Download Most Basic Observations Of the Sun

Most Basic Observations Of the Sun
Chapter 10
The Interiors of Stars
Sun has maintained
(i) its size,
(ii) energy it emits every second,
(iii) its surface temperature
all this while.
• Sun is a self-gravitating objects − each part of the sun
exerts force on each other part of the sun.
• Gravity always attracts
There must be other kinds of forces acting against Gravity to
prevent the sun from collapsing onto itself.
These inward and outward forces must be in perfect balance!
Hydrostatic Equilibrium
• Sun is radiating the same amount of energy every
second − 3 x 1026 Joule
It must be generating the right amount of energy every
second.
Energy Generation Rate
It must be making sure that each of its layer transports just
the right amount of energy to maintain this energy output.
Energy Transport Rate
• Sun is maintaining the temperature of its surface, and is
also maintaining some fixed temperature at each of its
radial distance from the Sun.
Since the transfer of fixed (energy) radiation from the center to
the surface in each layer would depend crucially on how
temperature in each layer varies, it must maintain the required
temperature gradient in all layers.
Temperature Gradient
• Mass conservation
Stellar Structure Equations
Hydrostatic Equilibrium
Mass Conservation
Energy Transport
Hydrostatic Equilibrium
Ex. 10.1.1 Make a crude estimate of the pressure at the
center of the Sun using the Hydrostatic Equilibrium.
Rigorous calculation shows the pressure is
(
)
Pressure Equation of State
Completely neutral gas,
Completely ionized gas,
In terms of mass fractions, for a neutral gas
In terms of mass fractions, for a completely ionized gas
Go through P. 293
Ex. 10.1.2 Make an estimate of the temperature at the
center of the Sun using the Gas pressure term alone and
using the value for pressure we derived in the previous
example.
Stellar Energy Sources
Gravitational Energy
Kelvin-Helmholtz Timescale
Assuming a spherical star of Radius R and M, the
gravitational potential energy of the star,
Kelvin-Helmholtz time scale ~ 107 years
Too short! From dating of meteorites we know that our solar
system is about 4.5 billion year old.
Nuclear Time Scale
Total Mass of four (4) Hydrogen atoms
Mass of one Helium atom
Ex. 10.3.2 Assuming Sun was all Hydrogen, and that
inner 10% of mass is hot enough to convert Hydrogen
into Helium, how long Sun can produce its current
luminosity?
~ 1010 year
Reasonable!