Transcript Lecture 1

Lecture 21
• 6.4 keV Fe line and the Kerr metric
• Satellite observatories
– Attitude and boresight
• X-ray instrumentation and calibration
(mostly XMM).
• (XMM users’ guide:
– http://xmm.esac.esa.int/external/xmm_user_
support/documentation/uhb/index.html)
NASSP Masters 5003F - Computational Astronomy - 2009
Fe lines in AGN – what this can tell us about GR
• Fe: iron of course. There is a fluorescence
line at 6.4 keV (in the rest frame).
• AGN: Active Galactic Nucleus.
– No-one has seen one close up – but almost
certainly, these are accretion disks about a
large black hole.
• GR: here this doesn’t mean gamma ray,
but General Relativity.
– We expect to see GR effects near a giant
black hole, because the gravitational force is
so extreme.
NASSP Masters 5003F - Computational Astronomy - 2009
(Tentative) cross-section through an AGN:
To us
Flare
Jet
Continuum background
from halo
Fe fluor.
Flare additional
continuum
Accretion disk
Accretion disk
BH
Very
Innermost stable orbits –
about 6rg for non-spinning BH;
closer in for spinning BH.
halo
hot
Jet
NASSP Masters 5003F - Computational Astronomy - 2009
Fluorescence from a ‘cool reflector’.
From A Fabian et al, PASP 112, 1145 (2000)
NASSP Masters 5003F - Computational Astronomy - 2009
How ionization modifies this
From A Fabian et al, PASP 112, 1145 (2000)
NASSP Masters 5003F - Computational Astronomy - 2009
A Doppler-broadened spectral line –
predictions of various theories:
An accretion disk seen from above:
Slow – small DS
Profiles just
for the two
dashed annuli.
Fast – large DS
Fainter outside
for whole disk
Brighter inside
From A Fabian et al, PASP 112, 1145 (2000)
NASSP Masters 5003F - Computational Astronomy - 2009
Theory - spinning vs non-spinning BH
Spinning (so-called
Kerr-metric BH)
From A Fabian et al, PASP 112, 1145 (2000)
Non-spinning (so-called
Schwartzschild BH)
NASSP Masters 5003F - Computational Astronomy - 2009
Time-varying behaviour in MGC -6-30-15.
This is a Seyfert I galaxy. From Tanaka et al (1995).
1994: time-averaged.
1997: time-averaged.
1994: in a deep minimum.
1997: at flare peak.
From A Fabian et al, PASP 112, 1145 (2000)
NASSP Masters 5003F - Computational Astronomy - 2009
Attitude
• The orientation of the spacecraft in the sky is
called its attitude.
• It isn’t just the direction it points to, attitude
specifies the roll angle as well.
– One way to define this is via a pointing vector and a
parallactic angle.
• However, as with any trigonometric system, this has
problems at poles.
– Better is to define a Cartesian coordinate frame of 3
orthogonal vectors.
•
•
•
•
Each vector defined by direction cosines in the sky frame.
Attitude is then an attitude matrix A.
This is isotropic (no trouble at poles).
Easy to convert between different reference frames.
– Whatever you do, avoid messing about with Euler
angles. Ugh.
NASSP Masters 5003F - Computational Astronomy - 2009
Sky frame or basis.
z at dec=90°
Unless you have good reason
not to, always construct a
Cartesian basis according to
the Right-Hand Rule:
y at RA=6 hr
xy screws toward z;
yz screws toward x;
zx screws toward y.
x at RA=0
“Direction cosines” really just
means Cartesian coordinates.
NASSP Masters 5003F - Computational Astronomy - 2009
RA/dec  Cartesian (ie, direction cosines).
z at dec=90°
 cos cos RA


vˆ sky   cos sin RA 


sin



vˆ
y at RA=6 hr
x at RA=0
To invert this:

  atan2vz , v  v
2
x
2
y

RA  atan2vy , vx 
NASSP Masters 5003F - Computational Astronomy - 2009
Spacecraft basis (green vectors).
zsky
Attitude matrix:
xs/c
ysky
 xˆs/c 
 sky 
A   yˆ s/c sky 
 zˆ

 s/c sky 
xsky
ys/c
zs/c
NASSP Masters 5003F - Computational Astronomy - 2009
Conversion from sky to spacecraft basis:
zsky
Attitude matrix:
xs/c
vˆ
ysky
 xˆs/c 
 sky 
A   yˆ s/c sky 
 zˆ

