X-Ray Spectroscopy
The need for high resolution
X-ray spectroscopy 1 eV
Astrophysical Plasmas:
Simulation of the emission from
a gas at T = 107 K with normal
abundances of elements.
An energy resolution of ~ 10 eV
is required to begin serious 10 eV
X-ray spectroscopy and a resolution
of ~ 1 eV is required for complete 100 eV
plasma diagnostics and velocity
measurements.
Energy (keV)
What’s a milliCrab?
• The second brightest X-ray (1-10 keV)
source in the sky is the Crab nebula
• Its photon intensity at the top of the
atmosphere of the Earth is ~ 10 cm-2 s-1
• There are about 1000 AGN (“quasars”) at
a level of about .01 cm-2 s-1 = 1 mC
Oxygen Shock-Heated to kT ~ 0.3 keV
ionized
H-like
He-like
Ionization
age
X-Ray Spectrum with 100 eV Resolution
4-6 keV
Cassiopeia A ACIS spectrum
Estimates of H- and He-Like Energies vs Atomic Number
X-Ray Spectrometers - I
• Proportional counters have
– High efficiency
– Imaging capability
– Multiplex spatial/spectral without confusion
But resolving power ≡ E/(δE) ≈ 6√E(keV)
X-Ray Spectrometers - II
• Bragg crystal spectrometers
– Dispersive, so they can use any detectors
– Can achieve R > 103
– Can have high efficiency (at one E at a time)
But no imaging or multiplexing capabilities
(i.e. can look at only one E at a time)
X-Ray Spectrometers - III
• Gratings
– Dispersive
– Can have moderate (few %) efficiencies
– Can multiplex (all E at the same time)
– Can have R > 103/√E(keV) (better for low E)
But image and spectral orders are mixed
Capella
Chandra HETG
X-Ray Spectrometers - IV
• Solid State (including CCDs)
– High efficiency (>90%)
– Non-dispersive, can multiplex all E
– Imaging capability without confusion with E
But cannot achieve better than R ≈ 25√E(keV)
(Resolution ≈ 40√E(keV) eV)
The need for high resolution
X-ray spectroscopy 1 eV
Astrophysical Plasmas:
Simulation of the emission from
a gas at T = 107 K with normal
abundances of elements.
An energy resolution of ~ 10 eV
is required to begin serious 10 eV
X-ray spectroscopy and a resolution
of ~ 1 eV is required for complete 100 eV
plasma diagnostics and velocity
measurements.
Energy (keV)
X-Ray Spectrometers - V
• Cryogenic Microcalorimeters
– High efficiency (>90%)
– Non-dispersive, can multiplex all E
– Imaging capability without confusion with E
And can achieve R > 103 √E(keV)
Physical Conditions Through X-Ray Spectroscopy
Fe-K lines provide very clean diagnostics.
w
He-like Fe “triplet” He-like Fe Expected
y, x with XRS
z
(12 eV)
Neutral Fe
w x
Counts
H-like Fe
y z
Chandra
HEG
(~ 60 eV)
Energy (keV)
One such diagnostic: excellent density-independent
temperature sensitivity in the range 107–108 Kelvin.
The X-ray Microcalorimeter
Features high resolution, non-dispersive spectroscopy with high quantum
efficiency over K- and L- atomic transition band.
Moseley, Mather and McCammon 1984
Simple Energy Resolution Argument
• δT = E/C (temperature rise for E deposition)
• C ≈ N(kT)/T (N = # of phonons with )
• N ≈ C/k (fluctuation in N is the “noise”)
• ΔN = √N (Poisson statistics)
• R = E/(ΔE) (resolving power)
• ΔE ≈ kT√N ≈ kT√(C/k) ≈ √(kT2C)
• More carefully, ΔE = 2.35 ζ √(kT2C)
Spectral Resolving Power:
Doped semiconductor
Depends on thermometer technology
R (ohms)
Temperature-sensitive resistance
Resolution limited by thermal
fluctuations between sensor and heat
bath and Johnson noise.
Temperature
E 2.35 kT 2C
T = operating temperature (50-100 mK)
R (ohms)
C = heat capacity
Superconducting
~ 2 - 4 for doped semiconductors Transition
~ 0.2 for transition edge sensors
For both thermometer schemes a spectral
resolution of few a eV is possible! Temperature
Basic requirements:
• Low temperature
• Sensitive thermometer
• Thermal link weak enough that the time for restoration of the base
temperature is the slowest time constant in the system yet not so
weak that the device is made too slow to handle the incident flux.
• Absorber with high cross section yet low heat capacity
• Reproducible and efficient thermalization
Types of thermometers:
• resistive
• capacitive
• inductive
• paramagnetic
• electron tunneling
Microcalorimeter Arrays
Implanted Traces
X-Ray Absorber
(HgTe)
Implanted Thermistor
Silicon Spacer
Silicon Pixel
Silicon Support Beams
.
.
.
XQC Array: 36 array of
0.5 2 mm pixels.
X-Ray Quantum Calorimeter Dewar
Deep implants using
silicon-on-insulator wafers.
625 m pixels
GSFC
Fit Parameters
200
6.4 eV FWHM
FWHM: 6.40 ± 0.15 eV
E_shift: -19.95 ± 0.069 eV
Mn Ka1
Amplitude: 208.8 ± 4 counts
y0: 0.0 ± 0 counts
150 2: 1.43
Ion beam
Counts
100
1.5 m Mn Ka2
50
E
0
40
Residual
20
0
(after anneal) -20
-40
5860 5870 5880 5890
Energy [eV]
~ 6 times deeper Energy (keV)
thermometer
RTS – Rotating Target Source
X-ray lines
continuum
X-ray source
X-ray continuum
rotating target
wheel
targets (one is open
for continuum)
motor
target wheel