The Effect of Magnetic Variability on Stellar Angular Momentum Loss I: The Solar Wind Torque During Sunspot Cycles 23 & 24
Summary (2 min read)
1. INTRODUCTION
- Angular momentum loss through stellar winds explains the rotational evolution of low mass stars (M∗ ≤ 1.3M ) on the main sequence.
- This allows, for the first time, a more continuous calculation of the angular momentum loss rate.
- Using the multitude of current observations of the Sun (this work), and multi-epoch studies of other stars from the ZDI community (Paper II), the authors can now evaluate the variation of stellar wind torques over decadal timescales.
2. SEMI-ANALYTIC TORQUE FORMULATIONS
- FM18 provides semi-analytic prescriptions for the angular momentum loss rate based on over 160 stellar wind simulations using the PLUTO magnetohydrodynamics (MHD) code (Mignone et al. 2007; Mignone 2009).
- As discussed in Pantolmos & Matt (2017) variations in the chosen wind speed, i.e. a wind comprised of all slow or all fast wind, differ by a factor of ∼ 2 in the predicted torque.
- For this work, the authors adopt the parameters derived originally in FM18, with a temperature between the extremes (see Pantolmos & Matt 2017), and accept potential discrepancies in the wind acceleration over the solar cycle.
- 2. Formulation Using Open Magnetic Flux Réville et al. (2015a) show that by parametrising the relationship for the average Alfvén radius in terms of the open magnetic flux, φopen, a scaling behaviour independent of magnetic geometry can be formulated.
- The simplicity of the semi-analytic derivation for the open flux torque formulation (see Pantolmos & Matt 2017) suggests that this method produces the most reliable torque for a given estimate of the open flux.
3. OBSERVED SOLAR WIND PARAMETERS
- Information regarding the magnetic properties of the Sun are used here in two forms.
- Measurements of the solar wind speed and density are also made in-situ by multiple spacecrafts, but here the authors focus on results from Ulysses and ACE.
- During the 22 years this averages to removing ∼ 1% of the data from each 27-day bin.
- This process produces complex coefficients αlm, which weight each of the spherical harmonic modes, Br(θ, φ) = l=lmax∑ l=0 m=l∑ m=−l αlmY l m(θ, φ), (7) where θ and φ represent the co-latitude and longitude of the magnetograms respectively.
- 2. Mass Loss Rates and Magnetic Open Flux Variability From ACE/Ulysses.
4. EVALUATING THE SOLAR WIND ANGULAR MOMENTUM LOSS RATE
- Here the authors consider three methods for determining the angular momentum loss in the solar wind.
- The authors aim to characterise any difference between these torque predictions, and attempt to determine the most accurate estimate of the solar wind torque and its variability.
- The average torque predicted using the open flux method is 2.28 × 1030erg, which is 3.26 times greater than the surface field method in the previous section.
- Shown in both the observations from ACE and Ulysses.
5. DISCUSSION
- Using the torque formulations from FM18, the value of the solar wind torque is shown to be lower than the empirical estimate based on the rotation of other Sunlike stars.
- The authors also find a disagreement between the two predictions from FM18, using either the surface or open flux method for calculating the torque.
- It is therefore generally accepted that magnetograms require multiplication by an uncertain factor or the inclusion of additional magnetic flux (typically coronal mass ejections or small scale surface fields) in order to bring observations in-line with the extrapolated field strength at 1AU (Wang 1993; Zhao & Hoeksema 1995; Cohen et al.
- Torques derived using stellar magnetic field observations and equation (3) may be lower than in actuality, due to the FM18 model producing a smaller value of unsigned open flux than measured in the solar wind.
6. CONCLUSION
- In this work the authors have utilised the wealth of current solar observations and the semi-analytic results from FM18 to produce an estimate of the current solar wind torque.
- The authors thank the ACE MAG and SWEPAM instrument teams and the ACE Science Center for providing the ACE data.
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"The Effect of Magnetic Variability ..." refers methods in this paper
...Figures within this work are produced using the python package matplotlib (Hunter 2007)....
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"The Effect of Magnetic Variability ..." refers background in this paper
...…= 6.2× 1030 erg ( I 6.90× 1053 g cm2 ) × ( Ω 2.6× 10−6 rad/s )( 4.55 Gyr t )( 2 p ) , (13) where we have input fiducial values for the solar moment of inertia (Baraffe et al. 2015), representative rotation rate (Snodgrass & Ulrich 1990), age (Guenther 1989), and p. Appendix B discusses the…...
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...…transport, it is worth noting that even in the most extreme case where the convective envelope is completely decoupled from the radiation zone implies a lower limit of 7.0×1029 erg (calculated by putting the moment of inertia of the convective zone from Baraffe et al. (2015) into equation (13))....
