Instruments: LETG

In The Kitchen At Parties
As a humble scientist associated with a high-flying satellite conceived by a Nobel Laureate and directed by prominent Rossi Prize winners, people often corner me at cocktail parties or stop me in the street to ask "How is the calibration of the spectrograph instrumental profile going?" One can of course answer such a complicated technical question in a variety of ways. I usually choose "I think you must be confusing me with someone else" , or "Mmmm, those cheese and spinach nibbly things look nice".

Unless, of course, the inquisitor is an expert, such as a Chandra Users Committee member, a taxi driver, or a pizza delivery person. In this case one might point out before heading to the bathroom that, among all the other aspects of the Chandra spectrographs that are rather difficult to calibrate, the instrumental profile, or "line response function" (LRF) as it is referred to, is perhaps about the trickiest bit. At the X-ray Calibration Facility (XRCF) at Marshall Space Flight Center, many tests of the imaging characteristics of the instrumentation were devised and carried out. However, on the ground the primary mirrors were distorted under their own weight, and the electron impact X-ray sources were not quite points. The ground-based testing could only verify complicated models of the mirror and detector imaging performance including the gravitational distortion. The true performance of the system was only revealed later, in orbit.

Once flying, X-ray point sources can, in principle, provide the point spread function in exquisite detail. While the realities of effective area and detector performance tend to mock such principles - pile-up effects in ACIS mean that fainter sources are best, but these require long exposure times - the LRF is only onedimensional and so should be easier. All that is needed is a bright point source with narrow, isolated lines spaced every couple of Ångstrom or so between 1.2 and 170 Å. At this point, something strong to wash down the rich cheese and spinach nibbly things is a good idea.

Our best hope of bright, narrow lines in a cosmic point source is in the hot coronae of stars. In these plasmas, non-thermal velocities are hopefully rather small and, provided we choose a source with a small v sin i, intrinsic source line profiles should be dominated by thermal (Gaussian) broadening. However, atoms of Fe at a temperature of 10 million K have a typical velocity of about 50 km s^-1, corresponding to roughly 1/5 of the instrumental line width at a typical Chandra grating resolving power of 1000 - small but sufficiently large that it must be taken into account when trying to understand the instrumental broadening component. Useful lines of H-like ions are also broadened by their doublet splitting: the O VIII 19 Å Lyman α doublet splitting is 0.0055 Å, for example, or about 1/3 of a line width - small, but sufficiently large that it justifies another stiff drink while pondering the complications.

Like line blends that inevitably distort the wings of spectral line profiles in even the best diagnostic lines that have been carefully selected by model calculations to be relatively blendfree ..... Close examination of high quality spectra of even the most well-behaved sources, such as the Chandra grating calibration target Capella (G1 III + G8 III), will show that there is no single line whose profile remains untainted down to less than 90% or so of peak intensity. This is almost guaranteed by the pseudo-continuum of Fe and Ni "L-shells" for wavelengths less than 18 Å or so, and at longer wavelengths in the LETG bandpass by analogous transitions in other abundant lighter elements Ne-Ar.

Another problem is simply that of photon statistics. Placing the diffraction gratings behind the mirrors produces a sometimes disappointingly small slice of effective area for the first orders. The Chandra mirrors are also very slightly asymmetrically aligned and this is reflected in spectral line profiles; to do the calibration properly requires looking at positive and negative orders separately. From the point of view of the source, we are interested in photons from only a few bright lines that cannot be easily coadded because the thermal and non-thermal line broadening contributions at different wavelengths and for lines of different species affect the observed profile to different extents.

Now that a firm foundation of excuses is in place, and since a large crowd of eager eavesdroppers is now hanging on every syllable (that looks like Beyoncé over there), how is the calibration of the spectrograph instrumental profile going? Like methods used to calibrate the PSF, the LRF calibration involves more a testing of model predictions, rather than measurement of a quantity that is then used to derive the calibration product. Coincidently, this approach also has the striking advantage of being much easier - innocent until proven guilty of calibration.

FIGURE 6: Capella MEG + ACIS-S profiles for the Fe XVII 15.01 Å resonance line, in both plus and minus orders (solid black), with theoretical profiles overplotted (dashed red).

