How Dim Can the Sun Be?
Philip R. Goode
Big Bear Solar Observatory
New Jersey Institute of Technology
The Sun’s Irradiance & Earth’s
Albedo ⇔ Climate Heat Engine
Net solar power reaching Earth
in
2
PEarth
= CSunπ REarth
(1 − A)
and re-radiated to space
out
2
4
in
PEarth
= 4π REarth
σε TEarth
= PEarth
Fractional Change in net to Earth
in
δ PEarth
in
Earth
P
=
δ CSun
CSun
−
δA
1− Α
-Global and seasonal average is A ~ 0.30
-Shortwave input (visible, 0.5 µ m, 6000 K)
-Longwave output (IR, 15 µ m, 255 K)
Big Bear Solar Observatory
15 January 2004
The Sun’s Irradiance Variations
are Small, but Hard to Explain
Big Bear Solar Observatory
15 January 2004
Sunspot Number
ƒ Sunspot number 1620 –
2000
Big Bear Solar Observatory
15 January 2004
Earthshine
ƒ Net Sunlight
Reaching Earth
Drives the Climate
ƒ About 30% of
Incident Sunlight
Reflected by Our
Blue Earth
ƒ Origin of
Earthshine First
Explained by
DaVinci
Big Bear Solar Observatory
15 January 2004
The Solar Cycle Changes in the
Sun – Is the Sun Hotter at Max?
ƒ Naively, luminosity varies like irradiance and the Sun is a
blackbody. Then, allowed size of the changes in the Sun’s
output
∆L 4 ∆ T 2 ∆ R
=
+
L
T
R
-In truth, we have cast the Sun’s changing magnetic field,
and resultant thermal structure and turbulent velocity
changes as temperature changes.
- Probing the role of the changing solar radius leads us out
of the wilderness, but first deeper into the wilderness.
ƒ Principal Collaborator:
-Wojtek Dziembowski, University of Warsaw
(new results here from Jan. 1, 2004 paper in ApJ)
Big Bear Solar Observatory
15 January 2004
Normal Modes of the Sun
( ν n ,l ∝ 2 n + l + ε )
n =1
n=0
Big Bear Solar Observatory
15 January 2004
Oscillation Frequencies Increase
with Increasing Activity
ƒ Goldreich et al. (1991) showed increasing near
surface, isotropic, random field could account for the
frequency changes of p-modes. Problem is rms field
growing by 250 G at photosphere is required,
whereas data say field from min. to max. grows by
about 50 G.
ƒ Dynamical changes driven by magnetic pressure, so
the field’s effect is an order of magnitude too large.
ƒ Forced to ad hoc solutions assuming changes driven
by the field are arbitrary.
Big Bear Solar Observatory
15 January 2004
f-mode Data Provide Critical Clue
ƒ f-modes are, asymptotically, surface waves
characterized by horizontal flows near the
surface, whereas p-modes confined to cavity.
ƒ f-modes from MDI data (l=100-300) confined
to band 5-10 Mm beneath the visible sun.
ƒ Response of band to growing activity is the
key.
Big Bear Solar Observatory
15 January 2004
Helioseismic Radius Using MDI
f-modes
ƒ ωl2≈l(l+1)GMs/Rl3 : Asymptotically surface waves,
but f-modes see different effective gravities –
depending on l .
ƒ ∆ν l /ν l=-3/2 ∆Rs/Rs : ∆ means model value minus
true value.
ƒ From this, Schou et al. (1997) determined Rs=
695.68±0.03 Mm.
