Transcript Lecture 1

Lecture 23
• XMM instrumentation and calibration
continued
– EPIC calibration quantities
• Quantum efficiency, effective area
– Exposure calculations
– The RGA
NASSP Masters 5003F - Computational Astronomy - 2009
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()
NASSP Masters 5003F - Computational Astronomy - 2009
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()
NASSP Masters 5003F - Computational Astronomy - 2009
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
NASSP Masters 5003F - Computational Astronomy - 2009
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
NASSP Masters 5003F - Computational Astronomy - 2009
Back to XMM.
Calibration quantities: (1) Quantum Efficiency
Silicon K edge
pn
MOS
Oxygen K edge
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(2) Effective area (no filter) (includes QE)
Gold M edge
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Effective Area change with filters
This is for pn – MOS is very similar.
NASSP Masters 5003F - Computational Astronomy - 2009
Exposure
• Relation between incident flux density S
and the photon flux density φ: most
general form is
dimensionless
erg s eV cm
cm
photons s eV
dE 
 E , r, t   A
dr X E , E , r, r, t  S E , r, t 
E   E of course is the photon energy.
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.
-1
-1
2
-1
-1
-2
– 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.
NASSP Masters 5003F - Computational Astronomy - 2009
Exposure
• A reasonable breakdown of AX is
AX  RE, E AEV E, rCr  r, r, EDt 
where
All dimensionless except A.
– 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.
NASSP Masters 5003F - Computational Astronomy - 2009
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
S E, r, t   S E, t  r  r0 
This gets rid of the integral over r, and the r‘
in V and ρ become r0.
NASSP Masters 5003F - Computational Astronomy - 2009
•
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:
I r    dt  dE  E , r, t   an image
t
qE    dt
t
Lt  
E
 dr  E, r, t 
 a spectrum
Region
 dr  dE  E, r, t 
E
 a light curve
Region
S   dt
t
 dr  dE  E, r, t 
E
 a source
Region
NASSP Masters 5003F - Computational Astronomy - 2009
Exposure map
• For XMM images we have
photons cm
photons
erg s eV cm
eV s erg
1
I r    r  E   dt S E , r, t 
s
t t
where the exposure map ε is
2
-1
-1
-1
-1
-2
 r   V  E , r C r  dt Dt 
t
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.
NASSP Masters 5003F - Computational Astronomy - 2009
ARF
• For XMM spectra
photons eV-1
qE    E   dt
t
 dr S E, r, t 
Region
where the ancillary response function (ARF) α is
1
 E   AE V E , r0  dr C r  r0 , r, E  dt Dt 
Reg
t
E
This is a bit more rigorous because the resulting
spectrum q is explicitly acknowledged to be preRM.
– And if S can be taken to be time-invariant, then this
expression follows almost exactly from the general
expression involving X.
NASSP Masters 5003F - Computational Astronomy - 2009
Fractional exposure
• For XMM light curves,
photons s
dE
Lt   f t  A E  dr 
S E , r , t 
Reg. E E
-1
where the fractional exposure f is
f t  V  E , r0  Dt  dr C r  r0 , r, E
Reg.

NASSP Masters 5003F - Computational Astronomy - 2009
Sources
• There is just a small modification to the
‘image’ approximation:
1
S   r  E   dr  r, r, E   dt S E, r, t 
t

t
Region
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’.
NASSP Masters 5003F - Computational Astronomy - 2009
•
Prescriptions to obtain ergs s-1:
Image:
1. Divide by exposure map
2. Multiply by ECF
•
Spectrum:
1. You don’t. Compare to forward-treated model
instead.
•
Light curve:
1. Divide by frac exp
2. Multiply by ECF
•
Source:
3. As for image but also divide by integral of ρC.
NASSP Masters 5003F - Computational Astronomy - 2009
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.
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RGA –
plot showing the event pixel locations:
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The ‘banana plot’
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An example RGS spectrum:
Spectral resolution:
about 2 eV
NASSP Masters 5003F - Computational Astronomy - 2009
An example EPIC spectrum:
Spectral resolution:
about 100 eV
NASSP Masters 5003F - Computational Astronomy - 2009
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':
S E    dE  RE , E S E 
• 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.
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MOS RM cross-section at 800 eV
Energy of the x-rays
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6.0 keV
1.5 keV
Evolution of the energy dispersion
Black: pn
Red and Green: the MOS chips
MOS temperatures were
lowered here.
NASSP Masters 5003F - Computational Astronomy - 2009