CHARTING THE INTERSTELLAR MAGNETIC FIELD CAUSING THE INTERSTELLAR BOUNDARY EXPLORER (IBEX) RIBBON OF ENERGETIC NEUTRAL ATOMS

The simplest approximation is to assume that there is a single ISMF that controls the optical interstellar polarizations for stars within 40 pc and 90° of the heliosphere nose, as was also assumed in Papers I and II. All of the qualifying observations are used in the evaluations of the ISMF direction, except for the 20th century data collected in the Heiles (2000) catalog where observations range in precision levels. Those data are not used if a more recent, and presumably more precise, measurement is available for the same star. Justification for the approximation of a single field direction is provided by the low column densities, N(H^o) < 10^18.7, of the ISM within ∼25 pc (e.g., Wood et al. 2005), and the fact that local clouds flow through space with roughly similar velocity vectors in the LSR, suggesting a common origin for the clouds (Frisch et al. 2002, 2011). It is shown below, however, that multiple magnetic structures appear to be present.

Analyzing the qualifying set of polarization data (Section 2), with the merit function ${F}_{\mathrm{II}}({B}_{i})$ (Equation (1)) based on weighted data points (Equation (2)), gives a best-fitting ISMF direction that is toward the direction ℓ = 163, b = 270 (Figure 4, left). The uncertainty on this direction is determined by the width of the minimum of ${F}_{\mathrm{II}}({B}_{i})$. Figure 5, left, shows the value of ${F}_{\mathrm{II}}({B}_{i})$ plotted against the angle from this best-fitting ISMF direction for each location in the sky. The uncertainty on the best-fitting ISMF direction is assumed to be the angle that clearly distinguishes the minimum of ${F}_{\mathrm{II}}({B}_{i})$ from an adjacent secondary minimum, or ±15° cm⁻². This new best-fitting direction differs by 276 ± 292 from the result of Paper II, which is not a significant difference. A test was also made to determine whether the use of ${F}_{\mathrm{III}}({B}_{i})$ changed the best-fitting ISMF direction from these data, and it gave a similar direction directed toward ℓ = 153, b = 270.

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As the sky coverage of the underlying polarization data set improves, it becomes more likely that inhomogeneities in the direction of the local ISMF will be sampled. Since the purpose of this study is to connect the ISMF that shapes the heliosphere with the local interstellar field, the analysis of the best-fitting ISMF to the polarization data needs to take into account the possibility there are multiple local ordered components of the magnetic field, so that polarizations clearly associated with a magnetic field that is different from the one that shapes the heliosphere can be omitted from the fits. In this section we identify a clearly identifiable secondary magnetic structure. The properties of this filament suggest that it is related to interstellar dust grains deflected around the heliosphere (Frisch et al. 2015a). In this section we justify the selection of these polarizations as belonging to a separate magnetic structure, and in the following section the magnetic field direction in the local ISM is evaluated for a data set that omits data that trace the polarization filament.

Using data from the PlanetPol polarimeter, Bailey et al. (2010) showed that the polarization strengths for stars in the region R.A. > 17H increase with the distance of the target star. In Paper II we showed that the stars that formed the upper envelope in the polarization versus distance relation for this subset of the PlanetPol data contains a group of stars within 40 pc that traces a magnetic structure with an ordered ISMF direction that extends to within 10 pc of the Sun. In Paper II, this ordered field was characterized by a position angle gradient of PA_R.A. of ∼−025 pc⁻¹ (based on the fit ${\theta }_{{\rm{R}}.{\rm{A}}.}$ = 36.0(±1.4) −0.25(±0.03)D for distance D and position angles expressed in the equatorial coordinate system, ${\theta }_{{\rm{R}}.{\rm{A}}.}$, e.g., with respect to R.A.).

Given this evidence for a magnetic structure suggested by the upper envelope to the polarization versus distance relation for the PlanetPol data, we have searched for additional stars within 40 pc in this spatial interval that might also show polarization position angles that vary systematically with distance indicating an ordered magnetic field. A total of thirteen stars (HD 131977, HD 161797, HD 120467, HIP 82283, HD 119756, HD 144253, HD 130819, HD 161096, HD 134987, HD 136894) were identified in the current data set by a systematic decrease of ${\theta }_{\mathrm{gal}}$ with distance (see below). The stars tracing the magnetic structure are located between 6 pc and 29 pc from the Sun and appear to form an elongated feature spanning an angle of ∼5° × 98°, where the polarization position angles are parallel to the axis of the structure (see the polarization data points that are circled in Figure 3). The geometric configuration of this structure is filamentary or edge-on. Since a filament would occupy the smallest volume of space, we suggest that it is filamentary.

The gradient in ${\theta }_{\mathrm{gal}}$ with distance is quantified by dividing the thirteen stars into two separate groups and performing a linear fit to the variation of polarization versus distance for each group of stars. A slightly different slope of the ${\theta }_{\mathrm{PA}}$ versus distance relationship was obtained for the two groups (Figure 6). The most slowly varying ISMF component is traced by seven stars and includes the original three PlanetPol stars from Paper II. The linear fit to ${\theta }_{\mathrm{PA}}$ versus distance for the first set gives ${\theta }_{\mathrm{gal}}$ = 106.8 (±1.5) − 0.53 (±0.08) D_star, with a reduced χ² of 1.217 (lower group of stars in Figure 6). The second set of six stars in the same extended filamentary-shaped feature can be fit by the line ${\theta }_{\mathrm{gal}}$ = 130.0 (±15.2) − 0.68 (±0.65) D_star, with a reduced χ² of 0.528 (upper group of stars in Figure 6). More than thirteen data points are plotted in Figure 6 because several of these stars have been observed multiple times.

