THE INTERSTELLAR MAGNETIC FIELD CLOSE TO THE SUN. II.

The characteristics of the interstellar magnetic field (ISMF) in the warm, low-density, partially ionized interstellar gas near the Sun are difficult to study. A new diagnostic of the magnetic field in the Local Interstellar Cloud (LIC) surrounding the heliosphere is provided by the giant arc, or "Ribbon," of energetic neutral atoms (ENAs) discovered by the Interstellar Boundary Explorer (IBEX) spacecraft (McComas et al. 2009, 2011). ENAs are formed by charge exchange between interstellar neutral hydrogen atoms and the solar wind and other heliospheric ions. The ENA Ribbon is observed toward sight lines that are perpendicular to the ISMF direction as it drapes over the heliosphere, and it is superimposed on a distributed ENA flux that traces the global heliosphere (Appendix A provides additional information on the Ribbon and Ribbon models). In Frisch et al. (2010a, Paper I), we showed that the measurements of interstellar polarization toward nearby stars yield a best-fit ISMF direction that is close to the field direction obtained from the IBEX Ribbon. In this paper, we further study the connection between the magnetic field sampled by the IBEX Ribbon and the magnetic field in the local ISM.

Starlight polarized by magnetically aligned dust grains in the ISM shows that the magnetic field in our galactic neighborhood has two large-scale components, a uniform field parallel to the galactic plane that is directed toward ℓ ∼828¹² and extends beyond a kiloparsec, and a giant magnetic structure, Loop I, that is within 100 pc and dominates the northern sky and probably reaches to the solar location. The ISMF of Loop I is traced by optical polarizations (Mathewson & Ford 1970; Heiles 1976; Santos et al. 2011; Berdyugin et al. 2011), the polarized radio continuum (Berkhuijsen 1973; Wolleben 2007), and Faraday rotation measures (Taylor et al. 2009; Mao et al. 2010). It is a superbubble formed by stellar winds and supernovae in the Sco-Cen association during the past ∼15 Myr (e.g., de Geus 1992; Frisch 1995, 1996; Heiles 1998a, 2009). The ISMF is swept up during superbubble expansion, creating a magnetic bubble that persists through the late stages of the bubble evolution (Tilley et al. 2006). Optical polarization and reddening data show that the eastern parts of Loop I, ℓ =3°–60°, b >0°, are within 60–80 pc of the Sun (Santos et al. 2011; Frisch et al. 2011). If Loop I is a spherical feature, the ISMF near the Sun should be associated with the Loop I superbubble (e.g., Frisch 1990; Heiles 1998a, 1998b). The magnetic structure of Loop I provides a framework for understanding the magnetic field in the local ISM and the relation between the galactic magnetic field and the magnetic field that shapes the heliosphere.

In this paper, we use high-sensitivity observations of the polarization toward nearby stars as a tool for determining the direction of the ISMF near the Sun within ∼40 pc. This study builds on our earlier study (Paper I), which presents a new method for determining the ISMF direction, based on testing for the best match between polarization position angles and the ISMF, where we found that the best-fit local ISMF direction in the galactic hemisphere regions agrees, to within the uncertainties, with the ISMF direction defined by the center of the IBEX Ribbon arc. Our new study differs from the first study in that the method is broadened to include weighted fits (Section 2), which is possible because of the inclusion of new data (Section 3). The best-fit ISMF direction found from both unweighted fits (Section 4.1) and weighted fits (Section 4.2) is close to the direction of the ISMF shaping the heliosphere (Section 5.1). We also look closely at the PlanetPol data (Bailey et al. 2010, Section 5.3) and use the upper envelope of the polarization–distance curve (Section 5.3.1, Appendix C) to show that there is an ordered component in the local ISMF with a direction that varies weakly with distance and extends to within 8 pc of the Sun (Section 5.3.2). The ordered component provides information on magnetic turbulence. An anti-correlation of polarization with radiation fluxes suggests ineffective radiative torques (Section 5.3.3, Appendix D). The best-fit ISMF direction is compared with the field direction derived from the IBEX Ribbon and the relation between the LIC and G-clouds (Section 5.1). For our new ISMF direction and the new IBEX heliosphere nose direction, the symmetry of the cosmic microwave background (CMB) dipole moment with respect to the heliosphere nose direction is still apparent (Section 5.3.4). The similar directions of the ISMF over scales of several hundred parsecs suggest an interarm-type field (Section 5.4.1). The local ISMF direction also appears to affect anisotropies observed in GeV–TeV galactic cosmic rays (GCRs; Section 5.4.2). Results are summarized in Section 6.

Optical polarization is an important probe of the direction of the ISMF in interstellar clouds, over both large spatial scales (Mathewson & Ford 1970) and the very local ISM (Tinbergen 1982; Frisch 1990; Frisch et al. 2010a). The observed polarization from aligned grains depends on the total column of dust and the grain size distribution (Mathis 1986), the fraction of asymmetrical dust grains and alignment efficiency of the grains (Whittet et al. 2008), and the projection of the magnetic field onto the sky. The axis of lowest average grain opacity is parallel to the ISMF direction (Davis & Greenstein 1951; Martin 1971; Roberge 2004; Lazarian 2007).¹³ Polarization is a pseudovector entity (always in the range 0°–180°), and in denser regions radiative transfer effects can influence the observed polarization both due to turbulence in the probed medium (Jones et al. 1992; Ostriker et al. 2001) and due to the influence of foreground depolarizing screens (Andersson & Potter 2006; Andersson 2012). The ISM within 10 pc has low average ISM densities, N(H) ≲ 10¹⁸ cm⁻² and 〈n〉 ∼ 0.1 cm⁻³, suggesting that there is very little nearby dust. Therefore, depolarizing foreground screens and collisional disruption of grain alignment are less likely locally compared to distant dense cloud regions. This low-density ISM is partially ionized (Frisch et al. 2011) so that gas and the ISMF will be tightly coupled.

Two properties of polarized starlight could in principle be exploited to obtain the ISMF direction causing the polarization: the position angle of the polarizations, which are measured with respect to a great circle meridian and increase positively to the east, and the polarization strengths that reach a maximum for sight lines perpendicular to the ISMF for a uniform medium. The drawbacks with using polarization strengths to determine the ISMF direction are that polarization varies with the dust column density of the sight line, and polarizations are weaker near the magnetic pole where the statistical significance of detections will be lower. Polarization directions are insensitive to the dust column density, but sensitive to magnetic turbulence that could distort the field over either small or large scales.

Paper I introduces a new method for determining the ISMF direction based on finding the best fit to an ensemble of polarization position angles. The analysis makes the assumption that the polarization position angle is parallel to the direction of the ISMF (Roberge 2004). This assumption is justified for the diffuse clouds in Loop I, where the field directions determined from optical polarization data and synchrotron emission in high-latitude regions agree (Spoelstra 1972). The ensemble of data used in the analysis is chosen to meet a set of selection criteria. These data and the criteria are discussed in the following section (Section 3). All measurements meeting the criteria are used in the analysis, including multiple measurements of the same star by different observers.

The ISMF direction is derived by assuming that a single large-scale ISMF close to the Sun is aligning the grains, so that the polarization direction would then be parallel to a great-circle meridian of the "true" magnetic field direction. The best-fit ISMF is calculated to be the direction that corresponds to the minimum value of

$$\begin{equation} F_\mathrm{i} = F(B_\mathrm{i}) = {N^{-1}} \sum _{n=1}^{N} \left | \frac{\mathrm{sin}(\theta _n(B_i))}{G_{n}}\right | , \end{equation} \tag{ 1 }$$

where θ_n(B_i) is the polarization position angle PA_n for star n, calculated with respect to the ith possible ISMF direction B_i, and where the sum is over N stars. G_n is the weighting factor for each star n based on the measurement uncertainties of the polarization position angle for that star. A grid resolution of 1° in longitude and latitude is used for the spacing of B_i values. An alternate approach to find the best-fit field direction B_{i = best} that maximizes the cosecants, i.e., maximizes $\overline{| G_{n}/\sin (\theta _{n}(B_{i}))|}$, generated numerical glitches related to dividing by zero and is not used.

