Time-varying Heliospheric Distance to the Heliopause

The solar wind is highly variable. During periods of short time variability in the solar wind, such as solar flares and CME disturbances as well as smaller-scale variations propagating outward in the inner heliosphere, these disturbances can merge and form a global merged interaction region (GMIR; Burlaga 1994). GMIRs are frequently observed by Voyager 2 (V2) in the distant heliosphere. It is anticipated that a series of GMIRs may change the outer heliospheric structure and distance to the heliopause (HP). The long time variations of the solar-wind ram-pressure are also expected to be important in determing the structure of the time-varying outer heliosphere. OMNI data show that the solar-wind ram-pressure at 1 au was 1.4 nPa in 2004 when Voyager 1 (V1) crossed the termination shock (TS) and increased to a maximum of 2.4 nPa around mid-2005, and then decreased to minimum of 1.3 nPa around 2009–2010. OMNI data are useful for analyzing the long-term variation of the distance to the HP because Ulysses observations show that solar-wind ram-pressure is independent of latitude (e.g., McComas et al. 2008). Since 2010, the ram-pressure began to increase again, reaching 2.6 nPa in late 2015. As the interplanetary plasma density decreases as R², R is the distance from the Sun by astronomical unit, the ram-pressure changes the distance to the HP by about a factor of 2^0.5. Hence, the OMNI data suggest that the ram -pressure change over the past 10 years will introduce a quite evident effect on the the distance to the HP.

The effect of the solar-wind ram-pressure on the outer heliospheric structure has been discussed (e.g., Karmesin et al. 1995; Wang & Belcher 1999; Zank & Müller 2003; McComas et al. 2008, 2010; Zank 2015; Pogorelov et al. 2017), but there has been no explicit study that includes the effects of a series of GMIRs and/or varying solar-wind ram-pressure on our heliospheric structure and distance to the HP using observational data from the inner heliosphere. In this Letter, we use a three-dimensional (3D) time-dependent MHD simulation. Initially, we simulate an MHD stationary outer heliospheric structure with no solar-wind disturbances. Thereafter, we introduce a series of GMIRs to determine outer heliospheric structure and the change in the HP distance with time.

Certainly when averaged over a sufficiently long scale, the presence of many GMIRs must contribute an average increased ram-pressure that will then place the HP at a more distant location. Why then is it important to include the dynamics of both the long-term solar-wind ram-pressure changes and the short-term GMIR ram-pressure changes? There are at least two reasons. (1) Other than changes to the internal energy of the supersonic wind related to the continued heating of the solar wind by multiple following shocks, the transmission of the disturbance across the TS considerably changes the dynamics of the TS and inner heliosheath (IHS). For example, the transmission of a GMIR shock (see Washimi et al. 2011 and references therein) produces a weakened transmitted shock propagating toward the HP, along with an advected contact or tangential discontinuity. The transmitted shock collides with the HP and is partially transmitted into the very local interstellar medium and partially reflected by the HP back toward the TS, with which it collides driving the TS toward the Sun. This example illustrates why a simple increase in the averaged ram-pressure associated with a sequence of GMIRs does not fully capture the response of the HP to multiple GMIRs. (2) Only a dynamical simulation based on temporal solar boundary conditions can provide an estimate of the speed with which the HP moves inward or outward. This is essential to estimate when Voyager 2, which has a fixed speed, can catch up to and cross the HP. In addition, we include recent solar-wind ram-pressure variations to determine the recent changes in the HP distance. Our simulations yield the distance between the HP and the V2 position at the present time, which allows us to estimate/predict when V2 will cross the heliopause.

As a typical example of a series of GMIRs in deep interplanetary space, V2 observations of solar-wind ram-pressure from the beginning of 2000 when V2 was 59.8 au from the Sun to the end of 2006 when V2 was 81.6 au are shown in the upper panel of Figure 1. More than 10 GMIRs are shown in this panel. The GMIR amplitudes were several nPa if normalized at 1 au, i.e., if they were estimated by (proton mass) × (density × R²) × (velocity)², and the largest one observed was the event of 2006 March and the amplitude was 10 nPa. GMIRs are exceptionally large disturbances in the outer heliosphere and probably occur during every solar cycle (SC). However, GMIRs do not appear very periodically and occur more frequently in the rising rather than the declining phase of an SC. We study the temporal distance to the HP due to a series of GMIRs. To model the series of GMIRs, a simplified GMIR of amplitude 6.0 nPa is introduced at a rate of one per year at the inner boundary of the simulation box.