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The angle found in Paper II for the rotation of polarization position angles with distance was ∼−025 pc⁻¹ for position angles presented in the equatorial coordinate system, whereas the slopes in the galactic coordinate system are −053 to −068 pc⁻¹, and the stars span an angular range of ∼98° (Section 4.2). The factor of at least two difference between the slopes suggests that neither the galactic coordinate system nor the equatorial coordinate system is the correct system for evaluating the characteristics of the magnetic structure traced by the filament stars. It appears as if some of the variation of the polarization position angle with distance is, instead, due to the rotation of the coordinate systems over the angular interval spanned by the star positions.

To remove this bias introduced by the coordinate system, we have applied the analysis method of Section 3 to the filament stars. Evaluating the minimum of ${F}_{\mathrm{II}}({B}_{i})$ for the filament-star data gives a magnetic field direction for the filament, ${B}_{\mathrm{FIL}}$, toward ℓ = 359°, and b = 19°. A better direction for the magnetic field direction traced by the filament stars is found in Frisch et al. (2015a, see Table 1), which incorporated new polarization measurements of three additional stars not used here. The polarization position angles expressed with respect to the pole ${B}_{\mathrm{FIL}}$ do not vary systematically with the distance of the star. Evidently the distance dependence of the polarization position angles defined by ${\theta }_{\mathrm{gal}}$ is partly due to the rotation of the galactic coordinate system over the 90° span of the filament.

Table 1.  Interstellar Magnetic Field Directions

Magnetic Field	Merita	ISMF Directionb
	Function	ℓ, b (deg)
Paper I	Unweighted fit	38, 23 (±35)
Paper II	${F}_{\mathrm{II}}({B}_{i})$	47 ± 15, 25 ± 20
All stars (${B}_{\mathrm{ALL}}$)	${F}_{\mathrm{II}}({B}_{i})$	16.3, 27.0 (±15)
Interstellar (${B}_{\mathrm{POL}}$, no filament stars)	${F}_{\mathrm{II}}({B}_{i})$	36.2, 49.0 (±16)
Filament (${B}_{\mathrm{FIL}}$, only filament stars)c	${F}_{\mathrm{II}}({B}_{i})$	359.3, 19.0 (±10.2)
IBEX (BIBEX)d	⋯	34.8 ± 4.3, 56.6 ± 1.2
Angle between ${B}_{\mathrm{POL}}$ and VCLIC,LSRe	⋯	76.8 (+23.5, −27.6)
Angle between ${B}_{\mathrm{POL}}$ and BIBEX	⋯	7.6 (+14.9, −7.6)
Angle between BIBEX and VLIC,LSRf	⋯	96.9 ± 8.5

Notes.

^aEquation (1). ^bThe quantities ℓ, b are the direction of the ISMF in galactic coordinates. ^cDirection of the ISMF traced by the polarization filament, from Frisch et al. (2015a). ^dISMF direction traced by the IBEX Ribbon, B_IBEX, corresponding to the weighted mean of the energy-dependent center of the IBEX Ribbon arc at λ = 219.2 ± 1.3, β = 39.9 ± 2.3 (Funsten et al. 2013). ^eBased on an upwind direction for the LSR CLIC velocity vector of ℓ = 335.6 ± 13.4, b = −7.0 ± 9.0, V = −17.3 ± 4.9 (Appendix D). ^fSee Appendix D for the LSR velocity of the LIC.

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Figure 6, right, shows the polarization position angle that is calculated with respect to the filament magnetic field direction, ${B}_{\mathrm{FIL}}$, and plotted against the angular distance between the star and the end of the filament. The filament end is defined by star HD 172167, located at ℓ, b = 67°, 19°. The steady variation of the polarization angle PA_filament along the filament length suggests that ${B}_{\mathrm{FIL}}$ provides a better coordinate system for expressing filament polarizations than does the north galactic pole (or north terrestrial pole). The best-fitting ISMF direction to the filament stars, from Equation (1), is directed toward the heliosphere nose defined by the inflow velocity vector of neutral interstellar He into the heliosphere. The magnetic turbulence associated with the filament polarizations is ±96, based on the harmonic mean of the measurement uncertainties and the dispersion of the polarization position angles with respect to the filament magnetic field direction. The polarization position angles of the filament are obviously not consistent with the local ISMF direction obtained in Paper II, or with the new fit to the entire data set in this paper (Figure 4, left).

Since the filament polarizations appear to define an isolated magnetic structure (see previous section), the fitting process has been repeated for a data set that is identical to that used to obtain ${B}_{\mathrm{ALL}}$ except that the thirteen stars that trace the filament polarizations are omitted. The results of the fit performed with the omission of the filament stars are shown in Figure 4, right, and the uncertainties on that fit are shown in Figure 5, right. For this new fit, the best-fitting ISMF direction is toward ℓ = 362, b = 490. Comparison of the distribution of ${F}_{\mathrm{II}}({B}_{i})$ for the evaluations with and without the filament stars (Figure 4), clearly shows that the merit function obtained from the star sample that omits the filament stars is more clearly defined than the irregularly shaped minimum of the merit function that is based on the entire data sample. The uncertainty on this best-fitting ISMF direction is assumed to occur where ${F}_{\mathrm{II}}({B}_{i})$ is 10% larger than the minimum, giving an uncertainty on this direction of ±16° (Figure 5, right). The directions of ${B}_{\mathrm{POL}}$ and the IBEX ISMF, B_IBEX, are the same to within the uncertainties (Table 1).

At first glance, the excellent agreement between the ISMF direction obtained from the polarization data ${B}_{\mathrm{POL}}$ after stars tracing a separate magnetic structure are omitted from the sample and the ISMF traced by the IBEX Ribbon almost seems too good to be correct. Since other unrecognized magnetic features may be present in these data, and the volume of space sampled by the polarization data is large, it is remarkable that the local ISMF field direction found from the polarization data is so close to the ISMF indicated by the IBEX Ribbon (Table 1). We therefore look more closely at the values of the individual parameters in Equation (1) to determine whether all of the polarization data with P/ΔP > 2.0 are tracing ${B}_{\mathrm{POL}}$, as opposed to ${B}_{\mathrm{POL}}$ being traced by only a subset of the polarization data.

