A Coarse 3D Model of E0102-72 Derived from HETG Data by Dan Dewey MIT Center for Space Research Thanks to "3D & SNR" collegues at MIT: Johns Davis & Houck, Mikes Noble, Nowak &Wise, Claude Canizares, Kathy Flanagan, Amy Fredericks, Glenn Allen, Norbert Schulz, Mike Stage Contact: dd@space.mit.edu Dan Dewey Poster 24.04, AAS HEAD Meeting, 2004

Poster 24.04, AAS HEAD Meeting, 2004 HETG Analysis of E0102 Ne X Analysis of the Ne X dispersed images suggests regions of red and blue shift appearing on the sky as displaced rings. Red: 900 and 1800 km/s Green: -900 km/s Blue: -1800 km/s See Flanagan et al. 2004, ApJ Interpret this as cylinder viewed almost end-on: "True-color" image (above); Ne X line "color-velocity" map: Dan Dewey Poster 24.04, AAS HEAD Meeting, 2004

O III Long-slit spectrum "Thanks to You-Hua Chu for the data! " FP image of E0102 Long slit spectrum in O III, 5007 Å, shows similar spatial- velocity structure to the Ne X X-ray line. - 1800km/s - 900km/s ? But where's the red-shifted emission in the optical flux. Perhaps … see next slide. + 900km/s - + 1800km/s Dan Dewey Poster 24.04, AAS HEAD Meeting, 2004

Poster 24.04, AAS HEAD Meeting, 2004 Transmission of gas & dust * An aside… O VI Perhaps there's equatorial dust absorbing the back-half of the ejecta in the optical? X-ray O III Dust attenuates the 5007 Å line but not X-ray or IR emission. Dust? Spitzer IR bands X-ray and IR black bodies Observer O, Ne, etc. ejecta Blastwave sphere Dan Dewey Poster 24.04, AAS HEAD Meeting, 2004

Poster 24.04, AAS HEAD Meeting, 2004 Constructing a 3D Model Analogous to the Ne X result construct cylinders of emission from each ion. From Flanagan et al. 2004 the radii of the cylinders vary from ion to ion, see Table below. Also include a Blastwave sphere of emission (Hughes 1994) with a vnei spectrum and abundances ~ 0.3 solar. ions Dan Dewey Poster 24.04, AAS HEAD Meeting, 2004

Cylindrical Components Ion Lambda (Å) T_e(keV) Cylinder average radius(") O VII ~21.8 0.34 12.50 O VIII 18.97 13.95 Ne IX ~13.57 0.58 13.40 Ne X 12.13 15.00 Mg XI ~9.17 0.50 14.50 Mg XII 8.42 16.20 Si XIII ~6.65 0.60 15.30 Dan Dewey Poster 24.04, AAS HEAD Meeting, 2004

Poster 24.04, AAS HEAD Meeting, 2004 Encoding the Model Spatial: O VII emission measure array: Each component is a 3-D array of values, (e.g., 87^3 elements) giving the "norm" of the spectral model in each local cell. Spectral: "Single ion" (or "vnei") spectra are created at nominal values of T_e and for v=0. local EM Dan Dewey Poster 24.04, AAS HEAD Meeting, 2004

Poster 24.04, AAS HEAD Meeting, 2004 "Evaluating" the Model Assume the source is optically thin: concatenate component photon/count outputs. Create "output" photons from each component as a: random spatial location determined by "norm" array values. and project to 2-D on sky location. random spectral wavelength based on spectrum assigned. number created determined by spectrum and optionally an "arf" as well. v ~ r los r Modify wavelengths using line-of-sight angle for Doppler: v ~ r spherical velocity field. Dan Dewey Poster 24.04, AAS HEAD Meeting, 2004

Comparing Model and Data Fold simulated photons through instrument, e.g., with a ray-trace. [Or: modify simulated counts to approximate the instrument effects.] Variety of HETGS observation outputs that can be compared, e.g., MEG minus order MEG plus order Zeroth-order image Zeroth-order spectrum Adjust "norms" of the components for overall coarse agreement of model to data - do it by hand with human "comparison". Use automated fitting to do fine adjustment of parameters. Dan Dewey Poster 24.04, AAS HEAD Meeting, 2004

Poster 24.04, AAS HEAD Meeting, 2004 Z-o Data and Model Data Comparing the Zeroth-order image and the Zeroth-order Spectrum. The real data includes background events and more spatial complexity than the simple model. Data Model Model [These images are in detector coord.s. Roughly, North is down and East is to left.] Dan Dewey Poster 24.04, AAS HEAD Meeting, 2004

MEG-Dispersed Data and Model O VII Ne X Data MEG -1 MEG +1 Fe needed? Ne X O VII Model MEG -1 MEG +1 Dan Dewey Poster 24.04, AAS HEAD Meeting, 2004

