What do we know about the orientation of the Local Interstellar Magnetic Field?

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1 **FULL TITLE** ASP Conference Series, Vol. **VOLUME**, **YEAR OF PUBLICATION** **NAMES OF EDITORS** What do we know about the orientation of the Local Interstellar Magnetic Field? Romana Ratkiewicz Space Research Center PAS, Bartycka 18a, Warszawa, Poland Lotfi Ben-Jaffel Institut d Astrophysique de Paris, CNRS, UPMC, 98bis Blvd Arago, Paris, France Jolanta Grygorczuk Space Research Center PAS, Bartycka 18a, Warszawa, Poland Abstract. About a decade ago first 3D MHD numerical simulations of the interaction of the solar wind with the magnetized interstellar plasma showed that the oblique local interstellar magnetic field (LIMF) introduces asymmetries in the heliospheric boundary. Since then, more and more observations confirm these predictions, offering a unique opportunity to uncover the strength and orientation of the LIMF. Using asymmetries observed in the spatial distribution of the Ly-α emission far from the Sun, Ben-Jaffel et al. (2000) first reported the detection of the bow shock and its deflection from upwind. It was an opportunity to estimate the direction of the unknown interstellar magnetic field to be 40 from upwind. This result now is checked with our 3D magnetohydrodynamic model with a constant flux of neutral particles. Our new analysis confirms our previous finding for the B is orientation. We compare our results with other recently reported observations. 1. Introduction Two counterflowing magnetized plasmas such as the solar wind (SW) and the local interstellar medium (LISM), in the ideal magnetohydrodynamic treatment, are separated by the tangential discountinuity surface called the heliopause (HP). The highly supersonic solar wind slows down through the termination shock (TS) to adjust to the outer conditions in the LISM. In case when the interstellar plasma is supersonic it slows down through the bow shock (BS). The region between the TS and BS is the heliospheric boundary layer (HBL). A basic MHD model of the interaction between the spherically symmetric SW and LISM includes the LISM magnetized plasma interaction with unmagnetized SW plasma. Since the neutral component of the interstellar medium plays an important role in this interaction, this factor has been added to some models subsequently. In general, the full MHD model should take into account the interplanetary magnetic field (IMF), anomalous component of cosmic rays (ACR s), galactic cosmic 1

2 2 rays (GCR s), also time-dependent phenomena and latitudinal dependence of SW. A first attempt to study the influence of the local interstellar magnetic field (LIMF) on the shape of the HBL was made by Fahr, Ratkiewicz & Grzedzielski (1986) using the so called Newtonian Approximation (NA). The main assumption of the NA (Fahr et al. 1986, 1988) is that the TS, HP, and BS are very close to each other, therefore can be described by a single surface called the heliopause, which represents them all. The basic equation of the NA expresses the fact of equality of the normal components of the total unperturbed hydromagnetic momentum flux on both sides of the heliopause. The obtained results showed that for the inclination angle α other than 0 and 90 (α is an angle between interstellar velocity and magnetic field vectors), the interstellar magnetic field causes a deviation of the nose of the heliopause from the apex direction. The first basic three-dimensional MHD model, with numerical simulations performed for α = 0, 30, 60, 90, presented by Ratkiewicz et al. (1998) revealed the complexity of the SW-LISM plasma interaction showing asymmetries of the heliospheric interface introduced by the LIMF for α = 30 and 60. The results for α = 0, 45, 90 were published by Pogorelov & Matsuda (1998). In both models it is assumed that the unperturbed solar wind is spherically symmetric, the SW ram pressure dominates, the interplanetary magnetic field is neglected, the neutral component of LISM is not included. Since the magnitude and direction of the LIMF are not known, in these computer simulations they are treated as