The properties of the polarization position angles referenced to the best-fitting ISMF direction, ${B}_{\mathrm{POL}}$, are viewed from two perspectives: (i) the three-dimensional statistical properties of ${F}_{\mathrm{II}}({B}_{i})$ as a function of the probability ${G}_{n}$, sine(${\theta }_{\mathrm{POL}}$), and ${F}_{\mathrm{II}}({B}_{i})$ evaluated for the polarization position angles calculated with respect to ${B}_{\mathrm{POL}}$. (ii) The probability of the position angle (Equation (2)) versus the position angle of the star with respect to ${B}_{\mathrm{POL}}$.

For the first approach, the statistical characteristics of the data set that yields the best-fitting ISMF can be represented by plotting the individual components of the merit function, ${F}_{\mathrm{II}}({B}_{i})$ (Equation (1), Figure 7), where the best-fitting ISMF direction ${B}_{\mathrm{POL}}$ corresponds to the minimum value of ${F}_{\mathrm{II}}({B}_{i})$. The function ${f}_{n}({B}_{i})$ (Equation (1)) achieves low values for either high-probability polarization position angles (${G}_{n}$, Equation (2)) or small sin(${\theta }_{n}$). Figure 7 shows the ${F}_{\mathrm{II}}({B}_{i})$ plotted against the probability ${G}_{n}$ that the data point traces ${B}_{\mathrm{POL}}$, and the sine of the position angle sin(θ_n,i) calculated with respect to the best-fitting ISMF B_n = ${B}_{\mathrm{POL}}$. The probability shows the probability ${G}_{n}$ (Equation (2)) for each star i, normalized to a maximum value of one. The right-hand axis labeled "sin(theta)" shows the sine of the polarization position angle for each star in the coordinate system defined with respect to the best-fitting ISMF at the north pole.¹⁵ The vertical axis labeled "merit function" shows the ${f}_{n}({B}_{i})$ for each individual star. Red points show stars where P/ΔP > 2.0. The lower statistical probabilities of outlying polarization position angles for significant detections (e.g., P/ΔP > 2.0) is apparent by the non-compliant position angles in the rear-left corner of the figure. Insignificant polarizations would not be expected in this corner since their position angles will tend to be statistically random so that sin(θ_n,i) > 0.

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The distribution in Figure 7 can be used to identify the set of nearby stars with polarization position angles that are consistent with ${B}_{\mathrm{POL}}$. These stars include stars where measurement uncertainties are either small, P/ΔP > 2.0, or are large but with small values of ${F}_{\mathrm{II}}({B}_{i})$ and P/ΔP $\ll 2.0$. Appendix A lists the identifications of the top third of the stars with polarization position angles that provide the best match to ${B}_{\mathrm{POL}}$ and have P/ΔP > 2.0. These stars are located on the front right of Figure 7. Stars with significant polarization position angles that do not comply with the direction of ${B}_{\mathrm{POL}}$ are in the rear left part of the figure, and represent candidate polarizations for tracing an unrecognized component of the local ISMF (see Section 4.6).

Figure 7 shows that the minimization method used to select out the best-fitting ISMF direction (Section 3), will be affected both by the compliant stars in the front right-hand corner of the figure, where the values of the merit function being minimized are small, and by the non-compliant stars in the rear left corner where the probability that the observed polarization position angle corresponds to the true polarization angle (given by ${B}_{\mathrm{POL}}$) is negligible. The general implication of Figure 7 is that a non-negligible fraction of the polarization position angles that are significant (P/ΔP > 2) do not have polarization position angles that conform to (or are compliant with) the best-fitting ISMF. Those points are represented by low probabilities and large sin(θ_n,i) values in the figure. Stars with small values of ${F}_{\mathrm{II}}({B}_{i})$ are refereed to as stars that "conform" to, or are "compliant" with, the dominant ISMF direction ${B}_{\mathrm{POL}}$.

Figure 8 shows the probability distribution of the stars as a function of the polarization position angle, ${\theta }_{\mathrm{POL}}$, evaluated with respect to the best-fitting ISMF, ${B}_{\mathrm{POL}}$. Clearly stars with large measurement uncertainties are more likely to be compliant with the best-fitting ISMF ${B}_{\mathrm{POL}}$ than stars with small measurement uncertainties and polarization vectors pointing in the wrong direction. This feature allows data with all levels of accuracy to be useful in the fitting process. The second salient property of Figure 8 is that there are numerous polarization position angles that have small mean errors and also clearly do not trace the same magnetic field direction as ${B}_{\mathrm{POL}}$ and the IBEX Ribbon ISMF.

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Figure 9 maps the stars in Figure 7 in the galactic coordinate system, and codes the symbol of the star as to whether or not the polarization position angle is compliant with ${B}_{\mathrm{POL}}$. The star set is divided into two halves, based on the median value of ${F}_{\mathrm{II}}({B}_{i})$ of 3.54. The best-matching half of the stars, where ${F}_{\mathrm{II}}({B}_{i})$ < 3.54, are plotted with solid symbols. The least-compliant half of the stars, ${F}_{\mathrm{II}}({B}_{i})$ > 3.54 are plotted with "X's" (also see Figure 7). Stars where P/ΔP > 2.0 are plotted with red symbols, and stars with P/ΔP < 2.0 are plotted with black symbols. The compliant stars with P/ΔP > 2.0 have a tendency to be located between galactic longitudes of 0° and 90° in the northern hemisphere, and follow that trend until they wrap around ℓ at negative latitudes of ∼−50° in the southern galactic hemisphere near the BICEP2 region (Section 5.6). The conforming polarization position angles tend to follow into two extended distributions, one located roughly between ℓ, b = 90°, 50°, and 60°, −60°, and the other extending roughly between 70°, 65° and −10°, −65°. There is a slight tendency for the southern hemisphere conforming polarization position angles to be located in the region of the original nearby dust "patch" identified by Tinbergen (1982) that extended to negative galactic latitudes in the fourth galactic quadrant (ℓ > 270°) of the galaxy.

