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Subsections

LETG+HRC-S Effective Area

Dispersion Relation

Operations and Processing

Cross-Calibration with XMM-Newton

References

Instruments: LETG

Every once in a while, when the Netscape home page pops up in a new window,
for those of us who never get round to completing the arduous 5 second task of
setting a more sensible local home page, and after the mouse, operating by
mysterious forces and surely of its own volition, clicks not on the invitingly
dull grey ``Chandra Science'' button on the title bar but on poll: which
famous celebrity is your dream date?, one's eye can be caught by
intriguing minor headlines--intriguing on the scale of being slightly more
interesting than washing the kitchen floor, but somewhat less so than poll:
which famous celebrity is your dream date?--that promise fascinating
new insights into the human condition. One such study involved hapless
participants playing a computer game which psychologists had cunningly
programmed to temporarily freeze at certain moments. (No, it was not at one of
the CIAO workshops.)

The test is to see whether participants applied only the single mouse click
they knew, logically, was necessary, then waited patiently for results, or
whether mouse clicks were repeatedly applied in an irrational frenzy of childish
impatience. Uncharitably, my wife has no hesitation in pre-assigning me to the
latter group, claiming to have watched me perform the test in numerous data
analysis scenarios (at one of the CIAO workshops.)

The truth, however, is that my behaviour has been modified from its usual
cool rationality by a paranormal psi talent, a power that lowers a veil
of negative influence on the goings on of any machinery in my immediate
vicinity. Bugs appear in software that had worked perfectly in the hands of
others, programs freeze, random numbers aren't, 99% confidence becomes somewhat
iffy. It goes without saying that the perfect code I write myself seems to get
perturbed into horrible states of error when run. Even, inexplicably, when run
by others. So, when called upon every year or so, it is with some considerable
relief and gratitude that I cut-and-paste into the Chandra Newsletter
draft the usual ``The last twelve months have seen flawless operation of the
LETG, and at the time of writing, the LETGS with both HRC-S and ACIS-S detectors
is operating nominally, blah blah blah.'' Fortunately, mine is not a long-range
force and the data the instrument is returning, happily insulated by thousands
of miles of near-vacuum in its high elliptical orbit, are jolly impressive.

LETG+HRC-S Effective Area

Well, most of it is anyway. One much anticipated Chandra event was the first
acquisition of a high resolution spectrum of an isolated neutron star. When
still X-ray bright, such objects are expected to have temperatures in the range
of a few hundred thousand to a million degrees K, and so their spectra are
expected to peak nicely in the LETGS bandpass. In 1997, Frits Paerels at
Columbia published an important paper pointing out that the gravity-sensitive
Stark broadening of X-ray lines of ionised metals in a neutron star atmosphere
could be used, together with their observed gravitational redshift, to provide a
simultaneous measurement of mass and radius--quantities that could provide
useful constraints for the equation of state of ultra-dense matter. A 55 ks
LETG+HRC-S observation of one of the more promising candidates in the isolated
neutron star pageant, RX J1856.5-3754, was finally obtained in 2000 March. The
spectrum was nicely analysed by Vadim Burwitz at MPE and collaborators.
Fascinatingly, it exhibited................. absolutely nothing and was
perfectly consistent with a blackbody spectrum.

Figure: The combined positive and negative order
spectra of RX J1856.5-3754 binned at 0.5 Å intervals shown with a best
fit blackbody model. After allowance for calibration uncertainties at the C K
edge and over broader wavelength intervals, the deviations from this model are
just about consistent with Poisson statistics. The apparent edge at 60 Å
results primarily from one of the HRC-S plate gap boundaries and small
residual QE differences between positive and relative negative order outer
plates. (Figure drawn by Herman Marshall).

LINK
TO POSTSCRIPT FILE for Figure 10.1

Last year's TAC subsequently declined a deluge of three proposals requesting
a significantly longer exposure to draw out those diminutive spectral features
lurking bashfully in the grassy noise of the 55ks exposure. It was then left to
Our Director to wield the noise-cutting scythe in the form of 450 ks of
discretionary time. The data were obtained in 2001 October, were carefully
shepherded through processing and, after a brief but intense V&V, the
co-added spectrum was finally ready for public release. Fascinatingly, it
exhibited.............. absolutely nothing and was perfectly consistent with a
blackbody spectrum (Figure 10).

