISN helium atoms sampled by IBEX during ISN seasons 2009-2020, we compare the observations with predictions of a parametrized model of ISN helium transport in the heliosphere. We account for the filtration of ISN helium atoms at the heliospheric boundaries by charge exchange and elastic collisions. We examine the sensitivity of the ISN helium fluxes to the interstellar conditions described by the pristine VLISM velocity, temperature, magnetic field, and composition. We show that comprehensive modeling of the filtration processes is critical for interpreting ISN helium observations, as the change in the derived VLISM conditions exceeds the statistical uncertainties when accounting for these effects. The pristine VLISM parameters found by this analysis are the flow speed (26.6 km s$^{-1}$), inflow direction in ecliptic coordinates (255.7$^\circ$, 5.04$^\circ$), temperature (7350 K), and B-V plane inclination to the ecliptic plane (53.7$^\circ$). The derived pristine VLISM He$^+$ density is $9.7\times10^3$ cm$^{-3}$. Additionally, we show a strong correlation between the interstellar plasma density and magnetic field strength deduced from these observations., Comment: 13 pages, 3 figures, 2 tables, accepted for publication in ApJ

We construct a free group of continuum many generators among those autobijections of $\mathbb{R}$ which are also Hamel bases of $\mathbb{R}^2$, with identity function included. We also observe two new cases when a real function is a composition of two real functions which are Hamel bases of $\mathbb{R}^2$.

Angular scattering in charge exchange and elastic collisions between interstellar ions and neutral (ISN) atoms has been assumed to be negligible in previous studies. Here, we investigated the momentum transfer associated with the angular scattering of H atoms using Monte Carlo calculations to simulate their transport through the outer heliosheath. We considered two cases where charge exchange and elastic collisions between ISN H atoms and protons occur with and without momentum transfer in the outer heliosheath. We then simulated the transport of ISN H atoms inside the heliosphere to simulate count rates observed in the lowest energy bin of IBEX-Lo. We studied the effect of radiation pressure on the ISN H measurements for the cases with and without momentum transfer and compared them with our previous findings. We found an effective radiation parameter ($\mu_{\scriptsize\textrm{eff}}$, which represents for force associated with radiation pressure relative to gravity) for the years 2009-2018 based on the longitudinal shift of the ISN H signal. The two cases with and without momentum transfer reproduce the longitudinal shift in accordance with variations in solar activity, in agreement with our previous results, and they result in similar values for the $\mu_{\scriptsize\textrm{eff}}$, which is $\sim21-22 \%$ larger than the value found based on Ly$\alpha$ observations.

A Ribbon of enhanced energetic neutral atom (ENA) emissions was discovered by the Interstellar Boundary Explorer (IBEX) in 2009, redefining our understanding of the heliosphere boundaries and the physical processes occurring at the interstellar interface. The Ribbon signal is intertwined with that of a globally distributed flux (GDF) that spans the entire sky. To a certain extent, Ribbon separation methods enabled examining its evolution independent of the underlying GDF. Observations over a full solar cycle revealed the Ribbon's evolving nature, with intensity variations closely tracking those of the solar wind (SW) structure after a few years delay accounting for the SW-ENA recycling process. In this work, we examine the Ribbon structure, namely, its ENA fluxes, angular extent, width, and circularity properties for two years, 2009 and 2019, representative of the declining phases of two adjacent solar cycles. We find that, (i) the Ribbon ENA fluxes have recovered in the nose direction and south of it down to ~ 25{\deg} (for energies below 1.7 keV) and not at mid and high ecliptic latitudes; (ii) The Ribbon width exhibits significant variability as a function of azimuthal angle; (iii) Circularity analysis suggests that the 2019 Ribbon exhibits a statistically consistent radius with that in 2009. The Ribbon's partial recovery is aligned with the consensus of a heliosphere with its closest point being southward of the nose region. The large variability of the Ribbon width as a function of Azimuth in 2019 compared to 2009 is likely indicative of small-scale processes within the Ribbon., Comment: 5 figures