ƒ Rate of Shrinking from f-modes follows from
∆ minν l
νl
3 ∆ min R f ∆ minγ f
=−
+
2 Rf
ν l Il
Big Bear Solar Observatory
15 January 2004
Evolution of f-mode Radius
ƒ With γ:
dRf/dt = -1.51±0.31 km/y
ƒ Without γ:
dRf/dt = -1.82±0.64 km/y
ƒ Results imply at a depth of 610 Mm, the sun shrank by
some 5 km during the rising
phase of this activity cycle
ƒ dγf/dt= 0.180±0.051 µHz/y,
noisy with some cross-talk
ƒ As small as it is, a shrinking
sun is not easy to explain
Big Bear Solar Observatory
15 January 2004
Variations in the Solar Radius
from Space
ƒ Emilio et al. (2000)
MDI limb observations:
annual radius increase
with increasing activity
of 5.9±0.7 Km/year
ƒ Consistent results from
HAO Solar Disk
Monitor, Brown &
Christensen-Dalsagaard
(1998)
Big Bear Solar Observatory
15 January 2004
Shrinkage Due to Variation in
the R.M.S. Magnetic Field
(Thermodynamically Induced
Shrinking Too Small)
ƒ For a purely radial random field, an
increasing field implies contraction.
ƒ For an isotropic random field, an increasing
field implies expansion! A non-trivial
constraint!
Big Bear Solar Observatory
15 January 2004
Role of Growing Magnetic Field
ƒ Radial random field is most economical field with a
value of ~100 G at the photosphere (but twice that in
active latitudes for l > 0 terms or for f-modes)
ƒ Required field increases with increasing random,
horizontal component.
ƒ Growing field reduces the turbulent pressure which in
turn reduces the near-surface temperature. Both
reduce required growth of field needed to account for
p- and f-mode frequency changes.
ƒ Calculate ~0.5% decrease in turbulent pressure from min. to
max. required to account for f-mode and p-mode frequency
changes!
ƒ Calculate that temperature changes reduce required field
growth, but can only partially account for frequency changes
Big Bear Solar Observatory
15 January 2004
Role of Decrease in Turbulent
Velocity
ƒ Roughly, relative change in turbulent velocity,
∆vt/vt=q, has same effect as relative temperature
change ∆T/T =0.5qM2, where M is the turbulent Mach
number.
ƒ Effect may be significant because we can expect a
decrease in vt with increasing activity, because the
magnetic field should inhibit convection.
ƒ ~1% decrease in turbulent pressure from min. to
max. required to account for f-mode and p-mode
frequency changes!
Big Bear Solar Observatory
15 January 2004
What about Limits on the Sun’s
Output?
ƒ Consider the higher order shape asymmetries.
We have focused on the spherically
symmetrical part
ƒ Connect to luminosity and to the spectacular
activity-related phenomena in the solar
atmosphere
Big Bear Solar Observatory
15 January 2004
Near-Surface Terms from
MDI p-modes
ƒ Note γ0 systematically rises,
but behavior is much more
muted than anisotropic terms
— this is a clue to the
shrinking of outermost layers
of the sun. For β=-1, the
splitting kernels (γk>0) are
much larger than those for
the isotropic part. This is
consistent with the anisotropic
γ’s (like γ3) being much larger
than for isotropic γ’s (γ0).
ƒ Also, note how small γ’s are at
activity minimum
Big Bear Solar Observatory
15 January 2004
BBSO Ca-K Image of the Sun
ƒ Proxy for
stellar
activity
ƒ Geometry
can be
decomposed
to be
compared to
seismic P2n indices
Big Bear Solar Observatory
15 January 2004
Left:
γ’s
Rt:
β’s
P2P18
Big Bear Solar Observatory
15 January 2004
Conclusions about the Sunshine
ƒ Required field growth agrees with observations
and drives/causes frequency change (pT)
ƒ Sun is hotter and smoother at activity minimum.
Picture that emerges is Spruit’s corregated
surface at high activity, so it is difficult to
imagine a sun that was significantly dimmer
during the holocene than at present activity
minima. What about response of the earth (see
solar cycle in ice core data, maybe effect on
climate is indirect)?: Difficult and requires longterm measurements!
Big Bear Solar Observatory
15 January 2004
The Earth’s Global Albedo
from Earthshine and ISCCP
Big Bear Solar Observatory
ƒ Precise,
integral
diagnostic
of climate
ƒ Cloud
cover,
thickness
and surface
reflectance
regression
ƒ Blue is pure
ES result
ƒ ES team:
Koonin,
Palle and
Rodriguez
15 January 2004
What about Climate Change?
Where Does the Sunlight Go?
Big Bear Solar Observatory
15 January 2004