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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:.

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Lecture 23

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Lecture 23 l.jpg

Lecture 23

  • XMM instrumentation and calibration continued

    • EPIC calibration quantities

      • Quantum efficiency, effective area

    • Exposure calculations

    • The RGA


Python cpickle l.jpg

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 cpickle3 l.jpg

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 l.jpg

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 l.jpg

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


Back to xmm calibration quantities 1 quantum efficiency l.jpg

Back to XMM.Calibration quantities: (1) Quantum Efficiency

Silicon K edge

pn

MOS

Oxygen K edge


2 effective area no filter includes qe l.jpg

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

Gold M edge


Effective area change with filters l.jpg

Effective Area change with filters

This is for pn – MOS is very similar.


Exposure l.jpg

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.


Exposure10 l.jpg

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.


Exposure11 l.jpg

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.


Exposure12 l.jpg

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 l.jpg

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


Slide14 l.jpg

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


Fractional exposure l.jpg

Fractional exposure

  • For XMM light curves,

    where the fractional exposuref is

photons s-1


Sources l.jpg

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 l.jpg

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 l.jpg

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.


Rga plot showing the event pixel locations l.jpg

RGA –plot showing the event pixel locations:


The banana plot l.jpg

The ‘banana plot’


An example rgs spectrum l.jpg

An example RGS spectrum:

Spectral resolution:

about 2 eV


An example epic spectrum l.jpg

An example EPIC spectrum:

Spectral resolution:

about 100 eV


Charge redistribution l.jpg

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 l.jpg

MOS RM cross-section at 800 eV

Energy of the x-rays


Evolution of the energy dispersion l.jpg

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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