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PH507Q UNIVERSITY OF KENT SCHOOL OF PHYSICAL SCIENCES CLASS TEST 3 2016, WEEK 24 1. The gravitational perturbation of a star's position by an unseen companion provides a signature which can be detected through precision astrometry. Calculate the mass of an exoplanet in earth masses which causes a 2 solar mass star’s wobble in the plane of the sky to describe a circle of 3 microarcseconds radius and orbital period of 2 years. Assume the star is at a distance of 20 parsecs. First, find the distance of the planet from the dstar. Use the formula æ m p öæ a ö ÷÷ç ÷ Dq = çç è M * øè d ø Here, a is the orbital semi-major axis of the planet. This has to be calculated from the period and the star’s mass using Kepler’s generalized law. This yields the period P =2 pi/ where W= G(M * + m p ) a3 to yield a / 1AU= (P /1 year)2/3 (M / 1 solar mass)1/3 = 2AU With d = 20 parsecs, a/d = 4.9 x 10-7 theta = 3 microarcseconds = 3 x 10-6 x (2 pi/ (360x60x60)) radians = 1.45 x 10-11 radians Therefore mp / M* = 1.45 x 10-11 / 4.9 x 10-7 = turn over 2 3 x 10-5 So mp = 6 x 10-5 solar masses = 20 earth masses. 2. State the statistical weights for the ground and first excited states of neutral hydrogen. For a gas of neutral hydrogen, determine the temperature for which the number of atoms in the first excited state is10% of the number in the ground state. 2, 8, (2n2) 1eV = 11,594K Second level is 10.19eV above the ground. So: Use Boltzmann equation: exp (-10.19 x 11,594/T) = 2xN2/ (8xN1) = 0.025 yields T = 32,000K 3. Taking Deneb to have a surface temperature of 8,500K and a radius of 200 solar radii, determine the present spectral class and luminosity class of Deneb. Investigate and state the stages through which Deneb is expected to progress. State the name of the pre-main-sequence track that Deneb would have followed. A, Ia 20 Msun, so supergiant, core-collapse supernova Depending on their initial masses and the rate of mass loss, they may explode as yellow hypergiants or luminous blue variables, or they may become Wolf-Rayet stars before exploding in a core collapse supernova. Identifying whether Deneb is currently evolving towards a red supergiant or is currently evolving bluewards again would place valuable constraints on the classes of stars that explode as red supergiants and those that explode as hotter stars. 3 As a massive protostar: Henyey or radiative track. 4. The temperature of an opaque cloud is measured to be 20K. Find the wavelength of the peak blackbody emission. In which part of the electromagnetic spectrum does the peak lie? max = 2.898 x 10-3 / T where max is in metres when T is in Kelvin. Or: max 2897 T wheremax is in units of 10-6 m, and T is in Kelvin. So 20K, yields a peak at 2900/20 microns = 145 microns In the far infrared or sub-millimetre is just acceptable. turn over