The IBEX-Lo instrument on the Interstellar Boundary Explorer (IBEX) mission measures interstellar neutral (ISN) helium atoms. The detection of helium atoms is made through negative hydrogen (H$^-$) ions sputtered by the helium atoms from the IBEX-Lo conversion surface. The energy spectrum of ions sputtered by ISN helium atoms is broad and overlaps the four lowest IBEX-Lo electrostatic analyzer (ESA) steps. Consequently, the energy response function for helium atoms does not correspond to the nominal energy step transmission. Moreover, laboratory calibration is incomplete because it is difficult to produce narrow-energy neutral atom beams that are expected for ISN helium atoms. Here, we analyze the ISN helium observations in ESA steps 1-4 to derive the relative in-flight response of IBEX-Lo to helium atoms. We compare the ratios of the observed count rates as a function of the mean ISN helium atom energy estimated using the Warsaw Test Particle Model (WTPM). The WTPM uses a global heliosphere model to calculate charge exchange gains and losses to estimate the secondary ISN helium population. We find that the modeled mean energies of ISN helium atoms, unlike their modeled fluxes, are not very sensitive to the very local interstellar medium parameters. The obtained relative responses supplement the laboratory calibration and enable more detailed quantitative studies of the ISN helium signal. A similar procedure that we applied to the IBEX-Lo observations may be used to complement laboratory calibration of the next-generation IMAP-Lo instrument on the Interstellar Mapping and Acceleration Probe (IMAP) mission., Comment: 17 pages, 8 figures, 1 table, accepted for publication in ApJS

The Interstellar Boundary Explorer (IBEX) images the heliosphere by observing energetic neutral atoms (ENAs). The IBEX-Hi instrument onboard IBEX provides full-sky maps of ENA fluxes produced in the heliosphere and very local interstellar medium (VLISM) through charge exchange of suprathermal ions with interstellar neutral atoms. The first IBEX-Hi results showed that in addition to the anticipated globally distributed flux (GDF), a narrow and bright emission from a circular region in the sky, dubbed the IBEX ribbon, is visible in all energy steps. While the GDF is mainly produced in the inner heliosheath, ample evidence indicates that the ribbon forms outside the heliopause in the regions where the interstellar magnetic field is perpendicular to the lines of sight. The IBEX maps produced by the mission team distribute the observations into $6\deg\times6\deg$ rectangle pixels in ecliptic coordinates. The overlap of the GDF and ribbon components complicates qualitative analyses of each source. Here, we find the spherical harmonic representation of the IBEX maps, separating the GDF and ribbon components. This representation describes the ENA flux components in the sky without relying on any pixelization scheme. Using this separation, we discuss the temporal evolution of each component over the solar cycle. We find that the GDF is characterized by larger spatial scale structures than the ribbon. However, we identify two isolated, small-scale signals in the GDF region that require further study., Comment: 27 pages, 13 figures, v2 accepted for publication in ApJS

On its journey through the Galaxy, the Sun passes through diverse regions of the interstellar medium. High-resolution spectroscopic measurements of interstellar absorption lines in spectra of nearby stars show absorption components from more than a dozen warm partially ionized clouds within 15 pc of the Sun. The two nearest clouds - the Local Interstellar Cloud (LIC) and Galactic (G) cloud - move toward each other. Their bulk heliocentric velocities can be compared with the interstellar neutral helium flow velocity obtained from space-based experiments. We combine recent results from Ulysses, IBEX, and STEREO observations to find a more accurate estimate of the velocity and temperature of the very local interstellar medium. We find that, contrary to the widespread viewpoint that the Sun resides inside the LIC, the locally observed velocity of the interstellar neutral helium is consistent with a linear combination of the velocities of the LIC and G cloud, but not with either of these two velocities. This finding shows that the Sun travels through a mixed-cloud interstellar medium composed of material from both these clouds. Interactions between these clouds explain the substantially higher density of the interstellar hydrogen near the Sun and toward stars located within the interaction region of these two clouds. The observed asymmetry of the interstellar helium distribution function also supports this interaction. The structure and equilibrium in this region require further studies using in situ and telescopic observations., Comment: 13 pages, 5 figures, 1 table, accepted for publication in ApJL

We prove that the coordinate functionals associated with filter bases in Banach spaces are continuous as long as the underlying filter is analytic. This removes the large-cardinal hypothesis from the result established by the two last-named authors ([Bull. Lond. Math. Soc. 53 (2021)]) at the expense of reducing the generality from projective to analytic. In particular, we obtain a ZFC solution to Kadets' problem of continuity of coordinate functionals associated with bases with respect to the filter of statistical convergence. Even though the automatic continuity of coordinate functionals beyond the projective class remains a mystery, we prove that a basis with respect to an arbitrary filter that has continuous coordinate functionals is also a basis with respect to a filter that is analytic., Comment: 9 pp

