Dark Matter and Particle Mass Bounds --- Quick notes I

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- Mean free path of stellar collision 

    collision time  ~$\frac{mean-free-path }{velocity-of-stars}$~${10^{21}} years$

- Circular velocity

   $\frac{v^2}{R} = \frac{GM(R)}{R^2}$

    $v = \sqrt{\frac{GM(R)}{R}}$

    $M(R) = \frac{v^2 R}{G}$


-rotation curves

     v(R)

-Contradicts observation  -- need new particles

         -Getting observed flattening of the curve for dark matter halo

                $M$ ~ $R$

                $V$ ~$ R^3$

                $\rho$ ~ $1/R^2$

     

-- Getting some data from experiments

     -$\rho ~0.3 \frac{GeV}{cm^3}$

     -$R_{halo}$ ~ $100$ kilo-parsec

                     - Halo mass is computable

                     - Average velocity is computable  ~ 200km/s

           

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