The standard processing of the ROSAT All-Sky Survey gives in addition to the position of the source the detected count rate and two hardness ratios as an estimator of the spectrum of the source.
The ROSAT pass band from 0.1 to 2.0 keV can be split into four bands
according to their Pulse Height Amplitude channels (PHA). Three of
these bands are independent:
A(0.1 - 0.4keV; PHA 11-40),
B (0.5-2.0keV; PHA 50-200),
C(0.5-0.9keV; PHA 50-200) and
D(0.9-2.0keV; PHA 90-200).
The two ROSAT hardness ratios HR1 and HR2 are defined as
the ratios of the number of detected photons in the respective band:
A soft source, dominated by photons in the soft band, has a negative hardness ratio, whereas a hard source has a positive value in its hardness ratio.
I was interested in how the distribution of the two hardness ratios
HR1 and HR2 evolves with count rate. I split my dark cloud sample
into four count rate intervals so that the number of sources per
interval was approximately equal. I then computed hardness ratio
histograms with a bin width of 0.2. I finally normalized the histograms
to the number of sources per 
. The histograms for
the two hardness ratios are shown in Fig. 1 (click here).
Figure 1: The evolution of HR1 (left) and HR2 (right) with
the source count rate
in the dark cloud sample (solid line) as compared to the
total galactic sample (dotted line). The histograms show
the number of sources per 1000 
per hardness
ratio interval. R gives the count rate in counts per second
Part of the obvious increase of harder sources with reduced count rate is instrumental. The combination of the ROSAT telescope and the proportional counter is most sensitive to photons around 1keV. Additionally, the point-spread function at higher energies is more narrow. This leads to a higher detection probability for harder sources in the source detection algorithm. A reliable estimate of these instrumental effects is difficult to access without extensive modeling of the detector and the source detection algorithm. I have therefore resolved to comparing the dark source sample with the average population of ROSAT sources in the galactic plane. Because these two samples differ only in their location on the sky, they will be equally affected by the instrumental response.
I used the ROSAT bright source catalog to select a galactic
reference sample. The ROSAT bright source catalog was published
by Voges et al. (1996) based on the ROSAT All-Sky Survey.
A total of 18,811 sources were detected above a limiting
count rate of 
. Of these 8547 sources are brighter than
. At this count rate level, the survey has a sky coverage
of 92 percent (Voges et al. 1996).
From this bright source list I selected all sources within 
of the Galactic plane. Of 18,811 sources in the bright source list,
5540 sources lie within 
.
I binned this much larger source sample in the same way as the
dark cloud sample. The histograms of the galactic sample are
plotted in Fig. 1 (click here) with a dotted line. Due to
the cut off at a rate of the galactic sample
is only shown in the three brighter count rate intervals.
Sources with count rates 
, that lie inside
the dark cloud fields, are in both source samples.
Figure 2: Logarithmic distribution of the number of detected
sources versus the count rate for sources in the galactic
plane (open histogram) and the dark cloud
sample (hashed histogram).
The galactic sample shows an artificial cut-off
at . The slope of the
galactic sample is -0.57, slightly steeper than -0.5
as expected for a uniform distribution in Euclidean space
Figure 2 (click here) shows the total distribution of count rates in the two samples. The dark cloud sample extends to lower count rates than the galactic sample from the bright source list. Due to the larger sampling area for the galactic sample there are a larger number of sources and more objects at the bright end of the distribution. The slopes of the two distributions are within the uncertainties the same. Both distributions are slightly steeper, -0.57 compared to -0.5, than expected for a uniform distribution in Euclidean space. This indicates that there is an excess of faint sources over the extrapolation from local sources.
The dark cloud sample contains 894 sources above a
count rate of within 
.
The bright source list contains 5540 sources above the same count rate
threshold within 
(). Thus I obtain
a source density of 
and 
respectively.
The two populations evolve quite similarly with count rate (see Fig. 1 (click here)). However at all count rate levels there is an excess of the hardest sources in the galactic sample compared to the dark cloud sample. A possible interpretation of this behavior are hard background sources that are screened out in the dark cloud sample due to the high extinction through the could.
The evolution in HR2 is quite different for the dark cloud sample and galactic sample. In all three count rate intervals the dark cloud sample shows a significant shift to softer sources. This is the opposite result that one would expect from a single source population, distributed isotropically in in the sample volume, differing only in absorption. I suggest that there are two populations present in this sample. A group of hard, distant sources that lie beyond the galactic dark clouds as indicated by the evolution in HR1. A second group of softer sources, preferentially coinciding with galactic dark clouds, dominates the evolution in HR2. However, these softer sources are not sufficiently soft to suggest the presence of accreting compact objects. More likely, they are due to coronal emission from stars.