Home | Bibliography | Links

Observations in the soft X-ray band (~.05-2 keV) reveal diffuse emission in all parts of the sky. The lower energy flux is most likely produced by widely distributed hot plasma at a temperature of around one million Kelvin.

Snowden et al. (1998) used the ROSAT all-sky maps in the R12 band (1/4 keV) to attempt to model the diffuse soft X-ray emission with three components: a local component, a galactic halo component absorbed by a slab of neutral hydrogen, and a similarly absorbed extragalactic component with emission scaling as a power law in energy.

Earlier Wisconsin rocket observations of softer X-rays (sky survey B and C bands, UXT Be and B' bands) showed that the 1/4 keV count rates were proportional to the lower energy rates (McCammon et al. 1983, Bloch et al. 1986, Juda et al. 1991). Because lower energy X-rays are more likely to be absorbed, this implied that the source material responsible for the emission was local in origin and unabsorbed. However, more recent shadowing observations with ROSAT have shown that, in some directions, up to half of the observed 1/4 keV flux comes from behind distant molecular clouds (e.g., Snowden et al. 1991).

The Snowden model followed up the shadowing results by placing a large fraction of the 1/4 keV flux behind an absorbing layer of neutral hydrogen. However, it was unclear that this physical picture would be able to reproduce the observed proportionality with the lower energy bands because of the energy dependance of the absorption (E^-3).

Therefore, this project attempted to evaluate whether the Snowden model was capable of predicting correct count rates in the low energy Wisconsin bands.

Soft X-Rays and Thermal Plasmas
Soft X-rays may be produced by several radiative processes, but the dominant mechanism in the production of the diffuse Soft X-Ray Background (SXRB) is emission by a thermal plasma. In a hot (one to ten million Kelvin) plasma, a variety of variously ionized heavy elements will be present. Excited electrons of an element may transition to lower energy levels and emit a photon of a characteristic energy. For plasmas at these temperatures, the dominant transitions release photons with energies in the soft X-ray regime.

A number of spectral models have been produced which attempt to predict the spectra of plasmas as a function of temperature. The Snowden model was generated using the 1991 version of the Raymond-Smith model; more recent models include MEKAL and APEC. All of these models are subject to some degree of uncertainty, as the quantum mechanical equations needed to predict the spectra cannot be solved exactly.

Additionally, the brightness of specific emission lines depends in part on the prevalence of that element in the source plasma. Presently, however, there is a great deal of uncertainty in the interstellar abundances of specific heavy elements. (Detectors with the energy resolution necessary to resolve individual spectral lines did not exist until recently.) Observations suggest that abundances in these hot plasmas may be depleted with respect to solar abundances (Sanders et al. 2001), but there is no current consensus on reasonable abundances for use in modeling. The 1991 Raymond-Smith spectra used to produce the Snowden model were undepleted, although the spectra were cut off at 70 eV, which artificially removed some bright iron lines.

Detector Responses
The instruments considered in this study utilized gas proportional counters to detect X-rays. In these instruments, higher energy photons created higher amplitude pulses. However, their energy resolution was poor, so in order to most effectively utilize a small number of counts, filters were employed to divide incoming photons into bands.

For the Wisconsin flights, the bands were named after the elements used in the filters which created the high energy cutoff with their K shell absorption edges. The lowest energy band was the Beryllium (Be) band, with an effective energy around 100 eV. The Boron (B) band sampled energies around 170 eV, and the Carbon (C) band measured the 1/4 keV flux. (Higher energy bands were employed as well, but are not of interest in this work.) The ROSAT R1+R2 (R12) band corresponded roughly to the C band.

Interstellar Absorption
The liklihood of a photon to be absorbed by a specific quantity of material is a strong function of energy and atomic number (z) of the absorber. At 1/4 keV and below, photons are most likely to be absorbed by the neutral hydrogen (NH) which exists in great quantities throughout the galaxy. Because of the E^-3 dependence of the absorption, however, the amount of absorption resulting from the same column density of NH varies quite sharply across bands. In particular, photons with energies in the Be band are completely absorbed by even the lowest column densities of NH observed out of the plane of the galaxy (~10²⁰ cm^-2). Thus, all photons observed in the Be band must originate locally. This constraint made it possible to evaluate the effectiveness of the Snowden model.

The Be Band
While it would have been possible to predict Be band count rates from the Snowden model directly, the number of counts predicted in a specific direction would just be proportional to the amount of emitting material in that direction. The constant of proportionality would be the ratio of the convolution (?) of the source spectrum with the two detector responses. To avoid additional reliance on the theorized spectrum, therefore, it was more useful to fit a ratio of Be band count rates to R12 count rates.