Paper I calculated the ISMF direction with the weighting factor G_n = 1. Statistical weights were ignored since the northern hemisphere data included a large number of recent high-sensitivity data collected at ppm accuracy, while the southern hemisphere data were dominated by data collected in the 1970s that are less sensitive (1σ > 60 ppm; Section 3). Weighting data points by the uncertainties yielded a magnetic field direction biased by the difference in uncertainties in the two hemispheres. The best-fit ISMF direction from Paper I is listed in Table 1. In this paper, new data (Section 3) are added and the unweighted fit is recalculated (Section 4.1).

New high-precision polarization data make it possible to evaluate the best-fit ISMF direction by utilizing all of the position angles in the sample, but weighting individual values according to their statistical significance. By combining data based on weighted values, the emphasis is implicitly placed on the ISMF field in the distant portions of the sampled ISM, where polarizations may be stronger relative to the measurement errors (depending on the patchiness of the ISM; Section 5.3). The probability distribution for position angles does not have a normal distribution for weak polarizations, P/dP <6. The weighting function is based on the results of Naghizadeh-Khouei & Clarke (1993) that give the probability distribution for the position angle of linear polarization. For true polarization p_o with a measurement uncertainty of σ and the true position angle in equatorial coordinates θ_o, the probability G_n(θ_obs; θ_o, P_o) of observing a position angle θ_obs (which will be 0° for the "true" value of a perfectly aligned PA) is

$$\begin{eqnarray} G_n(\theta _{\rm {obs}} ; \theta _{\rm {o}},P_{\rm {o}}) &=& \frac{1}{\sqrt{\pi }} \left\lbrace \frac{1}{\sqrt{\pi }} + \eta _{\rm {o}} \rm {exp} \big(\eta ^2_{\rm {o}}\big) [1 + \rm {erf}(\eta _{\rm {o}})]\right\rbrace\nonumber\\ &&\times \rm {exp}\left({-\frac{P^2_{\rm {o}}}{2}}\right), \end{eqnarray} \tag{ 2 }$$

where $\eta _\mathrm{o} = ({P_\mathrm{o}}/{\sqrt{2}}) \mathrm{cos} [2(\theta _\mathrm{obs}-\theta _\mathrm{o})]$ and P_o = (p_o/σ), and the function erf(z) is the Gaussian error function ${\rm erf} (Z) = ({2}/{\sqrt{\pi }}) \int _0^Z {\exp }({-t^2}) dt$. The goal is then to choose a procedure that maximizes the contributions of high-significance (e.g., high G_n) measurements and minimizes the contributions from data points with large values of sin θ_{n, i}. When B_{i = best} is calculated using weighted fits (Section 4.2), the function G_n in Equation (2) is adopted as the weighting factor for each star n in Equation (1).

The Local Bubble void appears as an absence of both interstellar gas and dust within ∼70 pc, particularly in the third and fourth galactic quadrants. Figure 1 shows the distribution of interstellar dust within 100 pc, as traced by color excess E(B − V). The interior of the Loop I superbubble appears as a void in the distribution of interstellar dust within 100 pc in the fourth galactic quadrant (ℓ >270°). Models of Loop I as a spherical object place the Sun in or close to the rim of the shell (Section 5.2). This combination of properties is the basis for selecting polarized stars for this analysis within 90° of the heliosphere nose and 40 pc of the Sun. The heliosphere nose is remarkably close to the direction of the galactic center. IBEX-LO measurements of the 23.2 ± 0.3 km s⁻¹ flow of interstellar He^o through the heliosphere provide the nose direction of ℓ =525 ± 024, b =1203 ± 051 (McComas et al. 2012). Most interstellar gas within 40 pc is also clumped within 20 pc of the Sun, as shown by interstellar H^o and D^o (Figure 2) and the fact that the average number of interstellar Fe⁺, Ca⁺, and Mg⁺ velocity components is independent of distance for stars within 30 pc and rises only slightly (∼20%) for stars that are 30–40 pc (Frisch et al. 2011). This spatial interval provides for a well-defined region for study, accepts most stars in the region of Tinbergen's original "patch" of nearby polarization (Tinbergen 1982; Paper I), includes the region where PlanetPol (Bailey et al. 2010) obtained very high sensitivity polarization data (Section 3), and includes nearby stars observed toward Loop I by Santos et al. (2011).

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These data show that the polarizations in the southern galactic hemisphere tend to be larger than polarizations in the northern galactic hemisphere. For the special case where the star sample is restricted to stars meeting the spatial and spectral criteria above, and to recent higher precision data, the polarizations of southern stars with P/dP >2.5 are 0.024% ± 0.017%, while for northern stars they are 0.003% ± 0.005%. Whether this difference, originally noted by Tinbergen (1982), is accurate will require additional high-sensitivity data. Note that P/dP gives the polarization strength divided by the 1σ uncertainty of the polarization.

New polarization measurements were also collected for this study using telescopes of the Laboratorio Nacional de Astropfisica (LNA) in Brazil and the Nordic Optical Telescope (NOT) on the island of La Palma in the Canary Islands. The LNA data were acquired with the CCD polarimeter (Magalhaes et al. 1996) on the 0.6 m telescope at Pico de Dios, during the months of 2008 June, 2010 August, 2010 September, and 2011 May. The NOT data were acquired using the TurPol polarimeter (Piirola 1973; Butters et al. 2009) on the 2.52 m telescope on the island of La Palma in the Canary Islands during 2010 June. Optical polarimetry is a differential measurement, and good observing conditions are not as critical as for high-accuracy photometry. ISM polarization data also sample a relatively constant polarization source, allowing repeated observations over different days or from different sites to maximize sensitivity and minimize systematic uncertainties. These new data are listed in Table 2. The columns in this table are HD number, galactic longitude and latitude, star distance, the polarization in units of 10⁻⁵, and the polarization position in the equatorial coordinate system. The last column gives the observatory where the data were acquired.

The CCD imaging polarimeter at Pico dos Dias provided polarizations in the B band. The instrument acquires CCD images of the orthogonal polarizations, in sets of eight waveplate positions, with several images at each plate position. In the case of constant polarizations such as interstellar polarizations, individual observations can be combined to reduce uncertainties. Stars brighter than ∼7 mag were observed through a neutral density filter.

The TurPol data were obtained using the UBV mode of the polarimeter with high voltage for the R and I photomultipliers switched off. The effective wavelengths of the UBV bands are 3600, 4400, and 5300 Å, respectively. With this mode, typical count rates of 10⁶ counts s⁻¹ were achieved, giving a precision of 0.01% for a 3σ detection. Observations of two zero-polarization standards were acquired each night at the same precision in order to determine the instrumental polarization. The position angle calibration was obtained with observations of two high-polarization standard stars. For interstellar polarizations, position angles do not depend significantly on the wavelength, allowing the use of weighted averages from the UBV bands to achieve the highest possible precision; these "broadband" position angle measurements are listed in Table 2.