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The turbulence in ${B}_{\mathrm{POL}}$ can be evaluated from the dispersion of the polarization position angles calculated with respect to the direction of the best-fitting ISMF direction ${B}_{\mathrm{POL}}$. The third of the data sample that consists of the stars with ISMF directions that provide the best fit to ${B}_{\mathrm{POL}}$ contains 114 stars. Twenty-nine of those stars (listed in Appendix A) have significant polarizations with P/ΔP > 2.0. A rough estimate of magnetic turbulence can be found by evaluating the polarization position angles in a coordinate system that is aligned with the pole of ${B}_{\mathrm{POL}}$. The average position angle for this 29-star subset is ${\theta }_{\mathrm{POL}}$ = 120 ± 66. This relatively small dispersion about the mean suggests that ${B}_{\mathrm{POL}}$ has a low level of magnetic turbulence, and is not twisted by the kinematical properties of the CLIC (Section 5.5).

A better estimate of magnetic turbulence is obtained by considering only 21st century data that tend to have smaller mean errors than the older data. In the ideal case, the magnetic turbulence can be recovered by comparing the observed position angle variations with the mean measurement errors, or

$$\begin{eqnarray}&&{{\rm{\Phi }}}_{\mathrm{IS}}^{2}=\mathrm{std}{({\theta }_{\mathrm{POL}})}^{2}-\mathrm{std}{(\delta {\theta }_{\mathrm{me}})}^{2}.\end{eqnarray} \tag{ 4 }$$

The quantity Φ_IS represents the calculated interstellar turbulence (in degrees), std(θ_POL) is the standard deviation of the polarization position angle ${\theta }_{\mathrm{POL}}$ evaluated for a coordinate system with the pole located at ${B}_{\mathrm{POL}}$, and std(δθ_me) is the standard deviation of the mean measurement errors of the data subset.

The amount of interstellar turbulence obtained from Equation (4) varies with the number of stars that are included in the data subsample. If this subgroup of high-quality polarization data is sorted numerically according to goodness-of-fit between ${\theta }_{\mathrm{POL}}$ and ${B}_{\mathrm{POL}}$, where the perfect measurement will have ${\theta }_{\mathrm{POL}}$ = 0°, then the end-point of the array that contains the stars with the very best matches between the polarization position angles and ${B}_{\mathrm{POL}}$ should also provide the best estimate of the interstellar magnetic turbulence using Equation (4). In Figure 10 we evaluate interstellar turbulence using Equation (4) and by starting with the highest quality data set established by setting some minimum value for P/ΔP. That data subset is then reevaluated by successively rejecting the lowest quality data points until a reasonable estimate for the interstellar turbulence is obtained. Figure 10 shows the estimates of interstellar turbulence (solid lines) for two data subsets with P/ΔP > 2.0 (black lines) and P/ΔP > 3.5 (purple lines). The horizontal axis shows the number of qualifying stars included in the numbers used in Equation (4), with the stars with polarization position angles that better match ${B}_{\mathrm{POL}}$ on the figure right, and those with poorer matches on the figure left. For a data subset that is restricted to stars with P/ΔP > 3.5, the minimum value of the interstellar turbulence is 8° and the seven stars that bracket this minimum have Φ_IS = 9° ± 1°.

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For a larger subset where P/ΔP > 2.0, the minimum of the interstellar turbulence decreases to ∼2° for the stars that best-comply with ${B}_{\mathrm{POL}}$. However, the turbulent component of the ISMF ${B}_{\mathrm{POL}}$ should be best defined by the most precise data, so we report the turbulence Φ_IS = 9° ± 1° from the P/ΔP > 3.5 data subset as the our best estimate of the turbulence of ${B}_{\mathrm{POL}}$.

The large number of non-conforming stars in Figure 9 suggests that one or more additional ISMF directions, not yet accounted for, must be influencing some of the polarization position angles. ${B}_{\mathrm{POL}}$ is based on 360 measurements, of which 33% have P/ΔP > 2.0. The set of stars with the largest third of the values of the ${F}_{\mathrm{II}}({B}_{i})$ (i.e., the one-third of the polarization data that are least compliant with the direction ${B}_{\mathrm{POL}}$) were selected to be tested independently for a direction of the ISMF using the method described in Section 3. The best-fitting ISMF direction for this third of the stars is toward ℓ = 2673, b = 330, which is 86° from the heliosphere nose and is marginally constrained since it is at the edge of the region that is included in this study.

IBEX measures ENAs created from charge-exchange between neutral interstellar atoms and heliosheath ions, including the solar wind and incorporated pickup ions (McComas et al. 2009; Livadiotis & McComas 2012). IBEX discovered an extraordinarily circular Ribbon of ENAs that is about 20° wide and several times more intense than the distributed flux of ENA emissions throughout the rest of the sky (Fuselier et al. 2009; McComas et al. 2009; Schwadron et al. 2011; Funsten et al. 2013). The locus of sightlines where the Ribbon is observed appear in directions where the ISMF draping over the heliosphere is perpendicular to the radial viewing sightline (Schwadron et al. 2009). There is no consensus agreement on the Ribbon formation mechanism (McComas et al. 2014). More recently, Schwadron & McComas (2013) and Isenberg (2014) have suggested that the Ribbon is created through retention of pickup ions, implying that the Ribbon reflects a true spatial structure, not an optical effect due to the prominence of the pickup ring, as previously discussed (McComas et al. 2009; Heerikhuisen et al. 2010). The Ribbon geometry is a sensitive diagnostic of the ISMF direction and strength, and the pressure and ionization of the interstellar cloud surrounding the heliosphere (Frisch et al. 2010b; Heerikhuisen & Pogorelov 2011; Ratkiewicz et al. 2012).

