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

effective area change with filters
Effective Area change with filters

This is for pn – MOS is very similar.

exposure
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
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
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
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
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
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
Fractional exposure
  • For XMM light curves,

where the fractional exposuref is

photons s-1

sources
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
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
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.
an example rgs spectrum
An example RGS spectrum:

Spectral resolution:

about 2 eV

an example epic spectrum
An example EPIC spectrum:

Spectral resolution:

about 100 eV

charge redistribution
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
MOS RM cross-section at 800 eV

Energy of the x-rays

evolution of the energy dispersion
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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