The Standard Solar Model
and Its Evolution
Marc Pinsonneault
Ohio State University
Collaborators:
Larry Capuder
Scott Gaudi
Summary
The Sun is predicted to become brighter
as it ages for fundamental stellar structure
reasons
This luminosity evolution is extremely
insensitive to assumptions about the input
physics, except mass loss…
…and the rotation of the Sun, and by
extension mass loss, was very similar to
the current values for the last 4 Gyr
Standard Solar Model
Initial Conditions: Mass, Composition,
Evolutionary State
Equations of Stellar Structure
– Conservation Laws
The Solar Calibration
– Reproduce current solar properties, adjust
model uncertainties
In the Beginning…
There are interesting problems around the
formation of the Sun
– Rotation:
Hydrodynamic assembly phase
Protostar-disk interaction
– Mixing and Light Element Depletion
– However, subsequent solar evolution is
insensitive to the initial conditions (VogtRussell theorem)
Standard Model Assumptions
and Ingredients
Equation of State: OPAL; close to ideal gas
Energy Generation: Adelberger et al. 2010;
primarily pp
Opacities: OP or OPAL; radiative core
Convection Theory: MLT; convective
envelope
Gravitational settling included
Rotation, rotational mixing, mass loss not
included
Standard Luminosity Evolution
Early transient
phase (~30
Myr) when the
Sun contracts
and heats up
Steady core H
burning phase
where the Sun
steadily
brightens
Why does the Sun brighten as it
ages?
Pressure gradient balances gravity
Sun remains hot through H fusion
4 1H => 1 4He has a necessary implication:
– 8 particles -> 3 particles
– To balance gravity fewer particles must
move faster and the density must rise
– These factors drive higher energy
generation rates and luminosities in stars
More Luminous
Hotter
Structural and Luminosity
Changes
Bahcall, Pinsonneault & Basu 2001
What Tools Do We Have to Test
the Sun?
Current Solar Properties: M, L, age,
composition, solar wind…
Neutrinos
Helioseismology
– Sound speed profile
– Core helium profile
– Scalar constraints: convection zone depth,
surface helium
Good
Agreement!
Solar neutrinos
Helioseismology
implies a high O
abundance
– Disagreement with
some recent models
claiming a lower solar
O, but only at ~ 2 s
– Sound speed
agreement to 0.1 – 1%
in any case
How Reliable is Solar Evolution?
Vary input ingredients within error ranges
Vary sources of input physics (opacities,
equation of state, heavy element mixture) to
test systematic errors
Net Result: Almost a Perfect
Invariant!
Solar L(t) is
within
0.5% or
better at all
points
during MS
evolution
What About Mass Loss?
Any change to solar evolution would
require a drastic alteration…
The current solar mass loss rate ~1.3 x
1012 g/s is far too small to impact evolution
What properties of the ancient Sun could
have been very different?
– Look at rotation
Young Stars Can Be Rapid
Rotators
Denissenkov, Pinsonneault & Terndrup 2010
Link With Mass Loss
More rapid rotation is linked with higher
coronal X-ray luminosities and mass loss
rates (Wood et al. 2005)
– dM/dt ~ Lx
– Lx measures coronal heating, and is observed
to up to 1000x larger than solar for young
stars
– Higher past mass loss is reasonable
Lx is a strong function of mass
and rotation rate
Rossby number
Rotation Period
Pizzolato et al. 2003
Angular Momentum Evolution
Protostellar initial state
Star-disk coupling
Core-envelope
coupling
Epstein & Pinsonneault 2012
Denissenkov, Pinsonneault & Terndrup 2010
Simple Extension of the
Standard Model with Mass Loss
Evolve assuming….
– dM/dt = (w/wsun)^a
*(dM/dt)sun
 w evolution from
standard
assumptions
– Observed saturation
in X-ray flux
Solar
Evolution
With Mass
Loss
Some Early Changes Possible
However….
Rapid spin down
Solar wind rapidly converges
to present-day value
What About More Severe Mass
Loss?
Basic issue:
– Enhanced solar mass loss
is most naturally driven by
more rapid rotation in the
younger Sun
– Solar analogs are observed
to reach a few times solar
rotation in a few hundred
Myr
– Implies mass loss rates of
order 10x solar or less for
90% of the solar age
Sackmann & Boothroyd 2003
Tests and Future Directions
Important tests of rotational history from
Kepler and CoRoT will be arriving soon
– Crucial check on old field stars
Experimental tests of solar interiors
physics
Improved Wind Models