The IBEX Ribbon is a highly circular feature, with a radius of 745 ± 20 that is centered on the ecliptic coordinates of λ = 2192 ± 13, β = 399 ± 23 (based on the weighted mean average over the energy passbands, Funsten et al. 2013). The Ribbon center corresponds to galactic coordinates of ℓ = 347 ± 43, b = 566 ± 12. The Ribbon center is energy dependent and shifts by 92 across the five energy bands of IBEX-HI, from ℓ = 347, b = 555 for the 0.7–1.7 keV bands, to ℓ = 201, b = 607 for the 4.3 keV band, in galactic coordinates.

The observed center of the Ribbon arc is likely to be within 5° of the true ISMF direction outside of the heliosphere. MHD simulations of the Ribbon formation by Heerikhuisen et al. (2014) show that the center of the Ribbon arc is offset from the direction of the ISMF far upstream of the heliosphere by 5° for interstellar field strengths of 3 μG. Comparisons between the pressures of the inner heliosheath plasma and the thermal and ram pressure of the LIC give an ISMF of ∼3.3 μG. A similar value of ∼3.1 μG is found from the magnetic distortion of the heliotail (Schwadron et al. 2011). Photoionization models of the LIC that include energy sinks and sources also predict a ∼2.7 μG magnetic field strength from the equipartition of energy (Slavin & Frisch 2008).

The direction of the best-fitting ISMF that is obtained from the data set that omits the filament stars, ${B}_{\mathrm{POL}}$, agrees remarkably well with the magnetic field direction that is obtained from the center of the IBEX Ribbon arc. The angular separation between the magnetic field direction that dominates the results obtained from the polarization data, ${B}_{\mathrm{POL}}$, and the IBEX Ribbon field direction is 76 (+149, −76) (Table 1). The uncertainties become larger if the energy variation of the Ribbon center is included. The alignment of ${B}_{\mathrm{POL}}$ and B_IBEX indicate that these two magnetic field directions are the same to within the uncertainties, and that the ISMF interacting with the heliosphere extends into the upwind interstellar regions with minimal distortion outside of the draping region. It is also possible that ${B}_{\mathrm{POL}}$ agrees with B_IBEX because B_IBEX is the nearest coherent magnetic structure in the sky and therefore has the largest angular extent of all possible ordered fields.

Stars with polarization position angles that differ from ${B}_{\mathrm{POL}}$, and therefore from B_IBEX, have slightly stronger polarization strengths than those that do not agree. However, there does not appear to be any difference between the distances of the two subsets of the data. The third of the polarization data that provides the worst match to ${B}_{\mathrm{POL}}$ consists of 114 measurements that have a mean P/ΔP of 2.4 ± 1.5. The third of the polarization set that provides the best match to ${B}_{\mathrm{POL}}$ has a mean P/ΔP of 1.5 ± 1.1. Both sets of stars have mean distances of approximately 25 ± 10 pc. The lower mean significance of the polarizations that provide the best match to ${B}_{\mathrm{POL}}$, and therefore B_IBEX, is not surprising since total dust column densities will be lowest for the ISM closest to the heliosphere.

The polarity of the ISMF is not given by either the IBEX Ribbon data or by the polarization data. Both the polarity of the ISMF direction found by Voyager 1 at the heliopause (Burlaga & Ness 2014), and the radio rotation measures of pulsars within several hundred parsecs in the fourth galactic quadrant (Salvati 2010), suggest a polarity for the local ISMF that is directed upwards through the galactic plane.

Asymmetries in the flux of TeV galactic cosmic rays at Earth are observed over both large (Nagashima et al. 1998; Abdo et al. 2009) and small (Vernetto et al. 2009; Abbasi et al. 2011; Tibet Asγ Collaboration et al. 2011) angular scales. The cosmic rays in the 1.5–10 TeV energy range have gyroradii of ∼100–700 AU in a 3 μG magnetic field, and probe the magnetic field in the same spatial region as the IBEX Ribbon (Schwadron et al. 2014). Schwadron et al. modeled galactic cosmic ray streaming along the ISMF, for a small ratio of the perpendicular-to-parallel component of diffusion, and showed that the observed TeV cosmic ray asymmetries show a general ordering about the equator of B_IBEX locally. Over larger spatial scales, interstellar magnetic turbulence may disrupt GCR streaming and reduce the magnitude of the GCR asymmetries.

The low level of magnetic turbulence found for ${B}_{\mathrm{POL}}$, Φ_IS ∼ 9° ± 1°, indicates that the IBEX magnetic field extends out into interstellar space where the low magnetic turbulence does not impede the flux of TeV GCRs into the heliosphere. Over spatial scales of several hundred parsecs, Salvati (2010) used the rotation measures of radio sources to determine a direction for the ISMF in the third galactic quadrant that is within ∼22°–24° of B_IBEX. Both the polarization data and the radio rotation measure data suggest that the IBEX Ribbon traces a non-turbulent magnetic field that extends into the third galactic quadrant from whence the GCR streaming arrives.

