The Response Matrix

The response matrix provides information about the probability that an incident photon of a particular energy will be observed in a particular instrument channel. A discussion of the in orbit performance and calibration of the PCA can be found by Jahoda et al. (1996) and Jahoda et al. (2006). The detector response matrix captures non-linearities in the detector and must account for:

1. The energy to channel relationship which is non-monotonic at energies close to absorption edges. The mean energy absorbed above an edge is greater than the mean energy just below the edge; energy goes into the potential energy of the absorbing atom resulting in the photoelectron having less kinetic energy and so producing a smaller avalanche. Data suitable for parameterising the energy scale and monitoring variations (Jahoda et al., 2006) comes from three regularly observed sources.

• Each PCU contains a small Americium-241 source along with two dedicated anodes in a parasitic proportional counter referred to as the alpha counter. The Americium- 241 provides continuous calibration lines with energies between 13 and 60 keV. The source undergoes an alpha decay emitting several X-ray lines. The alpha particle is detected and tagged by a the alpha counter and the X-rays lines are captured in the xenon layer. A set of 6 Gaussians provides an excellent fit allowing the gain and resolution to be monitored.

• The supernova remnant Cassiopeia A has a bright, strong iron line easily visible in the PCA count spectra, a power-law fit to the continuum and Gaussian line between 4 and 9 keV can be fit to the data. The fit energy centroid can be unambiguously converted to a mean channel.

• Due to diffusion a small amount of xenon is present in the front propane layer. Reg- ular monitoring of the Crab Nebula allows the measurement of energies near the xenon L edge, at 4.78 keV. Fits in energy can be used to determine the energy to channel relationship.

2. The quantum efficiency is a measure of how efficient the device is at converting photons hitting the device into photoelectrons that can be detected. To model the quantum effi- ciency of the detector each PCU is treated as a series of parallel slabs of material. Various parameters, including the amount of xenon, amount of xenon in the propane layer, rate of change of xenon in the propane layer, thickness of xenon between layers, amount of propane in the first gas volume and the thickness of front window are specified in the ma- trix generation configuration file. Parameter values can be found in table 3 of Jahoda et al. (2006). Frequent observations of the Crab Nebula were used to estimate the best values for the parameters, which were averaged over time and PCU.

3. The detector also detects additional ’false’ escape peaks as well as detecting authentic lines from the source. An incident X-ray photon with energy above the absorption edge displaces a K or L alpha electron from an atom. If the fluorescence produced by the atom escapes from the detector the measured signal is interpreted as coming from a lower energy photon. The energy of this photon, Eesc, is the difference between the incident photon, Ei, and the energy of the lost fluorescence photon, Ef, Eesc= Ei−Ef.

The width of the photopeak corresponds to the energy resolution of the detector, which goes as∆E/E=0.17(E/6keV)1/2where∆E is the FWHM. The matrix also accounts for events

that can be rejected because the photoelectron travels into a neighbouring anode volume. The anodes in the xenon volume were initially set to a nominal +2050 V which has since been reduced. After 70 days in orbit, two of the 5 detectors showed evidence of gentle

Table 2.1: Dates and voltages for the epochs during the RXTE mission. Voltage

Epoch Start date (UT) PCU 0 PCU 1 PCU 2 PCU 3 PCU 4

1 Launch 2030 2030 2026 2027 2048 2 1996 Mar 21, 18 : 34 2010 2010 2006 2007 2007 3A 1996 Apr 15, 23 : 06 1990 1990 1986 1987 1988 3B 1998 Feb 09, 01 : 00 - - - - - 4 1999 Mar 22, 17 : 39 1970 1970 1966 1967 1968 5 2000 May 12, 01 : 06 - - - - -

breakdown, to prevent further occurrences the gain was lowered by 35 per cent on all detectors and the detectors were operated at a warmer temperature. The overall gain setting has been changed twice since launch for operational reasons. Changes in the operating voltages mark periods of discontinuity in the detector response, referred to as epochs. Table 2.1 shows the dates of each epoch. The satellite orbit began to decay noticeably midway through epoch 3 so the epoch was split to distinguish background models with different time dependences; epoch 5 was also split into three sub epochs. The anodes of the main detector are connected alternately so each layer has two anode chains. The electronic system uses this to monitor the gain. The propane veto layer forms one chain and is maintained at a higher nominal voltage of+2800 V to compensate for higher gas leakage.

The net effective area and the effective area of the first layer of the PCA, as a function of energy, is shown in Figure 2.3. The useful energy range of the PCA is from_∼ 2.5 keV to_∼ 50 keV. The small jumps in the effective area in the lower energy range are the xenon L edges, with energies of 4.78, 5.10, 5.45 keV. The strong decrease below 34.6 keV is the xenon K edge. Just above the edges more energy goes into potential energy associated with the absorbing atom. The photoelectron has less kinetic energy and the number of electrons produced in the absorbing gas is smaller.