nassp masters 5003f - computational astronomy - 2009 lecture 21 6.4 kev fe line and the kerr metric...
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NASSP Masters 5003F - Computational Astronomy - 2009
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:
BHAccretion disk Accretion disk
Very hothalo
FlareContinuum background
from halo
Fe fluor.
To us
Flare additionalcontinuum
Innermost stable orbits –about 6rg for non-spinning BH;closer in for spinning BH.
Jet
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:
From A Fabian et al, PASP 112, 1145 (2000)
An accretion disk seen from above:
Fainter outside
Brighter inside
Slow – small DS
Fast – large DS
for whole disk
Profiles justfor the twodashed annuli.
NASSP Masters 5003F - Computational Astronomy - 2009
Theory - spinning vs non-spinning BH
From A Fabian et al, PASP 112, 1145 (2000)
Spinning (so-calledKerr-metric BH)
Non-spinning (so-calledSchwartzschild 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).
From A Fabian et al, PASP 112, 1145 (2000)
1994: time-averaged.
1997: at flare peak.
1997: time-averaged.
1994: in a deep minimum.
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.
x at RA=0
y at RA=6 hr
z at dec=90°
Unless you have good reasonnot to, always construct aCartesian basis according tothe Right-Hand Rule:
xy screws toward z;yz screws toward x;zx screws toward y.
“Direction cosines” really justmeans Cartesian coordinates.
NASSP Masters 5003F - Computational Astronomy - 2009
RA/dec Cartesian (ie, direction cosines).
x at RA=0
y at RA=6 hr
z at dec=90°
sin
sincos
coscos
ˆsky
RA
RA
v
v̂
22,atan2 yxz vvv
xy vvRA ,atan2
To invert this:
NASSP Masters 5003F - Computational Astronomy - 2009
Spacecraft basis (green vectors).
xsky
ysky
zsky
xs/c
ys/c
zs/c
skys/c
skys/c
skys/c
ˆ
ˆ
ˆ
z
y
x
A
Attitude matrix:
NASSP Masters 5003F - Computational Astronomy - 2009
Conversion from sky to spacecraft basis:
xsky
ysky
zsky
xs/c
ys/c
zs/c
skys/c
skys/c
skys/c
ˆ
ˆ
ˆ
z
y
x
A
Attitude matrix:
v̂
skys/cˆˆ vv A
s/c
1
skyˆˆ vv A
Inverting it:
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:
• then
skys/cinstˆˆˆ vvv BAB
inst
11
skyˆˆ vv BA
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.
Paraboloid Hyperboloid
Double reflection
Behaves like a thin lens set here.
Can nestmany shellsof differingdiameter.
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-e-
e-e-e- e-e-
e-
e-e- e-
e-e- e-
At optical wavelengths: At x-ray wavelengths:
...then read out.
...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 accumulationtime
Short readout time
NASSP Masters 5003F - Computational Astronomy - 2009
X-ray Observatories - detectors
• CCDs have to be read out sequentially (slow).
Columns
Row
s
Readout row
Digitizer(ADC) Out
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).