Detection and (Linear) Data Model Jörn Wilms Remeis-Sternwarte & ECAP Universität Erlangen-Nürnberg http://pulsar.sternwarte.uni-erlangen.de/wilms/ joern.wilms@sternwarte.uni-erlangen.de
Part 1: Why is X-ray and Gamma-Ray Astronomy Interesting?
Part 2: Tools of the Trade: Satellites
Earth’s Atmosphere Earth’s atmosphere is opaque for all types of EM radiation except for opti- cal light and radio. Major contributer at high energies: photoabsorption ( ∝ E − 3 ), esp. from Oxygen (edge at ∼ 500 eV). ⇒ If one wants to look at = the sky in other wave- bands, one has to go to space! CXC
The Present XMM-Newton (ESA): launched 1999 Dec 10 Chandra (NASA): launched 1999 Jul 23 Currently Active Missions: X-ray Multiple-Mirror Mission ( XMM-Newton ; ESA), Chandra (USA), Suzaku (Japan, USA), Swift (USA), International Gamma-Ray Laboratory ( INTEGRAL ; ESA), Fermi (USA), AGILE (Italy), MAXI (Japan), ASTROSAT (India), NICER (USA), Spectrum-X-Gamma (RU/D) We are living in the “golden age” of X-ray and Gamma-Ray Astronomy
The Present RadioAstron Longjiang-1/2 Queqiao/NCLE Spitzer Sofia HST Kepler/K2 Gaia TESS Solar Orbiter XMM-Newton Chandra Swift MAXI NuSTAR ASTROSAT POLAR XPNAV-1 NICER Insight-HXMT MVN HaloSat Kanazawa-Sat 3 Spectrum-X-Gamma INTEGRAL AGILE Fermi DAMPE Lomonosov/MVL-300 LOFAR ASKAP/MWA MEERKAT FAST IRAM/NOEMA ALMA APEX VLT H.E.S.S. Advanced LIGO/Virgo KAGRA IceCube/PINGU 2018 2020 2022 2024 2026 2028 2030 2032 Year
The Present RadioAstron Longjiang-1/2 Queqiao/NCLE Spitzer Sofia JWST SPHEREx WFIRST HST Kepler/K2 Gaia TESS Solar Orbiter CHEOPS WSO-UV Euclid PLATO Ariel XMM-Newton Chandra Swift MAXI NuSTAR ASTROSAT POLAR XPNAV-1 NICER Insight-HXMT MVN HaloSat Kanazawa-Sat 3 Spectrum-X-Gamma ASO-S IXPE SVOM XRISM Einstein Probe Athena INTEGRAL AGILE Fermi DAMPE Glowbug Lomonosov/MVL-300 M5 LOFAR ASKAP/MWA MEERKAT FAST IRAM/NOEMA SKA ALMA APEX VLT LSST E-ELT H.E.S.S. CTA Advanced LIGO/Virgo KAGRA LIGO-India Einstein Telescope IceCube/PINGU KM3NeT 2018 2020 2022 2024 2026 2028 2030 2032 Year
Part 3: Tools of the Trade: Mirrors and Detectors
Introduction How is X-ray astronomy done? Detection process: Imaging Detection Data reduction Data analysis
Introduction How is X-ray astronomy done? Imaging: • Wolter telescopes (soft X-rays up to ∼ 15 keV) • Coded Mask telescopes (above that) • Collimators
Introduction How is X-ray astronomy done? Detectors: • Non-imaging detectors Detectors capable of detecting photons from a source, but without any spatial resolution ⇒ Require, e.g., collimators to limit field of view. = Example: Proportional Counters, Scintillators • Imaging detectors Detectors with a spatial resolution, typically used in the IR, optical, UV or for soft X-rays. Generally behind some type of focusing optics. Example: Charge coupled devices (CCDs), Position Sensitive Proportional Counters (PSPCs)
X-ray Imaging Cassegrain telescope, after Wikipedia Reminder: Optical telescopes are usually reflectors: primary mirror → secondary mirror → detector Main characteristics of a telescope: • collecting area (i.e., open area of telescope, ∼ πd 2 / 4, where d : telescope diameter) • angular resolution, θ = 1.22 λ (1) d if surface roughness and alignment can be ignored
X-ray Imaging Optical telescopes are based on principle that reflection “just works” with metallic surfaces. For X-rays, things are more complicated... Snell’s law of refraction: sin α 1 = n 2 (2) = n sin α 2 n 1 n 1 α where n index of refraction, and α 1,2 angle wrt. 1 surface normal. If n ≫ 1: Total internal reflec- θ tion 1 Total reflection occurs for α 2 = 90 ◦ , i.e. for sin α 1,c = n cos θ c = n (3) ⇐ ⇒ n 2 < n 1 α with the critical angle θ c = π/ 2 − α 1,c . 2 Clearly, total reflection is only possible for n < 1 ⇒ θ c ∼ 50 ◦ = Light in glass at glass/air interface: n = 1 / 1.6 = ⇒ principle behind optical fibers.
X-ray Imaging In general, the index of refraction is given by Maxwell’s relation, n = √ ǫµ (4) where ǫ : dielectricity constant, µ ∼ 1: permeability of the material. For free electrons (e.g., in a metal), (Jackson, 1981, eqs. 7.59, 7.60) shows that p = 4 πnZe 2 � 2 � ω p ω 2 ǫ = 1 − with (5) ω m e where ω p : plasma frequency, n : number density of atoms, Z : nuclear charge. (i.e., nZ : number density of electrons) With ω = 2 πν = 2 πc/λ , Eq. (5) becomes ǫ = 1 − nZe 2 πm e c 2 λ 2 = 1 − nZr e λ 2 (6) π r e = e 2 /m e c 2 ∼ 2.8 × 10 − 13 cm is the classical electron radius.