A laser-driven spin-polarized 3He2+ beam source for nuclear-physics experiments and for the investigation of polarized nuclear fusion demands a high-density polarized 3He gas-jet target. Such a target requires a magnetic system providing a permanent homogeneous holding field for the nuclear spins plus a set of coils for adjusting the orientation of the polarization. Starting from a transport vessel at a maximum pressure of 3 bar, the helium gas is compressed for a short time and can be injected into a laser-interaction chamber through a non-magnetic opening valve and nozzle, thus forming jets with densities of about a few 10^19 cm-3 and widths of about 1 mm. The target comprises a 3D adjustment system for precise positioning of the jet relative to the laser focus. An auxiliary gas system provides remote target operation and flushing of the gas lines with Ar gas, which helps to reduce polarization losses. The design of the target, its operation procedures and first experimental results are presented., Comment: 12 pages, 20 figures, submitted to PRAB

The IBEX-Lo instrument on board the Interstellar Boundary Explorer (IBEX) mission samples interstellar neutral (ISN) helium atoms penetrating the heliosphere from the very local interstellar medium (VLISM). In this study, we analyze the IBEX-Lo ISN helium observations covering a complete solar cycle, from 2009 through 2020 using a comprehensive uncertainty analysis including statistical and systematic sources.W e employ the Warsaw Test Particle Model to simulate ISN helium fluxes at IBEX, which are subsequently compared with the observed count rate in the three lowest energy steps of IBEX-Lo. The $\chi^2$ analysis shows that the ISN helium flows from ecliptic $(\lambda,\beta)=(255.59^{\circ}\pm0.23^{\circ}, 5.14^{\circ}\pm0.08^{\circ})$, with speed $v_\text{HP}=25.86\pm0.21$ km s$^{-1}$ and temperature $T_\text{HP}=7450\pm140$ K at the heliopause. Accounting for gravitational attraction and elastic collisions, the ISN helium speed and temperature in the pristine VLISM far from the heliopause are $v_\text{VLISM}=25.9$ km s$^{-1}$ and $T_\text{VLISM}=6150$ K, respectively. The time evolution of the ISN helium fluxes at 1 au over 12 years suggests significant changes in the IBEX-Lo detection efficiency, higher ionization rates of ISN helium atoms in the heliosphere than assumed in the model, or an additional unaccounted signal source in the analyzed observations. Nevertheless, we do not find any indication of the evolution of the derived parameters of ISN helium over the period analyzed. Finally, we argue that the continued operation of IBEX-Lo to overlap with the Interstellar Mapping and Acceleration Probe (IMAP) will be pivotal in tracking possible physical changes in the VLISM., Comment: 31 pages, 6 figures, 8 tables, accepted for publication in ApJS

Direct sampling of interstellar neutral (ISN) atoms close to the Sun enables studies of the very local interstellar medium (VLISM) around the heliosphere. The primary population of ISN helium atoms has, until now, been assumed to reflect the pristine VLISM conditions at the heliopause. Consequently, the atoms observed at 1 au by the Interstellar Boundary Explorer (IBEX) were used to determine the VLISM temperature and velocity relative to the Sun, without accounting for elastic collisions with other species outside the heliopause. Here, we evaluate the effect of these collisions on the primary ISN helium population. We follow trajectories of helium atoms and track their collisions with slowed plasma and interstellar hydrogen atoms ahead of the heliopause. Atoms typically collide a few times in the outer heliosheath, and only ~1.5% of the atoms are not scattered at all. We use calculated differential cross sections to randomly choose scattering angles in these collisions. We estimate that the resulting primary ISN helium atoms at the heliopause are slowed down by ~0.45 km/s and heated by ~1100 K compared to the pristine VLISM. The resulting velocity distribution is asymmetric and shows an extended tail in the antisunward direction. Accounting for this change in the parameters derived from IBEX observations gives the Sun's relative speed of 25.85 km/s and temperature of 6400 K in the pristine VLISM. Finally, this paper serves as a source of the differential cross sections for elastic collisions with helium atoms., Comment: 15 pages, 5 figures, accepted for publication in ApJL

Assuming the existence of certain large cardinal numbers, we prove that for every projective filter $\mathscr F$ over the set of natural numbers, $\mathscr{F}$-bases in Banach spaces have continuous coordinate functionals. In particular, this applies to the filter of statistical convergence, thereby we solve a problem by V. Kadets (at least under the presence of certain large cardinals). In this setting, we recover also a result of Kochanek who proved continuity of coordinate functionals for countably generated filters (Studia Math., 2012)., Comment: 10 pp