free parameters. At present, besides the theoretical models of the HBL, we also have experimental data. It would be a lengthy process to enumerate the large sets of data gathered up to now. Here we mention only those which have been used for further interpretations to confirm independently that the orientation of the local interstellar magnetic field introduces asymmetries in the heliospheric boundary layer. They are: 2-3 khz radio emissions detected in , , and recently during the 23 solar cycle newly interpreted in Gurnett et al. (2006) and in Opher et al. (2007); observations of asymmetries in the spatial distribution of the Ly-α emission far from the Sun (Quemerais et al. 1995) used in Ben- Jaffel et al. (2000); detection of a slight deflection of the hydrogen flow inside the heliosphere (Quemerais et al. 1999) interpreted by Lallement et al. (2005); observations of ions streaming from the termination shock (Stone et al. 2005; Decker et al. 2005) discussed therein and in Opher et al. (2007). Modelers very soon realized that the observations confronted with theoretical models may constrain the direction of the LIMF and act as an interstellar magnetic compass. The first such attempt has been made by Ben-Jaffel et al. (2000) (called later BPR). 2. Estimations of the orientation of the LIMF 2.1. Updated BPR estimation of LIMF direction In the BPR paper the authors proposed that first-order Fermi acceleration of Lyα photons should occur at the interface region between the solar and interstellar winds. In this process, photons are Doppler-shifted toward shorter wavelengths each time they are scattered by hydrogen neutrals that have been decelerated by

3 charge exchange with protons in the transition region wrapping the heliopause. The Fermi process, first confirmed by HST spectral detection, was then used to interpret enigmatic asymmetries in the spatial distribution of the sky Lyman-α brightness as observed by Voyager 1 & 2 (Quemerais et al. 1995). In that frame, BPR derived that the heliopause nose is tilted 12 from the interstellar flow direction, a deflection that has been translated to 40 angle for B is direction using the simple NA approach (Fahr et al. 1986, 1988) and numerical simulations of the distribution of neutral hydrogen (Baranov and Malama 1993). In this paper this result is checked with our 3D magnetohydrodynamical model, which includes neutral particles constant flux impact on the heliospheric plasma configuration (Ratkiewicz & Ben-Jaffel 2002) for the boundary conditions from Baranov and Malama (1993). Following Ratkiewicz & Ben-Jaffel (2002), we use the same set of MHD equations with a source term S on the RHS describing charge exchange with the constant flux of hydrogen: U t + F = Q + S (1) where U, Q, and S are column vectors, and F is a flux tensor defined as: 3 U = ρ ρu B ρe F = ρu ρuu + I(p + B B 8π ) BB 4π ub Bu ρhu B(u B 4π ) Q = 0 B 4π u u B 4π B S = ρν c 0 V H u V H 2 + 3k BT H 2m H 1 2 u2 k BT (γ 1)m H Here, ρ is the ion mass density, p = 2nk B T is the pressure, n is the ion number density, T and T H (T H = const) are ion and H atom temperatures, and u and V H (V H = const) are the ion and H atom velocity vectors, respectively; B is the magnetic field vector, E = 1 p γ 1 ρ + u u 2 + B B 8πρ is the total energy per unit mass, and H = γ p γ 1 ρ + u u 2 + B B 4πρ is enthalpy. γ is the ratio of specific heats. I is the 3 x 3 identity matrix. The charge exchange collision frequency is ν c = n H σu, where n H (n H = const) is H atom number density, σ is the charge exchange cross-section, and u = ((u V H ) k B (T + T H )/(9πm H )) 1/2 is the effective average relative speed of protons and H atoms, assuming a maxwellian spread of velocities both for protons and H atoms. The flows are taken to be adiabatic with γ = 5/3. The additional constraint of a divergence-free magnetic field, B = 0, in the numerical simulations is accomplished by adding the source term Q to the RHS of (1), which is proportional to the divergence of the magnetic field. By adding Q to the RHS of (1) assures that any numerically generated B 0 is advected with the flow, and allows one to limit the growth of B 0.

