Solar Angular Momentum Loss Over the Past Several Millennia
Summary (4 min read)
- The observed rotation periods of most low-mass stars (M*1.3Me) on the main sequence can be explained by their magnetized stellar winds.
- The resulting strong dependence of torque on rotation rate leads to a convergence of rotation periods with age, as initially fast rotating stars generate strong magnetic fields and experience a larger braking torque than the initially slowly rotating stars.
- The authors employ reconstructions of solar wind properties from the literature, in order to estimate the solar wind torque further back in time than has been probed so far (more than two orders of magnitude).
- Braking law, hereafter FM18, in Section 2.
2. Angular Momentum Loss Formulation
- Considering a steady MHD flow, along a one-dimensional magnetic flux tube, mass and magnetic flux are conserved.
- The simulations of FM18, from which the authors derived Equations (6) and (7), correspond to a base wind temperature of ∼1.7 MK, which sits at the lower edge of this temperature range (where the torques are strongest).
3.1. Observed Solar Wind Properties
- Hourly near-Earth solar wind plasma and magnetic field measurements are available from the OMNIWeb service.
- The OMNI data set is compiled from the in situ observations of 4 https://omniweb.gsfc.nasa.gov/.
- The 27 day averages are shown with circles that are colored according to the different sunspot cycles in their data set.
- The open magnetic flux roughly declines in time over the past three cycles, with the current sunspot cycle hosting some of the weakest values recorded in the OMNI data set.
- Equation (9) assumes the mass flux evaluated at a single observing location in the solar wind is representative of all latitudes when averaged over 27 days.
3.2. Coronal Mass Ejections
- Equations (8) and (9) do not take into account the effects of coronal mass ejections (CMEs) in the data.
- These appear as impulsive changes (generally increases) in the observed solar wind properties, and clearly violate the assumed isotropy of wind conditions in Equations (8) and (9).
- Previous authors have removed these events through the use of CME catalogs (Cane & Richardson 2003) or clipping anomalous spikes (Cohen 2011).
- CMEs carry only a few percent of the total solar mass-loss rate (Cranmer et al. 2017), however, at solar maximum they can provide a significant fraction of the average mass flux in the equatorial solar wind (Webb & Howard 1994).
- They determined that the average open magnetic flux and mass-loss rate, over their ∼20 yr of data, decreased by ∼4% after these cuts were applied.
3.3. Decades of Solar Wind Torque
- The authors use the open magnetic flux and mass-loss rate estimates from Section 3.1 to compute the angular momentum loss rate in The Astrophysical Journal, 883:67 (9pp), 2019 September 20 Finley et al. the solar wind using Equation (7).
- The results from this calculation are shown in the bottom panel of Figure 1.
- The authors calculate the average torque on the Sun during the space age to be 2.97×1030 erg, which is larger than the value obtained by Finley et al. (2018) of 2.3×1030 erg, due to the fact that Finley et al. (2018) only examined the past ∼20 yr.
- Averaging over each individual sunspot cycle, the authors find values of 2.67×1030 erg, 3.66×1030 erg, 3.70×1030 erg, 2.69× 1030 erg, and 2.06×1030 erg, for cycles 20–24, respectively.
- From the in situ measurements of Pizzo et al. (1983) using the Helios spacecraft, to the recalculation of Li (1999) based on data from the Ulysses spacecraft.
4. Solar Wind Torque on Centennial and Millennial Timescales
- Up until now, the authors have examined only direct measurements of the solar wind.
- These observations have been facilitated by the exploration of near-Earth space, which began a few decades ago.
- These indirect measurements have limitations.
- In terms of the open magnetic flux, which is constructed using the range of observed values from Section 3.1.the authors.
4.1. Estimating the Mass-loss Rate, and Wind Torque with the Open Magnetic Flux
- Predicting the mass-loss rates for low-mass stars, such as the Sun, is a difficult challenge, which has been attempted by previous authors to varying success (Reimers 1975, 1977; Mullan 1978; Schröder & Cuntz 2005; Cranmer & Saar 2011; Cranmer et al. 2017).
- There is a large scatter around the fit of Equation (10), which the authors wish to propagate through their calculation.
- The authors show the 2σ limits of a log-Gaussian function, centered on the fit, with red dashed lines.
- When the authors estimate the mass-loss rate for the historical estimates of the open magnetic flux in Sections 4.3, they will use both Equation (10) and the 2σ bounds.
- This allows us to predict the torque on the Sun due to the solar wind solely from the value of the open magnetic flux.
4.2. Reconstructions of the Solar Open Magnetic Flux
- For the centuries and millennia pre-dating the space age, estimates of the open magnetic flux have been produced using a number of different indirect methods.
- To compare them with indirect methods and over a wide range of timescales, the authors plot the spacecraft data from Figure 1 also in Figure 3, which displays the solar wind parameters versus logarithmic look-back time since 2019.
4.2.1. Centennial Variability
- Geomagnetic disturbances, caused by the interaction of the solar wind and the Earth’s magnetosphere, have been found to The Astrophysical Journal, 883:67 (9pp), 2019 September 20 Finley et al. correlate well with solar activity, and thus the amount of open magnetic flux in the heliosphere (Stamper et al.
- It has been noted that during the last century the open magnetic flux has been at a sustained high with respect to the longer data set (Lockwood et al. 2009).
- The 2σ bound from the torque prediction, shown by red dashed lines, indicates a weak dependence of solar wind torque on the assumed mass-loss rate.
