BD+30 LETG-ACIS spectral images from 6A (left) to 36 A (right).
From bottom to top, the images are:
LEG+1 [+53], LEG-1 [+53], LEG+1 [-25], LEG-1 [-25],
where the approximate roll angle is given in [ ]'s.

This web page summarizes some further analyses of the Chandra LETG-ACIS observations of the planetary nebula BD+30 3639. See Yu et al. 2009 and references therein for more information on the observations.

This page is a beginning, some further questions/items are:

• Why is the Eastern region bright ? Due to N_H variation? Temp? Interaction with denser material?
• Implement a spatially-varying N_H "screen" in the model and simulate line-images due to it.
• Is there significant ionized absorption that would modify the X-ray spectrum ?
• Use a tri-axial ellipsoid in the model; this may not change the projected image very much but would be more similar to Li et al. 2002..
• Better determine the absolute coordinates in the data/model to locate the WC star and other emssion relative to the X-ray.
• Put these analyses into context of other BD+30 papers/results.

Absorption: Ionized and/or Multi-N_H

Two effects may complicate the simple "wabs" model of X-ray absorption: i) ioniztion and ii) spatial variation. The "absori" XSPEC model is compared with the usual wabs model for three values of N_H in the plot at right. The green curves are for absori and wabs at a low N_H value, black curves are for the nominal N_H = 2.4x10^21, and the blue curves are for a higher N_H. Note that the enhanced transmission for the absori below ~ 0.6 keV will have a large effect on the O VII and C VI fluxes in particular. Varying optical extinciton, A_v, is seen over BD+30, ranging from roughly 0.5 to 5.0. The fit value of N_H of 2.4 (Yu+ 2009) is in rough agreement with an average A_v of 1.2. To check the effect of, instead, having a range of N_H, the transmission of a simple two N_H model is compared with the single wabs model. The magenta and orange curves, also on the plot, are from a 2-wabs model: "0.75*wabs(1)+0.25*wabs(2)" with wabs(1).nH adjusted to give the same transmission at O VIII (0.65 keV) as the nominal single wabs model. Four curves are shown, with wabs(2).nH set to 0.5, 0.33, 0.25, and 0.125 times the wabs(1).nH value. As this number gets smaller the curves deviate more from the nominal wabs (lower black curve) model. These curves suggest that the variation of N_H may not make a very dramatic change in model fitting except at the C VI lines where fluxes might be over estimated by a factor of 2 to 5. This plot was made using: analysis_absori.sl .

3D Spheroid images and the Li+ 2002 ellipsoid

As a starting point a simple model was made with a fixed arc of emsission (as suggested in Fig.6 of Kastener+ 2002) plus an adjustable spheroid of emission. Note that the "origin" of the model is x-ray center determined by tgdetect applied to the zeroth-order data; this is why the model appears off-center (image at right). Here are some diagrams sketched in Keynote using rotated 3D images from this "K02fig6nocrop" model: 3d_images.key.pdf - 448 kb 3d_images.key.tar - 3.8 Mb See the simple commands in analysis_3dimages.sl.

MCMC Fitting Plots for "K02fig6nocrop" model parameters

An MCMC "exploration" (e2d_mcmc_explore) was carried out to determine the best-fit parameter values of the model. The low-Chi^2 range in parameter space, as well as parameter correlations, are shown in the plots from the MCMC process below.

• fomlog_vsiter_plot.ps - the Chi^2 (=FOM) is plotted at each iteration for accepted (red) and rejected (yellow) MCMC points. Points within an acceptable range of the minimum value are shown with an "o" symbol here and in the 2D parameter-parameter plots as well.
• fomlog_xc_yc_plot.ps - 2D plot of XC, YC values with color coding.
• fomlog_rout_ratio_plot.ps - 2D plot of R_out, axis-ratio values with color coding.
• fomlog_rout_efrac_plot.ps - 2D plot of R_out, East_fraction values with color coding.
• fomlog_pa_ratio_plot.ps - 2D plot of PA, axis-ratio values with color coding.
• fomlog_pa_efrac_plot.ps - 2D plot of PA, East_fraction values with color coding.
• fomlog_history_plot.ps - plots of each parameter's value vs iteration, same color code.
  
