1. Jul 23 - Aug 3, 2007 COSPAR Planetary Science Workshop, Montevideo, Uruguay 1 Phase Function of Comet Wild 2 from Stardust Data Jian-Yang Li

2. Jul 23 - Aug 3, 2007 2COSPAR Planetary Science Workshop, Montevideo, Uruguay What is Phase Function

3. Jul 23 - Aug 3, 2007 3COSPAR Planetary Science Workshop, Montevideo, Uruguay Examples of Phase Function

4. Jul 23 - Aug 3, 2007 4COSPAR Planetary Science Workshop, Montevideo, Uruguay Scattering Function See slide 4 and 5 in “DI-Projects.ppt” from Mike A’Hearn. See slide 4 and 5 in “DI-Projects.ppt” from Mike A’Hearn. Reflectance is usually represented by r=I/F, where I is the scattered intensity (energy/area/wavelength/solid angle), and πF is incident flux (energy/area/wavelength). I/F is a dimensionless value, or actually has a unit of sr -1. Reflectance is usually represented by r=I/F, where I is the scattered intensity (energy/area/wavelength/solid angle), and πF is incident flux (energy/area/wavelength). I/F is a dimensionless value, or actually has a unit of sr -1. For the easiness of measurement and model, r is usually decomposed to r=AΦ(  ), where A is geometric albedo, and Φ(  ) is phase function, normalized such that Φ(0)=1. For the easiness of measurement and model, r is usually decomposed to r=AΦ(  ), where A is geometric albedo, and Φ(  ) is phase function, normalized such that Φ(0)=1.

5. Jul 23 - Aug 3, 2007 5COSPAR Planetary Science Workshop, Montevideo, Uruguay Work with Stardust Data – Outline Find Stardust images: Find Stardust images: http://pdssbn.astro.umd.edu/ http://pdssbn.astro.umd.edu/ http://pdssbn.astro.umd.edu/ Calibrated encounter images from NAVCAM Calibrated encounter images from NAVCAM Collect aspect data Collect aspect data Exposure keywords – exposure start and end, exposure time Exposure keywords – exposure start and end, exposure time Geometry keywords – heliocentric distance, spacecraft range, phase angle, pixel scales Geometry keywords – heliocentric distance, spacecraft range, phase angle, pixel scales Quality keywords – saturation Quality keywords – saturation Measure total brightness of the nucleus Measure total brightness of the nucleus Define the boundary of nucleus Define the boundary of nucleus Estimate corrections and the uncertainty – take home Estimate corrections and the uncertainty – take home Plot phase function Plot phase function Analyze phase function – collaborations welcome Analyze phase function – collaborations welcome

6. Jul 23 - Aug 3, 2007 6COSPAR Planetary Science Workshop, Montevideo, Uruguay Find Stardust Images Go to PDS SBN website http://pdssbn.astro.umd.edu/, look for Stardust mission data, and download the 72 encounter images. Go to PDS SBN website http://pdssbn.astro.umd.edu/, look for Stardust mission data, and download the 72 encounter images. http://pdssbn.astro.umd.edu/ Or you can download them from the local server where Gonzalo put them, but make sure you know how to find it from PDS. Or you can download them from the local server where Gonzalo put them, but make sure you know how to find it from PDS. Understand the image data Understand the image data What unit the image have been calibrated? What unit the image have been calibrated? At what wavelengths? At what wavelengths? At what heliocentric distance and spacecraft range? You will probably need this information later in the processing. At what heliocentric distance and spacecraft range? You will probably need this information later in the processing.

7. Jul 23 - Aug 3, 2007 7COSPAR Planetary Science Workshop, Montevideo, Uruguay Collect Aspect Data From the index table From the index table Read the index label file to find out what the columns are. Read the index label file to find out what the columns are. Read index file into IDL by readpds. Read index file into IDL by readpds. From image headers From image headers Use headpds to read in image headers into a string array. Use headpds to read in image headers into a string array. Use IDL command sxpar to return the value of keywords. Use IDL command sxpar to return the value of keywords. Results = sxpar(header_array, ‘KEYWORD’) Results = sxpar(header_array, ‘KEYWORD’)

8. Jul 23 - Aug 3, 2007 8COSPAR Planetary Science Workshop, Montevideo, Uruguay Measure Total Brightness of the Nucleus For each image, sum up all pixels of the nucleus. You have several methods to do it, but none of them is perfect. For each image, sum up all pixels of the nucleus. You have several methods to do it, but none of them is perfect. Define a box that includes the nucleus. Define a box that includes the nucleus. Define the edge of the nucleus by a threshold brightness, above which the pixel is considered inside the nucleus. Define the edge of the nucleus by a threshold brightness, above which the pixel is considered inside the nucleus. Define the edge of the nucleus by the maximum brightness gradient (sharpest edge). Define the edge of the nucleus by the maximum brightness gradient (sharpest edge). Think about which way is the best (or you like the most), and what consequence it has on the measurement and why. This is related to further correction and error estimate. Think about which way is the best (or you like the most), and what consequence it has on the measurement and why. This is related to further correction and error estimate.

9. Jul 23 - Aug 3, 2007 9COSPAR Planetary Science Workshop, Montevideo, Uruguay Plot the Phase Function ! What is the unit of your measured total brightness? What is the unit of your measured total brightness? Since we only want to measure the phase function Φ(  ), which is normalized to Φ(0)=1, the absolute scale of these measurements is not important. But think whether you need any corrections for spacecraft range or heliocentric distance. Since we only want to measure the phase function Φ(  ), which is normalized to Φ(0)=1, the absolute scale of these measurements is not important. But think whether you need any corrections for spacecraft range or heliocentric distance. Finally, normalize it to Φ(  )=1. Since we do not have measurement at 0 phase angle, it is not possible to do this step. You can make a rough estimate and normalized it to that. Finally, normalize it to Φ(  )=1. Since we do not have measurement at 0 phase angle, it is not possible to do this step. You can make a rough estimate and normalized it to that. Plot the normalized measurement as a function of phase angle – this is your phase function. You can plot it in both linear brightness scale and magnitude scale. Plot the normalized measurement as a function of phase angle – this is your phase function. You can plot it in both linear brightness scale and magnitude scale.

10. Jul 23 - Aug 3, 2007 10COSPAR Planetary Science Workshop, Montevideo, Uruguay What to Do with the Phase Function Think about the following questions Think about the following questions Do you see anything interesting in the phase function you plot? (Hint: inbound leg and outbound leg) Do you see anything interesting in the phase function you plot? (Hint: inbound leg and outbound leg) What is the linear phase slope  (mag/deg) of the phase function? What is the linear phase slope  (mag/deg) of the phase function? Compare with the phase functions shown in slide 3, which one is the most similar one? Compare with the phase functions shown in slide 3, which one is the most similar one?

11. Jul 23 - Aug 3, 2007 11COSPAR Planetary Science Workshop, Montevideo, Uruguay Extending the Project What is the advantages and disadvantages of the different methods you can use to measure the total brightness of nucleus? Any other better way you can think of? What is the advantages and disadvantages of the different methods you can use to measure the total brightness of nucleus? Any other better way you can think of? How much does the faint jets and ambient coma affect your measurement of total nuclear brightness? How about the foreground coma that is on the line of sight? How much does the faint jets and ambient coma affect your measurement of total nuclear brightness? How about the foreground coma that is on the line of sight? What is the uncertainties of your measurement? And subsequently, what is the uncertainty of phase slope  ? What is the uncertainties of your measurement? And subsequently, what is the uncertainty of phase slope  ?