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Chapter 9
LETG: Low Energy Transmission Grating

9.1  Instrument Description

The Low Energy Transmission Grating Spectrometer (LETGS) comprises the LETG, a focal plane imaging detector, and the High Resolution Mirror Assembly discussed in Chapter 4. The Chandra High Resolution Camera spectroscopic array (HRC-S) is the primary detector designed for use with the LETG. The spectroscopic array of the Chandra CCD Imaging Spectrometer (ACIS-S) can also be used, though with lower quantum efficiency below  ∼ 0.6 keV and a smaller detectable wavelength range than with the HRC-S. The High Energy Transmission Grating (HETG) used in combination with ACIS-S  offers superior energy resolution and quantum efficiency above 0.78 keV. The HRC is discussed in Chapter 7, the ACIS in Chapter 6, and the HETG in Chapter 8.

The LETGS provides high-resolution spectroscopy (λ/∆λ > 1000) between 80 and 175 Å (0.07-0.15 keV) and moderate resolving power at shorter wavelengths. The nominal LETGS wavelength range accessible with the HRC-S is 1.2-175 Å (0.07-10 keV); useful ACIS-S coverage is 1.2 to roughly 60 Å ( ∼ 0.20-10 keV).

A summary of LETGS characteristics is given in Table 9.1.

9.1.1  Scientific Objectives

The high resolution (∆λ ≈ 0.05 Å) of LETGS  spectra at longer wavelengths (\mathrel > 100 Å) also permits detailed studies of spectral line profiles in the X-ray region. These studies may provide non-thermal velocities of stellar coronae, flow velocities along active-region loops, orbital velocities in X-ray binaries, and upflow velocities in stellar flares. The LETGS also allows time resolved spectroscopy, 1-D spatially resolved spectra, and spectra of multiple point sources within its  ∼ 4 arcmin field of best focus .

Since the ultimate spectral resolution can only be achieved for point sources, the prime candidates for study in our Galaxy mainly comprise stellar coronae, white dwarf atmospheres, X-ray binaries, and cataclysmic variables. Extragalactic sources include relatively bright active galactic nuclei (AGN) and cooling flows in clusters of galaxies.

9.1.2  Heritage

9.1.3  Operating principles

9.1.4  Physical configuration

Figure 9.1: LETG Grating Element Support Structure, a machined aluminum plate approximately 110 cm in diameter that holds grating modules on a Rowland torus behind the Chandra mirrors.

Figure 9.2: Detail of the LETG Grating Element Support Structure showing grating modules mounted on the inner annulus.

Figure 9.3: A closeup view of the LETG GESS showing nearly three complete grating modules. Each module holds three circular grating facets, and each facet contains approximately 80 triangular grating elements.

Figure 9.4: LETG  facet structure schematic showing the basic shape of the individual grating elements and the relative sizes of the support structures. The upper view shows the complete grating element, which comprises the triangular coarse support, the vertical fine supporting bars, and the (horizontal) grating bars. The grating bars themselves are not shown to scale. In the upper view every 50^th grating bar is drawn, in the lower view every 10^th bar.

To reduce aberrations, the GESS is shaped to follow the Rowland torus. The basics of the Rowland geometry are shown in Figure 8.4. The primary readout detector (HRC-S ) is made of three tilted array segments which also follow the Rowland circle in the image plane (see Figures 7.2 and 9.5). Because the detector array elements are flat, the distance from the Rowland circle changes with position, and so the spectral resolution changes very slightly with wavelength. The secondary readout detector, ACIS-S, has 6 CCDs, each of which is only one-quarter as long as an HRC-S segment, so the ACIS-S array follows the Rowland circle even more closely.

Figure 9.5: The front surfaces of the HRC-S detector segments and their relationship to the Rowland circle are shown schematically. The scalloped line beneath them is the difference between the detector surface and the Rowland circle.

9.2  Calibration

9.2.1  Pre-launch Calibration

9.2.2  In Flight Calibration

Calibration of the LETGS effective area (EA) and HRC-S quantum efficiency (QE) at energies above the C-K edge (0.28 keV, 44 Å) relies primarily on observations of the quasar continuum source PKS 2155-304 and (earlier in the mission) 3C 273 and Capella. PKS 2155-304 also has been regularly observed with LETG/ACIS-S to monitor contamination buildup on ACIS (see Section 6.5.1) and for cross calibration with other X-ray missions. Mkn 421 largely replaced PKS 2155-304 as an ACIS contamination monitoring source starting in 2010, and RX J1856 (neutron star continuum source) was recently added for the same purpose. For calibration of the LETG/HRC-S EA at longer wavelengths, observations of the hot DA white dwarfs HZ 43 and Sirius B are used.

Early in the mission, most calibration targets were observed at least twice per year to monitor LETGS operation, but calibration observations are now less frequent. Regularly observed sources and monitoring frequencies are listed in Table 9.2. Other targets are occasionally observed to meet specific calibration needs that might arise, and ACIS-S and HRC-S (see Table 7.3) are routinely calibrated by themselves (i.e., without gratings).

9.3  LETGS Performance

9.3.1  Usage

Overview

The net LETG transmission is  ∼ 28% at energies below  ∼ 1 keV (about 12.5% for zeroth order, the same for 1st order, and a few percent for all other orders) so counting rates are usually not a concern with respect to exceeding detector limits or telemetry saturation. However, some bright sources (e.g. Sco X-1) if observed for long exposure times could cause significant charge depletion in the HRC MCPs (see Chapter 7, especially Section 7.13), and even moderate rates may cause pileup problems when using ACIS-S (see Sections 6.15 and 9.4.1). Some observers may find it useful to insert the LETG for imaging observations simply to reduce the detected photon counting rate.

Detectors

In rare cases it might be useful to use the HRC-S Low Energy Suppression Filter (LESF), as discussed in Section 9.4, in order to obtain a predominantly higher-order (m > 1) spectrum. The LESF is a region on the HRC-S UV/Ion Shield (UVIS) where the aluminum coating is relatively thick, and corresponds to the upper part of the "T" in Figure 7.1. Note that the Al coating on the LESF is thicker on the outer plates than on the central plate. See Figures 9.17 and 9.19 for the effect of the LESF on 1st and higher order effective areas.