…Comments on Dispersed Data-Model * The Model reproduces the coarse structure of the Data. * The velocity Doppler effect (due to the cylindrical ion emission and spherical velocity field) shows up in both Data and Model as narrower/crisper minus- order ring images. * Is there a need to add some Fe lines in a ring component? E.g., to add emission between O VIII and Ne IX lines? Dan Dewey Poster 24.04, AAS HEAD Meeting, 2004

Poster 24.04, AAS HEAD Meeting, 2004 Model Calculations Given the coarse model, the product (n_e * n_i) for each ion species is determined in 3D space. At right the values along a radial slice are plotted. In the plot on the next page the values n_e(r) and n_i(r) have been self-consistantly calculated. Blastwave, n_e * n_H Ne IX Ne X O VIII O VII O IX O VI Mg XI Ne VIII Mg XII Mg X Dan Dewey Poster 24.04, AAS HEAD Meeting, 2004

Radial Profile of Densities n_e n_H, Blastwave Blastwave densities of elements (~0.3 solar) Mg XI O IX O VII O VIII O VI Ne X Ne IX Ne VIII Mg XII Mg X n_O n_Ne n_Mg Dan Dewey Poster 24.04, AAS HEAD Meeting, 2004

Calculating Element Masses Ion Mass, M_solar O IX 0.91 O VIII 2.43 O VII 1.92 O VI 1.03 O TOTAL 5.38 Ne X 1.04 Ne IX 0.66 Ne VIII 0.43 Ne TOTAL 2.13 Mg XII 0.08 Mg XI 0.35 Mg X 0.28 Mg TOTAL 0.71 Si XIII 0.12 Blastwave (H,He,etc.) 103.4 Using the values of n_ion obtained above, the mass of each element in the model can be calculated as the sum of masses of the individual ions, see Table at right. Note that non-X-ray visible ions such as O VI and Ne VIII have been included at levels with comparable densities to the X-ray visible ions --- compatible with a uniform homogeneous ejecta element distribution. Dan Dewey Poster 24.04, AAS HEAD Meeting, 2004

Poster 24.04, AAS HEAD Meeting, 2004 Further work… [Another aside: Is E0102's morphology/flux changing over the ~3 years between HETGS obervations ? Due to ionization changes rather than motion ?] Add spatial complexity to the model, e.g., azimuthal variation Note that the 3D array implementation allows adjusting each of the 3D array values to create essentially arbitrary emission distributions. Develop better comparison methods and tools There is a lot of information in the data - on small and large scales. Compare multiple data sets A single model can be used to output simulated HETGS, XMM/RGS, and Astro-E2/XRS data simulations. Compare each/all of these to their real data sets and adjust the model appropriately. Dan Dewey Poster 24.04, AAS HEAD Meeting, 2004

Hydra: The Bigger Picture The work to create a 3D model of E0102 described above is part of a larger effort we've named "Hydra". The block diagram at right shows the many heads of Hydra - the many components to the full 3D modeling process. The E0102 activies above are used to describe Hydra concepts and goals in the pages at right. (Hydra graphic from: http://www.pantheon.org/areas/gallery/folklore/greek_heroic/hydra.html) Dan Dewey Poster 24.04, AAS HEAD Meeting, 2004

Poster 24.04, AAS HEAD Meeting, 2004 Hydra: Block Diagram Dan Dewey Poster 24.04, AAS HEAD Meeting, 2004

Hydra: 3D Source Modeling and X-Ray "Rendering" The method of using 3D arrays to specify properties of the 3D model described above is just one of many ways to encode 3D information. Other possibilites include analytic descriptions with a component algebra. The generation of rays from the model can be viewed as a form of "rendering" and in the extreme it takes on all the complexity of radiation transport. Efficiencies in rendering may be improved by matching the source model properties with the method of encoding the problem. Dan Dewey Poster 24.04, AAS HEAD Meeting, 2004

Hydra: Comparing Data and Folded Model One issue to explore more is the method to compare multi-dimensional data sets, e.g., the dispersed images from "real data" with a forward folded (ray-traced) simulation output. It may be important and useful for human insight to guide the selection and definition of a fit metric for different fitting situations. For example, the ratio of flux (projected) interior to the E0102 ejecta ring compared with the flux in the limb of the blast wave may be very sensitive to, say, the blastwave shell thickness. Dan Dewey Poster 24.04, AAS HEAD Meeting, 2004

Hydra: Instrument(s) Modeling One goal of the Hydra effort is to allow and support multiple data sets from multiple observatories. As a simple example, the spectral image and histogram at left were created from the coarse E0102 model and folded through a simple approx- imation of the XMM RGS Grating response. O VIII Ne X O VII The width of the lines is due to both the spatial and velocity structure in the 3D model. Dan Dewey Poster 24.04, AAS HEAD Meeting, 2004