Interstellar neutral atoms provide a remote diagnostic of plasma in the outer heliosheath and the very local interstellar medium via charge exchange collisions that convert ions into atoms and vice versa. So far, most studies of interstellar atoms assumed that daughter hydrogen atoms directly inherit the kinetic properties of parent protons. This assumption neglects angular scattering of the interacting particles. However, for low relative velocities, as expected for charge exchanges in the outer heliosheath, this scattering is significant. In this study, we present how the parameters of daughter populations depend on the relative velocity and temperatures of parent populations. For this purpose, we numerically compute collision terms with and without this scattering. We find that the secondary population of interstellar hydrogen atoms, for the parent populations with the relative bulk velocity of 20 km s$^{-1}$ and equal temperatures of 7500 K, has ~2 km s$^{-1}$ higher bulk velocity if the scattering is taken into account. Additionally, temperatures are higher by ~2400 K and ~1200 K in parallel and perpendicular direction to the relative motion of parent populations, respectively. Moreover, a significant departure of secondary atoms from the Maxwell-Boltzmann distribution is expected for high relative velocities of parent populations. This process affects the distribution and density of interstellar atoms in the heliosphere and production of pickup ions. Thus, we show that angular scattering in charge exchange collisions is important to include in analyses of interstellar neutral atoms and pickup ions observed at 1 au and in the outer heliosphere., Comment: 22 pages, 13 figures, to appear in the Astrophysical Journal

Interstellar neutral gas atoms penetrate the heliopause and reach 1~au, where they are detected by IBEX. The flow of neutral interstellar helium through the perturbed interstellar plasma in the outer heliosheath (OHS) results in creation of the secondary population of interstellar He atoms, the so-called Warm Breeze, due to charge exchange with perturbed ions. The secondary population brings the imprint of the OHS conditions to the IBEX-Lo instrument. Based on a global simulation of the heliosphere with measurement-based parameters and detailed kinetic simulation of the filtration of He in the OHS, we find the number density of interstellar He$^+$ population at $(8.98\pm 0.12)\times 10^{-3}$~cm$^{-3}$. With this, we obtain the absolute density of interstellar H$^+$ $5.4\times 10^{-2}$~cm$^{-3}$ and electrons $6.3\times 10^{-2}$~cm$^{-3}$, and ionization degrees of H 0.26 and He 0.37. The results agree with estimates of the Very Local Interstellar Matter parameters obtained from fitting the observed spectra of diffuse interstellar EUV and soft X-Ray background., Comment: Accepted for ApJ

Let $X$ be a Banach space and $f,g:X\rightarrow X$ be contractions. We investigate the set $$ C_{f,g}:=\{w\in X:\m{ the attractor of IFS }\F_w=\{f,g+w\}\m{ is connected}\}. $$ The motivation for our research comes from papers of Mihail and Miculescu, where it was shown that $C_{f,g}$ is a countable union of compact sets, provided $f,g$ are linear bounded operators with $\pa f\pa,\pa g\pa<1$ and such that $f$ is compact. Moreover, in the case when $X$ is finitely dimensional, such sets have been intensively investigated in the last years, especially when $f$ and $g$ are affine maps. As we will be mostly interested in infinite dimensional spaces, our results can be also viewed as a next step into extending of such studies into infinite dimensional setting. In particular, unlike in the finitely dimensional case, if $X$ has infinite dimension then $C_{f,g}$ is very small set (at least nowhere dense) provided $f,g$ satisfy some natural conditions.

Generalizing Christensen's notion of a Haar-null set and Darji's notion of a Haar-meager set, we introduce and study the notion of a Haar-$\mathcal I$ set in a Polish group. Here $\mathcal I$ is an ideal of subsets of some compact metrizable space $K$. A Borel subset $B\subset X$ of a Polish group $X$ is called Haar-$\mathcal I$ if there exists a continuous map $f:K\to X$ such that $f^{-1}(B+x)\in\mathcal I$ for all $x\in X$. Moreover, $B$ is generically Haar-$\mathcal I$ if the set of witness functions $\{f\in C(K,X):\forall x\in X\;\;f^{-1}(B+x)\in\mathcal I\}$ is comeager in the function space $C(K,X)$. We study (generically) Haar-$\mathcal I$ sets in Polish groups for many concrete and abstract ideals $\mathcal I$, and construct the corresponding distinguishing examples. We prove some results on Borel hull of Haar-$\mathcal I$ sets, generalizing results of Solecki, Elekes, Vidny\'anszky, Dole\v{z}al, Vlas\v{a}k on Borel hulls of Haar-null and Haar-meager sets. Also we establish various Steinhaus properties of the families of (generically) Haar-$\mathcal I$ sets in Polish groups for various ideals $\mathcal I$., Comment: 71 pages