When used with the ACIS-S detector, the effective LETGS wavelength coverage is reduced because of the smaller detector size in the dispersion direction (ACIS-S is only half as long as the HRC-S) and the fact that the two outermost chips (S0 and S5) have essentially zero QE for detecting 1st order LETG photons (see Figure 9.6). Another consideration is that ACIS has lower temporal resolution than HRC, which may be important when observing periodic or rapidly varying sources. In some cases, however, those disadvantages may be outweighed by the lower effective background rate and intrinsic energy resolution of ACIS, which can be used to separate diffraction orders. Note that the CTI-degraded energy resolution of the ACIS FI CCDs (Section 6.7) does not pose a problem for LETG point-source observations, since the source can be placed close to the ACIS readout, where the energy resolution is best.

Figure 9.6: LETGS 1st order effective area (EA) with ACIS-S and HRC-S, showing plus and minus orders separately; lower panel shows low-EA regions in more detail. The effects of dither and ACIS bad columns are explicitly included. Dotted lines mark ACIS chip boundaries, and HRC plate gaps appear near −53 and +65 Å. ACIS curve is for Y-offset=+1.5′ and HRC curve is for Y-offset=0'. EAs are taken from mid-2012; the LETG+ACIS EA is very slowly decreasing over time because of increasing contamination. Note its abrupt decline beyond  ∼ 28 Å as longer wavelengths fall on the FI S4 chip, whereas the BI S1 chip provides useful EA well beyond 50 Å. Y-offsets may be chosen to tailor the coverage of BI chips (S1 and S3), which have significantly higher QE at low energies than the FI chips. See Section 9.4.2/Offset Pointing for more information regarding the choice of Y-offset. See also Figure 9.17 which plots effective areas for combined plus and minus orders.

Off-Axis and Multiple Sources

9.3.2  Wavelength Coverage and Dispersion Relation

With a dispersion of 1.148 Å/mm for the LETG, the standard wavelength range of the LETGS with HRC-S is −164 Å to +176 Å. Physical coverage with ACIS-S extends from −87 to +84 Å when using Y-offset=+1.5′, but the poor low-E response of the outlying front-illuminated chips limits the effective wavelength range to −60 Å for negative 1st order and less than about +30 Å for the positive order (see Figure 9.6). Outlying chips may be useful, however, for collecting higher-order spectra.

Off-Axis Pointing and Detector Gaps

As noted in Section 9.3.2, there are gaps between detector segments which create corresponding gaps in the wavelength coverage of each order. The gaps in + and − orders do not overlap so that the combined wavelength coverage is continuous. The location of the gaps (neglecting the effects of dither) are listed in Table 9.3, which also lists the location of the HRC-S UV/Ion Shield inner "T" filter edge. Dithering the spacecraft will partially smooth these gaps, but observers may wish to adjust the source pointing if a favorite line falls in a gap, or to tune the wavelength coverage of the higher-QE back-illuminated (S1 and S3) ACIS-S chips. Standard HRC dither amplitude (full width, in both directions) is 40^′′ (1.95 mm), which covers 2.3 Å, and standard ACIS dither is 16^′′ (0.78 mm), or 0.9 Å.

Please see the "Checking your LETG/ACIS Obscat Setup" web page at http://cxc.harvard.edu/cal/Letg/ACIS_params. An interactive tool for visualizing spectral feature placement on the ACIS array as a function of Y-offset and source redshift is available there.

Dispersion Calibration

Position errors occur in both dispersion and cross-dispersion axes, though for spectroscopy the latter are usually not important because data are generally summed in the cross-dispersion direction. The magnitude of position errors in the dispersion axis for the central HRC-S plate range from 0 to  ∼ 0.05 Å, with typical errors of  ∼ 0.01-0.02 Å . The outer plates ( > 60 Å ) tend to exhibit larger errors of typically  ∼ 0.02-0.08 Å. The size of the position errors changes over spatial scales of the HRC readout taps, which are 1.646 mm apart (see Chapter 7 for details of the HRC). Spacecraft dither moves dispersed monochromatic photons of a given order over a region of the detector that is roughly 2mm square. Within any given dither region, then, monochromatic light will fall on detector regions that have different position determination errors. As a result, a narrow spectral line could suffer some distortion of its line profile and/or a small shift of its apparent wavelength. Such distortions or shifts could occur at the spacecraft dither frequency (see Chapter 5); observers should therefore exercise caution in interpretation of such periodic effects. Care should also be taken when interpreting the results of combined spectra from + and − orders, since these effects are not symmetrical about zeroth order.

The position errors appear to be stable in detector coordinates and to repeat in different observations for which the aim points are very similar. An empirical correction for the effect based on accumulated calibration and GO observations has been derived and is implemented in CALDB 3.2.0 as part of the HRC-S degap map. Details on the derivation of the wavelength corrections can be found on the "Corrections to the Dispersion Relation" page at http://cxc.harvard.edu/cal/Letg/Corrlam. After correction, the RMS deviation between observed and predicted wavelengths lines observed in Capella are reduced from 0.013 to 0.010 Å across the entire wavelength range of the instrument. Corrections for the outer plates ( > 60 Å) are much less effective owing to a lack of reference lines with adequate signal-to-noise ratio. For the central plate alone, the RMS deviation amounts to 0.006 Å .

For the purposes of observation planning, it should be assumed that individual observed line wavelengths could be in error by up to about 0.02 Å for λ < 60 Å, and 0.05 Å for λ > 60 Å. Despite the observed repetition in pattern from observation to observation, observers are reminded that the exact wavelength error for any given line depends on the exact position of the target on the detector. Small differences in actual aim point that occur naturally between observations as a result of uncertainties in aspect and target acquisition (see Chapter 5) mean that wavelength shifts for a specific line are not generally repeatable from one observation to another and might also be subject to small secular trends.

