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Lecture 23

- XMM instrumentation and calibration continued
- EPIC calibration quantities
- Quantum efficiency, effective area
- Exposure calculations
- The RGA

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()

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()

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

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

(2) Effective area (no filter) (includes QE)

Gold M edge

Effective Area change with filters

This is for pn – MOS is very similar.

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.

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.

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.

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:

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

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

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’.

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.

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.

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.

MOS RM cross-section at 800 eV

Energy of the x-rays

Evolution of the energy dispersion

1.5 keV

6.0 keV

MOS temperatures were

lowered here.

Black: pn

Red and Green: the MOS chips

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