Direct-sampling observations of interstellar neutral (ISN) He by Interstellar Boundary Explorer (IBEX) provide valuable insight into the physical state of and processes operating in the interstellar medium ahead of the heliosphere. The ISN He atom signals are observed at the four lowest ESA steps of the IBEX-Lo sensor. The observed signal is a mixture of the primary and secondary components of ISN He and H. Previously, only data from one of the ESA steps have been used. Here, we extended the analysis to data collected in the three lowest ESA steps with the strongest ISN He signal, for the observation seasons 2009-2015. The instrument sensitivity is modeled as a linear function of the atom impact speed onto the sensor's conversion surface separately for each ESA step of the instrument. We found that the sensitivity increases from lower to higher ESA steps, but within each of the ESA steps it is a decreasing function of the atom impact speed. This result may be influenced by the hydrogen contribution, which was not included in the adopted model, but seems to exist in the signal. We conclude that the currently accepted temperature of ISN He and velocity of the Sun through the interstellar medium do not need a revision, and we sketch a plan of further data analysis aiming at investigating ISN H and a better understanding of the population of ISN He originating in the outer heliosheath., Comment: 20 pages, 5 figures, 5 tables, accepted for publication in the The Astrophysical Journal

Let $G$ consist of all functions $g \colon \omega \to [0,\infty)$ with $g(n) \to \infty$ and $\frac{n}{g(n)} \nrightarrow 0$. Then for each $g\in G$ the family $\mathcal{Z}_g=\{A\subseteq\omega:\ \lim_{n\to\infty}\frac{\text{card}(A\cap n)}{g(n)}=0\}$ is an ideal associated to the notion of so-called upper density of weight $g$. Although those ideals have recently been extensively studied, they do not have their own name. In this paper, for Reader's convenience, we propose to call them simple density ideals. We show that there are $\mathfrak{c}$ many non-isomorphic (in fact even incomparable with respect to Kat\v{e}tov order) simple density ideals. Moreover, we prove that for a given $A\subset G$ with $\text{card}(A)<\mathfrak{b}$ one can construct a family of cardinality $\mathfrak{c}$ of pairwise incomparable (with respect to inclusion) simple density ideals which additionally are incomparable with all $\mathcal{Z}_g$ for $g\in A$. We show that this cannot be generalized to Kat\v{e}tov order as the ideal $\mathcal{Z}$ of sets of asymptotic density zero is maximal in the sense of Kat\v{e}tov order among all simple density ideals. We examine how many substantially different functions $g$ can generate the same ideal $\mathcal{Z}_g$ -- it turns out that the answer is either $1$ or $\mathfrak{c}$ (depending on $g$).

Observations of energetic neutral atoms (ENAs) are a fruitful tool for remote diagnosis of the plasma in the heliosphere and its vicinity. So far, instruments detecting ENAs from the heliosphere were configured for observations of hydrogen atoms. Here, we estimate emissions of ENAs of the heavy chemical elements helium, oxygen, nitrogen, and neon. A large portion of the heliospheric ENAs is created in the inner heliosheath from neutralized interstellar pick-up ions (PUIs). We modeled this process and calculated full-sky intensities of ENAs for energies 0.2-130 keV/nuc. We found that the largest fluxes among considered species are expected for helium, smaller for oxygen and nitrogen, and smallest for neon. The obtained intensities are 50-10^6 times smaller than the hydrogen ENA intensities observed by IBEX. The detection of heavy ENAs will be possible if a future ENA detector is equipped with the capability to measure the masses of observed atoms. Because of different reaction cross-sections among the different species, observations of heavy ENAs can allow for a better understanding of global structure of the heliosphere as well as the transport and energization of PUIs in the heliosphere., Comment: 21 pages, 8 figures, 1 table, published in The Astrophysical Journal

We show that the Cantorvals connected with the geometric Cantor sets are not achievement sets of any series. However many of them are attractors of IFS consisting of affine functions.

