Xuepu Zhao sun.stanford/~xuepu Oct. 19, 2011

1. The Base of the Heliosphere:The Outer (Inner) Boundary Conditions of Coronal (Heliospheric) models Xuepu Zhao http://sun.stanford.edu/~xuepu Oct. 19, 2011

2. It was thought for decades that the heliopause extends in a long comet-like heliotail (left panel), but in 2009 data from the Cassini and IBEX show a different shape (right panel). Voyager 1 is expected to cross the heliopause by 2014.

3. 1. Introduction • The heliosphere is the immense magnetic bubble around the Sun. Its outer boundary, the heliospheric pause or heliopause, has been theoretically defined using the discontinuity between the outgoing solar wind and the incoming interstellar wind. The shape and location can be determined by the pressure balance between interstellar and solar winds (Axford, 1990) . • There is no theoretical definition of the inner boundary in the literature.

4. It has been shown that the success of MHD simulation of CME propagation in the inner heliosphere depends heavily on the initial and boundary conditions (Owens et al., 2008a), suggesting the importance of correctly determing the inner boundary and specifying the magnetic field and solar wind on the inner boundary. • I’ll show the mono-pole-like characteristics of the ambient radial HMF component, and define the heliobase and determine its shape and locationon on the basis of this mono-pole-like characteristics.

5. 2. Assumptions on Heliobase in literature In coronal (heliospheric) models, the heliobase, as a outer (inner) boundary of modeling domain, is often implicitly assumed to be a spherical surface located at various heliocentric distances based on different characteristics of plasma flow or/and magnetic field.

6. 2.1 In PFSS, the spherical source surface is assumed to be at 2.5 Rs where magnetic field radial and the plasma β becomes 0.03 as show in the following figure.

7. At cusp points around 2.5 Rs most of open field lines are not radial, approaching from higher to lower latitudes. Where should the source Surface be located??

8. 2.2 In heliospheric models, the inner boundary is usually set at ~21.5 Rs or 30 Rs, i.e., the transition from sub- to super-Alfvenic plasma flow is assumed to take place lower than ~21.5 Rs or 30Rs. 2.3 At the inner boundary of the heliospheric models, the magnetic field is extrapolated on the basis of the PFSS source-surface magnetic field, and the solar wind is obtained using HAN et al (1998) or WSA (2002) wind models.

9. The sonic critical points and Alfven critical points The lowest (highest) Alfven critical point occurs in the dipole equator (pole). The Alfven critical surface is not spherical

10. 3. Confirming mono-pole-like characteristics of ambient radial HMF • By using Alfven critical surface to define the heliospheric base separating super-Alfvenic solar wind from sub-Alfvenic coronal expansion, the heliospheric base must not be spherical and the magnetic field on the non-spherical surface must significantly differ from the source-surface field. • In situ observations of the HMF by Ulysses, STEREO & others have shown that the ambient radial HMF is definitely latitude-independent and probably longitude-independent (Owens..2008b).

11. To see if the ambient radial HMF is longitude-independent as well, we examine STEREO in situ observations from Jan. 2007 to 31 Oct. 2008 with longitude separation between A and B increasing from 0.5° to 80.6°. In order to obtain the ambient radial HMF component without dynamic effect,the hourly radial HMF component at various distances is first normalized to 1 AU and then averaged over 24 hours to smooth out the effects of large-amplitude Alfven fluctuations and various noise sources. Finally, the daily radial HMF components are running-averaged over one or three solar rotations to filter out he effects of stream-stream interaction and coronal mass ejections. The following figure shows the results. The thick blue line in the bottom panel show the difference between A and B.

13. 4. The Definition of Heliobase • Coronal magnetic field is multi-pole, as shown by the above figure, and heliospheric field is mono-pole-like, as confirmed here. • We use this different characteristics of magnetic field between the corona and the heliosphere to define the heliobase and to find out its shape and location.

14. 4.1 The shape of the heliobase It is well known that the spatial variation of mono-pole field depends only on 1/r². Thus the base where the global mono-pole-like HMF field is mapped back to or starts to occur must be a spherical interface. 4.2 The heliocentric distance of the heliobase The above figure shows that stream lines are bended from higher to lower latitude, and as heliocentric distance increases, stream lines approach radial individually .

15. The theory of coronal expansion has show that corona plasma pervaded by a frozen-in magnetic field, the stream lines coincide with magnetic field lines. To become solar wind, coronal expansion must pass continuously through three critical points associated with the sound, the Alfven speed, and the radial Alfven speed. Under the Alfven critical point, the magnetic stress dominates over the radial acceleration, and beyond the Alfven critical point, the radial expansion dominates magnetic stress, and final approaches radial at radial Alfven critical point. The heliocentric distances of the radial Alfven critical points are different for different field lines. The heliobase should be located at the farthest (highest) radial Alfven critical point.

16. As the heliocentric distance increases, the direction of each striation or ray becomes increasingly radial. Therefore, the latitudinal extent of coronal helmet streamer belts is expected to become smaller and smaller around the minimum phase, and the shape of streamer belts becomes is gradually flattening toward the equator. The heliocentric distance beyond which the shape of the streamer belts becomes height- independent should be an indication of the height beyond which all magnetic fields are purely radial. Following figures show the radial variation of streamer belts for CR1922, 1936 and 1947, i,e,, May 1997, May 1998, and March 1999.

17. Black curves are HCS calculated by HCCSSS model with a=0.2, Rcp=2.25 Rs Rss=14 Rs (Zhao & Hoeksema, 1995, 2002) May 1997

18. May 1998

19. May 1999

20. Comparison of HCSs calculated with Rss=2.50Rs (solid), (PFSS) 10.0Rs (dotted), (CSSS) 14.0Rs (dashed), (CSSS)

21. Latitude-independent Longitude-independent

22. 5. Conclusions • Confirming that ambient HMF is mono-pole-like in nature, which is significantly different from multi-pole coronal field. • Define the base of globally mono-pole-like field as the base of the heliosphere, where all stream lines bacome radial, i.e., the base of global super-Alfvenic radial solar wind. • The heliobase has been shown to be a spherical surface located at around 14 Rs.

23. Thank you !