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...The assumption of constant moment of inertia is correct to better than 2%, for solar-mass stars in the age range from 600 Myr to that of the Sun (Baraffe et al. 2015)....
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"The Effect of Magnetic Variability ..." refers background in this paper
...This is routinely observed for the Sun which is known to have a magnetic activity cycle (Babcock 1961; Wilcox & Scherrer 1972; Willson & Hudson 1991; Guedel et al. 1997; Güdel 2007; Schrijver & Liu 2008), moving from an activity maximum through minimum and back to maximum in roughly 11 years....
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Frequently Asked Questions (15)
Q2. What future works have the authors mentioned in the paper "The effect of magnetic variability on stellar angular momentum loss i: the solar wind torque during sunspot cycles 23 & 24" ?
The authors need additional information to discriminate between these possibilities. The required variability of ( a ) suggests the authors should observe stars like the Sun that are on average significantly more active ( i. e., that they have larger torques ) such that the average is correct. From the dynamical models, ( b ), uncertainties remain in the wind acceleration and effects of non-axisymmetric field components which both require further study to disentangle. Using the FM18 formula, predictions of the angular momentum loss rates for these stars based on their surface measurements may be smaller than in reality.
Q3. What is the reason for the differences in the modelled torque?
As the mass loss rate is typically evolved self consistently in these models, differences in the modelled torque value is often due to discrepant mass loss rates when compared to observations (as this is a challenging problem).
Q4. What is the way to measure the wind properties of distant stars?
In order to gain information about the mass loss rate and wind properties of these distant stars, the authors rely on proxies such as the strength of Lyman-α absorption at their astropauses (Wood 2004) and more recently the observed erosion of exoplanet atmospheres (Vidotto et al. 2011; Vidotto & Bourrier 2017).
Q5. What is the impact of the wind temperature on the torque formulas?
In general, variability in thewind temperature over the cycle will affect both torque formulas from FM18 and so represents an uncertainty on their results, i.e. for a fixed Ṁ , a faster wind will open more flux with a weaker resulting torque.
Q6. How many different observations can lead to the estimation of the angular momentum loss?
Magnetic variability can lead to estimates of the angular momentum loss which are, in the solar case, up to a factor of ∼ 10 different from one observation to another.
Q7. What is the PLUTO code used to generate a torque in the bottom panel of Figure?
The PLUTO code is used to construct 3D wind solutions for each WSO magnetogram, this produces global values for the mass loss rate and open magnetic flux (Réville, private communication), which are used to generate a torque in the bottom panel of Figure 1.
Q8. What is the effect of the long-term variability on the predictions of the stellar wind torques?
3. Long-time variability may also play a role, and with the difficultly ascertaining the true magnetic behaviour of other Sun-stars, i.e. if they are cyclic or stochastic, the corresponding estimate of their angular momentum loss rate may be discrepant from rotation evolution model predictions.
Q9. What is the impact of the non-axisymmetric components on the solar torque?
In their calculation of the solar torque, based on surface magnetogram observations, the authors include the strength of the non-axisymmetric components through equation (8)which adds the components in quadrature to produce a combined strength for each mode l.
Q10. How did the authors determine the impact of the non-axisymmetric components?
In order to assess the impact of including the nonaxisymmetric components with equation (8), the authors performed the torque analysis using both, only the axisymmetric components, and the combined strength approach of equation (8).
Q11. What is the average of the Alfvén radii predicted from the open flux method?
The averages of the Alfvén radii predicted from the open flux method are nearly constant between cycles, but as cycle 24 is currently moving into a minimum the average is expected to move lower as it becomes complete.
Q12. What is the reason for the difference in the dynamical torque estimates for the current Sun?
Differences in the dynamical torque estimates for the current Sun and the long-time-average value may then be due to magnetic variation on longer timescales than the 22 year magnetic cycle.
Q13. What is the torque controlled by the combined dipole field strength?
The torque calculated in Section 4.1 is controlled largely by the combined dipole field strength, which appears to be out of phase with solar activity, displayed in the top left panel of Figure 1 (note the use of absolute magnitude field strengths).
Q14. What is the difference between the present-day torques and the spin-evolution torques?
Differences in the average present-day torques to the spin-evolution torques, could be due to, (a) variability on a longer timescale than probed by the presentday variability presented here (but less than a spin-down time), (b) errors in using the dynamical models inferring present-day torque, or (c) that stars spin-down significantly different than Skumanich at ages of a few to several Gyr.
Q15. What is the effect of the angular momentum loss rate on the observations of other stars?
Observations of other Sunlike stars will therefore suffer from considerable uncertainty in their derived angular momentum loss rates based on a single or small number of observations.