9.3.3  Resolving Power

When all these effects are combined, the LETGS line response function is generally  ∼ 40 μm FWHM. With a conversion of 1.148 Å/mm for the LETG, a good figure of merit for LETGS resolution is therefore 0.05 Å. Because the three segments of the HRC-S can not perfectly follow the Rowland circle (see Figure 9.5), however, resolution varies slightly along the detector, and is lowest near the ends of each detector segment. Resolution degradation is almost negligible when using the ACIS-S, since its six segments more closely follow the Rowland circle, although the coarser ACIS pixel size (24 μm vs.  ∼ 40-μm-FWHM LRF) means that line profiles are barely adequately sampled. A plot of LETGS resolving power for an on-axis point source, based on results from an observation of Capella, is shown in Figure 9.7.

Figure 9.7: LETG spectral resolving power, as derived from observations of Capella (Obs ID's 1248, 1009, 58) and Procyon (Obs ID's 63, 1461) with the HRC-S. The analysis is based only on spectral lines thought not to be affected significantly by blending at the LETGS resolution. Measured line widths were corrected for source orbital, rotational, and thermal motions. The dashed line is an optimistic error budget prediction calculated from pre-flight models and instrument parameters. The conservative solid curve is based on in-flight values of aspect, focus, and grating period uniformity. The deviations from approximate linearity near ±60 Å and at the longest wavelengths arise from deviations of the HRC surface from the Rowland circle (see Figure 9.5). Deviations in the experimental data from a smooth curve are likely caused by hidden blends not predicted by the radiative loss model and by detector imaging nonlinearities discussed in Section 9.3.2.

(9.1)

Figure 9.10 illustrates the χ² of fits to the zeroth order profile vs. β, and shows a best-fit profile with an index of  ∼ 2.5. (Note that β = 1.0 yields a Lorentzian profile.) The best fit to the very high signal-to-noise-ratio zeroth order profile is far from being statistically satisfactory. However, spectral lines seen in first order generally contain orders of magnitude fewer counts than in the zeroth order of the well-exposed calibration spectrum shown, and the Moffat function nearly always provides a good match. Line response functions can also be generated within CIAO in the RMF FITS format. These are based on ray trace simulations using the MARX program and generally match observed line profiles to a level of 10% or better once intrinsic source broadening terms have been taken into account. Observers wishing to use line profile shapes as a diagnostic tool should keep in mind that, in the case of LETG+HRC-S observations, non-linearities in the HRC-S imaging can lead to significant distortions of observed line profiles (see Section 9.3.2).

Figure 9.8: Observed LETG zeroth-order LRF from in-flight calibration observations of the active late-type binary Capella. The model profile, the continuous curve, is a Moffat function (see Equation 9.1) corresponding to the best-fit value of β = 2.5. While this function represents a statically-poor fit to this extremely high S/N zeroth-order profile, it is a good approximation to the LRF for lines in the dispersed spectrum containing many fewer counts.

Figure 9.9: LETGS line response function as illustrated by two bright Fe lines (Fe XVII at  ∼  17 Å and Fe XVIII at  ∼  94 Å ) using in-flight calibration observations of Capella. The solid curves are best-fit Moffat functions with β = 2.5.

Figure 9.10: LETGS zeroth order profile goodness of fit vs. β, showing a best-fit profile with an index of  ∼  2.5 (see Equation 9.1).

Extended Sources

The effect of increased source size on the apparent LETG spectral resolving power has been simulated using the MARX program, and results are shown in Figure 9.11. Another illustration of the effect of source extent may be seen in Figure 9.30 (Section 9.4), which shows model spectra over a small wavelength range.

Figure 9.11: LETG spectral resolving power for extended sources. The predicted LETG resolving power (E/∆E) is shown versus wavelength for several source sizes. The MARX simulator has been used, and the source is represented by a β model (Equation 9.2). For comparison, the spectral resolution for ACIS front-illuminated CCD chips is shown (thick solid line). Note that the ACIS/FI curve does not include the effects of CTI, which progressively degrades resolution away from the readout edge (most of this degradation can be compensated for in data analysis).

(9.2)

Off-Axis Sources

Figure 9.12: LETG spectral resolving power for off-axis sources. The predicted LETG resolving power (E/∆E) is shown versus wavelength for various off-axis distances. For comparison, the spectral resolution for ACIS  front-illuminated CCD chips is shown. Note that the ACIS/FI curve does not include the effects of CTI, which progressively degrades resolution away from the readout edge.

9.3.4  Grating Efficiency

Fine and Coarse Support Structure Diffraction

The two support structures each diffract roughly 10% of the X-ray power, but the coarse-support diffraction pattern is so small that essentially all its photons are collected along with the primary spectrum during spectral-region extraction in data analysis. A significant fraction of the fine-support diffraction pattern, however, may lie outside the spectral extraction region, resulting in a loss of several percent of the total X-ray intensity (see, e.g., Figure 9.23). The fractional retention of X-ray power in the source extraction region is referred to as the spectral extraction efficiency and is discussed in Section 9.3.5.

Total Efficiencies

Figure 9.13: LETG grating efficiency. Combined positive and negative order efficiency is plotted versus wavelength and energy. For clarity, even and odd orders are plotted separately; the sum of orders 11-25 is also shown. Plotted values include all support structure diffraction. Net efficiency when using a spectral extraction region (see Figures 9.14 and 9.15) is 10-15% lower. Features near 6 and 80 Å are due to the partial transparency of the gold grating material at these wavelengths.

9.3.5  Effective Area

Of the contributors listed above, the HRMA EA (see Chapter 4) is the best calibrated within the LETGS energy band. The largest contributor to the LETG/HRC-S effective area uncertainty is the efficiency of the HRC-S, especially at longer wavelengths ( > 44 Å ; < 0.28 keV) where ground calibration is very difficult or impossible. In-flight calibration (see Section 9.2.2), particularly of the net 1st order effective area, has provided the best and most extensive data, and the effective area is now believed to be accurate to a level of approximately 10-15% or better across the entire bandpass.