In the Newsletter 10 (2003), I described some artifacts of the HRC-S imaging characteristics that lead to distortion and nonlinearity of the dispersion relation and distortion of line profiles. We therefore began looking seriously at the LRF using ACIS-S data - HETG+ACIS-S because few observations of stellar coronae have been taken with LETG+ACIS-S and there is not much data on which to base a calibration. The first step involves a spectral analysis of HETG+ACIS-S observations of Capella in order to understand its thermal structure, or emission measure distribution (EMD) with temperature. Using this function, thermal broadening profiles can be constructed. Capella is a binary system with a period of 104 days and a velocity separation of about 50 km s^-1 at quadrature - small but sufficiently large to be annoying - so we choose an observation taken at conjunction. We still need to consider the rotational broadening of the G1 component. We do not know the scale height of the coronal emission, or whether one star or other dominates the signal, but we can convolve in a surface rotational broadening function with half of our synthetic signal as a reasonable guess. Finally, the LRF is mixed in. This is available in CIAO in Response Matrix File (RMF) form. These files were produced by Bish Ishibashi of the HETG MIT group and are based on fits of analytical functions (Gaussians + Lorentzians) to the LRFs predicted by MARX raytraces. These raytraces also include the small blurring effects of imperfections in the Chandra pointing aspect reconstruction. The LRFs of both HETG and LETG are dominated by the mirror response; there appears to be no significant broadening from the gratings themselves and scattered light from the gratings is negligibly small. The observed and synthetic line profiles for the Fe XVII resonance line at 15Å are illustrated in Figure 6. This line is one of the brightest available in Capella, yet in one 30 ks observation we are down to 300 or so counts per pixel in the negative order. The synthetic profile appears to be largely innocent, and matches the observed one rather well in general, though there is perhaps a hint that the red inner wings are narrower than predicted. The outer wings have too little signal to provide a definitive LRF test. An equally good match to the observed line profiles from XRCF tests on the ground was found to be provided by the function

where a is the amplitude, Γ is a characteristic line width, I_λ is the observed intensity of a line centered on λ_c and β ~ 2.5. This function also translates nicely to flight data, though there is a bit of cheating here because the function width can be left free to vary to obtain the best match to the observed profile.

We can also compare the widths at half maximum intensity of observed and synthetic line profiles. The line FWHM is less sensitive to low-level blends than the full line profile, and we can measure it quite accurately in both observed and synthetic line profiles by fitting functions such as that in Equation 1. Line widths were derived in this way in a recent paper by Chung et al. (2004) for Capella and also for Algol (B8V + K2 IV; P_orb= 2.87d). While line widths for Capella were found to be fairly consistent with synthetic profiles, those observed in Algol seem systematically too large and indicate that extra broadening in the source is at work - either a radially extended corona or nonthermal plasma motion (Figure 7).

FIGURE 7: Illustration of the observed line widths of six emissionlines for negative, positive, and coadded orders, for Algol (upper panel) and Capella (lower panel). The negative and positive order wavelengths have been shifted slightly for clarity. The solid horizontal line indicates predicted line widths. While the theoretical and observed line widths are consistent with each other for Capella, the Algol observed line widths show a significant excess as compared to theoretical values.

The next steps will involve more rigorous tests from coadded data with greater signal-to-noise ratio and application to both ACIS-S and HRC-S LETG spectra. It can be argued that accurate knowledge of the LRF is more important for the LETGS than for the HETGS at wavelengths < 20 Å - spectral lines will be more blended in the former, and the accuracy of disentanglement depends more critically on the description of the instrumental profile.

"Now, Britney, did I tell you about the time when the Project Scientist..."

Analyze That
One of the most spectacular LETGS observations of the year must be that of the nova V4743 Sgr. It became the brightest X-ray source in the sky at wavelengths above 25 Å (< 0.5 keV) in early 2003, and was caught for 25 ks by the LETGS as a target of opportunity (P.I. S. Starrfield). A preliminary analysis of its spectrum (Figure 8) was presented by Ness et al. (2003). While prominent resonance lines of C, N and O can easily be identified, unlike the case of low-density plasmas, the higher density environment of the nova atmosphere in the gravity of its degenerate host can support substantial absorption from excited states that are more difficult to identify. Determining the origin of the multitude of weaker lines gouging the continuum presents a considerable challenge.

FIGURE 8: LETG+HRC-S spectra of the nova V4743 Sgr for two different segments of an observation made on 2003 March 19. Identifications of resonance lines of C, N and O are indicated by vertical lines (solid: rest wavelength; dotted: shifted by -2400 km s^-1; from Ness et al. 2003).

More mysterious was the light curve extracted from both the 0th and 1st orders that showed extreme oscillatory behavior followed by a dramatic decline after ~ 17 ks of observations when the count rate dropped from ~ 40 cts/sec to practically zero within ~ 6 ks (Figure 9). Ness et al. found a period of 1325 sec (22 min) in the bright phase of the light curve that they tentatively associated with the rotation period of the white dwarf, but they had no explanation for the dramatic decline in flux.

FIGURE 9: Light curve of the 25 ks exposure (25 sec bins) of V4743 Sgr extracted in the designated wavelength intervals. Top: Complete wavelength ranges in 0th and 1st order. Middle: This panel shows the same data but now broken into ``hard'' and ``soft'' regions of the spectrum. Bottom: The time evolution of the hardness ratio.

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

References
Chung, S., Drake, J.J., Kashyap, V.L., Lin, L., Ratzlaff, P.W., ApJ, in press
Ness, J.-U. et al. 2003, ApJL, 594, L127

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