The early Tinbergen (1982) survey, made during 1973–1974 from La Silla (Chile) and Hartebeespoortdam (South Africa) in the southern hemisphere and Leiden (The Netherlands) in the northern hemisphere, remains the most extensive all-sky survey of weak polarizations, with 1σ sensitivity on the Q and U Stokes parameters of 0.006%–0.009%, depending on the instrument and data set. These weak polarizations are biased toward larger polarization strengths, since P² = Q² + U² is always positive. Clarke et al. (1993) evaluated the statistics of stars observed from each observing station in the Tinbergen data set and concluded that residual instrumental polarizations may remain in the K-star data collected from Hartebeespoortdam. We have examined the data from Hartebeespoortdam for non-active K-stars that also have P/dP >2.5. The seven stars that match the data criteria are located at angles of 86° ± 32° from the ISMF direction defined by the center of the IBEX Ribbon arc. If the direction of the ISMF at the heliosphere is the same as in the local ISMF direction, then for a uniform ISM the maximum polarizations are expected at angles of 90° from the ISMF pole. We therefore assume that any contribution of instrumental polarization to the Hartebeespoortdam data is insignificant, while acknowledging that high-sensitivity observations and temporal monitoring of the polarizations of these stars are needed.

This study also includes the Bailey et al. (2010) polarizations of nearby stars obtained with the PlanetPol instrument at the William Herschel Telescope. These linear polarization data were collected over a broad red band (maximum sensitivities at 7000–8000 Å) and achieved typical accuracies of parts per million. PlanetPol data were also included in the Paper I analysis, but without screening for stellar activity. Twenty-six stars in the PlanetPol catalog that passed the selection criteria above were incorporated into our analysis of the local ISMF direction and are listed in Appendix B. Bailey et al. (2010) measured 18 northern hemisphere stars that were also observed by Tinbergen, and they detected weak polarizations toward roughly half of the stars that were unpolarized at the sensitivities of the Tinbergen data.¹⁴ PlanetPol data showed that polarizations in the R.A. > 17^H region increased with distance, and they measured a weak interstellar polarization of 17.2 ± 1.0 ppm toward α Lyr (Vega, HD 172167), 8 pc away. Bailey et al. argue that the face-on debris disk around Vega is unlikely to contribute to the observed polarization signal since the instrument aperture is 5'' and the radius of the central hole in the disk is 11'' ± 2''. We show that the α Lyr polarization data have follow polarization trends of other nearby stars (Section 5.3), so those data are retained in this sample.

Santos et al. (2011) surveyed interstellar polarizations toward Loop I for stars out to distances of 500 pc, using the imaging polarimeter at LNA. Typical mean accuracies 1σ = 0.05% were achieved in the V band. Forty stars in the Santos et al. catalog passed the regional and activity selection criteria above and are listed in Appendix B.

Polarizations of stars used in the determination of the local ISMF direction (within 40 pc) are plotted against the distance of the star in Figure 3 and on an Aitoff projection of the sky in Figure 4. For comparison, the polarizations of more distant stars (40–110 pc) within 90° of the heliosphere nose are also shown (from the catalogs of Santos et al. 2011; Heiles 2000; Leroy 1993, 1999). A general increase in polarization strength with distance is seen (this is discussed in more detail in Appendix C). The polarizations shown in Figure 3 were measured in different bandpasses. For the PlanetPol bandpass covering red wavelengths (Bailey et al. 2010), the Serkowski curve of polarization versus λ/λ_max predicts polarizations that are up to 30% below the peak polarizations at λ_max (λ is the wavelength of observation, and λ_max, which has a median value ∼5500 Å, is the wavelength of maximum polarization; Serkowski et al. 1975). The PlanetPol stars, located in the northern galactic hemisphere, include the largest set of detections of very weak polarizations, while the early Tinbergen (1982) data set provides the most detections in the southern hemisphere. For this reason, polarization strengths are not used in Paper I to trace the ISMF direction. With the addition of new high-sensitivity data in the southern hemisphere, all polarization position angle data can be included in the study using weighted fits (Section 4.2).

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Cool stars are included as target stars to provide adequate spatial coverage, but not all cool stars are suitable for the high-sensitivity interstellar polarizations of ∼0.01% needed for this study. Magnetic activity is observed in cool stars, especially late K and M stars. With the sensitivity levels for most observations used in this study there is no a priori reason to omit stars with active chromospheres from the sample; however, some cool stars are known to show polarizations in chromospheric lines (Clarke & Fullerton 1996). Stars of spectral types G and cooler, and with known active chromospheres, are usually omitted from the data sample used to evaluate the local ISMF direction. Screening for active stars was performed using the lists in Gray et al. (2006). For the same reason, variable stars with variations δV ⩾0.06 mag are omitted to avoid other intrinsic magnetic phenomena by requiring the coarse variability flag, word H6, in the Hipparcos catalog (Perryman 1997)¹⁵ to be H6 ⩽1. The analysis in Paper I did not screen for stars with known chromospheric activity.

4.1. ISMF Direction from Unweighted Fit

The first evaluation of the best-fit ISMF direction uses the same basic method as in Paper I, but applied to the larger set of data in this paper (Section 3). Equation (1) was evaluated for F_i with G_n = 1, using data points where P/dP >2.5. All observations meeting the selection criteria (Section 3) are used in the fit, including measurements of the same star by different observers. The application of Equation (1) to the polarization data set (Section 3) yields an ISMF direction toward ℓ,b = 37° ± 15°, 22° ± 15° (see Table 1 for ecliptic coordinates). There is no significant change in the direction obtained from the unweighted fit when compared to the results of Paper I. The values of F_i are displayed in Figure 5, in both ecliptic and galactic coordinates, and for each point in the possible ISMF grid using the 1° grid spacing discussed in Section 2.

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Because of the underlying data sample, the unweighted fit emphasizes southern hemisphere data acquired in the 1970s. For the best-fit ISMF direction, B_{i = best}, 48 stars contributed to give F_{i = best} =0.51 for the function being minimized. Of these 48 stars, 20% have new NOT and LNA data and contributed 25% of F_{i = best}, 35% have pre-1980 data from Tinbergen (1982) or Piirola (1977) and contributed 29% of F_{i = best}, 31% have PlanetPol data and contributed 32% of F_{i = best}, and 8% were observed by Santos et al. (2011) and contributed 12% of F_{i = best}. Note that no single set of observations appears to dominate this result.

4.2. ISMF Direction from Weighted Fit

The new high-precision polarization data in the southern hemisphere, as well as additional high-precision data in the northern hemisphere (Section 3), make it possible to evaluate the best-fit ISMF direction by utilizing all of the position angles in the sample by weighting each value according to the position angle probability distribution in Equation (2).

If the polarizing medium were to be homogeneous over the nearest 40 pc in the galactic hemisphere (which is not the case), combining polarization data using weighted values implicitly weights the resulting field direction toward more distant points where the signal-to-noise ratio (S/N) is larger. If in contrast there is no statistically significant field in the same spatial region, the resulting field direction based on weighted fits is close to the center of the spatial interval for randomly distributed polarization directions.

For the weighted fits, the polarization strengths in the combined set of all data were capped at 50 × 10⁻⁵ in order to minimize the possible biases due to unrecognized intrinsic stellar polarization. Fewer than 5% of the significant (P/dP >2.5) data points in the fit were affected by this cap. With the use of weighted fits, the best-fit direction is biased toward data sets that have low quoted uncertainties. To avoid overreliance on the PlanetPol data, which are quoted to a typical accuracy of ppm and are spatially clustered in the northern hemisphere, the P/dP value input to G_n was capped at 3.5, and a lower limit of 10⁻⁵ was set on G_n. With these constraints, the best-fit ISMF direction is oriented toward λ,β =263⁺¹⁵₋₂₀, 47 ± 15 or ℓ,b = 47° ± 20°, 25° ± 20° (Table 1). The values of F_i (Equation (1)) are plotted in Figure 6, using G_n given by Equation (2). It is seen that the minimum value of F_i is more clearly defined for G_n = 1 than for G_n given in Equation (2).