Effective areas for orders 2-10 have been calibrated relative to 1st order to an accuracy of 5-10% (best for 3rd order and generally worsening with increasing m), using both ground and flight data. Uncertainties for λ\mathrel < 6 Å, mλ\mathrel > 80 Å, and orders beyond 10th may be larger but are usually unimportant.

Instrument Spectral Features

Spectral Extraction Efficiency

Figure 9.14: A MARX simulation of a flat spectrum illustrating the broadening of the LETG+HRC-S  profile in the cross-dispersion direction, and showing the "bow-tie" spectral extraction window. Note that the vertical axis is highly stretched. The cross-dispersion profile of an LETG+ACIS-S spectrum is approximately constant across its smaller wavelength range and the default extraction window (not shown) is rectangular.

Figure 9.15: Spectral extraction efficiencies for LETG+ACIS for various extraction region half-widths (tg_d values listed in degrees). Approximately 10% of the total power is diffracted by the fine-support structure and most of it falls outside the extraction region; the peaks toward shorter wavelengths reflect the inclusion of progressively higher orders of cross-dispersed events within the extraction region. The otherwise general trend of declining efficiency toward short wavelengths is caused by increased scattering. The slight fall-off beyond  ∼ 60 Å is due to astigmatism, i.e., an increasing fraction of events are lost as the dispersion pattern broadens (see Figure 9.14). In 2010 the default spectral extraction region was narrowed from | tg_d | < 0.0020 to 0.0008 degrees after a slight misalignment between the dispersed spectrum and the extraction region was corrected.

Zeroth and First-Order Effective Areas

Figure 9.16: LETGS zeroth-order effective area for an on-axis point source for the LETG with HRC-S and ACIS-S detectors. The zeroth-order effective area for the HRC-S/LESF combination is the same as for the HRC-S. LETG+ACIS-S areas were computed using an effective area model that included the effects of contamination build-up extrapolated to the level expected in mid-2013.

Figure 9.17: LETGS 1st-order effective area for an on-axis point source, with HRC-S and ACIS-S  detector configurations with log (top) and linear (bottom) scaling. Positive and negative orders are summed. LETG+ACIS-S areas were computed using an effective area model that included the effects of contamination build-up extrapolated to the level expected in mid-2013. Note that the vertical scale of the linear plot has been truncated.

Off-Axis and Extended Sources

High-Order Diffraction Effective Areas

The relative contribution of higher-order photons with different detector configurations can be estimated by inspection of Figures 9.18, 9.19, and 9.20. As an example, say an observer plans to use the LETG/HRC-S configuration and wants to determine the intensity of a line at 45 Å, but knows that line may be blended with the 3rd order of a 15 Å line which has 10 times the emitted intensity of the 45 Å line. Looking at Figure 9.18, we read the 1st- and 3rd-order curves at mλ = 45 Å and see that the 3rd-order value is about one-tenth the 1st-order value. Multiplying by 10 (the ratio of the emitted intensities of the 15 and 45 Å lines), we compute that  ∼ 50% of the feature at mλ = 45 Å will come from the 15 Å line. A fuller explanation, with color figures and more examples for the LETG/HRC-S with line and continuum sources, can be found at http://cxc.harvard.edu/ciao/threads/hrcsletg_orders/.

Figure 9.18: The combined LETG/HRC-S effective area, illustrating the relative strengths of 1st and higher orders, plotted versus mλ (top) and λ (bottom). Positive and negative orders are summed. Light shading in top panel marks plate gaps around mλ = −53 and +64 Å. See the text for an example of how to determine the relative strength of overlapping lines from different orders, and http://cxc.harvard.edu/ciao/threads/hrcsletg_orders/ for color figures and further information.

Figure 9.19: The combined HRMA/LETG/HRC-S/LESF effective areas for 1st and higher orders. Positive and negative orders are summed.

Figure 9.20: The combined HRMA/LETG/ACIS-S effective areas for 1st and higher orders. LETG+ACIS-S areas were computed using an effective area model that included the effects of contamination build-up extrapolated to the level expected in mid-2013. Positive and negative orders are summed.

9.3.6  Background

HRC-S Exposure Windows, Deadtime, and Timing Resolution

As long as the total counting rate is below the 183 cts s⁻¹ telemetry limit, detector deadtime is negligible (and recorded as a function of time in the secondary science .dtf files-net exposure time is recorded in the image FITS file header). During background "flares" arising from an increased flux of solar wind particles, however, the background rate may rise above the 183 cts s⁻¹ telemetry limit. During these times detector deadtime may become significant. Current data processing algorithms correct for this deadtime with a typical accuracy of  ∼ 10% or better.

Time resolution approaching 16 μsec can be achieved with the HRC if the data rate is below telemetry saturation. To leave ample margin for telemetry in case of background flares, a special Imaging Mode (see Section 7.11) is used for high-resolution timing observations. This mode utilizes only the central region of the HRC-S detector and provides a field of view of approximately 7′ × 30′. However, if telemetry saturation does take place then the time resolution with HRC-S is approximately the average time between events.

HRC-S Background Reduction Using Pulse-Height Filtering

Data collected or reprocessed in the Archive after June 2010 were processed with a time-dependent HRC-S gain map, which allows use of an associated pulse-height filter. This filter removes more than half of the Level 2 background at wavelengths longer than 20 Å, with a loss of only 1.25% of X-ray events (see Figure 9.22). Details, including instructions on how to reprocess older data, may be found at http://cxc.harvard.edu/cal/Letg/Hrc_bg.

Note that the HRC-S high voltage was raised in Mar 2012. The gain map for observations after this date is not as accurate as before because temporal trends are not yet well established. The background filter is still safe to use but will be slightly less effective on these post-HV-change data. The gain map will be refined as more calibration data become available.

Figure 9.21: Solar cycle and HRC-S background. Top: Monthly sunspot numbers and with 6-month smoothing; dotted curve is predicted. Bottom: Level 1 background rate is for the LETGS standard spectroscopy region, derived from AR Lac monitoring data. The "typical" Level 2 (L2) rate is 1.0×10⁻⁶ cts s⁻¹ pixel⁻¹, but this varies with the solar cycle. A simple model of the HRC-S background rate based on sunspot number (with a 1-year lag corresponding to the approximate time for the solar wind to reach the heliopause, where its magnetic field helps deflect cosmic rays from entering the solar system) is shown by the solid and dotted curve. Rates in Figure 9.22 correspond to a Level 2 rate of 1.1×10⁻⁶ cts s⁻¹ pixel⁻¹.