4 4 Figure 1. The heliospheric configurations for the inclination angle α equal to 30 (left), 40 (middle), 50 (right) with the density contours (solid lines). The upper dotted line indicates the nose of the heliopause. The bottom dotted line indicates the angular distance of the center of the plasma island from the apex (middle dotted line), which is 25 for α=30, 16 for α=40, 11 for α=50. The three-dimensional set of equations describing the interaction of the solar wind with the interstellar magnetized plasma is solved using a spatial first order time-marching, implicit, upwind-differenced scheme based on a finite-volume approach (Ratkiewicz et al. 1998). The improved grid (Ratkiewicz et al. 2006) that is used for the computations is generated internally in the 3D MHD code, and is a spherical one containing 60 grid points in the azimuthal, 350 points in the radial, and 120 points in the meridional direction. The calculations have been made for the following set of the boundary conditions: for the unperturbed solar wind at 1AU, number density n E = 7cm 3, velocity V E = 450km s 1, and Mach number M E = 10. For the unperturbed interstellar magnetized plasma we take V is = 25km s 1, and M is = 2. The interstellar plasma number density n is = 0.07cm 3, the interstellar neutral hydrogen number density n H = 0.14cm 3, the local interstellar magnetic field strength B is = 1.8µG, and the inclination angle α is in the range between 0 and 90 in steps of 10. Detailed analysis for the above range of LIMF angle α showed that the role of the interstellar magnetic field is very important. However, one should remember that the interaction with neutral hydrogen by charge exchange reduces the asymmetries introduced by the LIMF (Pogorelov et al. 2007). Having the shapes of BS, HP, and TS, and the structure between them, we can analyze the distribution of the plasma between the heliopause and the bow shock, where the hydrogen wall appears (compare the streamlines and fieldlines in Ratkiewicz et al. (2000); Izmodenov et al. (2005)). In Figure 1 we show the heliospheric configuration for α = 30, 40, and 50. The highest density island appears near by the heliopause, where the plasma is most compressed. This island nicely reflects the asymmetry caused by the direction of LIMF. At such place the charge exchange between H and plasma has the highest efficiency. Therefore one can expect to see the excess intensity in the Lyman-α emission in this region. According to the Voyager 2 Lyman-α data the peak brightness has been found

5 at 20 ± 10 (Quemerais et al. 1995; Ben-Jaffel et al. 2000). Figure 1 confirms it, showing the 16 peak for α=40, in fact the same inclination angle, which we derive from the simple Newtonian approximation. The comparison of Voyager data shown in Fig. 4 of the Ben-Jaffel et al. (2000) paper with our MHD model definitely confirms that the heliopause is tilted and the bow shock exists. As shown in Figure 1, our calculations reveal that the Voyager brightness peak asymmetry 20 ± 10 can be obtained when the local interstellar magnetic field direction is about 30 to 50 from the upwind direction. Using the ecliptic coordinates of the planes where the V1 (246, 34 ) and V2 (284, 14 ) Lyα observations have been conducted, we derive that for both V1 and V2, the LISM B is orientation should be between 41 to 58 below the galactic plane. The galactic longitude of the field is found in a range around These numbers should be considered as a first order estimate and should be improved in the near future using more Voyager UVS data Other estimations of LIMF orientation and comparison After BPR published their results in 2000, other estimations of the orientation of the local inerstellar magnetic field have been reported in two studies based on different techniques (Lallement et al. 2005; Opher et al. 2007). Using an absorption cell, Lallement et al. (2005) measured the Doppler shifts of the interstellar hydrogen resonance glow to derive the direction of the neutral hydrogen flow as it enters the inner heliosphere. The neutral hydrogen flow has been found to be deflected relative to the helium flow by about 4. The most likely explanation of this deflection, according to the authors, is a distortion of the heliosphere under the action of an ambient interstellar magnetic field. The conclusion is that the helium flow vector and the hydrogen flow vector constrain the direction of the magnetic field, therefore it is