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One hundred and seventy-seven stars have contributed to this best-fit ISMF direction, B_{i = best}. For this fit the mean value of Equation (1) gives F_{i = best} = 485, using G_n from Equation (2). Of these 177 stars, 26% have new NOT and LNA data and contributed 11% of F_{i = best}, 39% have pre-1980 data from Tinbergen (1982) or Piirola (1977) and contributed 24% of F_{i = best}, 12% have PlanetPol data and contributed 60% of F_{i = best}, and 20% were observed by Santos et al. (2011) and contributed 0.3% of F_{i = best}. The PlanetPol contribution to the function being minimized, F_i, is dominated by four stars that have position angles nearly orthogonal (90⁺²⁵₋₁₅ deg) to the meridians of B_{i = best} and that make 86% of the PlanetPol contribution. Those four stars are HD 150680 at 10 pc and three high-latitude stars at 24–31 pc (HD 113226, HD 116656, and HD 120315).

This method of using weighted fits produces an ISMF direction that is biased by the distribution of measurement errors for diverse instruments. We have tested the effect of the weighting factor by raising the lower limit of G_n to 10⁻⁴ for P/dP ⩽3.5. This test increases the homogeneity of low-significance data points. Although the resulting ISMF direction is within 25° of B_{i = best}, it is closer to the center of the spatial interval indicating increased reliance on statistically insignificant measurements. The cap P/dP ⩽3.5 in G_n (Equation (2)) has the effect of de-emphasizing the PlanetPol data where the ppm-level uncertainties otherwise dominate the result. If instead we take G > 10⁻⁵ and a P/dP cap of 4–6, the magnetic pole is then directed toward ℓ =337° ± 10° and b =28° ± 7° and the F minimum (Equation (1)) becomes very poorly defined. We are quoting the best-fit ISMF direction for the weighted fit (Table 1) for values P/dP ⩽3.5 and G_n ⩾10⁻⁵, since these limits appear to present the best overall representation of the data given the differences in measurement sensitivities. With future high-sensitivity data, it should be possible to treat the analysis utilizing a broader range of the weighting factor.

5.1. Comparing the ISMF Directions Traced by the IBEX Ribbon and Polarizations

The very local ISMF direction provided by the center of the IBEX Ribbon arc is separated by 32⁺²⁷₋₃₀ deg from the direction of the best-fit ISMF (weighted fit in Table 1). MHD heliosphere models that successfully predict the location of the IBEX Ribbon yield offsets between the center of the Ribbon arc and the ISMF that shapes the heliosphere of between 0° and 15° (Heerikhuisen & Pogorelov 2011), so the direction of the very local ISMF found here is marginally consistent with the direction of the ISMF that shapes the heliosphere. Polarization of stars within 40 pc and 90° of the heliosphere nose has contributed to this result. Up to 15 interstellar clouds have been identified toward stars in this region of space (Lallement et al. 1986; Frisch et al. 2002, 2011; Frisch 2003; Redfield & Linsky 2008). The magnetically aligned dust grains causing the polarizations presumably are located in these clouds. Although local color excess values are too small to be measured, the variable gas-phase abundances of the refractory elements that make up the grains show that several types of interstellar grains must be present in these clouds (Frisch & Slavin 2012). The clouds are distinguished by the gas kinematics using the assumption of solid-body motion, and in some cases by temperature. Since most of the neutral ISM that is within 40 pc is also within 20 pc (Section 3, with the exception of the special region displyed in Figures 7, 8, and 9), the best-fit ISMF direction then may represent primarily the ISMF direction within ∼20 pc of the Sun. This would help explain the remarkably similar directions of the ISMF traced by the IBEX Ribbon and the polarization data.

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If the IBEX ENA Ribbon and interstellar polarizations trace the same ISMF direction, then polarization strengths should increase with ENA fluxes because interstellar polarizations and the IBEX Ribbon both reach maximum strengths in sight lines that are perpendicular to the magnetic field, e.g., where B · R = 0 for magnetic field B and radial sight line R. Figure 10 shows a plot of the mean value of 1.1 keV ENA fluxes that are in a 12° diameter region centered on stars that are within 40 pc, 90° of the heliosphere nose, and have P/dP >2.5. ENA fluxes with S/N >3.5 are included. The data points are color-coded according to the data source in the left panel. Data in the left panel of Figure 10, tend to be divided into four groups with different relations between the polarization and ENA fluxes. Group A consists of the highest-quality data, such as data collected for this study and the PlanetPol data (Section 3), and shows a general increase of polarization with ENA fluxes. The PlanetPol stars in group A are located in the R.A. = 16^H–20^H interval. Region D primarily represents 1970s polarization data, where uncertainties are substantially larger. The trend in region B is ambiguous. The four groups of data in the left panel of Figure 10, are plotted in galactic coordinates in the right panel of Figure 10, using a color-coding that shows the data group. The increase of ENA fluxes with polarization for stars in group A supports the hypothesis that the ISMF sampled by the polarization data and Ribbon ENA fluxes are tracing the same, or similar, ISMF directions. Results for the remaining stars are ambiguous.

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The difference between the ISMF directions from the polarization and ENA Ribbon data may reveal structural components of the local ISM. The polarization data set we use to determine the field direction (Section 3) may not sample the interstellar cloud surrounding the Sun, the LIC. The Sun is within 20,000 AU of the edge of the LIC (Frisch et al. 2011), and the LIC includes a minimal amount of ISM within 90° of the heliosphere nose (e.g., Redfield & Linsky 2008). It is possible that the ISMF direction traced by the center of the IBEX Ribbon arc represents the ISMF in the LIC, while the ISMF traced by the polarization data represents the ISMF traced by the next cloud in the upwind direction, the G-cloud that is observed toward the nearest star α Cen. The LIC is ∼22% ionized (Slavin & Frisch 2008; Appendix A), and the G-cloud is likely to be partially ionized, so that the ISMF will couple tightly to the gas in these clouds. The possible location of the ISMF traced by polarization data is discussed further below where a small rotation with distance of the local ISMF is found (Section 5.3.2). This rotation suggests that some of the small difference between the ISMF directions found from the IBEX Ribbon and polarization data may result from the volume-averaged ISMF direction implicit in our method for fitting the polarization data.

5.2. Local ISMF and Loop I

5.3. Ordered ISMF Near Sun

A detailed study of the behavior of interstellar polarizations and ISMF behavior with distance is possible with the sensitive PlanetPol data for stars located in the interval R.A. = 16^H–20^H, which contains the R.A. >17^H region where Bailey et al. (2010) found an increase of polarization with distance. This region overlaps the low-latitude part of the North Polar Spur, where aligned optical polarization vectors define the ISMF for distances 60–120 pc (Mathewson & Ford 1970; Santos et al. 2011). The behavior of the ISMF for distances <60 pc in the North Polar Spur direction is provided by PlanetPol data.

5.3.1. Polarization versus Distance and Column Density in 16^H–20^H Region

Bailey et al. (2010) found that the increase of polarization with distance was greater for stars with R.A. >17^H than for stars in other spatial intervals. The increase of polarization with star distance for PlanetPol stars in the R.A. = 16^H–20^H region and with P/dP >3.0 is shown in the right panel of Figure 7. For this set of uniform-quality data a maximum value for the polarization is found for each distance interval within ∼60 pc, and there are no observed points that lie above the upper envelope marked by the filled points. Polarizations of stars beyond that follow this trend. Stars that define this maximum are often referred to as the polarization "upper envelope" (e.g., Andersson 2012; also see Appendix C), and we use that term here. In general, polarization data tend to have an upper envelope when plotted against either distance or color excess due to either depolarization or patchy ISM. A rough estimate of the dependence of polarization on distance can be found by first binning stars into 10 pc intervals and then selecting the stars with the maximum polarization in each interval. Omitting bins with no stars, seven stars (filled circles in Figure 7) can be used to define the upper limit of polarization as a function of distance. A linear fit through the envelope stars gives the approximate distance dependence of the maximum polarization in the R.A. = 16^H–20^H region of

$$\begin{equation} \mathrm{log} P \sim 1.200 + 0.013 *D, \end{equation} \tag{ 3 }$$

where P is polarization in ppm and D is the distance in parsecs. The closest envelope star is α Lyr at 8 pc (Table 3 lists the envelope stars). The locations of the R.A. = 16^H–20^H stars are plotted in galactic coordinates in the left panel of Figure 7. Two unpolarized PlanetPol stars in this region are not plotted, HD 163588 and HD 188119, both of which are located at larger longitudes than the other stars. Stars that form the upper envelope of the polarization–distance relation are loosely confined between galactic longitudes of 30° and 80° and latitudes of −5° to 30°.