Figure 9.22: The Jan 2008 LETG+HRC-S background rate with and without pulse-height filtering. These Level 2 rates correspond to 1.1×10⁻⁶ cts s⁻¹ pixel⁻¹ (see Figure 9.21). Data are shown using the standard `bowtie' spectral extraction region (see Figure 9.14). X-ray losses from the observed spectrum as a result of the filtering for 1st order are  ∼ 1.25%; losses will be slightly higher for higher orders. See http://cxc.harvard.edu/cal/Letg/Hrc_bg for more information.

The mean of the pulse-height distribution increases weakly with photon energy, such that a factor of two difference in energy corresponds to a shift in the mean of  ∼ 8%. The mean of 8th order will therefore be about 25% higher than 1st order; the new PI filter removes 1.25% of 1st order at 160 Å, and about 11% of 8th order (λ = 20 Å, mλ = 160 Å). Extra filtering of higher orders will have negligible effect for nearly all analyses, but should be considered if deliberately studying wavelength ranges with very heavy higher order contamination.

Relevance for Observation Planning  

There are two backgrounds relevant for the LETG/HRC-S. The first is the Level 1 data event rate over the 3-plate standard spectroscopy region, which is 55-130 cts s⁻¹ during quiescence (see Figure 9.21), but can rise during background `flares' to cause telemetry saturation when the total (background plus sources) rate reaches 183 cts s⁻¹. The other is the filtered Level 2 background rate in the extracted spectrum. A "typical" rate of 1.0×10⁻⁶ cts s⁻¹ pixel⁻¹ (see Figure 9.21) corresponds to  ∼ 10-25 counts (depending on wavelength-see Figure 9.22) in a 0.07 Å spectral bin per 100,000 s integration during quiescence, which may be used for estimating signal-to-noise (see also the discussion in Section 9.5.1).

There is a third background rate which will be of interest when high time resolution (sub-msec) is required, which is the counting rate before any on-board screening is applied. See Sections 7.11 and 7.14.1 for more information on the HRC-S Timing Mode.

ACIS-S Background

9.3.7  Sample Data

Figure 9.23: HRC-S detector image of LETGS observation of Capella. In order to illustrate the stretching of the cross-dispersion axis, both axes are in Å with 1.148 Å/mm; only the central 30 mm of the central plate is shown. The full extent of the telemetered six-tap cross-dispersion window is shown and measures 9.9 mm. The areas of reduced background at top and bottom are due to dither effects. Star-shaped coarse support structure diffraction is seen around zeroth order, and "cat's whiskers" fine support structure diffraction is seen above and below the primary dispersion axis, as well as in the vertical line through zeroth order.

Figure 9.24: Detail of Figure 9.23, showing the LETG/HRC-S image of bright lines in Capella. Both axes are in Å with 1.148 Å/mm. The Fe XVII lines at  ∼  15 and 17 Å are the brightest in the LETG Capella spectrum. Faint features above and below the primary spectrum are due to fine support structure diffraction.

Figure 9.26: Extracted LETGS spectrum of Capella with some line identifications (from Brinkman et al. 2000, ApJ, 530, L111). Many of the lines visible between 40 and 60 Å are 3rd order dispersion of the strong features seen in 1st order in the uppermost panel.

Figure 9.27: LETG/HRC-S zeroth order image of Sirius A and B. The two stars are separated by  ∼ 4^′′. Flux from Sirius A is due to the small but finite UV response of the detector. The star-shaped structure is due to coarse support diffraction.

9.4  Observation Planning

9.4.1  Detector Choices

HRC-S  

• The HRC-S provides wavelength coverage from 1.2-175 Å  (10-0.07 keV).
• The HRC-S QE is smaller than that of ACIS-S in the 1.2-20 Å ( ∼ 10-0.6 keV) range, but larger at longer wavelengths (see Figure 9.17).
• The HRC-S provides the highest time resolution at 16 μs when telemetry saturation is avoided. The probability of avoiding saturation is significantly improved if only the central plate is utilized (see Section 7.11).
• The HRC-S suffers from small position non-linearities which may slightly distort or shift spectral features (see Section 9.3.2).
• HRC-S has essentially no intrinsic energy resolution and so overlapping spectral orders cannot be separated.
• The Level 1 HRC-S background count rate is typically 100 cts s⁻¹  in its windowed-down spectroscopic configuration during quiescence. (See Figure 9.21 for how this varies over the solar cycle). However, this can rise to exceed the HRC telemetry saturation limit of 183 cts s⁻¹ during background "flares". During telemetry saturation, deadtime is determined to an accuracy of 5-10%. Background flares can also be filtered out using CIAO or other software tools. These flares have been seen to affect 10-20% of some observations. Typical fractions are smaller than this; larger fractions are rare. If observing a very bright source where telemetry saturation is a concern, one can use a smaller than standard region of the detector (see Section 9.4.2).
• The LESF filter region in principle can be used to obtain a higher-order spectrum relatively uncontaminated by 1st order for wavelengths above 75 Å (E < 0.17 keV; see Figure 9.17). This could be useful either for observing features in a high order for high spectral resolution that cannot be easily observed with the HETG/ACIS-S combination, or for providing a direct observation of higher order contamination in conjunction with an LETG+HRC-S observation in its nominal configuration. NB: the LESF configuration has never been used in flight.

   Summary  

HRC-S is probably the best detector choice for spectroscopic observations in which one or more of the following observational goals apply:
-signal longward of 25 Å is of significant interest (see Figure 9.17);
-the highest time resolution is required.

