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2. Exercise 19-2: Flattened Salpeter IMF a. For the simple flattened Salpeter IMF, with (alpha = 2.35) for (m > 1) and (alpha = 0) for (m < 1), integrate DocOnotes eqn. (21.9) over all masses to obtain an expression for the normalization (K) in terms of the total number of stars (N_{tot}). b. Now use this to obtain an expression for the fraction of stars, (N(m > m_o)/N_{tot}), with mass greater than some mass lower limit (m_o) (assuming (m_o ge 1)). In particular, what fraction of stars have (m > 1)? c. For (m_o = 100), how many total stars must a cluster have for there to be at least one star with (m ge m_o)? How about for (m_o = 300)? What does this imply for observational efforts to determine whether there is an upper mass cutoff to the IMF?

          2. Exercise 19-2: Flattened Salpeter IMF
a. For the simple flattened Salpeter IMF, with (alpha = 2.35) for (m > 1) and (alpha = 0) for (m < 1), integrate DocOnotes eqn. (21.9) over all masses to obtain an expression for the normalization (K) in terms of the total number of stars (N_{tot}).
b. Now use this to obtain an expression for the fraction of stars, (N(m > m_o)/N_{tot}), with mass greater than some mass lower limit (m_o) (assuming (m_o ge 1)). In particular, what fraction of stars have (m > 1)?
c. For (m_o = 100), how many total stars must a cluster have for there to be at least one star with (m ge m_o)? How about for (m_o = 300)? What does this imply for observational efforts to determine whether there is an upper mass cutoff to the IMF?

$2. Exercise 19-2: Flattened Salpeter IMF a. For the simple flattened Salpeter IMF, with (alpha = 2.35) for (m > 1) and (alpha = 0) for (m < 1), integrate DocOnotes eqn. (21.9) over all masses to obtain an expression for the normalization (K) in terms of the total number of stars (Ntot). b. Now use this to obtain an expression for the fraction of stars, (N(m > mo)/Ntot), with mass greater than some mass lower limit (mo) (assuming (mo ge 1)). In particular, what fraction of stars have (m > 1)? c. For (mo = 100), how many total stars must a cluster have for there to be at least one star with (m ge mo)? How about for (mo = 300)? What does this imply for observational efforts to determine whether there is an upper mass cutoff to the IMF?$

Added by Betty C.

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