_{c}, r

_{c}, P

_{c}.

_{}

^{}

Soln. We have, for the three core parameters -

T = T

_{c}

_{ }q , q = ( r / r

_{c})

^{1/n }And q = (P/ P

_{c})

^{(1+ 1/n)}

At the interface (core-radiative boundary) one finds:

**q = 0. 7839768**

Then, for the (dimensionless) core temperature: t

_{c}

_{ }= t

**/**q

And, since 0.6969 = t

_{c}

_{ }q = t

_{c}(0.7839768) then: t

_{c}= 0.8876

The dimensional form is: T = T

_{c}

_{ }q

_{}

^{}

antilog (7.1643) = T = 1.46 x 10

^{7}K
And: T

_{c}_{ }= T**/**q
For which we set up the ratio:

(0.6969)/

**/**(0.8876) = (1.46 x 10^{7})/ T_{c}_{ }
Whence: T

_{c }= (1.46 x 10^{7}) (0.8876)/ (0.6969) = 1.86 x 10^{7}K
Take log T = log (1.86 x 10

^{7}) = 7.2695
Which is the core temperature log value we find at r /R = 0.0, i.e., See Table in Part 1

For core density:

q = ( r / r

_{c})^{1/n }^{}

Where: The polytropic index n can be defined: n = 1/ (g - 1)

where g is the ratio of specific heats. (g =

In a non-relativistic limit one will have g = 5/3 and

n = 1 / (5/3 - 1) = 1/ (2/3) = 3/2

where g is the ratio of specific heats. (g =

**C**/_{p}**C**)_{v }In a non-relativistic limit one will have g = 5/3 and

n = 1 / (5/3 - 1) = 1/ (2/3) = 3/2

Then write the core density as: r

_{c}= r / q^{3/2}
Now, take q = 0.7839 SO: q

^{3/2 }= 0.6941
Since we have, at r/R = 0.172, log r = 1.4033 then

antilog (1.4033) = r = 25.31 g/ cm

^{3}
Therefore: r

_{c}= r / q^{3/2 }= 25.31 g/ cm^{3}/ 0.6941
And: r

_{c}= 36.46 g/ cm^{3}
Now, take log (r

_{c}) = 1.5618
Which is the density log value we find at r /R = 0.0, i.e. the core (See Table in Part 1)

For core pressure, we have: q = (P/ P

_{c})^{(1+ 1/n)}
Since: q = (p/ p

Then: p

_{c})^{(1+ 1/n) }and n = 1.5 (assigned polytropic index - see top of*Lane-Emden**function table*)Then: p

_{c}= p / q^{5/2}and q^{5/2}= 0.5441
And, since we have, from the model table, at r/R = 0.172, log P = 16.6770 then

antilog (16.6770 ) = P = 4.754 x 10

^{16}dyne/ cm^{ 2}^{}

_{}

^{}

Therefore: P

_{c}= P / q^{5/2}= (4.754 x 10^{16}dyne/ cm^{2})/ 0.5441
P

_{c}= 8.737 x 10^{16}dyne/ cm^{2}
and the log is: 16.9414 or the value shown at r/R = 0.0 (the core)

_{}^{}
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