Let's assume that a cluster of total mass 2000 Msun follows a Kroup...

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Let's assume that a cluster of total mass 2000 Msun follows a Kroupa IMF, with stellar masses between 0.1 Msun and 100 Msun- Determine the number and total mass of stars between the following two mass ranges: [0.1- 1] Msun and [1-100] Msun . How does that compare to what vou would obtain if the IMF of that cluster was following the mass function of dN/dm is a = 1.3 for [0.1-1] Msun and a = 4.0 for [1-100] Msun). Where do you think the differences come from? As the cluster evolves, its luminosity changes. Determine the relation Lclus (t) (the cluster luminosity as a function of time) knowing that the luminosity of a star of mass m is given by 3.5 Lstar = 5/3 m Lo and its main sequence lifetime is tms =

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