An update of Owens et al. (2008) shows that the relationship between the coronal mass ejection (CME) rate and the heliospheric magnetic field strength predicts a field floor of less than 4 nT at 1 AU. This implies that the record low values measured during this solar minimum do not necessarily contradict the idea that open flux is conserved. The results are consistent with the hypothesis that CMEs add flux to the heliosphere and interchange reconnection between open flux and closed CME loops subtracts flux. An existing model embracing this hypothesis, however, overestimates flux during the current minimum, even though the CME rate has been low. The discrepancy calls for reasonable changes in model assumptions

Crooker, N. U.

Owens, M. J.

arXiv

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SOHO-23: Understanding a Peculiar Solar MinimumASP Conference Series, Vol. 428, c© 2010Steven R. Cranmer, J. Todd Hoeksema, and John L. Kohl, eds.Impact of Coronal Mass Ejections, InterchangeReconnection, and Disconnection on HeliosphericMagnetic Field StrengthN. U. CrookerCenter for Space Physics, Boston University, Boston, MA 02215, USAM. J. OwensSpace and Atmospheric Physics, Blackett Laboratory, Imperial College,London SW7 2AZ, UKAbstract. An update of Owens et al. (2008) shows that the relationshipbetween the coronal mass ejection (CME) rate and the heliospheric magneticfield strength predicts a field floor of less than 4 nT at 1 AU. This implies thatthe record low values measured during this solar minimum do not necessarilycontradict the idea that open flux is conserved. The results are consistent withthe hypothesis that CMEs add flux to the heliosphere and interchange recon-nection between open flux and closed CME loops subtracts flux. An existingmodel embracing this hypothesis, however, overestimates flux during the cur-rent minimum, even though the CME rate has been low. The discrepancy callsfor reasonable changes in model assumptions.1 IntroductionUsing an analytical, empirically-based model, Owens & Crooker (2006, 2007)demonstrated the feasibility of the idea that the rise and fall of magnetic fieldstrength in the heliosphere over the solar cycle could be caused solely by theaddition of closed magnetic loops from coronal mass ejections (CMEs) coupledwith a loss of flux through reconnection at the Sun. Either of two patterns ofreconnection can satisfy the constraints posed by observations of suprathermalelectrons, which can sense magnetic topology: (1) CME loops gradually open byinterchange reconnection with open field lines, or (2) open field lines of oppositepolarity reconnect, thus disconnecting flux from the Sun.The two options for flux loss through reconnection have different advan-tages. Option 1 is attractive because it restricts the rise and fall of field magni-tude to a single phenomenon, CMEs, and it conserves open flux, which serves asa backdrop. On the other hand, because option 2 calls upon a phenomenon sep-arate from CMEs for the loss of flux, that is, disconnection elsewhere, it has theflexibility of reducing the heliospheric flux to zero at solar minimum rather thanto some backdrop value. In view of the weakness of the heliospheric magneticfield strength during the present solar minimum, unprecedented in the ∼50-yearhistory of in situ measurements, we ask whether option 1 is still viable.A preliminary answer of “yes” to the question of option 1 viability wasprovided by Owens et al. (2008) using data through 5 July 2008. Since the279280 Crooker and OwensFigure 1. Updated plots of Carrington-Rotation-averaged data from Owenset al. (2008). Red (blue) points are from current (previous) solar minimum.Left: CME rate as function of time. Center, right: CME rate versus magneticfield strength at 1 AU. Solid curves are quadratic fits, with dashed curves at95% confidence intervals. Values in right panel are binned by CME rate.heliospheric field strength continued to drop after that date, this report updatesthe results of Owens et al. (2008) using data through 30 May 2009.2 AnalysisIf the rise and fall of heliospheric field strength is governed solely by the injec-tion of CME loops and the subsequent opening of those loops on time scales of40–50 days, as estimated by Owens & Crooker (2006), then the rate of injectionof CMEs should be proportional to magnetic field strength. The center panel ofFigure 1 shows this to be true in an update of the scatter plot of Carrington-Rotation averages of these parameters presented by Owens et al. (2008), wherethe most recent values are from the National Space Science Data Center’s OMNIdata set and STEREO data at http://cor1.gsfc.nasa.gov/catalog/. Al-though the correlation is fully expected, given the known solar cycle variationof the two parameters, there are two aspects of note. First, the relationshipbetween CME rate and field strength is nonlinear (fit with a quadratic curve),a point relevant to model development addressed in the next section. Second,for zero CME rate, the field strength has a finite value.The finite value of field strength for zero CME rate implies that the fieldhas a “floor” value (cf. Svalgaard and Cliver 2007). In the context of the Owens& Crooker (2006) model, this is the value it would reach during solar minimumif all the CME loops introduced during that cycle had opened by interchangereconnection and all that remained was the conserved open flux. According tothe smoothed plot in the right panel of Figure 1, the floor value is ∼3.7 nT. Thisis lower than the 4.0±0.3 nT found by Owens et al. (2008) owing to the additionof the most recent data points with lower values, but it is still considerablyabove zero. It seems unlikely that the curve in Figure 1 could steepen enoughto pass through the origin. Thus, the unprecedented