lecture7.2Astronomy 217 T h e I n f l u e n c e o f
t h e S u n
Solar Dominance In virtually all ways, the Sun dominates the solar system.
In mass, the Sun’s 1.99 × 1030 kg represents 99.8% of the mass in the solar system.
The gas giants; Jupiter (1.90 × 1027 kg), Saturn (5.68 × 1026 kg), Uranus (8.68 × 1025 kg) & Neptune (1.02 × 1026 kg), make up the bulk of the rest.
The Earth, at 5.97 × 1024 kg, is the most massive of the rocky planets, only 3/1,000,000 M.
Barycenter Because of Newton’s 3rd law, FSun→Planet = FPlanet→Sun, a careful derivation of Kepler’s laws reveals that both planet and Sun follow ellipses around the center of mass or barycenter.
Because M is >99.8% of the total mass of the solar system, the barycenter of the solar system lies quite close to the Sun.
For example, the center of mass of the Sun-Jupiter system lies 1.07 R from the center of the Sun. Even all of the planets in alignment, would offset the barycenter only 2.08 R.
3 > 53 ) , * 4
// > 22 , 33 , 2 , 3 ,
Solar Tides In the inner solar system, the Sun’s dominant mass leads to it providing a significant tidal force.
However, for the Earth, with its large Moon, the Sun is secondary.
For the large moons of the outer solar system, Saturn’s Titan and the Galilean moons of Jupiter (Io, Europa, Ganymede & Callisto) whose masses and lunar orbits are comparable to Earth’s Moon, the larger planetary orbits, aJ = 5.2 AU and aS = 9.5 AU result in more dominant lunar tides.
) * > 3 4
> 1 4 > 3/38
The Sun’s Luminosity is the most significant energy source in the solar system.
Each square meter at the Earth’s orbit collects 1400 W/m2, the solar constant.
Multiply by the area facing the Sun (πR⊕2), the total energy striking the earth is ~1.8 × 1017 W, though only ~70% is absorbed.
This is much larger than energy provided by tides (~1012 W).
Measuring neutrinos escaping from the Earth has recently shown that radioactive decay contributes 1.6 × 1013 W.
Light = Heat
Angular Momentum Surprisingly, the Sun’s angular momentum is a small fraction of the solar system total.
=1.0 × 1036 kg m2 s−1
In comparison, the orbital angular momentum of Jupiter is
M =3 × 1030 kg R = 7 × 105 m Prot ~ 28 days
MJ =1.9 × 1027 kg aJ = 5.2 AU Porb ~ 11.9 yr e = 0.048
=1.9 × 1037 kg m2 s−1
Lorb of the other gas giants are similar, thus Lrot, is only ~2% of the solar system’s total angular momentum.
- > > 36 3 3
- > > 3 3 2 3
Observations of the corona reveal a wealth of lines of species not seen elsewhere in the solar spectrum.
These lines came from highly ionized species, e.g. Fe15+, Si11+, Ca9+, Mg7+, etc., indicating the the corona is much hotter than layers below.
Suggestions for the heat source include photospheric sound waves and magnetically induced currents.
Coronal Heating
Mg7+ Fe12+
Too Hot to Hold Temperatures of millions of K at large radii from the Sun’s center is a recipe for escape.
An average thermal velocity is given by
for protons. This compares to the escape velocity
The high-energy tail of the coronal gas is free to escape, forming the solar wind.
23 3 > 43 > 4 23 271 LN T2 217 ,
23
Maxwell-Boltzmann Velocity Distrbution
)
1E-19
1E-17
1E-15
1E-13
1E-11
1E-09
0E+00 1E+05 2E+05 3E+05 4E+05 5E+05 6E+05 7E+05
T = 106 K T = 2 ×106 K
Solar corona changes with time as the photosphere and chromosphere change. For example, the corona changes along with sunspot cycle; it is much larger and more irregular at sunspot peak.
The Active corona
Maximum
Minimum
In general, closed magnetic field lines help keep the gas from escaping. Open field lines, however, enable particle escape.
Because gas is escaping, the parts of the corona through which these concentrations of open field lines pass are colder, darker, and lower-density than average, thus they are called coronal holes.
The high velocity component ( ~ 800 km/s) of the solar wind escapes along open field lines through these coronal holes.
Coronal Holes
Coronal holes are not the only source of the solar wind. Prominence and filaments, magnetic loops with trapped plasma as much as 100,000 km long, can also release burst of gas forming the low velocity component ( ~ 400 km/ s) of the solar wind.
Prominences
Coronal Mass Ejection When magnetic field lines “cross”, reconnection can occur, releasing energy and creating closed field loops. When a prominence experiences reconnection, a coronal mass ejection occurs, releasing a dense, high velocity cloud of gas.
1013 kg , 1024 J
Solar flare is a large explosion in the chromosphere, lasting minutes, emitting 1025J, mostly as UV, X-rays and γ-rays.
These are likely also powered by magnetic reconnection.
Solar Flares
Solar Mass Loss By picturing the solar wind as a thin expanding spherical shell, you can calculate the rate of mass loss.
The time rate of change is
which becomes
or, in the limit Δt → 0,
On Earth (r = a⊕), the solar wind is measured to have ~ 400 km s−1 and ρ ~ 10−21 kg m−3.
~ 108 kg s−1 ~ 10−14 M yr-1 ~ 10−5 M Gyr−1
or
~ 1014 yr
> 53 > 53 > 53
> 53 )* > 53
> At this rate, the Sun will evaporate in
LWind The solar wind, in addition to carrying of mass from the Sun, also carries angular momentum.
Could this be the way the Sun lost it’s angular momentum?
The timescale for the Sun to lose significant angular momentum is
Since dM/dt = 10−14 M yr−1, τL ≈ 4 × 1013 yr ~ τM
This is much longer than the Sun’s age, t = 5 × 109 yr.
- > 3
> - 2 > 3063 32
Magnetic Coupling Neutral gas would decouple from the Sun at the surface, hence
Plasma remains coupled the the Sun magnetic field, until the Alfvén radius, rA, where the wind’s kinetic energy equals the magnetic energy.
Magnetic Flux is conserved, thus 4πr2B(r) = 4πR 2B
=
= at rA
)*3 31 > 331
5 23 )*3 > 23 53 3 >
93 >
5331 203
Magnetic braking For the Sun, dM/dt = 10−14 M yr−1, ~ 400 km s−1 and B ~ 10−3 T,
≈ 140
Thus
With this much larger rate of loss of angular momentum, the timescale for angular momentum loss decreases.
τL ≈ 4 × 1013 yr /1402 = 2 × 109 yr
Thus the magnetized solar wind has significantly reduced the Sun’s angular momentum.
< t = 5 × 109 yr
203
- > 3 2513 3
Next Time