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In a gravitational potential, gas will settle into hydrostatic equilibrium. This question concerns the density distribution in a galactic gas disk obeying hydrostatic equilibrium in the direction perpendicular to the disk plane. For the purposes of this question you may ignore cooling, heating or gravitational collapse Consider a piece of this gas disk at radius R from the centre. Assume that the gas has a constant temperature To. Further, assume that near the disk, the gravitational acceleration perpendicular to the disk is well described by a constant, go (a) State qualitatively how the gas density p must change with height z above the disk plane. 1 mark. (b) Determine an expression for how the scale height, h, of the gas disk depends on go and To. Problem set up correctly: 1 mark Correct solution: 2 marks (C) Sanity-check your result: According to your result, what happens to the disk thickness when you vary T, or go? Does that match your expectation? 2 marks (Can achieve 0.5+0.5 marks for stating correct expectations.) (d) The gravitational acceleration perpendicular to the disk will certainly change with distance R from the centre. How will the disk thickness change with distance R from the centre if we assume a constant gas temperature? Give a very short qualitative answer with your reason. 1 mark. (Note: can be done even if you skipped the calculation above).