- Therefore, provided the 5 However, the additional complications did not statistically improve their Ṁ predictions.
4.2.2. Millennial Variability
- To go back further the open magnetic flux can only be reconstructed using cosmogenic radionuclides.
- Cosmogenic radionuclides, such as 14C and 10Be, are produced as a byproduct of the interaction of galactic cosmic rays and the Earth’s atmosphere.
- These smoothed values are plotted with dotted and dashed lines, respectively, in the top panel of Figure 3.
- It is worth noting that the authors have no physical justification for applying this linear shift to the reconstruction, which could introduce some systematic error.
- Examining all the values of open magnetic flux collected in Figure 3, the variability of the solar magnetic field appears to have a similar behavior across a range of timescales.
4.3. Centuries and Millennia of Solar Wind Torque
- To evaluate the solar wind torque during the last four centuries the authors use the open magnetic flux from Owens et al. (2017b).
- In Figure 3, the authors plot the mass-loss rate using Equation (10) and the resulting torque using Equation (11) with solid purple lines, and the 2σ bounds with dashed red lines.
- This is because the last four centuries also include multiple minima in solar activity, which host lower than average torques.
- Perhaps the most notable is the Maunder minimum (which spans the years 1640–1720), which has an average torque of 0.67×1030 erg.
- The authors find the solar wind torque during these activity minima have average values that span 0.62–1.73×1030 erg, in contrast to the activity maxima that have much larger average values ranging from 2.44 to 3.87×1030 erg.
- The authors explore potential caveats to their results, and then compare their torques to those prescribed by models of the rotation period evolution of Sun-like stars.
5.1. Reliability of Open Flux Proxies and Our Predicted Mass-loss Rates
- Indirect reconstructions of the solar open magnetic flux are by no means certain, and require careful examination and calibration.
- The interpretation of geomagnetic records as a proxy for open magnetic flux appears robust, at least for times where direct measurements are available for comparison .
- Sunspot number records, from which their centennial torque is ultimately generated, often suffer from historical periods that are incomplete or uncertain due to a lack of reliable observers (Vaquero et al.
- The fact that the various proxies agree with each other where they overlap is because they were calibrated to do so.
5.2. Impacts of Magnetic Variability on Short Timescales
- Reconstructions of solar activity based on the concentrations of cosmogenic radionuclides incur smoothing effects from the transport and deposition timescales of each radionuclide.
- Therefore, such records struggle to recover short timescales variability, such as the 11 yr sunspot cycle.
- Typically, this can be thought of as averaging the activity of the Sun over decadal timescales.
- The significance of this effect over the complete nine millennia can be probed in a few ways.
- By comparing the average torques from the smoothed reconstructions of Lockwood et al. (2014a) and Owens et al. (2017b) to their original data sets, the authors find the original data sets have a larger torque by ∼4% than their smoothed counterparts; a result of the nonlinearity of the torque on open magnetic flux.
5.3. Comparison to Rotation–evolution Torques
- One motivation for the present work was the finding of Finley et al. (2018), that the solar wind torque is less than that predicted by a Skumanich (1972) relation (a value of 6.2× 1030 erg).
- One possible solution to this is that the torque varies on a longer timescale than the ∼20 yr examined in that work.
- If the solar wind torque does indeed vary significantly on longer timescales than probed here, it suggests that the presentday wind torques of other stars should scatter (by at least a factor of ∼3) around the torque predicted by rotation–evolution models.
- If long-term variability in the angular momentum loss rate of Sun-like stars does not resolve this discrepancy, then it could indicate systematic errors in the wind models, or the observed wind parameters, although the origins of such errors are unclear.
- In this paper the authors have investigated the angular momentum loss rate of the Sun on a longer timescale than previously attempted.
- The average torque during grand maxima ranges from 2.4 to 3.9×1030 erg, with peaks of ∼5×1030 erg.
- The authors thank the many instrument teams whose data contributed to the OMNI data set, and the NASA/GSFC’s Space Physics Data Facility’s OMNIWeb service for providing this data.
- For the solar angular momentum loss rate generated using Equation (11) and the open magnetic flux reconstructions of Owens & Lockwood (2012) and Wu et al. (2018b), centennial and millennial-scale reconstructions, respectively, the authors list in Table 1 the average values during historical grand maxima and minima in solar activity.
- Sean P. Matt https://orcid.org/0000-0001-9590-2274.
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"Solar Angular Momentum Loss Over th..." refers methods in this paper
...MO is funded by Science and Technology Facilities Council (STFC) grant numbers ST/M000885/1 and ST/R000921/1 Figures in this work are produced using the python package matplotlib (Hunter 2007)....
"Solar Angular Momentum Loss Over th..." refers background in this paper
...…is the mass loss rate, Ω∗ is the stellar rotation rate, R∗ is the stellar radius, and 〈RA〉/R∗ can be thought of as an efficiency factor for the angular momentum loss rate which, under the assumption of ideal steady-state MHD, scales as the average Alfvén radius (Weber & Davis 1967; Mestel 1968)....
...…the dynamo mechanism) is strongly linked with rotation (Brun & Browning 2017), and the strength of the magnetic field is found to influence the efficiency of angular momentum transfer through the stellar wind (Weber & Davis 1967; Mestel 1968; Kawaler 1988; Matt et al. 2012; Garraffo et al. 2015)....
"Solar Angular Momentum Loss Over th..." refers background in this paper
...Furthermore, linking these results to the open magnetic flux requires careful calibration (e.g. Usoskin et al. 2003; Solanki et al. 2004)....
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