nassp masters 5003f - computational astronomy - 2009 lecture 21 6.4 kev fe line and the kerr metric...

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)


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.


(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


Fluorescence from a ‘cool reflector’.

From A Fabian et al, PASP 112, 1145 (2000)


How ionization modifies this



A Doppler-broadened spectral line – predictions of various theories:


An accretion disk seen from above:

Fainter outside

Brighter inside

Slow – small DS

Fast – large DS

for whole disk

Profiles justfor the twodashed annuli.


Theory - spinning vs non-spinning BH


Spinning (so-calledKerr-metric BH)

Non-spinning (so-calledSchwartzschild BH)


Time-varying behaviour in MGC -6-30-15.This is a Seyfert I galaxy. From Tanaka et al (1995).


1994: time-averaged.

1997: at flare peak.

1997: time-averaged.

1994: in a deep minimum.


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.


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.


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:


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:


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:


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.


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


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.


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.


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?


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.


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


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.


X-ray Observatories - detectors

• CCD operation is in frame cycles.

Long accumulationtime

Short readout time



• CCDs have to be read out sequentially (slow).

Columns

Row

s

Readout row

Digitizer(ADC) Out



• 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.


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 lecture 21 6.4 kev fe line and the kerr metric...

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direction cosines

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sky frame

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