6. X-ray Spectrometer (XRS)

Figure 6.1: The Astro-E2 XRS in the lab.

The XRS, shown in Figure 6.1, is the prime instrument onboard the Astro-E2 satellite, providing high resolution X-ray spectra for cosmic sources simultaneously over a broad range of energies, $\sim 0.3$ to 12 keV, at an unprecedented energy resolution of 6 - 7 eV (FWHM) with very good efficiency. It was constructed jointly by NASA/GSFC and ISAS/JAXA, based on principles of operation developed at NASA/GSFC and the University of Wisconsin. The XRS works by measuring the temperature difference resulting from an absorption of a photon, and thus it is a ``microcalorimeter'' (cf. Fig. 6.3). It will be the first such instrument flown on an orbiting observatory. While in principle it is a simple instrument, the details are complicated, as the sensors must be maintained at a precisely regulated cryogenic temperature. The X-ray sensors themselves, the signal processing electronics, the Adiabatic Demagnetization Refrigerator (ADR), and the liquid helium cryostat are supplied by GSFC. The cryogenic dewar, including the solid neon tank surrounding the helium tank, and the mechanical cooler, was built by ISAS and Sumitomo Heavy Industries in Japan, and the Filter Wheel was developed mainly at Tokyo Metropolitan University.

Figure 6.2: A schematic diagram of the entire XRS instrument, showing the main subsystems.

6.1 Principles of Operation of the XRS Detector

Figure 6.3: Principle of operation of the XRS. The deposited photon energy $E_{\rm ph}$ creates a temperature rise $\Delta T = E_{\rm ph} / C$, where $C$ is the heat capacity of the pixel. The pulse subsequently decays with the time constant $\tau$ of about $C/G$, where $G$ is the thermal conductance of the pixel supports.

The determination of the energy of the incident photon $E_{\rm ph}$ is accomplished by measuring the temperature rise $\Delta T$ (assumed to be much smaller than the heat sink temperature $T$) associated with its absorption. Schematically, the detector is illustrated in Fig. 6.2; it consists of a monolithic, etched silicon structure formed into an array of $6 \times 6$ pixels on a 0.64 mm $\times$ 0.64 mm grid. Only 30 of the 36 possible pixels in the grid are used as detectors^6.1. Each pixel consists of an etched silicon square with implanted thermistor with an absorber glued on top. The silicon thermistor is isolated from the heat sink by four etched silicon beams. The absorber is $\sim$ 10 $\mu$m above the plane of the silicon, and extends beyond the edges of the silicon beams.

The absorber size is 0.624 mm $\times$ 0.624 mm. If the thermal conductance between the thermistor and heat sink is $G$, and the heat capacity of the detector is $C$, then absorption of a photon with energy $E_{\rm ph}$ results in $\Delta T$ given by

$\Delta T = E_{\rm ph} / C$

and the detector returns to the heat sink temperature with a time constant

$\tau = C/G$.

The rise time of the temperature is $\sim$ 0.7 - 0.8 ms, and the $1/e$ fall time is about 3.5 ms, which determines the throughput as a function of the counting rate (see Sec. 2.3 and below).

The fundamental limit on the energy resolution of the detector is determined by the random transport of phonons between the detector and the thermal bath in the link connecting them and by the bandwidth of the measurement. For an ideal calorimeter with a resistive thermometer, this bandwidth is set by the Johnson noise. This is because the signal and phonon noise (which have the same frequency dependence) fall relative to the Johnson noise at high frequencies. For a detector of heat capacity $C$, operating at the bath (heat sink) temperature $T$, the limiting FWHM energy resolution is

$\Delta E = 2.35 \eta (k T^{2} C)^{1/2}$,

where $k$ is the Boltzman's constant. The variable $\eta$ is dependent on the design of the thermometer, and for XRS-like thermometers is of the order of 2. The XRS design uses an optimal filter technique, which requires multiple sampling of the pulse and weighted averaging of the samples over a time interval spanning several time constants. Since this must be done without an adjacent pulse present in the time series, this, in turn, sets the maximum counting rate.