 s/c sky 
xsky
ys/c
vˆ s/c  A vˆ sky
zs/c
Inverting it:
vˆ sky  A 1 vˆ s/c
NASSP Masters 5003F - Computational Astronomy - 2009
•
•
•
•
Boresights
Ideally, each instrument on a satellite
would be perfectly aligned with the
spacecraft coordinate axes.
In real life, there is always some
misalignment. This is called the boresight
of the instrument (I think it is an old
artillery term).
Define a set of Cartesian axes for each
instrument.
Components of these axes in the
spacecraft reference system (basis) form
the boresight matrix B for that instrument.
NASSP Masters 5003F - Computational Astronomy - 2009
Boresights
• With these matrices, conversion between
coordinate systems is easy. Suppose we have
an x-ray detection which has a position vector
v|inst in the instrument frame. If we want to find
where in the sky that x-ray came from, we first
have to express this vector in the sky frame
Cartesian system (new vector = v|sky). This is
simple. Since we have:
vˆ inst  Bvˆ s/c  BA vˆ sky
• then
vˆ sky  A 1B 1 vˆ inst
NASSP Masters 5003F - Computational Astronomy - 2009
Attitude and boresights
• NOTE that attitude varies with time as the
spacecraft slews from target to target – but there
is ALSO attitude jitter within an observation.
– XMM has a star tracker to measure the attitude.
• Attitude samples are available at 10 second intervals.
• So to build up a sky picture from x-ray positions
in the instrument frame, one has to change to a
new attitude matrix whenever the deviation
grows too large.
• Boresights can also change with time, due to
flexion of the structure, but this is slow.
– Calibration teams measure them from time to time.
NASSP Masters 5003F - Computational Astronomy - 2009
Other coordinate systems:
• The fundamental spatial coord system is
the chip coordinate system – in CCD
pixels.
• Note that for time and energy as well as in
the spatial coordinates, coordinate values
are ultimately pixellized or discrete.
– This defines the uncertainty with which they
are known (to ±half the pixel width).
– Rebinning can give rise to Moiré effects
(somewhat similar to aliasing in the Fourier
world).
• ‘Dithering’ can avoid this.
NASSP Masters 5003F - Computational Astronomy - 2009
X-ray Observatories
• You need to be in space, because the
atmosphere efficiently absorbs x-rays.
• Most of the currently interesting results are
coming from:
– Chandra (good images, so-so spectra)
– XMM-Newton (so-so images, good spectra)
– SWIFT (looks mostly at GRB afterglows)
although there are several more.
• How do you make an image from x-rays?
Don’t they go through everything? So how
can you make a reflector?
NASSP Masters 5003F - Computational Astronomy - 2009
X-ray Observatories - mirrors
• Wolter grazing-incidence mirrors:
– reflectivity of any EM radiation gets higher for a
low angle of incidence.
Double reflection
Can nest
many shells
of differing
diameter.
Paraboloid
Hyperboloid
Behaves like a thin lens set here.
NASSP Masters 5003F - Computational Astronomy - 2009
X-ray Observatories - detectors
• Charge Coupled Devices (CCDs) are used, just
as for optical. The workings are slightly different
though.
e-
e- e-
e- e-
e-
e- e-e- e-
e- e- e-e- e-
e- e- e-e-e- e-
...then read out.
At optical wavelengths:
At x-ray wavelengths:
e-
e- e-e- -e--e- -e- e-eee- e
e
...then read out.
Time
NASSP Masters 5003F - Computational Astronomy - 2009
X-ray Observatories - detectors
• Basic substance of the CCD is silicon – but
‘doped’ with impurities which alter its electronic
structure.
• There are several sorts, eg:
– Metal Oxide Semiconductor (MOS)
– pn
• The CCD surface is divided into an array of
pixels.
• A photon striking the material ejects some
electrons which sit around waiting to be
harvested.
– The number of ejected electrons is proportional to the
energy of the photon.
NASSP Masters 5003F - Computational Astronomy - 2009
X-ray Observatories - detectors
• CCD operation is in frame cycles.
Long accumulation
time
Short readout time
NASSP Masters 5003F - Computational Astronomy - 2009
X-ray Observatories - detectors
• CCDs have to be read out sequentially
(slow).
Rows
Columns
Digitizer
(ADC)
Out
Readout row
NASSP Masters 5003F - Computational Astronomy - 2009
•
X-ray Observatories - detectors
The readout operation consists of the
following steps:
– For each CCD row, starting with that nearest
the readout row, move the charges into the
next lowest row.
– In the readout row, starting at the pixel nearest
the output, shift the charges into the next lowest
pixel.
– Convert the analog charge quantity (it is an
integer number of electrons, but such a large
integer that we can ignore quantum ‘graininess’)
to a digital number.
– This is done in an Analog to Digital Converter (ADC).
– Send that number to the outside world.
NASSP Masters 5003F - Computational Astronomy - 2009
X-ray Observatories - detectors
• For x-ray detection, we want to arrange the
frame duration so that we expect no more than 1
x-ray per pixel per frame.
• Why? Because if we can be pretty sure that all
the charge per pixel per frame comes from a
single x-ray, we can determine the energy of the
x-ray.  x-ray spectroscopy.
• XMM example:
– Spatial resolution is ~1 arcsec (fractional ~10-3).
– Spectral resolution is ~100 eV (fractional ~10-2).
– Time resolution is ~1 second (fractional ~10-5).
NASSP Masters 5003F - Computational Astronomy - 2009