low values of field strengthduring the current solar minimum period do not discount the possibility thatinterchange reconnection of CME loops is the means by which flux is reduced inthe heliosphere (option 1, above) and that open flux is conserved.CMEs and the Heliospheric Magnetic Field 2811994 1996 1998 2000 2002 2004 2006 2008456789|B| (nT)  Figure 2. Modeled (red) and observed (black) magnetic field strength at 1AU as function of time. Shaded intervals indicate gaps in CME rates used inmodel calculation (after Owens & Crooker 2006).3 DiscussionThe Owens & Crooker (2006) model implies that the reason the heliosphericfield strength did not come close to the deduced floor value in Figure 1 duringprevious solar minima is that CMEs continued to feed loops into the heliosphere,albeit at a reduced rate, throughout the minima periods. A look at the CME rateas a function of time in the left panel of Figure 1 confirms that CMEs occurredthroughout the two minima for which we have CME data. On the other hand,against expectations based upon the Owens & Crooker (2006) model, the rateduring the current minimum is only marginally lower and more extended thanin the previous minimum. This contrasts with the much more pronounced dipin field strength during the current minimum compared to the previous one, asshown by the black trace in Figure 2. The contrast is also apparent in the centerpanel of Figure 1, where the red points from the current minimum sit at a lowerlevel of field strength than the blue points from the previous minimum. Theimpact of these contrasting levels at solar minimum on the model is that themodel overestimates the field strength during the current minimum, as indicatedby the red trace in Figure 2. The overestimate begins as early as late 2005.The overestimate of magnetic flux from CMEs by the Owens & Crooker(2006) model for the current solar minimum may be owing to its assumption ofconstant magnetic flux per CME. Recent observations indicate a secular changein CME properties which may reflect a decrease in flux content. Compilers of theautomated “CACTUS” CME catalog (Robbrecht et al. 2009) noted that CMEsare slower and coming from weaker field regions during the current minimum(E. Robbrecht, private communication, 2009), and A. Vourlidas, (2009 SHINE282 Crooker and OwensWorkshop) reported a significant drop in mass density. It is conceivable thatCMEs with less mass and speed also have weaker magnetic fields.Aside from the issue of differences between the current and previous min-ima, the Owens & Crooker (2006) model needs to accommodate the quadraticrelationship between magnetic field strength and CME rate shown in Figure 1.The model relationship is linear owing to the combined assumptions of constantmagnetic flux per CME, discussed above, and a constant rate for the interchangereconnection that gradually opens the CME loops. Figure 1 implies that duringperiods of high CME rate, near solar maximum, each CME increases the fieldstrength by a lesser amount than during periods of low CME rate, near solarminimum. A possible reason for this pattern is that the interchange reconnec-tion which opens the loops occurs at a faster rate during solar maximum, whenthe solar magnetic field configuration is complicated and evolving rapidly com-pared to minimum. Changing the model rate of interchange reconnection fromconstant to a function of solar cycle should bring consistency with Figure 1.Finally, we add that the assumption of a constant rate of interchange re-connection may also be a factor in the overestimate of flux from CMEs by theOwens & Crooker (2006) model for the current solar minimum, in addition to theassumption of constant flux per CME. The configuration of the solar magneticfield during the declining phase of the solar cycle and into the current minimumwas more complicated than during the previous cycle, with higher-order fieldsdominating the pattern. This configuration may be more conducive to a higherrate of interchange reconnection and, hence, a faster rate of flux loss, comparedto the dipole-dominated pattern of the previous minimum.4 ConclusionsThe unprecedented low magnetic field strength in the heliosphere during thecurrent solar minimum does not eliminate the possibility that open flux is con-served. Nor does it render invalid the hypothesis that the heliospheric fieldstrength depends solely upon the rate of injection of loops from CMEs and therate those loops open by interchange reconnection. According to this view, thefield floor reflecting the background open flux is never reached during solar min-ima owing to a residual influx of CME loops. As modeled by Owens & Crooker(2006), however, the extended lower CME rate during the current minimum can-not fully account for the depressed field strength. Assumptions of constant fluxper CME and/or rate of interchange reconnection must be relaxed, as seemsreasonable owing to apparent changes in CME properties during the currentminimum.Acknowledgments. The authors thank O. C. St. Cyr for advance valuesof CME rates. This research was supported in part by the US National Sci-ence Foundation under grant ATM-0553397 and by NASA under grant NNG06-GC18G.ReferencesOwens, M. J., & Crooker, N. U. 2006, JGR, 111, A10104Owens, M. J., & Crooker, N. U. 2007, JGR, 112, A06106CMEs and the Heliospheric Magnetic Field 283Owens, M. J., Crooker, N. U., Schwadron, N. A., Horbury, T. S., Yashiro, S., Xie, H.,St. Cyr, O. C., & Gopalswamy, N. 2008, GRL, 35, L20108Robbrecht, E., Berghmans, D., & Van der Linden, R. A. M. 2009, ApJ, 691, 1222Svalgaard, L., & Cliver, E. W. 2007, ApJ, 661, L203

Impact of coronal mass ejections, interchange reconnection, and disconnection on heliospheric magnetic field strength

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