Observations of energetic neutral atoms (ENAs) allow for remote sensing of plasma properties in distant regions of the heliosphere. So far, most of the observations have concerned only hydrogen atoms. In this paper, we present perspectives for observations of helium energetic neutral atoms (He ENAs). We calculated the expected intensities of He ENAs created by the neutralization of helium ions in the inner heliosheath and through the secondary ENA mechanism in the outer heliosheath. We found that the dominant source region for He ENAs is the inner heliosheath. The obtained magnitudes of intensity spectra suggest that He ENAs can be observed with future ENA detectors, as those planned on Interstellar Mapping and Acceleration Probe. Observing He ENAs is most likely for energies from a few to a few tens of keV/nuc. Estimates of the expected count rates show that the ratio of helium to hydrogen atoms registered in the detectors can be as low as 1:10^4. Consequently, the detectors need to be equipped with an appropriate mass spectrometer capability, allowing for recognition of chemical elements. Due to the long mean free paths of helium ions in the inner heliosheath, He ENAs are produced also in the distant heliospheric tail. This implies that observations of He ENAs can resolve its structure, which seems challenging from observations of hydrogen ENAs since energetic protons are neutralized before they progress deeper in the heliospheric tail., Comment: 31 pages, 12 figures, 3 tables, published in The Astrophysical Journal

Observations of energetic neutral atoms (ENAs) allow for remote studies of the plasma condition in the heliosphere and the neighboring local interstellar medium. The first IBEX results revealed an arc-like enhancement of the ENA intensity in the sky, known as the ribbon. The ribbon was not expected from the heliospheric models prior to the IBEX launch. One of the proposed explanations of the ribbon is the mechanism of the secondary ENA emission. The ribbon reveals energy-dependent structure in the relative intensity along its circumference and in the position. Namely, the ribbon geometric center varies systematically by about 10$^\circ$ in the energy range 0.7-4.3 keV. Here, we show by analytic modeling that this effect is a consequence of the helio-latitudinal structure of the solar wind reflected in the secondary ENAs. Along with a recently measured distance to the ribbon source just beyond the heliopause, our findings support the connection of the ribbon with the local interstellar magnetic field by the mechanism of the secondary ENA emission. However, the magnitude of the center shift in the highest IBEX energy channel is much larger in the observations than expected from the modeling. This may be due to another, not currently recognized, process of ENA generation., Comment: 14 pages, 8 figures, 1 table, v3: corrected caption to Figure 3

Maps of Energetic Neutral Atom (ENA) fluxes obtained from Interstellar Boundary Explorer (IBEX) observations revealed a bright structure extending over the sky, subsequently dubbed the IBEX ribbon. The ribbon had not been expected from the existing models and theories prior to IBEX, and a number of mechanisms have since been proposed to explain the observations. In these mechanisms, the observed ENAs emerge from source plasmas located at different distances from the Sun. Since each part of the sky is observed by IBEX twice during the year from opposite sides of the Sun, the apparent position of the ribbon as observed in the sky is shifted due to parallax. To determine the ribbon parallax, we found the precise location of the maximum signal of the ribbon observed in each orbital arc. The obtained apparent positions were subsequently corrected for the Compton-Getting effect, gravitational deflection, and radiation pressure. Finally, we selected a part of the ribbon where its position is similar between the IBEX energy passbands. We compared the apparent positions obtained from the viewing locations on the opposite sides of the Sun, and found that they are shifted by a parallax angle of $0.41^\circ\pm0.15^\circ$, which corresponds to a distance of $140^{+84}_{-38}$ AU. This finding supports models of the ribbon with the source located just outside the heliopause., Comment: 26 pages, 10 figures, 1 table, submitted to ApJ

With the velocity vector and temperature of the pristine interstellar neutral (ISN) He recently obtained with high precision from a coordinated analysis summarized by McComas et al.2015b, we analyzed the IBEX observations of neutral He left out from this analysis. These observations were collected during the ISN observation seasons 2010---2014 and cover the region in the Earth's orbit where the Warm Breeze persists. We used the same simulation model and a very similar parameter fitting method to that used for the analysis of ISN He. We approximated the parent population of the Warm Breeze in front of the heliosphere with a homogeneous Maxwell-Boltzmann distribution function and found a temperature of $\sim 9\,500$ K, an inflow speed of 11.3 km s$^{-1}$, and an inflow longitude and latitude in the J2000 ecliptic coordinates $251.6^\circ$, $12.0^\circ$. The abundance of the Warm Breeze relative to the interstellar neutral He is 5.7\% and the Mach number is 1.97. The newly found inflow direction of the Warm Breeze, the inflow directions of ISN H and ISN He, and the direction to the center of IBEX Ribbon are almost perfectly co-planar, and this plane coincides within relatively narrow statistical uncertainties with the plane fitted only to the inflow directions of ISN He, ISN H, and the Warm Breeze. This co-planarity lends support to the hypothesis that the Warm Breeze is the secondary population of ISN He and that the center of the Ribbon coincides with the direction of the local interstellar magnetic field. The common plane for the direction of inflow of ISN gas, ISN H, the Warm Breeze, and the local interstellar magnetic field %includes the Sun and is given by the normal direction: ecliptic longitude $349.7^\circ \pm 0.6^\circ$ and latitude $35.7^\circ \pm 0.6^\circ$ in the J2000 coordinates, with the correlation coefficient of 0.85., Comment: Accepted for publication in Astrophysical Journal Supplement Series

