Lecture 23

1. Lecture 23 • XMM instrumentation and calibration continued • EPIC calibration quantities • Quantum efficiency, effective area • Exposure calculations • The RGA

2. Python: cPickle • This module provides a convenient way to store python objects to a disk file. • Writing a ‘pickled’ file: import cPickle as cp import numpy ... pklFileName = <some file name> ... fred = numpy.array([1.2, 0.9, -4.0]) mary = (‘src’,33,0.7) bill = {‘blee’:99,’blah’:’mystr’} sue = ‘some string’ ... output = cp.open(pklFileName, 'wb') cPickle.dump((fred,mary,bill,sue), output, -1) output.close()

3. Python: cPickle • Reading a ‘pickled’ file: import cPickle as cp import numpy ... pklFileName = <some file name> ... inFile = cp.open(pklFileName, 'rb') (fred,mary,bill,sue) = cPickle.load(inFile) inFile.close()

4. X-ray interaction with matter • Can break it into continuum and resonant. • Both sorts generate ions. • ‘Continuum’ absorption scales with • Density • 1/E. • Resonant absorption: • electron is kicked out from an inner orbital. X-ray e- Atom + + M L K

5. Resonant absorption continued: • Because it is an inner orbital, doesn’t much matter if atom is in a gas or a solid. The inner orbitals are pretty well insulated from the outside world. • X-ray must have energy >= the amount needed to just ionize the electron. • Hence: absorption edges located at energies characteristic of that orbital (labelled eg K or L) and that element. Absorption X-ray energy

6. Back to XMM.Calibration quantities: (1) Quantum Efficiency Silicon K edge pn MOS Oxygen K edge

7. (2) Effective area (no filter) (includes QE) Gold M edge

8. Effective Area change with filters This is for pn – MOS is very similar.

9. Exposure • Relation between incident flux density S and the photon flux density φ: most general form is where A is an effective area and the fractional exposure kernel X contains all the information about how the photon properties are attenuated and distributed. • Note I didn’t include a t' because in XMM there is no redistribution (ie ‘smearing’) mechanism which acts on the arrival time. • Vector r is shorthand for x,y. dimensionless erg s-1 eV-1 cm-2 cm2 photons s-1 eV-1  E of course is the photon energy.

10. Exposure • A reasonable breakdown of AX is where • R is the redistribution matrix; • A is the on-axis effective area (including filter and QE contributions); • V is the vignetting function; • C holds information about chip gaps and bad pixels; • ρ is the PSF (including OOTE and RGA smearing); and • D is a ‘dead time’ fraction, which is a product of • a fixed fraction due to the readout cycle, and • a time-variable fraction due to blockage by discarded cosmic rays. • the fraction of ‘good time’ during the observation. All dimensionless except A.

11. Exposure • This includes a number of assumptions, eg • The spacecraft attitude is steady. • Variations between event patterns are ignored. • No pileup, etc etc • Now we try to simplify matters. First, let’s only consider point sources, ie This gets rid of the integral over r, and the r‘ in V and ρ become r0.

12. Exposure • What we do next depends on the sort of product which we want. There are really only 4 types (XMM pipeline products) to consider:

13. Exposure map • For XMM images we have where the exposure mapε is and the energy conversion factor (ECF) ψ is calculated by integrating over a model spectrum times R times A. • Hmm well, it’s kind of roughly right. photons cm2 eV s-1 erg-1 photons erg s-1 eV-1 cm-2 s

14. ARF • For XMM spectra where the ancillary response function (ARF) α is This is a bit more rigorous because the resulting spectrum q is explicitly acknowledged to be pre-RM. • And if S can be taken to be time-invariant, then this expression follows almost exactly from the general expression involving X. photons eV-1

15. Fractional exposure • For XMM light curves, where the fractional exposuref is photons s-1

16. Sources • There is just a small modification to the ‘image’ approximation: This is probably the least rigorous of the three product-specific distillations of X. • To some extent, this idiosyncratic way of cutting up the quantities is just ‘what the high-energy guys are used to’.

17. Prescriptions to obtain ergs s-1: • Image: • Divide by exposure map • Multiply by ECF • Spectrum: • You don’t. Compare to forward-treated model instead. • Light curve: • Divide by frac exp • Multiply by ECF • Source: • As for image but also divide by integral of ρC.

18. The Reflection Grating Spectrometer (RGA) • Each MOS has one. • They divert about ½ the x-rays. • Diffraction grating  array of 9 CCDs. • Pixel position in the dispersion direction is a function of x-ray energy. • But not a linear function (I think there is a cosine term in it). • Energy resolution is much sharper than via amount of charge the photons generate. • Spectral orders overlap – • but the 2nd order has even finer resolution.

19. RGA –plot showing the event pixel locations:

20. The ‘banana plot’

21. An example RGS spectrum: Spectral resolution: about 2 eV

22. An example EPIC spectrum: Spectral resolution: about 100 eV

23. Charge redistribution • Photons of a single, narrow energy give rise to broadened charge redistribution spectrum. • Partly because of Poisson (quantum) statistical variation; • Partly because of smearing out during the transfer of charges from row to row during readout. • The relation between true spectrum S and measured spectrum S': • R is called the redistribution matrix (RM). • As the chips degrade with age (due mostly to particle impacts), the RM changes and has to be recalibrated. • The philosophy with x-ray spectra is not to subtract background or deconvolve RM, but to begin with a model, and add background and RM-convolve this before comparing it with the measured spectrum. • See the program XSPEC.

24. MOS RM cross-section at 800 eV Energy of the x-rays

25. Evolution of the energy dispersion 1.5 keV 6.0 keV MOS temperatures were lowered here. Black: pn Red and Green: the MOS chips