10.000 Si Si+am.ice Si+cr.ice Si+porosity Si+C+Porosity Si+C+ice Si+C+ice+porosity 1.000 B 0.100 0.010 0.001... 0.1 1.0 100.0 1000.0 10.0 grain size a [um] Figure 2: Radiation pressure over gravity factor B calculated for grains of different composition in the HD 181327 debris disk. The horizontal dashed line denotes the limit between gravitationally bound (B 0.5) grains. Adapted from Lebreton et al. (2012). 3. [3 points) Assume that the material in the disk of HD 181327 has a Bond albedo A 0.4, consistent with a mix of ice and rock. Calculate the equilibrium temperature of the disk, and compare it with the temperature that you would estimate from the spectral energy distribution in Figure 1 (right panel). Hint: assume that the disk is made of small particles with black body emissivity e 21. If you could not solve the previous problem, you can assume a debris disk radius Rd 80 AU. 4. [2 points] Estimate the blowout size of the grains orbiting in the HD 181327 debris disk. Hint: the blowout size is the maximum size of the grains in a debris disk that are rapidly ejected from the system due to radiation pressure. Use the 3-components porous grains composition indicated by the thick solid line in Figure 2. 5. [2 points) You had enough of 2020 and decide to take a very long off-world vacation. You " borrow" a cheap spaceship with cryogenic life support and embark on a trip to HD 181327 that will take 100 Myr to get to destination. Assuming that the grains in the HD 181327 are not continuously replenished by some parent Kuiper belt body population, what is the smallest object that you expect to find in the disk once you wake up at destination? Hint: grains smaller than the blowout size are removed quickly from the system by radiation pressure, you should not expect to find those. However, larger grains are subject to the slower orbital decay due to Poynting-Robertson drag. Use again the 3-components porous grains composition indicated by the thick solid line in Figure 2. 10.000 Si Si+am.ice Si+cr.ice Si+porosity Si+C+Porosity Si+C+ice Si+C+ice+porosity 1.000 B 0.100 0.010 0.001... 0.1 1.0 100.0 1000.0 10.0 grain size a [um] Figure 2: Radiation pressure over gravity factor B calculated for grains of different composition in the HD 181327 debris disk. The horizontal dashed line denotes the limit between gravitationally bound (B 0.5) grains. Adapted from Lebreton et al. (2012). 3. [3 points) Assume that the material in the disk of HD 181327 has a Bond albedo A 0.4, consistent with a mix of ice and rock. Calculate the equilibrium temperature of the disk, and compare it with the temperature that you would estimate from the spectral energy distribution in Figure 1 (right panel). Hint: assume that the disk is made of small particles with black body emissivity e 21. If you could not solve the previous problem, you can assume a debris disk radius Rd 80 AU. 4. [2 points] Estimate the blowout size of the grains orbiting in the HD 181327 debris disk. Hint: the blowout size is the maximum size of the grains in a debris disk that are rapidly ejected from the system due to radiation pressure. Use the 3-components porous grains composition indicated by the thick solid line in Figure 2. 5. [2 points) You had enough of 2020 and decide to take a very long off-world vacation. You " borrow" a cheap spaceship with cryogenic life support and embark on a trip to HD 181327 that will take 100 Myr to get to destination. Assuming that the grains in the HD 181327 are not continuously replenished by some parent Kuiper belt body population, what is the smallest object that you expect to find in the disk once you wake up at destination? Hint: grains smaller than the blowout size are removed quickly from the system by radiation pressure, you should not expect to find those. However, larger grains are subject to the slower orbital decay due to Poynting-Robertson drag. Use again the 3-components porous grains composition indicated by the thick solid line in Figure 2