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We initially develop a 3D stationary outer heliospheric MHD solution, and then introduce a series of GMIRs at the inner boundary of our simulation box. Our 3D MHD simulation utilizes a TVD scheme (Tanaka 1994), in which charge exchange (Pauls et al. 1995) between protons and interstellar neutral H is taken into account. The inner and outer boundary distances are 50 au (=R₀) and 900 au, respectively. At the inner boundary, a typical set of solar-wind parameters at 1 au is assigned, i.e., velocity v is 400 km s⁻¹ (=v_0l) and density n is 5/cc (=n_0l) for latitudes less than 60°, and velocity is 700 km s⁻¹ (=v_0h) and density is $5.0\cdot {(4/7)}^{2}/{cc}(={n}_{0h})$ for latitudes greater than 60°. This ensures that the ram-pressure is 1.34 nPa in all latitudes. Both the toroidal and radial interplanetary magnetic fields at 1 au are taken to be 3.54 nT, so that the total field intensity is 5.0 nT. For the outer boundary LISM conditions, following Möbius et al. (2012) and McComas et al. (2013), the proton and hydrogen velocity and temperature are assumed to be 23.2 km s⁻¹ and 6300 K, respectively, with values for proton density 0.078/cc, hydrogen density 0.176/cc, and magnetic field intensity 0.28 nT. The magnetic field lies in the hydrogen deflection plane (Lallement et al. 2010), and the angle to the LISM flow is 45°.

Using the above parameters, an MHD stationary solution of the outer heliosphere is obtained. The upper panel of Figure 2 shows the radial distance dependence of the solar-wind plasma and VLISM quantities along the Sun–V2 line. In interplanetary space, the radial component of the solar-wind speed, Vr, is the same as the solar-wind speed, V, because the solar wind expands radially. In the IHS, the absolute value of the toroidal component of the magnetic field, B_T, is almost the same as the magnetic field intensity, B. The plasma density, N, is found to increase at the TS and to further increase near the HP. The location of the TS is identified by a sharp decrease in solar wind speed and an increase in thermal pressure, at R ∼ 66 au. The location of the HP is identified where the magnetic field sharply decreases and, at the same time, the thermal pressure sharply increases at R ∼ 104 au. In the VLISM, except for very near the HP, all quantities change monotonically with distance, tending at large distances to be outer boundary values.

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For the GMIR of 6.0 nPa at the inner boundary, we assume a triangular shape with a sharp increase for a time of 0.01 years, increasing from 1.34 to 6.0 nPa and then slowly decreasing to the initial intensity, 1.33 nPa, over a time of 0.19 years. Hence, the total pulse width is 0.2 years. This assumed pulse width and shape corresponds to the V2 observed GMIR event of 2006 March. At the peak intensity, the plasma density at the inner boundary is assigned to be $2.44\times {n}_{0l}\times {R}_{0}^{-2}$ or $2.44\times {n}_{0h}\times {R}_{0}^{-2}$ with a velocity of 1.36 × v_0l or 1.36 × v_0h for the low or high latitudes, respectively.

If a GMIR is introduced at the inner boundary, it propagates outward until it collides with the TS. The TS is driven outward and the GMIR shock is transmitted and propagates into the IHS as discussed in Whang & Burlaga (1994), Story & Zank (1995), Zank & Müller (2003), and Washimi et al. (2007). It takes about a year for the GMIR disturbance to propagate from the inner boundary at 50 au to the HP (see also Zank et al. 2001). The first GMIR is initiated at time of 0.00 years in the stationary heliospheric solution. The lower panel of Figure 2 shows heliospheric structure at the time of 1.22 years. The first transmitted shock has already reached the HP, and a large disturbance is found in the VLISM just outside the HP. The disturbance propagates outward in the VLISM with a speed of ∼50 km s⁻¹, which corresponds approximately to the magnetosonic wave speed in this region. A set of contact discontinuities, driven by the GMIR at the TS, is present in the IHS, and they are advected in the slow heliosheath flow where they persist for several years.