HRC-I  

• When used with the LETG, the HRC-I provides wavelength coverage from 1.2-73 Å (10-0.17 keV).
• The raw HRC-I quiescent background event rate per unit area is lower than that of the HRC-S by about a factor of 4. After moderate filtering in both detectors, the ratio is about a factor of 2. This may be important for very weak sources.
• The HRC-I imaging capabilities are similar to those of the HRC-S, but its single flat detector plate cannot follow the Rowland geometry as well as the HRC-S. At nominal focus this results in slightly poorer spectral resolution for wavelengths > 50 Å. In principle, small focus offsets can be used to optimize the focus of the dispersed spectrum either within a specific wavelength range, or to average defocus blurring over the full wavelength range. No simple focus optimization prescription currently exists; interested readers should contact the CXC for assistance.
• The details of the LETG+HRC-I effective area have been less well-studied in general than for the LETG+HRC-S combination. The polyimide used in the HRC-I UV/Ion shield is about twice as thick as that used with the HRC-S, resulting in lower transmission at long wavelengths.
• The HRC-I offers a broad detector in the cross-dispersion direction and this might be a consideration for observation of sources with extended components exceeding  ∼ 2 arcmin or so. Note, however, that the Chandra spectrographs are slitless, and the effective spectral resolution is severely degraded for large sources (see Figure 9.11).

   Summary  

HRC-I is possibly the best detector choice for sources in which signal longward of 73 Å (0.17 keV) is not of primary interest and accurate effective area knowledge for > 44 Å ( < 0.28 keV) is not a strong concern, and in addition one or more of the following observational goals apply:
-the source is very weak with interesting spectral features at wavelengths beyond the limit of the LETG+ACIS-S coverage;
-high resolution timing is not required;
-a larger detector area in the cross-dispersion direction than is provided by the HRC-S is required.

ACIS-S  

• Contamination build-up on the ACIS-S detector has significantly reduced the effective area of the LETG+ACIS-S combination longward of  ∼ 20 Å since launch (see Section 6.5.1 for details). ACIS-S  provides an effective LETG 1st order wavelength limit of about 60 Å (0.20 keV) because longward of this the ACIS-S QE is essentially zero (see Figures 9.6 and 9.17). ACIS-S is not as well-calibrated for wavelengths longward of the C edge ( ∼ 44 Å).
• The intrinsic energy resolution of ACIS-S allows for discrimination between different and otherwise overlapping spectral orders. For dispersion longward of mλ ∼ 60 Å the LETG+ACIS-S  response is dominated by higher order throughput (Figure 9.17) and ACIS-S can therefore be useful for observing these higher spectral orders.
• ACIS-S allows several modes of operation (see Section 6.12) including continuous clocking (CC) if high time resolution is desired, or to avoid pileup.
• If using the full frame 3.2 s exposure of ACIS-S in TE mode, photon pileup can be a serious consideration, especially in zeroth order. Proposers should also be aware that there is a potential for pileup in bright lines and continua and not assume that, because of dispersion, the flux is too spread out to be affected. For observations using Y-offset=+1.5′, 1st order pileup losses in continuum spectra can be estimated as < rate in counts/frame/dispersion-axis-pixel > times roughly 3 for FI chips (4 for BI chips). As an example, if the counting rate of the 1st order spectrum is expected to be 0.01 counts/frame in a wavelength interval of 0.0275 Å (one pixel wide along the dispersion axis), about 3% of those events will be lost to pileup (in FI chips). While the example rate is observed only in very bright continuum spectra (such as Mkn 421 near 6.5 Å), pileup can be a concern for bright features in line-dominated spectra. Some of these events can be recovered by examining higher order spectra but most pileup events will have "migrated" out of the standard grade set. Pileup can affect both the shape of the PSF and the apparent spectral energy distribution of your source. Pileup may be reduced by opting for a "sub-array" that reads out a smaller area of the detector for a decrease in the frame time. See Section 9.4.2 and also Section 6.15 for details concerning pileup, its effects, and how best to avoid it.
• ACIS-S time resolution is lower than that of HRC and depends on the control mode adopted. In timed exposure (TE) mode the full frame exposure is 3.2 s. This is reduced when using a subarray due to the shorter read-out time for the smaller detector region (see Section 6.12 for details). Using fewer chips (e.g., dropping S0 and S5 because of their negligible effective area for 1st-order photons) may also slightly reduce the frame time. The highest time resolution possible with ACIS-S (2.85 ms) is obtained in continuous clocking (CC) mode, but imaging information in the cross-dispersion direction is lost and the background will be higher due to the implicit integration over the entire cross-dispersion column of the detector.
• The energy resolution of the FI chips degrades as distance increases from the CCD readout because of CTI (see Section 6.7). The LETG dispersion axis is parallel to the ACIS-S readout and the spectrum of a point source can be placed close to the readout such that the energy resolution degradation is no longer a significant problem; a default SIM-Z offset of −8 mm is routinely applied to LETG+ACIS-S point source observations. If observations with extended sources are under consideration, or if for other reasons a SIM offset is undesirable, the resolution in the FI CCDs of the ACIS-S array might be a point to consider. From an LETG perspective, the effects of concern are a degradation of the CCD energy resolution that is employed for order sorting, grade migration that can make for difficult calibration of detector quantum efficiency, and, at longer wavelengths (\mathrel > 50 Å), a loss of events that have pulse heights below that of the ACIS event lower level discriminator. These effects render the effective area at wavelengths longward of the C edge ( ∼ 44 Å) less well-calibrated than at shorter wavelengths.
• The ACIS-S energy resolution enables removal of the vast majority of background events in LETG spectra; the effective ACIS-S background is consequently much lower than that of HRC-S or HRC-I.

   Summary  

ACIS-S is possibly the best detector choice for sources for which signal longward of 25 Å (0.5 keV) is of little interest and one or more of the following observational goals apply:
-Particular spectral features of interest occur where the LETG+ACIS-S effective area is higher than that of LETG+HRC-S
-High time resolution beyond the 3.2 s exposure of TE mode (less if a subarray is used), or the 2.85 ms of CC mode (if applicable), is not important
-A low resolution zeroth order spectrum from the S3 BI chip is of high scientific value, in addition to the dispersed LETG  spectrum
-Order separation is important
-Pileup can either be avoided or mitigated or is not likely to be a problem.

