Painting the jungles of the imagination seems a wise choice compared with navigating the jungles of X-ray calibration. Excuse my cringeworthy metaphors, this article is late, and I have a poor set of standard candles.
The irony of the term ``standard candle" is actually quite appropriate here---what candle could ever be a standard? In an uncontrolled environment, like my office, which appears to be entirely out of my control, a candle flame flickers like any good cosmic point source of X-rays. The British Parliamentary Standard Candle of 1860 called for spermaceti with a melting point of 112-115° F mixed with a small amount of beeswax. The length was 10 inches, the bottom diameter 0.9 inches and the top diameter 0.8 inches. Even under controlled conditions its burn rate varied by 5% - still a good enough number for most X-ray calibration work though. Using paraffin wax and controlling the precise chemical composition of the candle helps with luminous stability (and keeps the sperm whales happy), as does a more precise specification of diameter and wick. Using the standard lamps and candles to light big fat cigars and adopting a simple definition of luminance based on the power of the source is even better, which is more or less what those Systéme International folk did in 1979.
Hot white dwarfs make the best point source standard candles in
the EUV and very soft X-rays. The LETGS uses two of them,
Sirius~B and HZ~43, as effective area calibrators in the
60 - 170 Ã… range. The HRC-S detector used with the LETG
was not absolutely calibrated on the ground below the
energy of the C inner shell K alpha line at 277 eV (44.76
Ã…). However, the LETG+HRC-S effective area can be
derived simply by dividing the observed raw spectrum of a
standard candle by its model spectrum. Model spectra are
computed for the appropriate stellar parameters using the
fully non-LTE radiative and hydrostatic equilibrium model
atmosphere programs PRO2 (developed by Klaus Werner and
co-workers, University of Tübingen) and TLUSTY (developed
by Ivan Hubeny and Thierry Lanz, NASA GSFC). We can
obtain sufficient signal for a quite precise calibration
(to a few percent on a ~ 1Ã… scale) in about 50ks of
exposure time: the problem is not
precision but
accuracy - like the difference between “precision
cosmology’’ and “accurate cosmology’’. While
the stars
themselves are, for our purposes at least, constant, unwavering X-ray
beacons of hope, the models of their emission are not.
These models flicker in the winds of model atmosphere
change. In the last several years, both atmosphere
modelling groups have reported improvements, such as in
the treatment of Lyman and Balmer line blanketing, and in
Gaunt factors. These lead to palpable changes in predicted
soft X-ray spectra. Fanned by a strengthening gale of
model atmosphere change, our standard candles seemed to be
going Roman at the 6 Years of Science with Chandra
Symposium at the beginning of November last year
(appropriately close to Guy Fawkes Night.
Electron scattering is an important opacity source in hot DA white dwarf atmospheres. Models currently employ Thomson isotropic scattering, whereby only the direction of photon propagation changes as the result of a scattering event. More rigorously, finite electron mass instead implies that both momentum and energy exchange should actually occur. Photon energies are reduced by each scattering event, such that emergent spectra are expected to be softer in X-rays when Compton Scattering is accounted for (though it is not quite so simple since Compton Scattering also induces a change in atmospheric temperature structure). Estimates made by Jerzy Madej (1998) for HZ43 suggested the frequency redistribution effects would only become significant at wavelengths < 50Å, where the flux is too low to be of any use for calibrating Chandra. At the Calibration Workshop, Jelle Kaastra (SRON) and co-workers suggested, based on new calculations, that Compton Scattering might be important after all, causing differences at wavelengths > 50 Å of more than 20% in emergent soft X-ray flux for both Sirius B and HZ43 compared with models using Thomson scattering. Jerzy Madej (University of Warsaw Astronomical Observatory) and Valery Suleimanov (Tübingen University) managed to dowse the flames by re-examining the problem with their customary rigour: new calculations, designed to avoid numerical pitfalls of earlier methods, show Compton scattering to be completely negligible for wavelengths longer than ~25 Å or so, where the flux is so weak and dependent on the exact temperature structure of the atmosphere model that other uncertainties dominate predictions by orders of magnitude. So, I think we can draw a line under that one. Now, if only people would let sleeping dog stars lie.
FIGURE 18: LETG+ACIS-S spectrum of PG 1211+143, transformed to the rest frame, in the 4 - 6 keV range, binned at 0.0125 Å intervals. Data (filled circles), error bars (dotted lines) and the best-fit absorption-line model are shown. If identified with Fe XXVI Lyα, the redshift of each line would correspond to velocities of 0.26c and 0.40c. Such redshifts could result from matter from a massive outflow falling back onto the central black hole. From Reeves et al. (2005).