The upper panel of Figure 3 shows the IHS–VLISM structure at time of 2.21 years. In addition to the first disturbance, a second disturbance associated with the second GMIR is found in the VLISM near the HP. A second set of contact discontinuities is also found in the IHS. After 35.18 years of introducing GMIRs at the inner boundary, a series of disturbances is present in the VLISM up to a distance of ∼200 au from the Sun, illustrated in the lower panel of Figure 3.

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The lower panel of Figure 1 shows how the distance to the HP increases with time from the introduction of the first GMIR at time 0. The increase in distance to the HP saturates at ∼14 au 30–40 years after the first GMIR. The series of GMIR-induced disturbances adds an additional increase of the averaged solar-wind ram-pressure in the IHS, and it also induces disturbances propagating into the surrounding interstellar plasma, which results in reducing the pressure acting on the HP. As a result, the distance to the HP increases by ∼14 au when compared to the stationary solution in lower panel of Figure 1. The saturation time of the increased distance due to the solar-wind ram-pressure increase corresponds to the IHS plasma exchange time for new plasma of 7–10 years, which is shown as an initial phase of the HP distance increase in the lower panel of Figure 1, while the long-timescale saturation of 30–40 years probably corresponds to a relaxation time of the surrounding interstellar plasma near the HP due to the series of GMIRs.

Multiple contact discontinuities are also shown in lower panel of Figure 3. The location of the TS also changes rapidly as shown by Washimi et al. (2007, 2011, 2012). The time dependence of the HP distance along the Sun–V1 and Sun–V2 lines in the lower panel of Figure 1 is similar, which suggests that the north–south asymmetry of the HP structure is maintained through this process. The stationary model (Figure 1) suggests a steady increase in B across the heliosheath. This is possibly consistent with V1 observations of B across the heliosheath (Burlaga 2015, Figure 3). V1 observed increasing trends in B for about 1.5 years after V1 crossed the TS and again from halfway through 2010 until the HP crossing. These observations are made over an ∼8 year period and do not obviously correspond to the instantaneous snapshot of B across the entire heliosheath provided by the simulations. We have not included the complex magnetic field dynamics at our inner boundary that might account for the complicated variable evolution of B in the IHS. Nonetheless, this discrepancy is not important because the location and dynamics of the HP is determined primarily by the ram energy of the solar wind, which is significantly larger than the internal energy and magnetic field energy.

The solar-wind ram-pressure is closely related to the distance to the HP. OMNI data of the solar-wind ram-pressure at 1 au on the ecliptic plane show an increase from ∼2.0 nPa in late 2004 when V1 crossed the TS to a maximum value of ∼2.4 nPa by mid-2005, after which it decreased to a minimum value of ∼1.3 nPa during mid-2009 and early 2010. After this period, the ram-pressure began to increase again in mid-2010, reaching ∼2.4 nPa in 2015. This recent ram-pressure increase is expected to increase the distance to the HP.

For a more realistic simulation, we introduce a series of simplified ram-pressure increases as shown by the red step-lines in Figure 4, i.e., the ram-pressure is 1.34 nPa (first step) before 2010.4, corresponding to a solar-wind speed of 400 km s⁻¹ and density of 5/cc, as used for our stationary heliosphere model shown in the upper panel of Figure 2. The ram-pressure changes to 1.7 nPa (second step) during 2010.4–2014.8, and after 2014.8 is 2.4 nPa (third step). Because OMNI data are given at 1 au and our inner simulation boundary is at 50 au, a time shift of 0.55 years is simply assumed to model the solar-wind propagation from 1 to 50 au in this analysis. Hence, we do not account for stream–stream interactions between 1 and 50 au in our analysis. V1 crossed the HP on 2012 August 25 at a distance of 122 au from the Sun (Stone et al. 2013). The distance to the HP in our MHD simulation was 126.9 au. To fit the simulation result with V1 observations, a correction factor = 122/126.9 = 0.961 is applied to all our simulation distances.