X-ray Imaging � 1 − nZr e λ 2 ∼ 1 − nZr e ρ r e 2 π λ 2 = 1 − 2 π λ 2 =: 1 − δ (7) n = ( A/Z ) m u π Z : atomic number, A : atomic weight ( Z/A ∼ 0.5), ρ : density, m u = 1 amu = 1.66 × 10 − 24 g Critical angle for X-ray reflection: cos θ c = n = 1 − δ (8) Since δ ≪ 1, Taylor (cos x ∼ 1 − x 2 / 2): � 1 / 2 √ � ρ λ 2 δ = 5.6 ′ (9) θ c = 1 g cm − 3 1 nm So for λ ∼ 1 nm: θ c ∼ 1 ◦ .
X-ray Imaging Typical parameters for selected elements Z ρ nZ g cm − 3 e − Å − 3 C 6 2.26 0.680 Si 14 2.33 0.699 Ag 47 10.50 2.755 W 74 19.30 4.678 Au 79 19.32 4.666 After Als-Nielsen & McMorrow (2004, Tab. 3.1) To increase θ c : need material with high ρ ⇒ gold ( XMM-Newton ) or iridium ( Chandra ). = For more information on mirrors etc., see, e.g., Aschenbach (1985), Als-Nielsen & McMorrow (2004), or Gorenstein (2012)
X-ray Imaging 1.0 0.2deg 0.8 0.5deg Reflectivity 0.6 0.4deg X-rays: Total reflec- 0.4 1deg tion only works in the soft X-rays and 0.2 only under grazing incidence 0.0 0 5 10 15 20 ⇒ grazing inci- = Photon Energy [keV] dence optics. Reflectivity for Gold
Wolter Telescopes Hyperboloid Incident paraxial Paraboloid radiation Focus Hyperboloid after ESA To obtain manageable focal lengths ( ∼ 10 m), use two reflections on a parabolic and a hyperboloidal mirror (“Wolter type I ”) (Wolter 1952 for X-ray microscopes, Giacconi & Rossi 1960 for UV- and X-rays). But: small collecting area ( A ∼ πr 2 l/f where f : focal length)
Wolter Telescopes Recycle Mandrel Metrology Super Polished Mandrel Hole Drilling Gold Deposition Mandrel − + Separation (cooled) Cleaning Ni Ni Electroforming Integration Au Handling on Spider Mirror Production Integration (after ESA) Recipe for making an X-ray mirror: 1. Produce mirror negative (“Mandrels”): Al coated with Kanigen nickel (Ni+10% phos- phorus), super-polished [0.4 nm roughness]). 2. Deposit ∼ 50 nm Au onto Mandrel 3. Deposit 0.2 mm–0.6 mm Ni onto mandrel (“electro-forming”, 10 µ m/h) 4. Cool Mandrel with liquid N. Au sticks to Nickel 5. Verify mirror on optical bench. numbers for eROSITA (Arcangeli et al., 2017)
Wolter Telescopes
Wolter Telescopes Characterization of mir- ror quality: Half Energy Width, i.e., circle within 50% of the detected en- ergy are found. Note: energy dependent! for XMM-Newton: 20 ′′ at 1.5 keV, 40 ′′ at 8 keV. for eROSITA: 16 ′′ at 1.5 keV, 15.5 ′′ at 8 keV Ground calibration, e.g., at PANTER
Detection of X-rays Energy Semiconductors: separa- tion of valence band and E Fermi conduction band ∼ 1 eV (=energy of visible light). Absorption of photon in Si: Energy of photon released photo electron(s) + scattering off e − Space + phonons... Number of electron-hole pairs produced: Problem: normal semiconductor: e − -hole pairs recombine immediately
Detection of X-rays Energy “Doping”: moves valence- Acceptors and conduction bands. Connecting “n-type” and E Fermi Donors a “p-type” semiconductor: pn-junction. In pn junction: electron- n-type p-type hole pairs created by ab- sorption of an X-ray are Space separated by field gradient ⇒ electrons can then be collected in potential well away from the junc- = tion and read out.
Detection of X-rays Material Band gap E /pair Z (eV) (eV) Si 14 1.12 3.61 Ge 32 0.74 2.98 CdTe 48–52 1.47 4.43 HgI 2 80–53 2.13 6.5 GaAs 31–33 1.43 5.2 Number of electron-hole pairs produced determined by band gap + “dirt effects” (“dirt effects”: e.g., energy loss going into bulk motion of the detector crystal [“phonons”]) N pair ∼ E photon (10) E pair • optical photons ( E : few eV): ∼ 1 e − -hole-pair per absorption event • X-ray photons: ∼ 1000 e − -hole-pairs per photon But: Since band gap small: thermal noise = ⇒ need cooling (ground based: liquid nitrogen, − 200 ◦ C, in space: more complicated...)
Detection of X-rays Photon Polysilicon electrodes 1 2 3 conductors; ~0.5 m deep µ SiO insulator 2 0.1 m deep µ 3 1 2 3 1 2 3 1 2 3 1 e _ e _ e _ n−type (+) silicon (depleted) ~2 m µ e _ Atom ~10 m p−type (−) silicon µ (depleted) Potential energy 1 pixel for an electron photoelectrons (~15 m) µ ~250 m µ Photoelectron track p−type (undepleted) After Bradt Two-Dimensional imaging is possible with more complicated semiconduc- tor structures: Charge Coupled Devices (CCDs).
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