9.4.2  Other Focal Plane Detector Considerations

Instrument Features and Gaps

Dither

In special cases, different dither amplitudes can be specified by the observer, though it must be kept in mind that detector safety constraints, such as accumulated dose per pore in the HRC (see Section 7.13), must not be violated.

SIM-Z Offsets

In the case of LETG+ACIS-S, a standard SIM-Z offset of −8 mm is applied to point source observations, unless otherwise requested by the observer, in order to place the source closer to the ACIS readout. In the case of extended sources, this offset might not be desirable as it could place part of the source off the detector. The effects of spacecraft dither should always be considered when choosing a SIM-Z offset.

Offset Pointing

Pointing off-axis in the observatory y axis can be used to change the wavelengths at which detector gaps occur, or to change the wavelength corresponding to the ends of the detectors. Examples of offset pointings are shown in Chapter 3. When choosing offsets, an increase of +1 arcmin in Y-offset corresponds to a shift of +3.36 Å in wavelength. As an example, by invoking a +2 arcmin offset pointing (see Chapter 3 for the convention), the long-wavelength cut-off of the HRC-S can be extended in the + order from approximately 176 Å for on-axis pointing to 183 Å. This, of course, is obtained at the expense of a commensurate shortening of coverage in the − order.

Offset pointing leads to degradation of the PSF, and consequently the spectral resolution-see Figure 9.12. For offsets of 2 arcmin or less this degradation is very small. For offsets of > 4 arcmin, spatial and spectral resolution will be considerably degraded.

In the case of the LETG+ACIS-S configuration, certain offsets might be useful, e.g., in order to place features of interest on (or off) backside-illuminated chips for better low energy quantum efficiency. Table 9.3 and Figure 9.6 can be used to determine what offsets are required. There is also an extremely useful visualization tool on the `Checking Your LETG/ACIS-S Obscat Setup' page (http://cxc.harvard.edu/cal/Letg/ACIS_params), which incorporates the latest detector aimpoint calibration (see Section 6.10). Four particularly important Y-offsets are the following:

+0.15′ This is the default Y-offset value and provides the highest possible resolution while avoiding dither across the node0/node1 boundary on the S3 chip.
+1.50′ This is the most commonly used offset, as it keeps O K-edge features on the S3 backside chip. Zeroth order is moved toward the S2 chip by 4.5 mm and changes the S3 coverage to −0.7 to +26.5 Å (after excluding 0.45 Å on each dithered edge of the chip). Spectral resolution is  ∼ 20% worse than with Y-offset=0.
+1.55′ This is the largest offset that can be used and still have zeroth order  ∼ completely on S3 (using the standard 16^′′ dither and an extraction region with 5-pixel (2.5^′′) radius) while allowing an adequate margin ( ∼ 5^′′) for errors in target acquisition and aimpoint scatter. Resolution is very slightly worse than with +1.50′.
+1.91′ This puts zeroth order in the gap between S2 and S3; a small fraction of zeroth order events will fall on each chip because of dither. There will be uninterrupted spectral coverage (apart from chip-edge dither effects around 29 Å) by the BI chips (S1 and S3) from 0 to 57 Å. Spectral resolution is degraded by  ∼ 25% (see Figure 9.12).

ACIS-S Modes

Frame times as short as 0.6 s can be used with four ACIS-S chips, or 0.5 s with three chips. See Section 6.12.1 for further information on ACIS frame times. Users should always refer to "Checking your LETG/ACIS-S Obscat Setup" (http://cxc.harvard.edu/cal/Letg/ACIS_params) for the most current information regarding subarray setups, including the optimal ACIS Start Row parameter, which slowly drifts with the telescope aimpoint over time (see Section 6.10).

Optional ACIS-S Chips and Scheduling Flexibility

As described in more detail in Section 6.20.1, the continuing gradual degradation of the Chandra thermal environment means that a steadily increasing fraction of observations are experiencing scheduling constraints with regard to the allowable exposure time per orbit. One way to increase the scheduling flexibility of LETG+ACIS-S observations is to use fewer than the full array of 6 CCDs, which reduces the temperature of the ACIS electronics and focal plane. To achieve this, users may denote some ACIS chips as "Optional." In cases where thermal limits might otherwise be breached, Optional chips will be turned off for an observation; this allows Mission Planning more flexibility when setting up observing schedules and makes the process more efficient. Problematic observations with Optional chips are thus less likely to be split into multiple pieces than they would be if all the chips are required.

Note that chips S0 and S5 have negligible QE for LETG 1st order dispersed photons; those outermost chips are only useful for collecting higher-order spectra, or perhaps in other very special circumstances. The web page "Checking your LETG/ACIS-S Obscat Setup" (http://cxc.harvard.edu/cal/Letg/ACIS_params) and the Spectrum Visualizer tool linked there are helpful in determining which CCDs may be unnecessary. As of Cycle 13, the S0 chip will turned off in all LETG+ACIS-S observations unless the observer provides a compelling reason for its use. We also recommend that S5 be turned off or marked as Optional.

HRC-S Windowing

Likewise, a smaller detector region can be used if, for example, the source is very bright and telemetry saturation is a concern. In such a case, the number of cross-dispersion taps could be reduced, since the source only dithers across 2 or 3 taps. There would be less area for the background extraction region, but with a bright source this would not be a problem.

One can also specify that a subset of taps along the dispersion direction be used, particularly if the source spectrum is expected to be cut off at long wavelengths and higher-order spectra are not needed. The most commonly used (though still rare) non-default configuration is simply to use only the central plate with the standard 6 cross-dispersion taps, usually referred to as the Imaging Mode.

When considering defining a special HRC-S window, it is reasonable to assume that the detector background is spatially uniform for the purposes of computing the total source plus background count rate. The telemetry capacity of 183 cts s⁻¹ should be kept in mind to avoid telemetry saturation by using a window that is too big.

9.4.3  General Considerations

Complications from Other Sources

In some circumstances, photons from bright sources outside of the direct field of view of the HRC or ACIS might be dispersed by the LETG onto the detector.

