Deep Impact Projectsmfa - 1 Deep Impact Projects (2) Mike A’Hearn

Deep Impact Projectsmfa - 2 Problem 1 Optical Depth & Albedo of Ejecta from DI

Deep Impact Projectsmfa - 3 Optical Depth Well known and widely used in astronomy but often ignored in cometary science because the coma is usually optically thin I/I 0 = e - where  = optical depth For simple scattering and absorption  = N  where  = extinction cross section and N = column density A typical photon travels  = 2/3 before being absorbed or scattered

Deep Impact Projectsmfa - 4 Scattering Function A single particle (grain of dust or whatever) scatters light anisotropically The phase function describes the distribution of light with scattering angle, both for microscopic particles and for large bodies like cometary nuclei and asteroids Phase function is often approximated by many different simple functions of the scattering angle For a single particle, –I = F sun  p f( where p = geometric albedo and f() is the scattering function or I = F sun **A( –Be careful of confusion between geometric albedo and Bond albedo - geometric is backscattering and Bond is integrated around the sphere. –The widely used quantity Af uses Bond albedo as A, even though this is not well defined for microscopic particles

Deep Impact Projectsmfa - 5 Phase Functions Sample phase functions appropriate to comets –There is variation from one comet to another –Dust from Ney & Merrill, comet West (1976 VI) –Nucleus from Lumme- Bowell law These are normalized to unity at phase = 0° –correct for use with geometric albedo –Renormalize to unity of integral over 4 for use with Bond albedo

Deep Impact Projectsmfa - 6 Albedo Solving for the albedo from  and I is a matter of algebra left to the student –Use the approximation that the optical depth is not large ( < 1) so that I(column) = N*I(particle) –Be very careful of the units! I has units of radiance (see the image labels for the exact units) Look up solar flux for a typical wavelength (look at a document that describes the bandpass or use the label values for center wavelength and bandpass) –Remember that phase = 180° - scattering angle

Deep Impact Projectsmfa - 7 Making the Measurements - 1 Consider MRI images just before and just after the impact (ID _050 is before, ID _080 is after) You may wish to register the images first –IDL has, e.g., a cross-correlation function that you can use to determine the offset as long as the ejecta are not too bright –There are numerous other ways to do this if you are familiar with image processing –If the images are registered, you can make the measurements in the same pixels on all images Alternatively, you can choose a feature on the surface or the limb and make sure that you make all measurements at the same feature

Deep Impact Projectsmfa - 8 Making the Measurements - 2 Measure the profile of brightness across the limb of the nucleus at your “feature” Extrapolate the coma brightness to the brightness just inside the limb Measure the height, I, of the limb above the extrapolated coma –Extrapolation should only be a few pixels –Call it I 0 for the pre-impact image (or averaged over a few pre-impact images) –Use I/I 0 to determine  –Use I and  to determine p*f() and use the table of scattering functions to get p, the geometric albedo

Deep Impact Projectsmfa - 9 Extending the Project Ultimately, the interesting question is the variation of albedo with position around the limb and with time –This can show variations in the type of particles (ice vs. dust and organics) both with direction of ejection and with depth of excavation Optical depth is >1 after about 5-10 seconds –The problem is much messier because one must allow both for the attenuation of the incident sunlight from one direction and the attenuation of the scattered light along the line of sight Any other sharp boundary (a crater or a scarp) on the nucleus can be used to measure the optical depth but –the contrast is lower –One must use features on the sunward side of the impact site or the “true” brightness of the surface will change

Deep Impact Projectsmfa - 10 Problem 2 Plot the Light Curve of an Outburst

Deep Impact Projectsmfa - 11 Scientific Goal We do not understand what causes the natural outbursts Determine how long the emission of material continues, which is important in choosing a mechanism for producing the outburst, and whether the outflow of material explains the drop in brightness after the outburst

Deep Impact Projectsmfa - 12 Outbursts on July 1 & 3

Deep Impact Projectsmfa - 13 Outburst Motion July 3 outburst has most data Lightcurve best done from MRI data Images best done from HRI data, but requires deconvolution

Deep Impact Projectsmfa - 14 Making the Measurements Select the images that include the outburst plus a couple before and after On each image –Locate the nucleus of the comet - usually at the photocenter –Add up the intensity within a box centered on the comet’s nucleus Try boxes of several sizes, e.g., 5, 9, 15, 25 pixels Plot the intensities vs. time to see the light curve A circular aperture is better than a box, but requires a little more programming in IDL or use of procedures in the GSFC library for IDL (probably also in IRAF)

Deep Impact Projectsmfa - 15 Interpreting the Result Calculate the distance (in m or km at the comet) from the nucleus to the edge of the aperture Use the time from beginning of outburst to end of outburst to estimate the velocity of the material Verify that the deduced velocity is the same for various apertures

Deep Impact Projectsmfa - 16 Extending the Project The HRI images can be used to trace the material in time - see the deconvolved images shown in a previous slide –Not many images during the outburst –Requires subtracting a pre-outburst, registered image and then doing the deconvolution for the focus problem –Mapping the intensity variation with time can provide further constraints on the motion of the ejecta - need a true simulation Finding all the outbursts and coordinating them with rotational phase of the nucleus Tracing the outbursts to specific locations on the nucleus Simulating a mechanism to produce the outbursts