Apparently bereft of any spectroscopic foothold on its glassy, precipitous
slopes, if we really knew that RX J1856.5-3754 was a pure blackbody spectrum in
the X-ray range it would make an excellent, though rather faint, calibration
target, peaking as it does in the 40-50 Å range and with no significant
higher order contamination shortward of 80 Å or so. The 25-70 Å range
is especially difficult to calibrate in-flight because of a lack of standard
candle point source targets. White dwarfs are too cool and show no appreciable
flux here, and one is left hoping for featureless AGN continua that, with luck,
are still described by simple power laws in this very soft range. Even if luck
holds, such spectra inevitably are complicated by higher spectral orders that
cannot be separated in the LETG+HRC-S combination.

As it is, based on the blackbody hypothesis, RX J1856.5-3754 does illustrate
nicely the current state of the LETG+HRC-S effective area calibration. The
effective area of this combination depends on the effective area of the HRMA,
the diffraction efficiency of the LETG, the transmission of the HRC-S UV/Ion
shield, and on the microchannel plate quantum efficiency. As outlined in an
earlier Newsletter article, this last quantity completely dominates the
calibration uncertainties in 1st order spectra. The comparison of the blackbody
fit to the observed data in Figure 10 shows areas of some systematic deviation
beyond the counting statistics amounting to about 10% or so, as well as areas of
smaller discrepancy. In this range, both the HRMA area and LETG efficiencies are
relatively flat with wavelength. We note, in particular, the apparent edge at 60
Å. This feature occurs at the HRC-S plate gaps and at, in this plot of summed +
and - orders, the transition from seeing only the +1 order in the approximate
range of the -1 order gap (-58 Å) to seeing only the -1 order in the approximate range of the
+1 order gap (-66 Å). This effect results from a residual discrepancy in the +1
vs -1 quantum efficiency calibration.

More globally, absolute calibration uncertainties are determined by the
normalizations and power law slopes adopted for AGN calibrators--with most
weight placed on our primary calibrator PKS2155-304--and at longer wavelengths
on knowledge of the absolute flux of our primary white dwarf calibrators
Sirius B and HZ 43. At shorter wavelengths ( 20 Å) cross-calibration with HETGS suggests the LETG+HRC-S
effective area is good to about 10 % or so, absolute. Toward longer
wavelengths, and in higher spectral orders, uncertainties are likely to be
larger--we estimate about 15 % or so for the former. Higher order
calibration uncertainties result from both the HRC-S QE and the LETG diffraction
efficiencies which have proved both difficult to model and to calibrate
empirically. Uncertainties range from about 20% in third order to factors of two
or more in still higher orders.

The LETG+ACIS-S calibration is currently more certain than LETG+HRC-S by
virtue of the QE calibration of ACIS-S, and again, for 1st order, is presently
at a level of about 10 % in absolute terms. Progress in improving this
calibration will be presented in a future Newsletter.

A major milestone in the LETG+HRC-S calibration was recently achieved with
the inclusion of a spatially non-uniform HRC-S QE map. This map was based on
data obtained by the HRC team in flat field tests immediately prior to the
instrument delivery, and now enables a fairly accurate HRC-S effective area,
with or without the LETG, to be constructed for general off-axis angles using
the CIAO tools fullgarf (previously mkgarf) and mkarf.

The LETG group has also recently made available response matrices that
we have constructed for LETG+HRC-S combined orders 1-6. We emphasise response
matrices here because these are crucially different from the RMF/ARF
approach adopted by CIAO, in which effective area and spectral response
functions are separated into two separate entities. As will be well-known to the
majority of readers, a response matrix is comprised of an instrument
spectral response function normalised to its effective area. The difference is
important because the CIAO fitting engine Sherpa cannot at this time
model the overlapping spectral orders in the LETG+HRC-S response that requires
combining multiple RMF's/ARF's, whereas utilising a response matrix to
describe multiple orders is straightforward (as it is in XSPEC). The drawback to
the response matrix approach is the number of elements required in the
matrix to describe accurately the response in the higher spectral orders that
have higher resolving powers. The current matrices include orders 1-6. The
importance of orders above 6 will depend on the source spectrum, but for most
sources their omission should be of little consequence for wavelengths 50 Å. At longer wavelengths, omission of
higher orders could be a bit more important; if in doubt, the best approach is
to compute a trial model for increasingly higher orders until the incremental
change by adding further orders is small compared to the other uncertainties.
Such an operation can be done within CIAO, for example by using fakeit
for each spectral order in turn, then summing the resulting spectral orders
using SLANG. An analysis thread describing more precisely the exact steps
is in preparation. The effective areas for individual spectral orders are of
course available to perform the same type of computation in custom-written
software.