Particular attention should be paid to optically-bright and UV-bright sources, even if these are some distance off-axis. The ACIS-S and HRC-S filters are much more transparent to optical and UV light than are those of HRC-I and ACIS-I (the HRC-S central "T" segment is closer in performance to that of HRC-I, but has completely different thicknesses of polyimide and Al layers). As an example, an observation of the bright A0 V star Vega (V=0.03) in one of the outer HRC-S UVIS segments gave a count rate of about 475 count s⁻¹.

The energy resolution of the ACIS-S detector enables removal by filtering of all photons except those in a fairly narrow wavelength or energy range corresponding to the wavelength or energy of photons in a spectrum dispersed by the LETG. This means that contamination of the dispersed spectrum by, for example, the zeroth order or dispersed spectrum of other sources might not be a significant problem.

However, a much better solution to problems of source contamination is, if it is possible within other observation constraints, to choose a roll angle (Chapter 3) that avoids the source contamination issue.

Roll Angle Considerations

Owing to spacecraft thermal degradation and increasing difficulty in scheduling constrained observations, proposers are reminded that only a very limited number of constrained observations can be accomodated. Technical justification for requested constraints must be provided. It is also important to remember that roll angle constraints will also impose restrictions on the dates of target availability as discussed in Chapter 3. Exact restrictions depend on celestial position. Their impact can be examined using the observation visualizer tool, downloadable from the CIAO home page at http://cxc.harvard.edu/ciao/.

High Order Throughput

   Scientific Utility:   Higher spectral orders provide higher spectral resolving power than the 1st order spectrum by the approximate factor of the order number m. For observations in which features are expected to be seen in higher orders, this capability could be scientifically useful.

   LESF:   The LESF (the region of thicker Al coating on the HRC-S UVIS) is untested in flight, but could be useful for obtaining a spectrum containing mostly higher order flux.

   Source Spectrum:   For some sources higher orders will contain very little flux and will not be an issue. Typical examples are hot white dwarfs or relatively cool stellar coronae with T ∼ 10⁶ K. Sources whose spectra are fairly weak in the region where the effective area of the LETG+HRC-S is highest ( ∼ 8-20 Å ; 1.5-0.6 keV) but gain in strength toward longer wavelengths will also be less affected by higher order throughput. Typical examples are blackbody-type spectra with temperatures T ∼ 10⁶ K or less, such as might characterize novae or isolated neutron stars.

   Estimates:   Figure 9.18 can be used to estimate high order contamination. PIMMS can be used for gross estimates of higher order count rates; the PIMMS higher order calculation uses an effective area curve for orders m > 1 combined.

   Instrumental Capabilities:   Order separation is straightforward with ACIS-S. With HRC-S orders cannot be separated.

   Spectral Modeling and Higher Orders:   Unlike ACIS-S, the HRC-S does not have enough energy resolution to allow order sorting of LETG spectra. However, by folding a spectral model through an LETG+HRC-S instrument response that includes all significant higher orders (generally ≤ 10), the whole spectrum can be modeled at once. The capability to generate and simultaneously utilize response matrices for multiple orders (which can be created for plus and minus orders 1-25) is available within Sherpa/CIAO, and these response matrices can also be used with other spectral analysis software such as XSPEC. Note that the response matrices do not include the small-scale wavelength distortions discussed in Section 9.3.2, and hence care must be taken when analyzing some details of line-dominated spectra, particularly line profiles.

ISM Absorption

Figure 9.28: The ISM transmittance within the LETGS bandpass for different values of neutral hydrogen column density 10¹⁷-10²² cm².

9.5  Technical Feasibility

Some additional technical limitations in MARX modeling of LETG+HRC-S spectra are detailed below.

9.5.1  Simple Calculation of Exposure Times and Signal-to-Noise Ratio for Line and Continuum Sources

Emission Line Sources  

The source signal S in a bin is the difference between the total counts and the background counts B. The estimated standard deviation of the source counts S in a spectral bin is given by Poisson statistics as:

Spectrometer count rates for emission features are given by

Using Equations 9.3 and 9.4, the signal-to-noise ratio for an integration time t is then

The exposure time required to achieve a given signal-to-noise ratio is then provided by inversion of Equation 9.5,

(9.6)

Using the signal count rate s_l, provided by the product of source flux (at the telescope aperture) and effective area as stated in Equation 9.4, we then obtain the two equations for the signal-to-noise ratio S/σ_S resulting from an exposure time t,

(9.8)

In this case one can of course simply chose a new bin size w′=Nw.

The difference between the continuum and the emission line case above lies in the units of F_c, which is a flux density. The equations corresponding to the line source Equations 9.7 and 9.8 are, for the signal-to-noise resulting from an exposure time t

(9.12)

PIMMS for Rough Planning Purposes

MARX Simulations

MARX has an important limitation for LETG+HRC-S observations in that instrument, sky, and particle backgrounds are almost always significant (see Section 9.3.6 and Figure 9.22) but are not directly included and need to be simulated or otherwise accounted for by the user. Background can be simulated by approximating it as a flat field and adding this simulation to that of the source (see http://space.mit.edu/CXC/MARX/). Another way of simulating background is to scale the background in Figure 9.22 after adjusting for solar-cycle variations in the background rate.

Figure 9.29: This figure shows the extracted 1st order spectrum for an 80 ksec observation of the AGN NGC5548. The input spectrum consists of a power-law plus a "warm" absorber (shown in the top panel). The simulated spectrum (bottom panel) has been corrected for the instrument response to give the flux from the source.

Figure 9.30: MARX simulation of spectra showing the effect of source extent. The panels show (a) computed input spectrum, (b) a MARX output of LETG spectrum of a point source, (c) the same as (b) except that the source is a disc of uniform brightness with radius of 4", and (d) the same but with radius of 8". See Figure 9.11 and Section 9.3.3 for a discussion of extended sources.

9.6  References

• CXC Home
• Chandra: Public
• Astronomy Links
• iCXC (CXC only)
• Helpdesk

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