This paper is one of three companion papers presenting the results of our in-depth analysis of the interstellar neutral helium (ISN He) observations carried out using the IBEX-Lo during the first six Interstellar Boundary Explorer (IBEX) observation seasons. We derive corrections for losses due to the limited throughput of the interface buffer and determine the IBEX spin-axis pointing. We develop an uncertainty system for the data, taking into account the resulting correlations between the data points. This system includes uncertainties due to Poisson statistics, background, spin-axis determination, systematic deviation of the boresight from the prescribed position, correction for the interface buffer losses, and the expected Warm Breeze (WB) signal. Subsequently, we analyze the data from 2009 to examine the role of various components of the uncertainty system. We show that the ISN He flow parameters are in good agreement with the values obtained by the original analysis. We identify the WB as the principal contributor to the global $\chi^2$ values in previous analyses. Other uncertainties have a much milder role and their contributions are comparable to each other. The application of this uncertainty system reduced the minimum $\chi^2$ value 4-fold. The obtained $\chi^2$ value, still exceeding the expected value, suggests that either the uncertainty system may still be incomplete or the adopted physical model lacks a potentially important element, which is likely an imperfect determination of the WB parameters. The derived corrections and uncertainty system are used in the accompanying paper by Bzowski et al. in an analysis of the data from six seasons., Comment: 43 pages, 9 figures

We analyzed observations of interstellar neutral helium (ISN~He) obtained from the Interstellar Boundary Explorer (IBEX) satellite during its first six years of operation. We used a refined version of the ISN~He simulation model, presented in the companion paper by Sokol_et al. 2015, and a sophisticated data correlation and uncertainty system and parameter fitting method, described in the companion paper by Swaczyna et al 2015. We analyzed the entire data set together and the yearly subsets, and found the temperature and velocity vector of ISN~He in front of the heliosphere. As seen in the previous studies, the allowable parameters are highly correlated and form a four-dimensional tube in the parameter space. The inflow longitudes obtained from the yearly data subsets show a spread of ~6 degree, with the other parameters varying accordingly along the parameter tube, and the minimum chi-square value is larger than expected. We found, however, that the Mach number of the ISN~He flow shows very little scatter and is thus very tightly constrained. It is in excellent agreement with the original analysis of ISN~He observations from IBEX and recent reanalyses of observations from Ulysses. We identify a possible inaccuracy in the Warm Breeze parameters as the likely cause of the scatter in the ISN~He parameters obtained from the yearly subsets, and we suppose that another component may exist in the signal, or a process that is not accounted for in the current physical model of ISN~He in front of the heliosphere. From our analysis, the inflow velocity vector, temperature, and Mach number of the flow are equal to lambda_ISNHe = 255.8 +/- 0.5 degree, beta_ISNHe = 5.16 +/- 0.10 degree, T_ISNHe = 7440 +/- 260 K, v_ISNHe = 25.8 +/- 0.4$ km/s, and M_ISNHe = 5.079 +/- 0.028, with uncertainties strongly correlated along the parameter tube., Comment: Updated references

Neutral interstellar helium has been observed by the Interstellar Boundary Explorer (IBEX) since 2009 with a signal-to-noise ratio well above 1000. Because of the geometry of the observations, the signal observed from January to March each year is the easiest to identify. However, as we show via simulations, the portion of the signal in the range of intensities from 10^{-3} to 10^{-2} of the peak value, previously mostly left out from the analysis, may bring important information about the details of the distribution function of interstellar He gas in front of the heliosphere. In particular, these observations may inform us about possible departures of the parent interstellar He population from equilibrium. We compare the expected distribution of the signal for the canonical assumption of a single Maxwell-Boltzmann population with the distributions for a superposition of the Maxwell-Boltzmann primary population and the recently discovered Warm Breeze, and for a single primary population given by a kappa function. We identify the regions on the sky where the differences between those cases are expected to be the most visible against the background. We discuss the diagnostic potential of the fall peak of the interstellar signal, reduced by a factor of 50 due to the Compton-Getting effect but still above the detection limit of IBEX. We point out the strong energy dependence of the fall signal and suggest that searching for this signal in the data could bring an independent assessment of the low-energy measurement threshold of the IBEX-Lo sensor., Comment: This paper is a part of the special issue of Astrophysical Journal Supplement Series on interstellar neutrals measured by IBEX