The thermometers in the XRS detectors are resistive, operating on the principle of phonon-assisted electron hopping conduction, where the conductivity rises rapidly with an increase in temperature. In such a thermometer the resistance $R$ depends on temperature $T$ such that

$R = R_{\rm o} {\rm exp} ((T_{\rm o}/T)^{1/2})$.

These thermometers are ion-implanted into the individual pixels, and the contacts to the thermometer are brought out by conductive traces. The thermometer is biased at an approximately constant current via a voltage divider, and the increase in the temperature will appear as a change of voltage across it. The thermometers under bias have a resistance of the order of 30 M$\Omega$. The voltage across each thermometer is applied to the gate of a JFET source follower amplifier, with an output impedance of $\sim 2000 \Omega$. The JFET amplifiers are housed in a separate enclosure, since silicon JFETs need to operate at temperatures $\sim130$ K for the lowest noise, and thus need to be thermally isolated from the detectors and the ADR. The signal is subsequently sent to the Calorimeter Analog Processor (CAP). The CAP provides power to the detectors and further amplifies the signals (by a factor of 20,000). The CAP has 32 channels, each of which handles data from a single calorimeter pixel.

The energy resolution of the detector improves with decreasing heat capacity of the materials chosen for the substrate and for the absorber, and thus one of the challenges of the design is to find material of the lowest possible heat capacity that is sufficiently opaque to X-rays. Many materials, including silicon, the material used for the detector structure, have extremely low heat capacities at low temperatures. However, silicon is not suitable for X-ray absorption, since the large electronic bandgap allows many long-lived trap sites for the electrons, precluding rapid and efficient conversion of the X-ray to thermal energy. Thus, a separate absorber is needed. For the XRS, mercury telluride (HgTe) was chosen as the absorber, providing a relatively large opacity to X-rays with a relatively low heat capacity. The thickness of the absorber is $\sim$ 8.0 $\mu$m; this will stop 95% of 6 keV X-rays and achieve an energy resolution of 6 - 7 eV at 60 mK. The drop in the efficiency of the XRS at high energies is due to the absorber becoming transparent.

6.2 Details of the XRS Design

6.2.1 XRS Cryogenic System

In addition to the need to keep the heat capacity of the absorber to the minimum, the XRS must operate at a low temperature to minimize the phonon noise and maximize the sensitivity of the resistive thermometer. To achieve the required energy resolution ($\sim 6$eV FWHM) with the required detector size implies that the operating temperature must be below 0.1 K. For the XRS, there are four stages of cooling. The primary source of cooling is a 130 liter solid neon dewar. The life of the neon is extended by the use of a mechanical cooler which cools the outer radiation shield of the dewar. The solid neon maintains a temperature of $\sim$ 17 K, and surrounds a $\sim$ 32 liter tank filled with liquid helium. The liquid helium is vented to space, and maintains a temperature of $\sim 1.3$ K. The final stage of cooling is accomplished via the use of an adiabatic demagnetization refrigerator (ADR). This allows operation down to 50 mK; for the XRS, the nominal operating temperature will be 60 mK. Accurate temperature regulation is crucial, as the detector response depends directly on its temperature. A change in temperature results in a corresponding change in the energy scale calibration. Therefore the ADR is specified to maintain the temperature to better than 10 $\mu$K rms over a 10s to 10min timescale. Longer term temperature drifts are accounted for by a dedicated calibration pixel. Temperature control is accomplished by adjusting the magnetic field via a feedback loop. The expected lifetime of the on-board cryogens is $\sim 2.5$ years. This corresponds to operating the cooler 50% of the time; a slightly longer lifetime is expected if the cooler can operate at all times.