Dispersion Relation

In contrast to RX J1856.5-3754, and back to the jolly impressive, is the
LETG+HRC-S spectrum of the dwarf nova WZ Sge that undergoes an outburst
every 30 years or so. Caught in its latest at the Director's Discretion
following multiple TOO requests (PI P. Wheatley, Leicester University,
pressed Send first), its spectrum (Figure 11) is replete with a feast of
crinkly bits Slartibartfast could have won an award for had he turned to
astrophysics, and also bears more than a passing resemblance to a Stegosaurus'
rib cage. When time filtered and split into different orbital phases, the ribs
also wiggle about. While the identifications of some of the more prominent ribs
is straightforward by comparison with appropriate spectral line lists, there is
still much in there to discover for the spectroscopist/paleontologist, let alone
those studying the nova outburst itself.

Figure 11: The dwarf Nova WZ Sge.

LINK TO POSTSCRIPT FILE for Figure 11

To what accuracy could you measure the wiggling of the ribs? The answer
depends on the accuracy and stability of the dispersion relation. While now
perhaps the most difficult part of the LETG+HRC-S combination to understand and
calibrate, the dispersion relation is already pinned down to fairly good
accuracy for the central HRC-S plate. Geometrically, it is simple enough.
However, it was clear soon after launch that there were complications when one
or two narrow lines in the spectrum of Capella did not quite land exactly where
they should. Differences were small ( Å or less, compared to an instrument resolution of  Å), but measurable. Further study using
different targets that probe different wavelength regions has indicated that the
problem lies in detector spatial non-linearities localised to certain regions
with a millimetre scale size. One particular ``glitch'' occurs in the negative
order between about 17 and 22 Å. Work is ongoing to map out these spatial
non-linearities and to determine their exact cause and how to correct for them.
Outside of these problem areas, the dispersion relation for the HRC-S centre
plate is good to an accuracy of  Å. The outer plates also appear to show signs of spatial
non-linearity and exhibit larger departures from the dispersion relation of the
central plate. In particular, a primary departure appears to be that their
underlying dispersion relations are slightly different from that of the central
plate, with deviations reaching up to 0.05 Å. Again, we are working to map
out these effects, though analysis of the dispersion relation in the 70-170 Å
range is hampered by a lower instrument effective area and consequent paucity of
very bright spectral lines.

There is evidence that the LETG+ACIS-S dispersion relation could be
systematically different from that of LETG+HRC-S, based on the current sets of
parameters that describe the two instruments. This is impossible physically,
since both instruments share the same Rowland geometry; the discrepancy lies
elsewhere and work is ongoing to pin down the cause (likely due to a residual
small error in the pixel sizes of one, or both, of the instruments, or in the
ACIS-S plate gaps). The difference in the implied dispersion relations amounts
to a maximum of about 0.04% .

Regarding stability, we have never seen any significant shifts of spectral
lines from one observation to the next of the primary wavelength calibration
source Capella with either HRC-S or ACIS-S, confirming that the instruments are
very stable.

Operations and Processing

LETG operations were once again back to normal at the end of July 2001 when
the spacecraft systems group succeeded in implementing a software work-around
that enabled a return to commanded insertion and retraction. The original
problem was due to a HETG (rather than LETG) limit switch failure that onboard
software safety procedures used to prevent an undesirable clanging together of
LETG and HETG support structures should either be accidentally activated at the
wrong time. The software patch replaced the temporary procedure of inserting the
LETG ``by hand'' through commands that nudged it gradually into place.

The entire set of LETG+HRC-S data has recently been reprocessed in order to
correct for two problems found with earlier automatic processing. The first
problem pertained to filtering on status bit 21, which we found to be
appropriate for HRC-I but which was found to remove a significant number of
valid events in a spatially non-uniform way for HRC-S. This filter has now been
switched off for the S detector. The second regards the area of the detector
passed on to level 1.5 processing, which turned out to be slightly too small to
accommodate all of the region required for estimating the background spectrum.
The AP problems were corrected in the DS6.1.0 software release.

Cross-Calibration with XMM-Newton

A number of people have asked about cross-calibration with the other
X-ray observatory, the purpose of which is of course for the staff of the two
observatories to argue about whose calibration is best. Together with the
XMM-Newton Science Operations Centre, we have performed simultaneous calibration
campaigns starting in early 2000 on Capella, 3C 273 and PKS 2155-304.
The comparison is only waiting for the XMM-Newton data to become available.

Observer and proposer information and news on the performance of the Chandra
LETGS can be found on the instruments and calibration page:

http://cxc.harvard.edu/cal/Letg/

- Jeremy Drake

References
Burwitz, V.,
Zavlin, V. E., Neuhäuser, R., Predehl, P., Trümper, J., & Brinkman,
A. C. 2001, A&Ap, 379, L35

Paerels, F., 1997, ApJ, 476, L47

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