You cannot be Sirius
At the time of the launch of Chandra, both Sirius B and HZ 43 appeared
to have fairly well-defined physical parameters based on
optical, UV and EUV observations. The most important for
understanding the soft X-ray flux is effective
temperature, though surface gravity (controlling the
atmospheric gas pressure) also interferes in the process.
In the case of Sirius B, many years of astrometric
measurements of the binary enable a reasonably accurate mass estimate.
The precise (and hopefully accurate) parallax
enables comparison of spectroscopic and astrometric
mass estimates and accordance inspires a greater
degree of confidence in the fidelity of the absolute
flux of model atmosphere predictions outside of the
ranges amenable to accurate absolute flux
measurement - soft X-rays perhaps.
The effective temperature and surface gravity of a DA white dwarf can be determined from the Balmer series. Until recently, the glare from Sirius A has prevented acquisition of a high quality uncontaminated visible light spectrum of Sirius B. However, since 1993 the trajectories of Sirius A and B have been taking them farther apart on the sky and Barstow et al. (2005) were recently able to obtain an HST STIS spectrum of Sirius B. From this they estimated a temperature Teff= 25,193 ± 37 K and gravity log g = 8.556 ± 0.010 - extremely precise measurements, though the formal uncertainties do not account for modelling systematics and uncertainties in underlying input data and physics in the atmospheric and radiative transfer modelling. The formal uncertainties also do not encompass the earlier temperature estimate of 24790 ± 100 K derived by Holberg et al. (1998) from IUE and EUVE observations (the surface gravity instead agrees with the older estimate of log g = 8.57 ± 0.06). The 1.5% difference between new and older temperatures seems a bit picky - it does not change the UV-optical spectrum appreciably - but unfortunately we are interested in the Wien tail which is exponentially sensitive to temperature.
Collaborations with Martin Barstow (University of Leicester) and Klaus Werner and Thomas Rauch (Tübingen University) aimed at a better understanding of the X-ray spectral energy distributions of HZ43 and Sirius B are ongoing. Catastrophic implications for the low energy LETG+HRC-S calibration are avoided by the necessity of matching existing EUVE data in the 100 Å range. EUVE detectors were calibrated on the ground to an absolute accuracy of 20% or so, so any changes to the lowest energy calibration of Chandra should be no larger than this. The existing stated uncertainty of the LETG+HRC-S effective area in the 60-170 Å range is 15%. A revision of this magnitude over the next 12 months is quite possible.
LETG Science: LETG Observes
Purple Haze
AGN are versatile
fellows: disks, winds, jets, putative black holes,
absorption lines, emission lines; they have it all.
A couple of years back, Pounds et al. (2003)
observed the narrow emission line quasar PG1211+143
with XMM-Newton and found blueshifts of
24000 km s-1 in the absorption lines of
H- and He-like ions of Fe, S, Mg, Ne, O, N and C.
Pounds et al. interpreted the absorption as arising
in a massive outflow---with a mass and kinetic
energy comparable to the accretion mass and total
luminosity of the source. PG 1211+143 was
observed again in June 2004, this time using the Chandra LETG+ACIS. From this
observation, Reeves et al. (2005) detected
absorption lines at 4.22 and 4.93 keV, corresponding
to 4.56 and 5.33 keV in the rest frame of PG
1211+143. Since there are no obvious transitions at these
energies that would be expected to give rise to such
absorption, either in the rest frame or at 24000 km s-1,
Reeves et al. concluded that the most likely culprit is
highly redshifted ionized Fe XXV or Fe XXVI. The
relativistic velocity shifts required for such redshifts
are rather large - 0.40c and 0.26c. To explain such
redshifts by gravity alone would require matter in a
stable orbit within 6 gravitational radii of the black
hole. As Reeves et al. note, this is within the last
stable orbit around a Schwarzschild black hole and would
require a Kerr metric.
Alternatively, Reeves et al. suggest the data could also be
explained by matter falling directly onto a central black
hole. One possible origin for such matter might be
fall-back from part of the massive 24000 km s-1 outflow
found from the XMM-Newton observation that does not escape
the central gravitational potential. Redshifts and
blueshifts at the same time. Or, as concisely summarised
by Jimi Hendrix,
"Purple haze all around, Don't know if I'm comin up or down".
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/Links/Letg/User/
Jeremy Drake for the LETG team
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