The ADR operates by aligning the magnetic moments (electron spins) of the molecules in the salt pill with a superconducting magnet, running at $\sim 2$ A and providing a magnetic field of $\sim 2$ Tesla. At the start of a cycle, the magnet is ramped up to a full field and the salt pill is connected to the liquid helium bath via a gas-gap heat switch, transferring the heat to the liquid helium bath. Once the salt pill has reached an equilibrium, the heat switch is opened, and at this point the magnetic field is reduced to nearly zero. This allows the spins of the electrons in the salt molecules to randomize adiabatically, causing the salt to cool as they do. It is expected that the Astro-E2 ADR can maintain the 60 mK temperature while in orbit for $\sim$ 1 day, at which point the magnetic spins are completely randomized, and no more heat can be absorbed. At this point, a ``recharge'' of the refrigerator is necessary, and the cycle is started again. The ``recharge'' of the refrigerator, typically lasting $\sim 1$ hour, can be done partially while the observed astrophysical target is behind the Earth.

6.2.2 XRS blocking filters

The XRS detectors must be kept at their operating temperature, so they have to be shielded from the ambient radiation field (even deep space is warmer than the operating XRS detectors!). More significantly, the Poisson noise associated with the discrete nature of ambient photons would appear as additional noise in the signal detected from individual X-rays; from a practical standpoint, it is also necessary to keep the heat load on the cryogenic system to a minimum. To prevent this, the calorimeter pixels are shielded from the ambient radiation field via a set of blocking filters, located in the field of view of the detectors. These filters have to be sufficiently thick to block (either by absorbing or reflecting) infrared radiation from the spacecraft and the dewar as well as geocoronal UV, while allowing for good transmission of X-rays. The XRS employs five blocking filters made of thin films of aluminized polyimide. From the outside to inside, these are located on the Dewar Main Shell (DMS), on the Inner Vapor Cooled Shield (IVCS), at the Neon tank, on the outside of the Calorimeter Front End Assembly (FEA), and on the Calorimeter Thermal Sink (CTS) (on the lid of the detector box). The filter transmission determines the lowest observable energy by the XRS. It is expected that the XRS filters will allow throughput down to $\sim$ 0.3 keV.

6.2.3 XRS Filter Wheel and In-flight Calibration

As discussed above, the XRS detectors require a relatively long time after an absorption event to recover for the next event. In addition, as noted in §4.5, sufficiently bright sources will cause the XRS resolution to degrade. This is due to X-rays hitting the silicon frame outside of the pixels and thermal crosstalk from other pixels which is a source of noise that at very high incident flux begins to degrade the XRS resolution in the Hi-res and Mid-res grade events. For an observation of a point source, we project that the resolution will degrade to $\sim 10$ eV for source fluxes F(0.3-12 keV) $\sim 10^{-8}$ergs/s/cm$^2$. Therefore, to observe bright sources with the XRS while avoiding event pile-up the X-ray flux must be reduced.

This can be accomplished with the Filter Wheel, a circular plate made of aluminum with six mounting positions for the filter elements. As summarized in Table 6.1, two positions (position # 1 and # 2) out of the six remain open, another two (# 3 and # 4) are filled with 300$\mu$m thick Beryllium (Be) filters, and the other two (# 5 and # 6) are provided with Neutral Density (ND) filters which are made of a 200 $\mu$m thick molybdenum plate with 1802 small pin-holes, and have nominal transmission of 10 %.

In order to monitor the calibration of the XRS detector in orbit, we have attached $^{55}$Fe isotopes for the positions # 1, # 3 and # 5 at the center of the filter elements. In addition, we have further equipped the open position already having the $^{55}$Fe isotope with a $^{41}$Ca isotope at the end of the mounting position, for calibrating the energy-dependence of the XRS gain. The expected intensity is 0.1-0.2 cps/pixel for $^{55}$Fe and $\sim 0.1$ cps/XRS for $^{41}$Ca. The introduction of these Filter Wheel calibration sources is one of the changes from Astro-E.