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The simulated distances to the time-varying HP along the Sun–V1 and Sun–V2 lines are then obtained and shown in Figure 5. The trajectories of V1 and V2 are also shown. The HP distance is found to fluctuate with an amplitude ∼±1 au even when the ram-pressure is constant. This fluctuation is partly due to disturbances in the VLISM that were driven by solar wind GMIRs. In addition to the fluctuations, the HP distance is clearly found to increase after the year of ∼2012. Specifically, the speed at which the increase occurs is found to happen in two steps: during the period beginning in 2012 to the end of 2016, the increased speed of the HP along both of the Sun–V1 and Sun–V2 lines is rather slow and is ∼0.6 au yr⁻¹, whereas during the period of 2017–2020, the speed is ∼2 au yr⁻¹. These speeds are slower than the Voyager speeds. The first, and slow, increase of the HP distance probably corresponds to the first increase in the ram-pressure from the first level to the second level, while the second, and fast, increase in the HP distance is due to the second increase in ram-pressure. It is interesting that the present V2 location, i.e., mid-2017 March, appears to be very near the HP, as shown in Figure 5. Because this moment corresponds to the critical period when the expansion speed of the HP changes from the first to the second step, it is not easy to predict precisely when V2 will cross the HP, but the crossing is likely to occur within a year.

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The time-dependent model (Figure 3) shows a decrease of V_R to near zero and less, starting ∼10 au before the HP. The decrease in V_R is a consequence of the complicated interaction and reflection of shocks and heliosheath flow with the HP. Such a low V_R region was observed before the V1–HP crossing and was in fact captured for the simulations presented here (plots of along the Sun–V1 line reveal a negative V_R in the IHS ahead of the HP; because of space, these are not presented here). Our simulations cannot capture all of the details observed by V2, but they indicate that the radial velocity in the vicinity of the HP is quite variable because of the incident GMIRs that are partially transmitted and partially reflected. The overall dynamic of the cumulative interactions of the time-dependent solar wind and the GMIRs with the HP provide an averaged effect that determines the location of the HP despite the lack of very detailed agreement with specific V2 observations. As illustrated in Figure 4, the time-averaged location of the HP is predicted to be close to the current location of V2.

We point out that the ram energy of the solar wind flow, both in the supersonic solar wind and in the IHS, dominates the energy in the magnetic field (and thermal component—the pressure), and it is this that determines primarily the location of the HP—the pressure of the magnetic field in the IHS is a minor effect. In fact, we find that the dominating magnetic field effect is contributed by the orientation of the LISM field, essentially accounting for the different distances to the HP along the Sun–V1 and Sun–V2 lines. We find that the HP distance does not depend greatly on the magnetic field intensity in the IHS. For these reasons, we believe that our HP location prediction should be essentially correct despite the inadequacies of the magnetic field modeling in the IHS.

The outer heliospheric structure and distance to the heliopause varies temporally on scales associated with long- and short-time solar activity. This Letter shows the variability explicitly by using a series of GMIRs as suggested by Voyager 2 observations of the distant solar-wind and ram-pressure observations at 1 au by OMNI.

We have modeled a series of GMIRs over a ∼30 year period, finding that it increases the plasma ram-pressure in the IHS, and at the same time it reduces the surrounding interstellar medium pressure acting on the heliopause. The estimated distance to the heliopause becomes ∼14 au larger. Recent OMNI observations show that the solar-wind ram-pressure started to increase from 2010. Our MHD simulation shows that the distance to the heliopause is increasing accordingly. However, the increasing distance to the heliopause was slower than the speed of Voyager 2, and our simulation shows that Voyager 2 is now very close to the heliopause. It is expected that the Voyager 2 crossing of the heliopause will occur soon, possibly within the year.

Numerical computations were performed using the Polar Science Computer System of the National Institute of Polar Research. We used solar-wind NASA OMNI data during years 2004–2015 and of the MIT V2 plasma experiment data during SC23. H.W. thanks Q. Hu and M. Tokumaru for discussions. G.P.Z. acknowledges the partial support of NASA grants NNX14AJ53G, NNX17AB04G, NNG05EC85C, and NNX16AG83G.