Comparing the fit Be/Snowden local R12 ratio and the fit Be/total R12 ratio provided a way to evaluate the accuracy of the physical picture assumed by the Snowden model. (R12 count rates were determined by averaging the rate maps over 15 degree triangularly collimated fields of view in the 25 Be observation directions.) If, as assumed in the Local Bubble model, all of the 1/4 keV counts originated locally, then the best fit should occur between the Be band rates and the total R12 rates--the Snowden model's placement of some of the emitting material behind an absorbing cloud would leave too few local R12 counts behind.

However, the best fit was in fact with the Snowden local R12 rate, suggesting that the multiple component picture is indeed plausible. The plots below show the two fits; marked points were excluded from the fits because of their proximity to unusual features. Note that the plot of Be vs. total R12 suggests a change in slope as the count rates increase, with the slope becoming shallower due to excess R12 counts from behind the absorbing material.

Be/R12(I0)=0.0139 (all points); Be/R12=0.0132 (low latitude points)


Be/R12=0.0096 (all points)

The B Band
Evaluating the effectiveness of the Snowden model for bands intermediate in energy between the Be and R12 bands is difficult, as absorption has decreased to the point where counts originating from the halo are significant. Thus, it is not sufficient to compare with single components of the Snowden model. Additionally, spectral models become even more important at this stage. As the initial fit of the components of the model required choice of a spectral model, reabsorbing the halo contribution would require the use of the same model. For reasons discussed below, though, use of that model did not seem worthwhile.

It was still possible to evaluate whether the data favored the Local Bubble schematic or the multiple component model, though. While counts will be observed in both the intermediate bands (here, the B band) and the R12 band, if absorption is present the the ratio of the counts from the halo will vary with the intervening column density due to the energy dependence of absorption. If both bands originate only locally, however, the ratio should be essentially constant.

The plot below shows the ratio (Observed B band - predicted local B band)/(Observed R12 - predicted local R12) plotted vs. average column density of NH. The ratio is equivalent to (Predicted Absorbed B band)/(Predicted Absorbed R12 band) vs. NH. The local R12 rates were obtained from the Snowden model local component map, while the local B band rates were calculated by scaling the local R12 map by the average ratio of B/R12 for low galactic latitude points (0.0946).

The overplot curve is the predicted band ratio vs. absorbing column, generated by an undepleted Raymond-Smith spectrum from XSPEC v.11. The temperature of the spectrum was chosen to give an identical R2/R1 ratio as the distant component of the Snowden model.

Constraints on Spectral Models
The Snowden model was generated from an undepleted 1991 Raymond-Smith spectrum, and temperatures for each component were chosen by matching the modeled R2/R1 ratios seen there. However, these spectra are fundamentally flawed, as they cannot predict correct band ratios for the lower energy bands.

By fitting band ratios for points at low galactic latitudes, it is possible to obtain band ratios for purely local emission, as the high column densities of absorbing material in the plane of the galaxy make contributions from outside the local component negligable. These ratios can then be compared with a convolved spectrum and detector response to test the accuracy of the spectrum.

This work computed low latitude band ratios of Be/R12=0.0132, B/R12=0.0946, C/R12=0.202, and B/C=0.471. For undepleted spectra, the Be/R12 ratio was characteristically high, while B/R12 was generally low. (One exception was the 1991 R&S spectrum; the version used began at 70 eV, leaving out several important iron lines and creating an artificially low Be/R12 ratio.)

Additionally, band ratios changed between versions of a spectrum; this is apparent when comparing the B/R12 ratios generated by the 1991 R&S and the undepleted XSPEC v.11 R&S, shown below.

Use of two depleted abundance spectra improved the band ratios for the appropriate local R2/R1 ratio. The depletions used were from Savage and Sembach 1996. The light depletions were computed from the abundances measured towards warm Zeta Ophiuchi, the heavy depletions from cool Zeta Ophiuchi. The plots below show Be/R12 and B/R12 as a function of temperature and spectrum. (UD=undepleted, LD=light depletion, HD=heavy depletion; X R&S refers to the Raymond-Smith model generated by XSPEC v.11.)

Correct local spectrum should predict Be/R12=.0139. Note that '91 R&S is inaccurate due to missing lines in the omitted lower energies.


A fit to about 17 fields of view in the plane of the galaxy gives a B/R12 value for the local component of .0946.

Perhaps surprisingly, this work found that the physical picture presented in the Snowden model (local emission plus absorbed distant emission) could model the lower energy Wisconsin bands. However, the spectral models used are inaccurate, as they do not predict band ratios which are consistant with earlier data. As the component fit of the Snowden model depended on the spectrum used, the inaccuracy of the spectral model means that the predicted components must also be inaccurate. Thus, it would be worthwhile to generate a new spectrum which would satisfy the band ratio constraints, then redo the component fitting with the new spectral model.

Update
Results published:
Bellm, E. C., & Vaillancourt, J. E. 2005, ApJ, 622, 959