Table 6.1: Filter Element and Calibration Source on Filter Wheel

Position	1	2	3	4	5	6
Filter	Open	Open	Be 300 $\mu$m	Be 300 $\mu$m	ND 10 %	ND 10 %
Cal Source	--	$^{55}$Fe, $^{41}$Ca	--	$^{55}$Fe	--	$^{55}$Fe

The effect of these filters on the effective area of the XRS is shown in Fig. 2.3. Regarding the types of sources for which the filter wheel may be needed, we note again that except for the Crab nebula, there are no known diffuse sources, such as clusters of galaxies or supernova remnants which need the filter wheel; it may be needed for the bright Galactic binaries with a flux in excess of $\sim 50$ milliCrab (cf. Figs. 2.10 and 2.11).

6.2.4 In-flight gain-tracking of the XRS

The XRS includes an on-board calibration pixel to track variations in the gain, which could be caused by a drift in the temperature of the detector heat sink. Unlike the calibration sources on the filter wheel (which are too weak to be effective for this purpose), this pixel is not in the field of view. The calibration pixel is offset several millimeters from the imaging array, and is illuminated by a collimated $^{55}$Fe source. The decay of $^{55}$Fe to $^{55}$Mn produces 5.899 and 5.88 keV (K$\alpha_1$ and K$\alpha_2$) and 6.490 keV (K$\beta$) lines (with a half-life of 2.73 years). The count rate on the calibration pixel will be $\sim 4.5$ counts per second at launch, falling to $\sim 2.4$ after the nominal 2.5 year mission lifetime. Again, it is important to note that the imaging portion of the array is not illuminated at all by this internal calibration source.

The pulse height data from the calibration pixel (collected whenever the detector is on) will be used to create the XRS gain history files. It is anticipated that an absolute determination of the energy of a narrow monochromatic line (at energies below $\sim 7$ keV) can be made with a precision of $\lesssim$ 2 eV.

6.3 On-board Signal Processing in the XRS

The analog signals from the detectors, amplified by the CAP, are sent to the Calorimeter Digital Processor (CDP) for processing. Both analog and digital signal processing chains are split into two independent 16-channel sides. Each channel of the CDP consists of a low-pass antialiasing filter, analog-to-digital (A/D) converter and a Digital Signal Processor (DSP). The antialiasing filter cuts off frequencies above 2 kHz. The A/D part of the DSP samples and digitizes the data at a rate of 12288 Hz with 14-bit resolution. For High Resolution events (see the next section), 2048 samples are required to analyze a single pixel. Therefore, the amount of raw data in a single pulse is 2048 samples $\times$ 14 bits/sample= 28672 bits. The DSP determines the pulse height and arrival time, and outputs a digital event packet. A single event packet is 64 bits in length, which compares favorably to the amount of the raw data. Parenthetically, the default telemetry limit for the XRS is 10240 bits/sec, which corresponds to about 160 events/s/array, or an average of 5 events/s/pixel. The data stream is compressed before transmission, so the exact maximum count rate will depend on the data itself. It should be noted that in addition to this telemetry limit, above this count rate the energy resolution will degrade due to pileup effects. Independently, the XRS has an inherent hardware limit on the counting rate of 50 counts/s/pixel; counts in excess of this limit are simply discarded. Note that there are no user-specified parameters for the XRS, except for the setting of the filter wheel.

6.3.1 Searching for X-ray events

In order to provide the X-ray event data to the telemetry, the DSP has to detect the presence of X-ray pulses in the data stream. To do this, the DSP calculates a smoothed derivative of the data. The initial pulses are detected when the derivative exceeds a fixed threshold. An additional task of the DSP is to find secondary events which might be superposed on the tails of the initial pulses. If a secondary pulse is not recognized as such, this may affect the determination of the pulse heights of the initial pulses. Hence it is important for the DSP to detect secondary pulses even if they are much smaller than the initial pulses.

Figure 6.4: Calibration spectrum from the XRS flight detector array showing the resolution and centroiding for emission lines between 4.5-12 keV.

To search for secondary pulses, the DSP/CDP compares the smoothed derivative with a template of the single-pulse derivative shape stored in the CDP. The derivative shape template is subtracted from the measured derivative by scaling the peak values to form the adjusted derivative. If the adjusted derivative rises above a threshold and then falls below within a specified length of time, a secondary pulse is detected. The secondary pulses are flagged so that they can be discriminated from initial pulses.

