n(r) = nge where r represents the distance from the centre of the Galaxy, Ro is the distance of the Sun from the centre of the Galaxy, Ra is the typical size of disk and no is the stellar density of disk at the position of the Sun. All distances are expressed in kpc. An astronomer observes the center of the Galaxy within a small field of view. We take a particular type of Red giant stars as the standard candles for the observation with approximately constant absolute magnitude of M = -0.2, %3D (a) A telescope has a limiting magnitude of m = 18. Calculate the maximum distance to which this telescope can detect these red giant stars. For simplicity we ignore the presence of interstellar medium so there is no extinction. %3D (b) Assume an extinction of 0.7 mag/kpc for the interstellar medium. Repeat the calculation as done in the part 5a and obtain a rough number for the maximum distance these red giant stars can be observed. (c) Give an expression for the number of these red giant stars per mag- nitude within a solid angle of N that we can observe with apparent magnitude in the range of m and m + Am, (i.e. AN). Red giant stars contribute fraction f of overall stars. In this part assume no extinction in the interstellar medium as part 5a. Assume the size (109 - T17 - C) of the disk is infinite. Hint: The Tylor series expansion, for r «1 1 log10(1+1) = In 10 (8.2) + %3! 3

n(r) = nge where r represents the distance from the centre of the Galaxy, Ro is the distance of the Sun from the centre of the Galaxy, Ra is the typical size of disk and no is the stellar density of disk at the position of the Sun. All distances are expressed in kpc. An astronomer observes the center of the Galaxy within a small field of view. We take a particular type of Red giant stars as the standard candles for the observation with approximately constant absolute magnitude of M = -0.2, %3D (a) A telescope has a limiting magnitude of m = 18. Calculate the maximum distance to which this telescope can detect these red giant stars. For simplicity we ignore the presence of interstellar medium so there is no extinction. %3D (b) Assume an extinction of 0.7 mag/kpc for the interstellar medium. Repeat the calculation as done in the part 5a and obtain a rough number for the maximum distance these red giant stars can be observed. (c) Give an expression for the number of these red giant stars per mag- nitude within a solid angle of N that we can observe with apparent magnitude in the range of m and m + Am, (i.e. AN). Red giant stars contribute fraction f of overall stars. In this part assume no extinction in the interstellar medium as part 5a. Assume the size (109 - T17 - C) of the disk is infinite. Hint: The Tylor series expansion, for r «1 1 log10(1+1) = In 10 (8.2) + %3! 3