A3002_2017_PS4 (2).pdf - A3002 \u2013 Black Holes and Cosmology \u2013 Part 2 \u2013 Problem Set 4 due Tue 31 October 11:55pm \u2013 submit on Wattle No extensions

A3002_2017_PS4 (2).pdf - A3002 u2013 Black Holes and...

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A3002 – Black Holes and Cosmology – Part 2 – Problem Set 4 due Tue 31 October 11:55pm – submit on Wattle No extensions. Problem 1: The Super- Neutrino 1.1: (1pt) In the year 2017 the IceCube detector registered a neutrino with an energy of 290 TeV that was attributed to an outburst in an AGN called TXS 0506+056. The proper distance to this AGN has now been measured to be 4 billion light years. Assuming a rest mass of 0.1 eV for neutrinos, calculate the velocity of the neutrino relative to the vacuum speed of light. Assuming space between the AGN and Earth was perfect vacuum, how much later would the neutrino arrive after simultaneously emitted photons? 1.2: (1pt) In reality, even intergalactic space is not a perfect vacuum, but filled with low-density plasma that increases the refractive index of the intergalactic medium (assume an electron density of 1 per m3). How much is the arrival of UV-blue light from TXS 0506+056 (wavelength: 300 nm) delayed as a result? Which arrives first at Earth: the neutrino from problem 1.1, or UV-blue light? How far is the 100 MHz-radio wave away from Earth in the moment when the UV-blue light arrives? Problem 2: The Centre of the Milky Way Near the centre of the Milky Way a star called S2 is seen to orbit around an invisible mass around 8 kpc away from the observers on Earth. Its orbital period is approx. 16 years, and its orbit is inclined by ~45 degrees against the plane of the sky (and rotated around the RA axis) as you can infer from two ways of measuring the eccentricity of an ellipse. 2.1: (2pt)Measure and calculate the semi-major axis of the actual orbit as well as roughly its eccentricity from the plot on the next page, taking the inclination into account. Derive the mass of the invisible mass at Sgr A* assuming Keplerian motion
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