We have developed a refined and optimized version of the Warsaw Test Particle Model of interstellar neutral gas in the heliosphere, specially tailored for analysis of IBEX-Lo observations. The former version of the model was used in the analysis of neutral He observed by IBEX that resulted in an unexpected conclusion that the interstellar neutral He flow vector was different than previously thought and that a new population of neutral He, dubbed the Warm Breeze, exists in the heliosphere. It was also used in the reanalysis of Ulysses observations that confirmed the original findings on the flow vector, but suggested a significantly higher temperature. The present version model has two strains targeted for different applications, based on an identical paradigm, but differing in the implementation and in the treatment of ionization losses. We present the model in detail and discuss numerous effects related to the measurement process that potentially modify the resulting flux of ISN He observed by IBEX, and identify those of them that should not be omitted in the simulations to avoid biasing the results. This paper is part of a coordinated series of papers presenting the current state of analysis of IBEX-Lo observations of ISN He. Details of the analysis method are presented by Swaczyna et al. 2015, and results of the analysis are presented by Bzowski et al. 2015., Comment: This paper is a part of the special issue of Astrophysical Journal Supplement Series on interstellar neutrals measured by IBEX

The modeling of the heliosphere requires continuous three-dimensional solar wind data. The in-situ out-of-ecliptic measurements are very rare, so that other methods of solar wind detection are needed. We use the remote-sensing data of the solar wind speed from observations of interplanetary scintillation (IPS) to reconstruct spatial and temporal structures of the solar wind proton speed from 1985 to 2013. We developed a method of filling the data gaps in the IPS observations to obtain continuous and homogeneous solar wind speed records. We also present a method to retrieve the solar wind density from the solar wind speed, utilizing the invariance of the solar wind dynamic pressure and energy flux with latitude. To construct the synoptic maps of the solar wind speed we use the decomposition into spherical harmonics of each of the Carrington rotation map. To fill the gaps in time we apply the singular spectrum analysis to the time series of the coefficients of spherical harmonics. We obtained helio-latitudinal profiles of the solar wind proton speed and density over almost three recent solar cycles. The accuracy in the reconstruction is, due to computational limitations, about 20%. The proposed methods allow us to improve the spatial and temporal resolution of the model of the solar wind parameters presented in our previous paper (Sok\'o{\l} et al. 2013) and give a better insight into the time variations of the solar wind structure. Additionally, the solar wind density is reconstructed more accurately and it fits better to the in-situ measurements from Ulysses., Comment: Accepted to Solar Physics (doi:10.1007/s11207-015-0800-2). 26 pages, 13 figures

We investigate the signals from neutral He atoms observed from Earth orbit in 2010 by IBEX. The full He signal observed during the 2010 observation season can be explained as a superposition of pristine neutral interstellar He gas and an additional population of neutral He that we call the Warm Breeze. The Warm Breeze is approximately two-fold slower and 2.5 times warmer than the primary interstellar He population, and its density in front of the heliosphere is ~7% that of the neutral interstellar helium. The inflow direction of the Warm Breeze differs by ~19deg from the inflow direction of interstellar gas. The Warm Breeze seems a long-term feature of the heliospheric environment. It has not been detected earlier because it is strongly ionized inside the heliosphere, which brings it below the threshold of detection via pickup ion and heliospheric backscatter glow observations, as well as by the direct sampling of GAS/Ulysses. Possible sources for the Warm Breeze include (1) the secondary population of interstellar helium, created via charge exchange and perhaps elastic scattering of neutral interstellar He atoms on interstellar He+ ions in the outer heliosheath, or (2) a gust of interstellar He originating from a hypothetic wave train in the Local Interstellar Cloud. A secondary population is expected from models, but the characteristics of the Warm Breeze do not fully conform to modeling results. If, nevertheless, this is the explanation, IBEX-Lo observations of the Warm Breeze provide key insights into the physical state of plasma in the outer heliosheath. If the second hypothesis is true, the source is likely to be located within a few thousand of AU from the Sun, which is the propagation range of possible gusts of interstellar neutral helium with the Warm Breeze characteristics against dissipation via elastic scattering in the Local Cloud., Comment: submitted to ApJS