The origin of the filamentary structure (or structures) defined by the polarization position angles plotted in Figure 6 is not firmly established. The filament polarizations trace an ISMF direction that is aligned with the direction of the heliosphere nose, and the filament stars are spatially arranged along a direction that is perpendicular to the ${B}_{\mathrm{ismf},\mathrm{helio}}-{V}_{\mathrm{vel},\mathrm{helio}}$ plane that marks the heliosphere asymmetry created by the ISMF at the heliosphere, B_ismf,helio and the heliocentric interstellar gas velocity at the heliosphere, V_vel,helio. These properties led to the proposal that the filament polarizations are evidence for the deflection of the polarizing interstellar dust grains around the heliosphere (Frisch et al. 2015a). Confirmation of a filament origin in the outer heliosheath will require modeling the alignment and transport of interstellar dust grains during their approach to, and interaction with, the heliosphere. As this modeling is not yet available, other possible origins for the filament are briefly mentioned.

An alternate origin for the filament polarizing grains could be that the grains are near the Sun and embedded in the LIC flow, but outside the influence of the heliosphere. Since the ISMF that is the best fit to the filament polarizations coincides with the heliosphere nose direction, which is defined by the inflowing interstellar He°, this interpretation requires that either the ISMF traced by the filament is parallel to the heliocentric LIC gas velocity, or that the assumption of polarization vectors parallel to the magnetic field direction is invalid. The first requirement invokes a random coincidence between the filament ISMF direction and the LIC heliocentric velocity and violates the result that the LIC magnetic field and LSR velocity are perpendicular based on IBEX data (Table 1, Schwadron et al. 2015a). The second requirement may be fulfilled if radiative alignment is significant (e.g., Hoang & Lazarian 2014; Andersson 2015).

Alternatively, if ${B}_{\mathrm{FIL}}$ is not associated with the LIC but is located at a distance of ∼5 pc from the Sun, then the filament extent is about 1.7 × 7.1 pc in the plane of the sky. If this feature has the same density as the LIC (n ∼ 0.26 H^o nucleii cm⁻³, Model 26 in Slavin & Frisch 2008), then the column density associated with the feature would be log N(H^o) = 18.14 cm⁻². Such a column density would be consistent with other column densities through the very local ISM (Wood et al. 2005). However, the coincidence between the filament ISMF direction and the heliosphere nose would remain puzzling.

The filament could be associated with an unidentified magnetic field component, perhaps associated with a shock front related to Loop I that extends very close to the Sun. For this possibility, again, it is a coincidence that the best-fitting ISMF to the filament polarizations is toward the heliosphere nose. The shock could be associated with the ISM in front of one of the filament stars, α Oph (HD 159561, A5 III, 14 pc), where high abundances of refractory elements in the gas, a strong Mg^o line indicating high temperature or electron densities, and temperatures up to 23,000–60,000 K indicate the processing of dust through interstellar shocks (Frisch 1981; Frisch et al. 1987, 1999; Crawford 2001). The polarizations of the star HD 159561 that traces the filament was measured at high sensitivity by both PlanetPol (Bailey et al. 2010) and POLISH2 (Wiktorowicz et al. 2015), with good agreement between the polarization position angles.

Figure 11 compares polarization directions with the configuration of dust reddening that is associated with the parts of Loop I within ∼100 pc (Appendix B contains additional information about the figure). Some of the filament stars have polarizations that are loosely parallel to the edge of the cavity in the distribution of the dust extinction. The sample of polarized stars within 40 pc has been divided into two parts, and the half with polarization position angles in best agreement with the very local ISMF ${B}_{\mathrm{FIL}}$ are circled. The filament polarizations for stars between ℓ = 20° and ℓ = 90° are not aligned with strong gradients in the cumulative color excess in Figure 11, so a possible association between the filament and Loop I requires further study.

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Measurements of starlight that has been polarized in the ISM provide one of the few viable methods for determining the distribution of nearby interstellar dust grains and understanding the relative distributions of interstellar gas and dust over parsec-sized scale lengths. Polarization efficiencies in the local ISM can be found by comparing polarization strengths with color excess E(B − V), and E(B − V) with hydrogen column densities. Column densities of H^o for stars within 40 pc are typically less than N(H^o+2H₂) ≤ 10^18.7 (Wood et al. 2005). Using the mean ratio between N(H^o)+2NH₂ and E(B − V) (Bohlin et al. 1978), and the upper envelope of the relation between polarization and E(B − V) (Serkowski et al. 1975) yields E(B − V) ≤ 0.0009 mag and ${P}_{\%}$ ≤ 0.008 for the very local ISM. Using instead the analogous relations that apply to low-extinction stars with low column densities of foreground H₂ predicts E(B − V) ≤ 0.001 mag and ${P}_{\%}$ ≤ 0.014 in the local ISM. A quantitative discussion of the relations in this subsection that link hydrogen column density and polarization strength is given in Appendix C.

It might be expected that interstellar polarizations of nearby stars will be more effective than the polarizations of distant stars since the ISM toward distant sources is likely to be more complex, with different magnetic field directions or strong radiation fields in the sightline depolarizing a polarized beam. Variations in alignment efficiency are also indicated by theoretical calculations of perfectly aligned infinite cylinders that show approximately a factor 3–4 larger ${P}_{\%}$/E(B − V) than is observed (Mathis 1979; Kim & Martin 1994). The efficiency of nearby interstellar polarization can be tested using stars where both polarization data and hydrogen column density are available. Two variables are introduced to trace the efficiency of the polarization in a sightline, α and α'. The ratio ${P}_{\%}$/E(B − V) is proportional to α and α' for high-column density and low column density sightlines, respectively. Since N(H^o) will be used as a proxy for E(B − V) for the nearby stars (Appendix C) a third variable γ = N(H⁺)/N(H^o) is included to account for the possible presence of ionized hydrogen.