Once an initial pulse has been detected, the CDP begins counting down the length of a Hi-resolution data record (2048 samples). If the pulse count reaches zero without detecting any secondary pulses during 2048/12288=167 msec, the event is flagged as a Hi-res record (see Fig. 6.5 and the next section). If a secondary pulse does occur, the initial (primary) pulse will be processed and flagged as either a Mid-res or Low-res event, and the counter will reset to the full Hi-res length. The secondary pulse will then be graded as well. As noted below, Mid-res secondary pulses have lower energy resolution than Mid-res primary events.

Figure 6.5: Diagram showing the event grade determination in the XRS data processing chain.

6.3.2 Pulse Height Determination:

The main task for the CDP is to get the best possible estimate of the height of each pulse. The zeroth-order estimate of the pulse height is the peak value of the pulse minus the baseline value, but this is not a good measure because of noise. In order to determine the pulse height value as precisely as possible using all the samples in the pulse, the XRS uses the optimal filtering technique. In this technique, noise is reduced by weighted averaging of all the samples in the pulse. This requires an accurate template of a ``clean'' pulse. The Hi-res grade applies only when there is only a single pulse in the block of 2048 samples.

To create the optimal filter, the average pulse (2048 samples in 167 msec) is Fourier transformed and in Fourier space the pulse is divided by the power spectrum of the noise. Finally the result is inverse Fourier transformed to create the Hi-res template. In order to estimate the noise power spectrum, a relatively large number (100-200) of individual noise power spectra, each of which is made from a single noise record of 2048 samples, are averaged. The average pulse is made by averaging similar pulses which fall in a limited range on the pulse-height vs rise-time plane. The optimal filtering template for the Hi-res grade thus has 2048 samples in time space. The optimal pulse height is calculated by multiplying the data and optimal filter sample-by-sample and adding them up. This procedure cancels out the interference of the noise component in the pulse.

The above method of pulse-height calculation cannot be used when there are two or more events in the train of 2048 samples. If two pulses are closer than 2048 samples but not ``too close,'' a shorter optimal filtering template, typically 512 samples long, is used (see Fig. 6.5). This method of pulse height calculation is called Mid-res grade. In general, shorter templates are less effective in determining and rejecting the interference of noise at particular frequencies. In the absence of noise induced externally (such as microphonics or 60 Hz interference) the Mid-res primary pulses will give approximately the same resolution as the Hi-res grade.

When pulses are too close even for the Mid-res grade, pulse heights are determined simply measuring the heights of the peak over the baseline level; these are the Low-res grade. The baseline and the magnitude of the peak are measured by taking an average of typically eight samples.

Each XRS event has flags indicating which of the three methods of pulse height determination was used. Hi-res events provide a resolution that is limited by the detector and amplifier electronics, and this has been as good as 5 eV (FWHM) at 1 keV. In the absence of noise, the Mid-res grade (primary events only) provides better than 6 eV resolution at 1 keV. The Low-res grade gives a resolution around 30 eV. Mid-res secondary events have a large low-energy tail which reduces their resolution significantly relative to Mid-res primary events. These secondary events require a post-processng correction that is still under development, which could restore most of the lost energy resolution. However, for AO-1, we encourage proposers to exclude secondary events from their simulations. The relative fraction of events in the Hi-, Mid-, and Low-res grades as a function of the XRS counting rate (per pixel) are given in Fig. 2.11.

Figure 6.6: [Left] XRS spectral resolution at Mg K$\alpha$ using Hi-res events only. [Right] The same plot using Mid-res (primary) events only.