Table 3. PlanetPol^a Stars in Polarization Envelope

HD	Name	Coordinates	Distance	Polarization	PARA
		(deg)	(pc)	(ppm)	(deg)
172167	α Lyr	67.4, 19.2	7.8	17.2 ± 1.1	34.5 ± 1.4
159561	α Oph	35.9, 22.6	14.3	23.4 ± 2.0	30.8 ± 2.4
161868	γ Oph	28.0, 15.4	29.1	40.8 ± 3.1	28.5 ± 2.1
164058	γ Dra	79.1, 29.2	45.2	73.3 ± 1.2	145.0 ± 0.5
186882	...	78.7, 10.2	52.4	108.0 ± 2.0	22.8 ± 0.5
168775	...	63.5, 21.5	70.4	106.5 ± 2.7	6.1 ± 0.7
189319	...	58.0, −5.2	84.0	199.5 ± 1.4	56.1 ± 0.2

Note. ^aBailey et al. (2010).

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The upper envelope of the polarization–distance relation (Figure 7) can be used to estimate the gas density gradient along the ISM holding the ISMF, since dust and gas have similar spatial distributions in diffuse clouds. Few of the PlanetPol stars have measured H^o or D^o column densities (e.g., Wood et al. 2005), so column densities are estimated by converting polarization to color excess and then converting color excess to N(H), using standard relations for diffuse clouds. The polarization for dust grains aligned by an ordered ISMF, with no random component, provides an upper envelope of the P versus E(B − V) relation of P(%) = 9 E(B − V) (Fosalba et al. 2002). Interstellar gas and dust have similar spatial distributions in the low-opacity ISM. Copernicus observations of the saturated H^o Lyα absorption line and molecular hydrogen lines showed that N(H)/E(B − V) = N(H^o+ H₂)/E(B − V) =5.8 × 10²¹ cm⁻² mag⁻¹ (Bohlin et al. 1978).¹⁷ The Copernicus value underestimates hydrogen column densities for partially ionized gas since independent measurements of ionized gas are not available for most sight lines. The relation between polarization and column density is estimated by combining the distance–polarization fit with the empirical P versus E(B − V) and E(B − V) versus N(H) relations, giving

$$\begin{equation} \mathrm{log} N(\mathrm{H})=18.01+0.013*D \end{equation} \tag{ 4 }$$

for stars tracing the upper envelope of the P–E(B − V) relation and P–distance relation. For other stars, foreground depolarization can lead to lower values for N(H^o). This gas–distance relation can be checked against three nearby stars in the R.A. = 16^H–20^H region with N(H^o) values determined by Wood et al. (2005), HD 155886 (36 Oph), HD 165341 (70 Oph), and HD 165185. The ratio of the predicted N(H) (Equation (4)) to the observed N(H^o) for these three stars is 1.35 ± 0.35, indicating that depolarization and/or inhomogeneous ISM is present nearby.

5.3.2. Polarization versus Position Angle in 16^H–20^H Region

Optical polarization data that trace the H^o filamentary structure of Loop I beyond ∼80 pc reveal an ordered ISMF that follows the axis of an H i filament of Loop I (Heiles 1998a). Optical polarization vectors (Figure 4) and the location of the R.A. = 16^H–20^H region toward the North Polar Spur suggest that the very local ISMF direction may also be ordered. Figure 8 displays the polarization position angles, PA_RA, for PlanetPol stars with P/dP >3.0 in this interval, as a function of distance. With the exception of the outlier star HD 164058, which has PA_RA = 145° ± 05 and a distance of 45 pc, the envelope stars within 55 pc display a smooth rotation of polarization position angle with distance. HD 164058 is a K5III star and belongs to a spectral class where intrinsic polarization occurs because of chromospheric magnetic activity and was omitted from the fit in Equation (5) as an obvious outlier (see below). A linear fit to position angles versus distance gives

$$\begin{equation} {{\rm PA}}_\mathrm{RA} (D) = 35.97 (\pm 1.4) - 0.25 (\pm 0.03) \cdot D \end{equation} \tag{ 5 }$$

and a χ² of 0.559, where PA_RA is in degrees and the distance D is in parsecs. The small value of χ² per degree of freedom (2) suggests that the uncertainties on PA_RA quoted by Bailey et al. (2010) may be generous.¹⁸ The probability that the computed χ² value would have a value larger than 0.559 is 0.76, indicating that parameters of the fit in Equation (5) are believable. After excluding HD 164058, the relation between the polarization direction and star distances of the four envelope stars within 55 pc appears to be linear. The large difference of 7.8σ_pp between the position angle of the outlier star and the best-fit line (Equation (5)), where σ_pp is the mean difference between the best-fit line and the position angles of PlanetPol stars within 55 pc except for the outlier, justifies omitting HD 164058 from the calculation of Equation (5). The envelope stars are partly self-selected by the fact that they represent sight lines where intervening depolarization is minimized, so the linear fit to the polarization position angles suggests the existence of a nearby ordered ISMF that rotates ∼025 pc⁻¹. This rotation is confined to the small region of space (filled dots in Figure 7, left) where Bailey et al. (2010) found the systematic increase in polarization strengths with distance (Figure 7, right). The envelope stars appear to sample the uniform part of an extended medium that contains a magnetic field and reaches to within 8 pc of the Sun.

The standard deviation of position angles around the ordered component is a measure of the magnetic turbulence in this region. For all stars in the R.A. = 16^H–20^H region and within 55 pc, excluding the outlier star, the standard deviation of polarization position angles about the best-fit line is 23°, which we interpret as magnetic turbulence.

The smooth variation of the ISMF direction over distance suggests that the four nearest envelope stars are embedded in the polarizing medium, which extends between α Lyr (Vega, 8 pc) and δ Cyg (52 pc). The sight lines to all of the envelope stars sample either the S1 shell, the S2 shell, or both shells, according to the Wolleben (2007) model and the shell configurations plotted in Frisch (2010). The angular spread on the sky of the envelope stars is 50°, which suggests that the ISMF in the nominal S1 and S2 shells consists of a homogeneous "matrix" component of smooth material that is sampled by the envelope stars and patchy material and/or a turbulent ISMF that produces depolarization of, and turbulence in, the position angles of non-envelope stars.

If the polarizations of the envelope stars are tracing matrix ISM in this region, this material should be detectable as interstellar absorption features. Absorption lines have been measured toward the four envelope stars in the fit. All four stars show absorption at or close to the velocity of the Apex cloud defined by Frisch (2003),¹⁹ so it is tempting to assume that the "Apex cloud" represents the smooth ISM filling the local region of the S1 and S2 shells. Interstellar absorption lines have also been measured toward a fifth polarized star, HD 187642, in region R.A. = 16^H–20^H, where a component at the Apex cloud velocity is also found. Toward the envelope star HD 159561, the Apex cloud component is characterized by weak Ca⁺ absorption and a typical ratio Ti⁺/Ca⁺= 0.41, suggesting that it contains some neutral gas since Ti⁺ and H^o have the same ionization potential (Welty & Crowther 2010). A more recent and complete cloud identification scheme was developed by Redfield & Linsky (2008), where three of the Apex cloud components toward envelope stars are instead assigned to the MIC cloud, while the fourth component is left as unassigned. Three of the four stars in Redfield & Linsky (2004b) that are in the R.A. = 16^H–20^H region have components at the Apex velocity; however, the cloud temperature ranges from ∼1700–12,500 K for these components. A second possible carrier of the ordered field is the "G" cloud since it has a wide angular extent in the upwind direction, is within 1.3 pc of the Sun, and is observed toward the envelope stars. The identification of the cloud carrying the ordered component of the ISMF requires additional study.