Both polarization and UV absorption line data are available for the nearby star HD 34029 (α Aur, Capella, 13 pc Wood et al. 2002). Combining UV and FUV data on Capella, and adopting a model for the cloud length, Wood et al. determined column densities of log N(H^o) = 18.24 ± 0.07 cm⁻² and log N(H⁺) = 18.08 ± 0.65 for the LIC in this direction, corresponding to γ ∼ 0.69 (with large uncertainties, ±1.47). The polarization of Capella is P(%) = 0.024 ± 0.009 (Piirola 1977). Combining these values with Equations (8) and (12) in Appendix C for reddened and unreddened sightlines respectively gives alpha ∼5.3 and α' ∼ 2.6, where both estimates have large uncertainties. These large values for polarization efficiency compared to the expected values of one for the upper envelope of the relation between polarization and color excess of distant stars (Appendix C) suggest that polarization mechanisms in the local ISM are more efficient than for distant reddened and low-extinction stars. These results are nevertheless highly uncertain both because measurement uncertainties are large and Capella is a G1III+K0III binary system where intrinsic polarization is possible.

A second test of alignment efficiency in the local ISM is made using the two stars with spectral types not associated with intrinsic polarization, HD 11443 (F6IV, 20 pc) and 39587 (G0V, 9 pc) that have polarizations of ${P}_{\%}$ = 0.02 ± 0.009 and 0.019 ± 0.008 respectively (Piirola 1977). For these stars log N(H^o) = 18.33 cm⁻² and log N(H^o) = 17.93 cm⁻², respectively (Wood et al. 2005). Information on H⁺ toward these stars is not available so the Capella value for γ is assumed. The resulting alignment efficiencies are α = 3.6, and α' = 1.9 for HD 11443, and α = 8.5 and α' = 3.7 for HD 39587. If lower ionization levels had been assumed, such as γ ∼ 0.29 corresponding to the fractional ionization of the LIC near the heliosphere (Model 26 in Slavin & Frisch 2008), these values of α and α' would increase.

These estimates of the polarization efficiency in the local ISM, where α > 1, are consistent with the results of Fosalba et al. (2002) who found a nonlinear increase in polarization as extinction approached zero for low column density stars (see Appendix C). The low column density values of α' > 1 found in the previous paragraph could be spurious, resulting from the combination of the large uncertainties and this nonlinear behavior of polarization strengths at low column densities. Further data on both interstellar column densities and polarizations toward the same stars are needed to establish the efficiency of the polarization mechanisms in the local ISM.

The agreement between B_IBEX and ${B}_{\mathrm{POL}}$ (Table 1) indicates that B_IBEX extends into the ISM without significant distortion. The low level of magnetic turbulence for ${B}_{\mathrm{POL}}$ (Section 4.5) suggests that the ratio of the plasma thermal to magnetic pressure, β, is ≤1. A LIC magnetic field strength of ∼3 μG is consistent with the total interstellar pressure required to balance the inner heliosheath plasma traced by IBEX ENAs, and the deflection of the heliotail to the port side¹⁶ of the heliosphere (Schwadron et al. 2011), and also the equipartition of energy between the LIC thermal gas and magnetic field (Slavin & Frisch 2008). Nearby polarized stars with significant polarizations that do not trace ${B}_{\mathrm{POL}}$ (Section 4.6) may indicate local regions where the magnetic field has been distorted by cloud motions that create high magnetic pressure (Figure 13), or by cloud collisions (Figure 12).

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The local magnetic field, ${B}_{\mathrm{POL}}$, provides a probe of the physical properties and origin of the interstellar cloudy material in the immediate solar neighborhood. The bulk motion through space of the nearby interstellar material associated with the CLIC, <30 pc, has been determined from the velocities for interstellar optical and UV absorption lines and the flow of interstellar dust through the heliosphere (Frisch et al. 2011). The angle between ${B}_{\mathrm{POL}}$ and the upwind direction of the CLIC LSR velocity (V_CLIC,LSR, Appendix D) is 768 (+235, −276). Although the uncertainties are large, the bulk motion of local interstellar gas relative to the LSR is therefore perpendicular to the ISMF direction. The flow of the CLIC relative to the LSR originates in a direction that is within 214 ± 208 of the nominal center of the Loop I superbubble. For the Loop I bubble center, we use the S1 shell feature, centered at ℓ = 346° ± 5°, b = 3° ± 5° as defined by (Wolleben 2007). The S1 bubble model places the Sun in the rim of the S1 shell. The relative configurations of ${B}_{\mathrm{POL}}$, V_CLIC,LSR, and the S1 bubble form a self-consistent picture where local ISM, consisting of the CLIC, is part of the rim of the Loop I superbubble and ${B}_{\mathrm{POL}}$ represents the magnetic field swept up in the rim of the expanding superbubble.

The IBEX measurements of the LIC velocity and LIC magnetic field provide a precise set of data for comparisons between the LIC interstellar gas velocity and magnetic field vectors. The heliocentric velocity determined by IBEX for interstellar He° flowing through the heliosphere corresponds to a LIC velocity with respect to the LSR of V_IBEX,LSR = 17.2 ± 1.9 km s⁻¹ toward ℓ, b = 1411 ± 59, 24 ± 42 (based on the velocity in Schwadron et al. 2015b). The direction of the ISMF that shapes the heliosphere is given by the weighted mean center of the IBEX Ribbon, at ℓ = 348 ± 43, b = 566 ± 12 (Table 1, Funsten et al. 2013). The perpendicular angle between the LIC velocity with respect to the LSR, and the IBEX magnetic field direction (969 ± 85, also see Schwadron et al. 2014) indicates that the motion of the LIC through space is consistent with a scenario where the partially ionized LIC sweeps up and carries a frozen-in magnetic field through space (Model 26 in Slavin & Frisch 2008, indicates that ∼22% of the hydrogen and ∼39% of the helium are ionized).