  
• See the commands in analysis_mcmc.sl.
  Other files: bd30_data.sl , bd30_model_neivers2.sl

Spectral-line Images

Using the simple "K02fig6nocrop" model, it is possible to compare simulated dispersed line images with the actual data. Because the number of counts in the dispersed line-images is low (50 to 290) it is useful to combine the roll sets and focus primarilly on any differences between data and model in the bright (Eastern arc) region versus the more extended region. Because the "center" of the data/model is near the bright X-ray region, different rolls will have their bright region events overlap while the more extended emission will be separated. As an example, the three images below show the O VIII (~ 19A) line image as seen in the LEG+1 image for each roll angle and for their combination.

LEG+1, roll ~ +53 deg.

LEG+1, roll ~ -25 deg.

LEG+1, Combined rolls

The table below gives line-images for 12 lines in the BD+30 spectra and the C VI RRC region (25.0 to 25.7 A, see Nordon et al. 2009, arXiv:0901.1039). These are generally from the combined LEG+1 orders because of their greater sensitivity ("dat15" is in the filename of their 1d plots.) In four cases the combination of all 4 LEG spectra ("dat17") were used and for the C VI 33.73 A line the LEG-1 orders were used.

Besides the images, plots of 1D projections along the two axes, wavelength and cross-dispersion ("TG_D" in arc seconds), are given as well. Note that the data and model have been finely binned and smoothed, this helps show the individual events in the images.

The second plot, below the projection, is a K-S test plot showing the cummulative fraction of data and model events; the smoothing is not applied here. The "p-value" shows the chance that these are from the same underlying distribution and is generally greater than 0.1, suggesting that the data and model agree to the level of the statistics.

Looking at the images and K-S p-values, there are some images where the data (yellow dots) appear to have a significantly different distribution from the model (green):

• The O VIII Ly-beta line, 16.006 A. This line-image shows a clear concentration of events near the "bright" region and fewer in the more difuse regions. This is pretty significant with the K-S p-values of 2.4e-4 and 0.013 in the two projections. This 3--1 emission from oxygen may indicate enhanced recombination at that location ?
• The Ne IX He-beta line, 11.544 A. This line-image seems to be "hollow" with fewer than expected events near the center of the image. The 1D projections would not be the best way to test this, but even so the K-S p-value for the cross-dispersion distribution is low at 0.015 . Perhaps more humanly suggestive is the comparison of this with the other two Ne line-images: Ne X Ly-alpha (12.132) and Ne IX resonance (13.447). These three seem different with the Ne IX r spread out, the Ne X Ly-alpha somewhat more centrally peaked, and the Ne IX He-beta more ring-like in these images.
• The C VI RRC region, 25.0-25.7 A. There seems to be a clear "line" at about 25.5 A that is offset from the RRC (25.30) and is also separated from the series limit. Note that this excess also shows up in Fig.2 of Nordon+ 2009.

These analyses/plots were made with analysis_lineimages.sl .

Mg XI r 9.169 A (53 cts)
Ne IX He-beta 11.544 A (108 cts)
Ne X Ly-alpha 12.132 A (114 cts)
Ne IX r 13.447 A (289 cts)
Ne IX f 13.698 A (219 cts)
O VIII Ly-beta 16.006 A (75 cts)
O VII He-beta 18.627 A (83 cts)
O VIII Ly-alpha 18.967 A (221 cts)
O VII r 21.602 A (133 cts)
O VII f 21.101 A (69 cts)
C VI RRC 25.30 A (70 cts)
C VI Ly-beta 28.46 A (17 cts)
C VI Ly-alpha 33.73 A (57 cts)

Extended view of the RRC and the Lyman series limit

To get a better perspective on the 25.5 A events near the C VI RRC, the images and plots below cover from 24.3 A (left) to 26.6 A (right); the RRC is just left-of-center.
The data events are shown as yellow dots and the (higher-density) predicted MC model events are in green.
The highest Lyman series line in the model, Ly-delta, is near the right edge (n=5 --> n=1, ~ 26.35 A).
Data from the two rolls (see O VIII example above) are shown separately - because the 25.5 A events show up at each roll this rules out that they are due to a single contaminating source.
The 25.5 A events corespond to n ~ 11 --> n=1 transitions and the n=11 level is about 3000 A from the series limit.

Roll +53, LEG +1, C VI RRC region (90 cts)
Roll -25, LEG +1, C VI RRC region (84 cts)

These analyses/plots were made with Event-2D s/w using the files: analysis_rrc.sl, bd30_model_wRRC.sl, and bd30_data.sl .