5.3.3. Polarization versus Interstellar Radiation Field in 16^H–20^H Region

Radiative torques are known to play a role in the alignment of dust grains in dense clouds where the radiation field has a preferred direction (e.g., Andersson & Potter 2006; Draine & Weingartner 1997; Andersson et al. 2011; Lazarian & Hoang 2008), but this does not appear to be the case locally. The interstellar radiation field extrapolated to the location of each star in the R.A. = 16^H–20^H region appears to anticorrelate with polarization strengths. We believe that this correlation is a chance coincidence of the relative locations of the brightest radiation sources and polarized stars. Figure 9 shows polarizations for stars inside (filled symbols) and outside (open symbols) of the R.A. = 16^H–20^H region, plotted against the total far-UV 975 Å flux that has been extrapolated to the position of each polarized star, while ignoring any possible opacity effects. The 975 Å radiation flux is given by the 25 brightest stars at this wavelength (Opal & Weller 1984), which are primarily located in the third and fourth galactic quadrants because of the geometry and low opacity of the Local Bubble (see, e.g., the interstellar radiation field at the Sun from the S2 UV survey; Gondhalekar et al. 1980). These polarization data show a trend for linear polarization to increase as radiation flux decreases. The rough anticorrelation between radiation fluxes and polarizations is shown by the fit log P =4.61–0.054*F₃ (dashed line in Figure 9), where P is in units of 10⁻⁶ and F₃ is the radiation flux at 975 Å in units of 10³ photons cm⁻² s⁻¹ Å⁻¹. This apparent anticorrelation appears to be the result of the relative locations of the brightest hot UV-bright stars and the most distant polarized stars that define the low-flux region of the trend (see Appendix D for more details).

5.3.4. CMB Dipole Anisotropy and the Local ISMF

Large-scale global deviations from a uniform blackbody spectrum of the CMB radiation define a dipole anisotropy that is oriented toward ℓ =26385 ± 01 and b =4825 ± 004 (Bennett et al. 2003). The great circle on the sky that is midway between the two poles of the CMB dipole displays a striking symmetry around the direction of the heliosphere nose direction defined by the flow of interstellar He^o through the heliosphere (Frisch 2007). The best direction of the heliosphere nose is defined by the new IBEX consensus direction for the interstellar He^o flow, which includes correction for propagation and ionization effects (McComas et al. 2012; see Appendix A). This new consensus IBEX direction for the heliosphere nose more closely aligns the nose direction with the great circle that is midway between the hot and cold poles of the CMB dipole moment. The angle between the heliosphere nose and dipole anisotropy direction is 915 ± 06. The probability that the great circle that is evenly spaced between the poles of the CMB dipole anisotropy, which is defined to within ∼ ± 010, would pass through the ∼3° × 3° area on the sky that includes the heliosphere nose direction is less than 1/200. Figure 11 shows the great circle in the sky that is equidistant from the antipodes of the CMB dipole moment (gray line), as well as the hot (red) and cold (blue) dipole directions.

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The 90° great circle midway between the dipole directions also passes through the best-fit ISMF direction, when uncertainties are included (Table 1). The ISMF direction from the weighted fit is plotted as a purple dot in Figure 11, together with the uncertainties on this direction (purple polygon) and the 90° circle. The probability that the great circle dividing the antipodes of the CMB dipole moment would also pass through the ISMF pole, which is defined by an area of ∼300 deg², including uncertainties, is less than one in 10⁴. A deeper knowledge of the configuration and properties of the global heliosphere and local ISMF will elucidate whether additional CMB foregrounds might be present.

Although a possible relation between the CMB dipole and heliosphere may seem far-fetched, a number of studies have shown that the symmetries traced by the low-ℓ CMB moments are not consistent with the predictions of Gaussianity of the universe based on standard cosmological models, and in particular the quadrupole and octopole moments show evidence of the ecliptic geometry (e.g., Schwarz et al. 2004; Starkman et al. 2009, and citations to these articles). Since the ISM flows through the heliosphere from a direction 5° above the ecliptic plane, these low-ℓ symmetries are equivalent to symmetries around the heliosphere nose (e.g., see Figures 6 and 7 in Frisch 2007). Unrecognized CMB foregrounds related to the heliosphere may be present, with the most likely candidate being emission from interstellar dust inside the heliosphere since the dust traces both the gas flow and ISMF direction (Slavin et al. 2010, 2012; Frisch & Slavin 2012).

5.4. Speculative Implications

We have determined the direction of the ISMF within 40 pc of the Sun and 90° of the heliosphere nose (∼15° from the galactic center) using starlight polarized by magnetically aligned interstellar dust grains. The analysis is based on the assumption that the polarization E-vector is parallel to the direction of the ISMF and builds on the analysis in Paper I (Frisch et al. 2010a). The new technique for finding the ISMF direction minimizes the mean of an ensemble of sines of polarization position angles (Section 2). The use of an expanded data set, including new polarization data that have been acquired at several observatories for this study (Section 3), permits the use of weighted fits to the ISMF (Section 4) as opposed to the unweighted fit used in Paper I. The best-fit ISMF from the weighted fit is toward ℓ, b =47° ± 20°, 25° ± 20°. The direction obtained from the unweighted fit is consistent with the results of the weighted fit (Table 1).

The best-fit ISMF directions obtained from the weighted fit and from the center of the IBEX Ribbon arc (Table 1) are separated by 32⁺²⁷₋₃₀ deg (Section 5.1). Although heliosphere models indicate that there could be a small offset between the direction of the ISMF shaping the heliosphere and the Ribbon arc center (0°–15°), the agreement between these two field directions is remarkable considering that the polarization-based measurement is determined from light of stars up to 40 pc away. The similarity of these directions encourages the conclusion that the nearby ISMF is coherent over decades of parsecs, while the difference indicates that the local ISMF either has a curvature or is turbulent.

Interstellar optical polarizations reach maximum strengths in directions parallel to the ISMF, and the IBEX Ribbon extends in directions perpendicular to the ISMF draping over the heliosphere. Hence, if the directions of the best-fit ISMF and magnetic field traced by the IBEX Ribbon are related, the polarization strengths and ENA fluxes will be proportional. In one region of the sky that touches the Ribbon, where the ISMF is observed within 8 pc of the Sun, ENA fluxes and polarization strengths are found to increase together (Section 5.1). This effect is seen only in the most sensitive polarization data.

In one region of the sky in the right-ascension interval R.A. = 16^H–20^H, Bailey et al. (2010) used their high-sensitivity PlanetPol data to conclude that polarization systematically increases with distance (Section 5.3.1). Using stars that form the upper envelope of the polarization versus distance relation in that region, we find that log P = 1.200 + 0.013*D. For standard relations between polarization and color excess, and color excess versus N(H), the distance-dependent increase in column density in this spatial interval becomes log N(H) = 18.01 + 0.013 * D; the relation overpredicts the actual N(H^o) measured for several stars by ∼35%.