possible to estimate it. However, this conclusion was questionned by Pogorelov & Zank (2006) who used self-consistent MHD-neutral fluid model to show that this deflection can exist for virtually any orientation of the LIMF with respect to the LISM velocity vector. It is not the scope of this short paper to discuss in depth the two competing analyses as both have several weaknesses and thus the conclusions so far derived are not definite. In the following, we thus assume that Lallement et al. s conclusions regarding the orientation of LIMF are still competing. Lallement et al. derivations are based on the following: (1) B is is contained in the plane defined by the H and He flow vectors; (2) the magnetic field from the interstellar side toward the inner heliosphere is oriented like secondary flow of neutral H with respect to the wind axis; (3) α is between 30 and 60 It follows that, in fact, Lallement et al. only constrain the plane that contains the LIMF but not its orientation, which is assumed in (3). Therefore, if any comparison has to be made is to check if the proposed plane, defined by Lallement et al. to be perpendicular to (λ, β) =(167, 30 ), is compatible with our findings. For our range of LIMF orientation obtained above, we derive that the normal to the plane containing the LIMF and the He flow directions should be around (λ, β) =(168.5, 36.5 ). Obviously, our ecliptic coordinate estimation for the normal to the plane that contains both the helium flow direction and the LIMF, as well as the angle between this and galactic planes (about 64 ) 5

6 6 compare nicely with Lallement et al. (2005). Using a distinct technique based on 2-3 khz radio emissions and ions streaming from the termination shock, Opher et al. (2007) also suggested that the plane that contains the LIMF is 60 to 90 from the galatic plane. Concluding remarks The analysis above shows that the local interstellar magnetic field has the inclination angle from the interstellar flow direction in the range The observations so far obtained tend to establish that the local interstellar magnetic field has a galatic latitude in the range 41 to 58 and a longitude range around It is important to stress that we provide a real estimation of the α angle on the basis of the Voyager Lyman-α data. Other estimations provide constraints that are consistent with our findings. Further analyses of Voyagers, HST, Ulysses, and the future Interstellar Boundary Explorer (IBEX) missions data together with more sophisticated models including the latitudinal dependence of SW, time-dependent phenomena, interplanetary magnetic field effects, and necessarily neutral particles in a self-consistent way should constrain much more accurately these numbers. Acknowledgments. Authors acknowledge the support from PAN/CNRS no project and LEA ASTRO-PF project. RR and JG acknowledge the support from Prof. Gary Zank from the IGPP-UCR. References Baranov, V. B., and Malama, Y. G. 1993, JGR, 98, Ben-Jaffel, L., Puyoo, O., & Ratkiewicz, R. 2000, ApJ, 533, 924 Decker, R. B., Krimigis, S. M., Roelof, E. C., Hill, M. E., Armstrong, T. P., Gloeckler, G., Hamilton, D. C., & Lanzerotti, L. J. 2005, Science, 309, 2020 Fahr, H. J., Ratkiewicz, R. & Grzedzielski, S. 1986, Adv. Space Res., 6, No. 1, 389 Fahr, H. J., Grzedzielski, S. & Ratkiewicz, R. 1988, Annales Geophys., 6, 337 Gurnett, D. A., Kurth, W. S., Cairns, I. H., & Mitchell, J. 2006, AIP, 858, 129 Izmodenov, V., Alexashov, D., & Myasnikov, A. 2005, A & A, 437, L35 Lallement, R., Quemerais, E., Bertaux, J. L., Ferron, S., Koutroumpa, D., & Pellinen, R. 2005, Science, 307, 1447 Opher, M,. Stone, E. C., & Gombosi, T. I. 2007, Science, 316, 875 Quemerais, E., Sandel, B. R., Lallement, R., & Bertaux, J. L A & A, 299, 249 Quemerais, E., Bertaux, J. L., Lallement, R., Berthe, M., Kyrola, E., & Schmidt, W. 1999, JGR, 104, Pogorelov, N. V., & Matsuda, T. 1998, JGR, 103, 237 Pogorelov, N. V., & Zank, G. P. 2006, Ap.J, 636, L161 Pogorelov, N. V., Stone, E. C., Florinski, V., & Zank, G. P. 2007, Ap.J, 668, 611 Ratkiewicz, R., Barnes, A., Molvik, G. A., Spreiter, J. R., Stahara, S. S., Vinokur, M., & Venkatesvaran, S. 1998, A & A, 335, 363 Ratkiewicz, R., Barnes, A., & Spreiter, J. R. 2000, JGR, 105, Ratkiewicz, R. & Ben-Jaffel, L. 2002, JGR, 107, SSH 2-1 Ratkiewicz, R., Grygorczuk, J., & Ben-Jaffel, L. 2006, AIP, 858, 27 Stone, E. C., Cummings, A. C., McDonald, F. B., Heikkila, B. C., Lal, N., & Webber, W.B. 2005, Science, 309, 2017