Figure 6.6 shows the effective resolution of both Hi- and Mid-res primary events, using data taken from Mg K$\alpha$ lines at 5.8876 and 5.8988 keV. The XRS line shape is very nearly Gaussian, as can be seen in Figure 6.7. Unlike grating spectrometers the line shape is determined by the XRS detector itself, and is totally independent of the X-ray mirror. Although Fig. 6.6 shows results only from pixel 2 and Fig. 6.7 is from pixel 5, the pixels in the XRS array are quite uniform with the exception of two pixels. For 28 of the pixels, the resolution is only slightly energy dependent, 5.5-6 eV at low ($< 1$keV) energies and rising slowly to about 6-7 eV at 6 keV. Two pixels, #11 and #20 (see Fig. 2.5) have an energy that is much more energy dependent, as shown in Table 6.2. The energy resolution of these two pixels is not included in the proposal response matrix. However, after in-flight calibration is complete, it is expected that response matrices will be available for individual pixels as needed.

Table 6.2: The energy-dependence of XRS pixels; 1$\sigma$ measurement uncertainties are 0.3 eV. Note that the two unusual pixels are on the perimeter of the array and should have minimal impact on most observations.

Pixel	$E<\sim1$keV	$E=3.3$keV	$E=6$keV
11	$\sim 5.5$eV	$\sim 7$eV	8 eV
20	$\sim 5.5$eV	$\sim 10$eV	14 eV
others	$\sim 5.5$eV	$\sim 6$eV	$\sim 6.5$eV

Figure 6.7: XRS measurement of Cu K$\alpha$ emission line on a logarithmic scale compared to a simple Gaussian fit.

6.3.3 XRS Timing Accuracy

Each event time is reconstructed from a number of intermediate values, and represents Coordinated Universal Time (UTC) at the spacecraft when the photon was absorbed. The absolute time accuracy will be $\sim 100 \mu$s, a limit set by the spacecraft clock and electronics in the XRS. The relative timing accuracy within a single observation should be $\sim 10 \mu$s. However, there may be a statistically significant (10s of $\mu$s) systematic error in time-tagging as a function of photon energy, so proposers should assume the timing accuracies of $\sim 100 \mu$s.

6.4 XRS Background

While the XRS is physically a small detector, it can still be subject to background events. Most likely the strongest contribution will be from energetic protons depositing some of their energy in the XRS. The planned Astro-E2 orbit is quite similar to ASCA's, so the particle background also should be similar. Outside of the SAA the background rate in the ASCA SIS was roughly 1 count cm$^{-2}$ s$^{-1}$. With this, and given the expected proton spectrum, it is expected that the XRS may experience as many as $4 \times 10^{-3}$ counts s$^{-1}$ per pixel, with $\sim 60$% depositing more than 10 keV. While this is still a low rate, the XRS features an anti-coincidence detector for an added insurance against sudden increases in flux (and, possibly, allowing the data acquired during the SAA passages to be usable). To be useful, this device has to be located close to the XRS, and so it has to operate below 0.1 K. The XRS anti-coincidence detector is a 1 cm$^{2}$, 0.5 mm thick ionization detector made of doped Si, and placed directly behind the XRS array. The device is configured as a PIN diode operating in a reverse bias configuration (although at these low temperatures such a diode acts essentially as a capacitor).

Simulations with the high-energy physics tool GEANT4 show that the anti-coincidence detector will be triggered by 98% of the particles which pass through a pixel. In addition, because the particles which miss the anti-coincidence detector are mostly those which pass through the X-ray pixels at a steep angle, 90% of them will deposit more than 10 keV in the pixel, and will thus be rejectable strictly on an energy basis. Thus our total unrejected particle background is 0.2% of the particle rate. Individual events from the anti-coincidence detector are not telemetered to the ground, but XRS X-ray events that were recorded within a set time window of the anti-coincidence event are flagged ``ANTICO.'' In addition, one can use the timing information to reject events that occurred nearly-simultaneously in multiple adjacent pixels (the so-called ``pixel-to-pixel'' events), as those are likely to be particle-induced. One-minute totals of the number of anti-coincidence detector events are also telemetered to the ground.

The expected performance of the anti-coincidence detector suggests that the background should be dominated by secondary particles (i.e. electrons and photons). In combination with our knowledge of the ASCA unrejected background, we expect this to be a few counts/pixel/day.