This same region, which overlaps a low-latitude portion of Loop I, appears to contain an ordered ISMF that extends to within 8 pc of the Sun (Section 5.3.2). Stars forming the upper envelope of the polarization–distance relation define a unique group where foreground depolarization is minimized. For the nearby envelope stars, the polarization angle depends on the star distance with the relation PA_RA =35.97(± 1.4) − 0.25(± 0.03) · D (Section 5.3). The ISMF rotates by ∼025 pc⁻¹, yielding a 10° ISMF rotation over a 40 pc thick magnetic layer. The nearest polarized star showing the ordered ISMF is HD 172167 (α Lyr, 8 pc), where the polarization direction is consistent with the direction of the best-fit ISMF field. The dispersion of position angles about this nearby ordered ISMF component suggests that the turbulent ISMF component is ∼ ± 23°. These results are conditioned on the exclusion of a 7.8σ outlier star from the analysis and on the small number of stars (4) used for defining the position angle rotation. Confirmation of this result would require observations at ppm accuracy toward very faint stars, V >6 mag, in the spatial interval ℓ ∼25°–70°, b ∼0°–35°.

The best-fit magnetic field direction, the flow of local ISM past the Sun, and variable abundances of refractory elements in the local ISM all suggest that the local ISM is associated with an expanding fragment of the S1 shell of the Loop I superbubble (Section 5.2). The bulk LSR flow of the local ISM past the Sun has an upwind direction within 15° of the center of the S1 shell. The best-fit ISMF makes an angle of ≈76° with the flow direction, suggesting that the field is parallel to the rim and perpendicular to the flow velocity. Such a configuration would be expected for an ISMF swept up and compressed in an expanding superbubble shell. Variable abundances of refractory elements in the local ISM indicate recent shock destruction of some of the local dust grains. A consistent interpretation of the kinematics of the local ISM and the direction of the best-fit ISMF would be that the ordered component represents the ISMF that was swept up in the expanding S1 superbubble shell. The flow of ISM past the Sun is decelerating, as shown by the deviations of velocity components from a rigid-body flow (Frisch et al. 2011). Cloud collisions in the decelerating flow may generate the observed magnetic turbulence of ±23°, with the ordered component representing the matrix ISM between the clouds.

Polarization strengths for the envelope stars in region R.A. = 16^H–20^H anticorrelate with the interstellar radiation field at 975 Å (Section 5.3.3). This anticorrelation is probably due to the fact that those stars are in the first galactic quadrant and, by chance, the most distant of those stars are also the most distant from the bright stellar far-ultraviolet and extreme-ultraviolet radiation sources that are mainly located in the third galactic quadrant.

The ISMF direction from pulsars in the third galactic quadrant is within 22° of the ISMF direction from the IBEX Ribbon. A common field strength of ∼3 μG is found from the pulsar data, a range of heliosphere diagnostics including plasma pressure and the deflection of the heliotail, and models of the ionization of the ISM surrounding the heliosphere. This suggests that the ISMF near the Sun is coherent over large spatial scales, such as expected for interarm regions. One source of uncertainty is the polarity of the field, since the polarity derived from pulsar data is opposite in direction from the polarity that is assumed by several of the MHD heliosphere models.

The new ISMF direction, together with the new consensus direction for the ISM flow through the heliosphere derived from IBEX observations of interstellar He^o, strengthens the spatial coincidence between the geometry of the CMB dipole moment, the heliosphere nose, and the local ISMF (Section 5.3.4). The great circle that divides the two poles of the CMB dipole moment passes within 15 ± 06 of the heliosphere nose defined by the IBEX measurements of the flow of interstellar He^o in the heliosphere and passes through the best-fit ISMF determined by weighted fits to polarization position angles to within the uncertainties.

The axis of the best-fit ISMF direction from polarization data extends through the direction of the "tail-in" excess of GeV–TeV cosmic rays that has been attributed to the heliotail. The direction of the tail-in excess coincides poorly with the flow of interstellar He^o through the heliosphere.

High-sensitivity interstellar polarization data provide an opportunity to explore the ISMF and magnetic turbulence in the very diffuse ISM close to the Sun and our very local galactic environment. The implications of understanding this field may affect our understanding of the most distant reaches of the universe. The domain of the heliosphere and the local ISM are filters through which all observations about our more distant universe must pass.

This work was supported by the IBEX mission as part of NASA's Explorer Program, and by NASA grants NNX09AH50G and NNX08AJ33G to the University of Chicago. We are grateful for observations made with the Nordic Optical Telescope, operated on the island of La Palma jointly by Denmark, Finland, Iceland, Norway, and Sweden, in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofisica de Canarias. We are also grateful for observations made with telescopes at the Observatorio do Pico dos Dias of the Laboratorio Nacional de Astrofisica of Brazil.

Heliosphere models predict the density and ionization of the LIC and the ISMF that shapes the heliosphere (e.g., Opher et al. 2009; Pogorelov et al. 2009; Ratkiewicz et al. 2008; Prested et al. 2010) and originally showed that the Ribbon forms where the sight line is perpendicular to the direction of the interstellar field draping over the heliosphere (Schwadron et al. 2009; Heerikhuisen et al. 2010; Chalov et al. 2010; Grygorczuk et al. 2011; Heerikhuisen & Pogorelov 2011; Ratkiewicz et al. 2012). The exact mechanism generating the Ribbon is a conundrum, partly because the properties of turbulence upstream of the heliopause are unknown (Gamayunov et al. 2010; Florinski et al. 2010), so that several possible scenarios for the formation of the Ribbon have been suggested (e.g., McComas et al. 2010; Schwadron et al. 2011; Grzedzielski et al. 2010). One possible Ribbon formation mechanism requires outflowing ENAs to escape from the heliosphere and charge exchange with interstellar protons in the outer heliosheath. These ENAs subsequently create secondary inflowing ENAs from another quick charge exchange with interstellar neutrals before the ring-beam distribution of the ions (with a pitch angle of ∼90°) is disrupted by turbulence, therefore giving the B · R =0 alignment. Testing for such a model, Heerikhuisen & Pogorelov (2011) varied the strength and direction of the ISMF, and the interstellar neutral H and proton densities, to obtain a best fit to the geometry of the Ribbon. These models suggest that the Ribbon is formed roughly ∼100 AU beyond the heliopause, by a local ISMF that is directed away from the galactic coordinates ℓ, b = 33° ± 4°, 53° ± 2°, for a field strength of 2–3 μG. For comparison, an earlier MHD model of the heliosphere asymmetries implied by the deflection of the solar wind in the inner heliosheath gave an ISMF direction of ℓ =10°–22°, b =28°–38°, and field strength ∼3.7–5.5 μG (Opher et al. 2009). For the Heerikhuisen & Pogorelov (2011) models, the angle between the center of the Ribbon arc and the ISMF direction is ∼0°–15°.

The global heliosphere provides an in situ diagnostic of the magnetic field and plasma shaping the heliosphere. The ∼48° offset between the ISMF direction given by the Ribbon arc center and the velocity of the inflowing neutral interstellar gas creates asymmetries that can be predicted using MHD models (e.g., Pogorelov et al. 2009; Opher et al. 2009; Ratkiewicz et al. 2008; Prested et al. 2010). The data tracing the heliosphere asymmetries include the different distances of the solar wind termination shock found by Voyager 1 in the northern ecliptic hemisphere and by Voyager 2 in the south (94 AU versus 84 AU; Stone et al. 2008; Richardson & Stone 2009), the ∼8° offset between the upwind directions of the neutral interstellar H^o and He^o flowing into the heliosphere (using data from Lallement et al. 2010; McComas et al. 2012), and the preferential alignment exhibited by the 3 kHz plasma emissions from the ISM beyond the heliopause that were detected by both Voyagers (e.g., Kurth & Gurnett 2003). The ISMF directions from these models are generally consistent with the field direction from the IBEX Ribbon.

