# Energy carried by solar wind

What are the velocity, mass, and charge distribution of the solar wind.

1. Near the earth within the magnetosphere in the ecliptic
2. Near the earth but outside the magnetosphere in the ecliptic
3. Outside the ecliptic at 1 AU

I would like to understand the energy content of the solar wind, and how it compares with the solar radiation(solar constant is $1360\, Wm^{-2}$)?

• It might be tough to find a precise answer as estimates to the mass of coronal mass ejections (CMEs) vary and the energy would be proportional to the amount of ejected material. I found this table with kinetic energy of some CMEs. spacemath.gsfc.nasa.gov/weekly/4Page17.pdf By comparison, the Sun emits about 3.8 x 10^26 joules per second, so the largest CME listed there is about 1/4 second of solar energy. Other than saying it's quite tiny, I wouldn't want to guess a percentage though. Jul 18 '16 at 0:06
• @userLTK Thanks for the nice link! It is my understanding that the solar wind is a relatively constant stream of particles, and that CMEs are "mere" fluctuations. I am interested in the constant stream. Even a rough annual average would do. Jul 18 '16 at 13:59

What are the velocity, mass, and charge distribution of the solar wind.

Velocity
The solar wind speed has a large range of variation, between ~250–820 km/s [e.g., Chen et al., 2014; Gopalswamy, 2006; Jian et al., 2011, 2014; Kasper et al., 2012; Maksimovic et al., 1998; Marsch, 1983; McComas et al., 2013; Schwenn, 1983; Stverak et al., 2008, 2009] near the ecliptic plane. These values are not including interplanetary shocks, which can have speeds exceeding 2000 km/s.

The speed is generally higher at higher latitudes out of the ecliptic plane, tending to be over 650 km/s [e.g., McComas et al., 2008; 2013].

Number Density
The number density also has a large range of values, from ~2–90 $cm^{-3}$ [e.g., Chen et al., 2014; Gopalswamy, 2006; Jian et al., 2011, 2014; Kasper et al., 2012; Maksimovic et al., 1998; Marsch, 1983; McComas et al., 2013; Schwenn, 1983; Stverak et al., 2008, 2009]. Again, these do not include interplanetary shocks or coronal mass ejections (CMEs).

Charge State
The alpha particle to proton number density ratio varies between ~1-5%, depending on solar cycle and solar wind speed [e.g., Kasper et al., 2012; Schwadron et al., 2014].

We have also measured the ratio of $O^{7+}/O^{6+}$ and $C^{6+}/C^{5+}$, finding ~1-30% and ~20-200%, respectively [e.g., Schwadron et al., 2014].

Near the earth within the magnetosphere in the ecliptic

The properties of the terrestrial magnetosphere vary so widely, you would need to narrow down this question. For instance, the charge states are completely different (e.g., we observe $O^{1+}$ but not $O^{7+}$) but the number densities range from ~$10^{-2}-10^{3} \ cm^{-3}$.

Near the earth but outside the magnetosphere in the ecliptic

See responses above to first part.

Outside the ecliptic at 1 AU

We don't have any measurements near 1 AU that are at high latitudes. Some spacecraft have done out of ecliptic polar orbits with high apogees, but the heliocentric latitudes were still within ~$10^{\circ}$ of the ecliptic plane. The notes above discuss our only real measurements out of the ecliptic by the Ulysses spacecraft.

I would like to understand the energy content of the solar wind, and how it compares with the solar radiation(solar constant is 1360 W $m^{-2}$?

The solar wind ram(dynamic) pressure is typically only ~1 nPa or $10^{-9} \ J \ m^{-3}$. This is highly variable and can change in milliseconds (e.g., interplanetary shocks), but that would still only be $10^{-6} \ W \ m^{-3}$. If we make a hand-wavy argument that this drops to zero in ~3 $R_{E}$ (i.e., upper bound on thickness of magnetosheath), then the power per unit area can be up to ~20 W $m^{-2}$. However, I would not read too much into that number as the actual power dissipated per unit area is different for numerous reasons.

# References

• C.H.K. Chen et al., Geophys. Res. Lett. 41, pp. 8081, 2014.
• N. Gopalswamy, Space Sci. Rev. 124, pp. 145, 2006.
• L.K. Jian et al., Solar Phys. 274, pp. 321, 2011.
• L.K. Jian et al., Astrophys. J. 786, pp. 123, 2014.
• J. C. Kasper et al., Astrophys. J. 745, pp. 162, 2012.
• M. Maksimovic et al., Geophys. Res. Lett. 25, pp. 1265, 1998.
• E. Marsch, Fifth International Solar Wind Conference 228, pp. 355, 1983.
• D.J. McComas et al., Geophys. Res. Lett. 35, pp. L18103, 2008.
• D.J. McComas et al., Astrophys. J. 779, pp. 2, 2013.
• N.A. Schwadron et al., J. Geophys. Res. 119, pp. 1486-1492, 2014.
• R. Schwenn, Fifth International Solar Wind Conference 228, pp. 489, 1983.
• v. Stverak et al., J. Geophys. Res. 113, pp. 3103, 2008.
• v. Stverak et al., J. Geophys. Res. 114, pp. 5104, 2009.

I'm not sure such a detailed answer to your question is available.

1. This book cites this paper as a source for the mass loss due to the solar wind:

$$\dot{M} \sim 2.5 \times 10^{-14}\,M_\odot/yr$$.

This book cites this paper as the source for the following data at 1 AU:

1. Kinetic energy density of the solar wind:

$$\frac{1}{2}N_\mathrm{p}m_\mathrm{p}v^2 = 1.44 \pm 0.09 \times 10^{-8}\,$$erg cm$$^{-3}$$.

2. Thermal energy density for protons, electrons and helium atoms:

$$\frac{3}{2} N k T \approx 4.8 \pm 3.2 \times 10^{-10}\,$$erg cm$$^{-3}$$.

3. Wind velocity:

$$v_\mathrm{w} = 468 \pm 116\,$$km s$$^{-1}$$.

The numbers in 2. and 3. indicate that the thermal energy contributes for about 3%, and can be ignored given the uncertainties involved. Using 1. and 4. we get a kinetic 'wind luminosity' of

$$~~~ L_\mathrm{w} \approx \frac{1}{2} \dot{M} v_\mathrm{w}^2 \approx 1.7 \times 10^{27}\,$$erg s$$^{-1} \approx 4.5 \times 10^{-7} L_\odot.$$