Different aspects of this picture emerge when the 15-cloud model of Redfield & Linsky (2008) is compared with the direction of the interstellar field. The angles between the LSR velocities of the fifteen clouds (given in Frisch & Schwadron 2014) and B_IBEX are plotted in Figure 12 against ${V}_{\mathrm{LSR}}$. The magnetic field direction is represented by the IBEX value, as B_IBEX is known more precisely than the field determined from the polarization data, ${B}_{\mathrm{POL}}$, and the two field directions agree (Table 1). A prominent characteristic of Figure 12 is that, except for the Aur cloud, the LSR velocities of these clouds tend to increase as the angle between ${V}_{\mathrm{LSR}}$ and the interstellar field increases if the uncertainties are included. The mean angle between the 15 LSR velocities and B_IBEX is 1075.

If we assume that deviations of the velocities of the 15 individual clouds from the bulk CLIC motion are caused by the injection of energy into the CLIC gas, and that the energy injection is ordered by the pole of the IBEX ISMF direction ${B}_{\mathrm{POL}}$ (Table 1), then the most effective acceleration is directed toward the antipode of ${B}_{\mathrm{POL}}$ at ℓ = 216°, b = −49°. The largest deviations from the perpendicularity of the gas and magnetic field therefore occurs for higher velocities that are more pointed toward the third galactic quadrant, where gas and dust densities are extremely low (e.g., Fitzgerald 1968; Frisch & York 1983; Vergely et al. 2010).

The CLIC is a decelerating flow of interstellar gas so that cloud collisions supply an opportunity for shock formation (Frisch et al. 2002; Linsky et al. 2008; Redfield & Linsky 2008; Gry & Jenkins 2014; Frisch et al. 2015c). Stars that are compliant with ${B}_{\mathrm{POL}}$ are preferentially located in the first galactic quadrant, ℓ = 0°–90° (Figure 13). Some of the stars that have polarizations that are compliant with ${B}_{\mathrm{POL}}$ (Section 4.4, and are circled in Figure 9) are also located in kinematically active regions. The elongated feature of compliant stars with ℓ = 60°–90° (Section 4.4) occupies a kinematically quiescent region (Figure 13) dominated by the LIC, while the second elongated feature with ℓ = −10°–70° occurs in a kinematically active region where multiple clouds and large differences in absorption component velocities in the same sightline indicate cloud collisions at up to 50 km s⁻¹.

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It is notable that there is minimal nearby polarization associated with the G-cloud centered near ℓ, b = 315°, 0° (Figures 13, 14). Two stars with polarization position angles that comply with ${B}_{\mathrm{POL}}$ are found toward the G-cloud (Figure 13). Two layers of nearby polarizing dust are found in the direction of the G-cloud, at ∼19 and ∼55–65 pc (Figure 14). The G-cloud extends in front of α Cen, at 1.3 pc, but the polarizing grains are much more distant.

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The G-cloud region shows evidence of dust grain destruction by interstellar shocks. The average volume densities of interstellar Fe and Ca are systematically larger in the third and fourth galactic quadrants where the G-cloud is located, compared to ℓ < 180° (Frisch 2010). Destruction of dust grains in interstellar shocks preferentially returns refractory elements such as Fe and Ca to the gas phase (Jones et al. 1994; Frisch et al. 1999), so that the higher Fe and Ca densities in the G-cloud region may indicate recent shock activity and magnetic turbulence.

Interstellar polarization data provide one technique for selecting the dust-free sightlines that provide the optimum conditions for measurements of the B-mode polarization of the cosmic microwave background (CMB). BICEP2 has studied the B-mode polarization in a southern region centered near R.A. = 0°, decl. = −575 (Ade & the BICEP2 team 2014). The BICEP2 field coincides roughly to the region defined by decl. between −68° and −48°, and R.A. between 322° and 38°. This field, centered on galactic coordinates ℓ, b = 3161, −583, is outlined with dotted lines on a smoothed map of color excess E(B − V) for stars within 100 pc in Figure 11 (also see Figure 3). Figure 15 shows that the BICEP2 region contains significant polarization within 40 pc of the Sun, and with increasing polarization strengths out to 300 pc. The star that is circled at the high-longitude end of the BICEP2 region (Figure 11) indicates a star with a polarization position angle that conforms to ${B}_{\mathrm{POL}}$, and therefore to B_IBEX, which suggests that B_IBEX extends up to the edge of the BICEP2 region. A slightly different ISMF direction is traced by most of polarized stars in the BICEP2 region.

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We have tested the dust content of the BICEP2 field using two markers of interstellar dust, optically polarized starlight and the color excess E(B − V) of stars. The polarization data for stars in this field are plotted against distance in Figure 15, using the data sources mentioned in Section 2. Both significant polarization detections where P/ΔP ≥ 2.0, and lower polarization strengths that are not statistically significant are found. Polarizations are up to ∼0.2%, corresponding to color excess values of E(B − V) ≥ 0.028 mag (using the low extinction relations of Equation (9) for α' ≤ 1), optical extinction A_V = 3.1 ∗ E(B − V) ≥ 0.087 mag for an assumed selective-to-total extinction of 3.1, and column densities of N(H) ≥ 1.4 × 10²⁰ cm⁻². The starlight reddening data that give the color excess values in Figure 11 (see Appendix B) indicate larger color excesses of E(B − V) > 0.2 mag through the BICEP2 field, or optical extinctions of A_V > 0.6 mag for a selective-to-total extinction ratio of 3.1.

Although the extinction of the BICEP2 region is negligible when compared to molecular clouds, the polarization data show that the dust that is present produces detectable amounts of optical polarization in the starlight. Both ${B}_{\mathrm{POL}}$ and the lower latitudes of Loop I extend into the BICEP2 region where they indicate that the local contributions to polarizations are likely to trace an ordered magnetic field with directions that can be predicted from the measurements of the very local ISMF ${B}_{\mathrm{POL}}$ and the southerly portion of Loop I.