McComas et al. (2012) have determined a new consensus direction for the velocity vector of interstellar He^o flowing through the heliosphere. The He^o gas velocity, 23.2 ± 0.3 km s⁻¹ (Table 1), agrees with the (less precise) velocity of interstellar dust traveling through the heliosphere, after correction for propagation effects, of 24.5^+1.1_−1.2 km s⁻¹ from galactic coordinates ℓ, b =8° ± 15°, 14° ± 4° (Frisch et al. 1999; Kimura et al. 2003). It also agrees with the velocity of interstellar H^o interacting with the heliosphere found from the first spectrum of Lyα emission from interstellar H^o inside of the heliosphere, 22.5 ± 2.8 km s⁻¹, after correction for H^o propagation and to the consensus IBEX upwind direction (Adams & Frisch 1977).

The outer boundary conditions of the heliosphere models are set by the physical properties of the LIC, which must be reconstructed from ISM observations using photoionization models because of the low opacity of the cloud. Ribbon models are highly sensitive to the interstellar boundary conditions of the heliosphere; 15% variations in the interstellar parameters lead to pronounced differences in the location and width of the Ribbon (Frisch et al. 2010b). Photoionization models indicate that the LIC is a low-density, n ∼ 0.27 cm⁻³, partially ionized cloud, H⁺/H ∼ 22% and He⁺/He ∼ 39% (Model 26 in Slavin & Frisch 2008). Observations of the ISM inside of the heliosphere also probe the LIC properties. When the IBEX measurements of interstellar O^o and Ne^o are corrected for propagation effects through and entering the heliosphere and ionization in the LIC using photoionization models, the interstellar abundance ratio O/Ne =0.27 ± 0.10 that is recovered agrees with other local ISM measurements and suggests that over 50% of the O is depleted onto interstellar dust grains (Bochsler et al. 2012). IBEX and Ulysses measurements of interstellar He^o indicate that the LIC is warm, 6300 ± 390 K (Witte 2004; McComas et al. 2012).

New IBEX-LO observations of the flow of interstellar He^o through the inner heliosphere (McComas et al. 2012) indicate that ISM flow is ∼12% slower than found from earlier Ulysses data (Witte 2004), which lowers the interstellar ram pressure on the heliosphere by ∼22% and may affect the models of the Ribbon location. The value of the He^o flow vector is given in Table 1, together with the 1σ uncertainties for longitude, latitude, and velocity. The new IBEX upwind direction has shifted to 36 east of the Ulysses direction. The uncertainties are somewhat larger when the bounding range constraints are included; these constraints set the limits as ℓ =5.25^+1.48_−1.37 deg, b =12.03^+2.67_−3.19 deg, the velocity to −23.20^+2.5_−1.9 km s⁻¹, and the temperature to 5000–8300 K.

The stars within 40 pc from the PlanetPol catalog included in this study are HD 97603 (HR 4357), HD 140573 (HR 5854), HD 139006 (HR 5793), HD 116656 (HR 5054), HD 156164 (HR 6410), HD 95418 (HR 4295), HD 112185 (HR 4905), HD 161096 (HR 6603), HD 177724 (HR 7235), HD 127762 (HR 5435), HD 153210 (HR 6299), HD 120315 (HR 5191), HD 113226 (HR 4932), HD 112413 (HR 4915), HD 163588 (HR 6688), HD 95689 (HR 4301), and HD 131873 (HR 5563).

The nearby stars from the Santos et al. (2011) catalog that have been used in this study include HD 223889 (HIP 117828), HD 120467 (HIP 67487), HD 173818 (HIP 92200), HIP 65520, HD 127339 (HIP 70956), HIP 82283, HIP 50808, HIP 106803, HD 162283 (HIP 87322), HIP 114859, HIP 83405, HIP 96710, HIP 90035, HIP 87745, HD 176986 (HIP 93540), HD 175726 (HIP 92984), HIP 61872, HIP 95417, HD 155802 (HIP 84303), HD 166184 (HIP 88961), HD 161098 (HIP 86765), HD 182085 (HIP 95299), HD 164651 (HIP 88324), HD 119638 (HIP 67069), HD 125184 (HIP 69881), HD 95521 (HIP 53837), HIP 66918, HD 177409 (HIP 94154), HD 144660 (HIP 78983), HD 151528 (HIP 82260), HD 95338 (HIP 53719), HD 127352 (HIP 70973), HD 183063 (HIP 95722), HD 105328 (HIP 59143), HD 204385 (HIP 106213), HD 145809 (HIP 79524), HD 172675 (HIP 91645), HD 149013 (HIP 81010), HD 185615 (HIP 96854), and HD 138885 (HIP 76292).

The seven PlanetPol stars that define the upper end of the region R.A. = 16^H–20^H polarization envelope (Section 5.3) are listed in Table 3.

Polarization of optical starlight in the ISM is due to magnetically aligned dichroic dust grains, so that there is a correlation between the upper envelope of polarization and interstellar extinction for a given set of observations (Serkowski et al. 1975; Fosalba et al. 2002; Andersson 2012). The usual term "upper envelope" describes the relation between the maximum observed polarizations for a set of stars as a function of extinction, i.e., for a given extinction no polarization is found above the upper envelope value by definition. Figure 7 shows that an upper envelope is also present in the polarization–distance plot. The scatter of polarization strengths for a given extinction is due to the patchy nature of the ISM and magnetic turbulence. Likewise, the presence of an upper envelope to the polarization–distance plot in Figure 7 likely results from either the patchy nature of the nearby ISM (Frisch et al. 2011), magnetic turbulence, or both.

The polarization data represented in Figure 3 were collected over a time span of half of a century, using a diverse set of instruments with unknown systematics. The reasonableness of the statement that polarization increases with distance has been tested for the stars shown in the figure using the nonparametric Kendall's tau measure of bivariate correlation. For the set of stars where Pol/d Pol ⩾3, the rank correlation coefficient is τ = 0.86, where a value of one indicates that there is a perfect association of increasing polarization with increasing distance. Selecting only the most accurate data points, Pol/d Pol ⩾5, yields τ = 0.89. However, for the nearest stars used in this analysis, <40 pc, this association is not demonstrated (τ = 0.14 P/dP ⩾3), an effect that we attribute both to influence of systematic uncertainties on weak polarization measurements and to the patchy nature of the nearby ISM. In Section 5.3.1, we discuss an especially nearby region where increasing interstellar polarization is shown to be associated with increasing distance for stars within 40 pc.

The asymmetry of the local interstellar radiation field is related to the overall opacity of the Local Bubble. The brightest of the far-UV sources are located in the third and fourth galactic quadrants (ℓ =180°–360°; Gondhalekar et al. 1980) because of the distribution of massive stars with respect to the Local Bubble void. Those same stars are bright at the 13.6 eV ionization edge of H^o so that in the absence of interstellar opacity the ℓ =180°–360° interval will be more highly ionized (Frisch 2010). This distribution of radiation sources explains the relation between polarization and the radiation field at each star that is displayed in Figure 9.

Figure 12 shows the different levels of far-UV radiation at 975 Å between galactic quadrants I and II (ℓ =0°–180°) and III and IV (ℓ =180°–360°). The sum of the stellar fluxes is shown at spherical surfaces around the Sun with radii of 25 pc and 45 pc and displayed using an Aitoff projection. The mapped fluxes represent the sum of stellar fluxes at each position, based on the 25 brightest OB stars at 975 Å (Opal & Weller 1984). Flux units are photons cm⁻² s⁻¹ Å⁻¹. The fluxes are plotted with the same color-coding in both figures. The minimum and maximum flux values on the color bar correspond to 4.0 × 10⁴ and 8.0 × 10⁴ cm⁻² s⁻¹ Å⁻¹, respectively. Low radiation fluxes in the region of large PlanetPol polarizations are the result of the locations of hot stars.

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