High-energy astrophysics

Transcription

1 High-energy astrophysics III Imaging IV Spectroscopy Stéphane Paltani With lots of help from Marc Audard!

2 Overview Imaging: Telescopes and mirrors Spectroscopy: Grating

3 Slide origin and courtesy Several slides are original, i.e., created by Marc Audard for this course Many are, however, taken (or adapted) from presentations made by others Figures were also borrowed from the web Sources have been identified as much as possible and apologies for missing credits

4 Techniques for imaging X-rays Collimators (and scanning) Coded masks Grazing incidence Gamma-rays Collimators Compton telescope

5 Passive collimators Shield Shield Mechanical collimator (e.g., rectangular tubes) Angular resolution is very poor (about 1 ) Flux limit is erg cm-2 s-1 (probability of 5% to have 2nd source in the FOV) Frequently used also for gamma-rays Detector

6 Modulating Aperture Systems

7 Giacconi et al. (1971)

8 Giacconi et al. (1971)

9 4.8 s modulation Schreier et al. (1972)

10 RXTE

11 HEAO-1 A2

12 Occultation Techniques Flux Collimation / Source Localization (cont.) Fsource For example: Earth Occultation Technique t Source From M. Böttcher

13 coded mask imaging measured parameters : x,y: int. location on the detector E : energy deposited t : arrival time astronomy : encoding of a two dimensional source distribution (i,j) into a 2-D dataspace (k,l) for sources at finite distance (nuclear medicine, tomography of X-ray emitting plasmas) coded mask techniques can be used to extract depth information for volumetric object reconstruction.

14 Field of view characteristics of a coded mask instrument Good simultaneous measurement of background and source Large field of view Bad Limited range of spatial frequencies (bad for diffuse emission and for small sources) Detector background contributing significantly

15 Advantages of focusing optics versus direct-view detectors B =background flux, Tint = integration time, E = integration bandwidth Moreover: much better imaging capabilities!

16 Focusing X/gamma-Rays

17 Simulation of two sources in a Einstein field as seen by a direct view detector With the direct view detector the second weak sources is lost in the background

18 X-ray astronomical optics history in pills (I) 1895: Roentgen discovers X-rays 1948: First succesfull focalization of an X-ray beam by a total-reflection optics (Baez) 1952: H. Wolter proposes the use of two-reflection optics based on conics for X-ray microscopy 1960: R. Giacconi and B. Rossi propose the use of grazing incidence optics for Xray telescopes 1962: discovery by Giacconi et al. of Sco-X1, the first extra-solar X-ray source 1963: Giacconi and Rossi fly the first (small) Wolter I optics to take images of Sun in X-rays 1965: second flight of a Wolter I focusing optics (Giacconi + Lindslay) 1973: SKYLAB carry onboard two small X-ray optics for the study of the Sun

19 X-ray astronomical optics history in pills (II) 1978: Einstein, the first satellite with optics entirely dedicated to X-rays 1983: EXOSAT operated (first European mission with X-ray optics aboard) 1990: ROSAT, first All Sky Survey in X-rays by means of a focusing telescope with high imaging capabilities 1993: ASCA, a multimudular focusing telescope with enhanced effective area for spectroscopic purposes 1996: BeppoSAX, a broad-band satellite with Ni electroformed optics 1999: launch of Chandra, the X-ray telescope with best angular resolution, and XMM-Newton, the X-ray telescope with most Effective Area 2004: launch of the Swift satellite devoted to the GRBs investigation (with aboard XRT) 2005: launch of Suzaku with high throughput optics for enhanced spectroscopy studies with bolometers

20 Imaging experiments using Bragg reflection from replicated mica pseudo-cylindrical optics E. Fermi Thesis of Laurea, Formazione di immagini con i raggi Roentgen ( Imaging formation with Roentgen rays ), Univ. of Pisa (1922) Thanks to Giorgio Palumbo!

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22 X-ray optical constants complex index of refraction to describe the interaction X-rays Linear abs. coeff. /matter: ñ = n + i = i changes of phase ( cm -1) absorption at a boundary between two materials of different refraction index n1, n2 reverse of the momentum P in the z direction: h p1 k1 2 k1 2 p z 4 n1 sin inc 2 n1 momentum transfer the amplitute of reflection is described by the Fresnel s equations: r12s n sin 1 n2 sin 2 1 n1 sin 1 n2 sin 2 s-polarized (perp plane) r12p n1 sin 2 n2 sin 1 n1 sin 2 n2 sin 1 p-polarized (parallel plane)

23 Total X-ray reflection at grazing incidence if vacuum is material #1 (n1 = 1) the phase velocity in the second medium increases beam tends to be deflected in the direction opposite to the normal. Snell s law (n1 cos 1 = n2 cos 2) to find a critical angle for total reflection: crit 2 r0 2 N Av A = wavelength = density A = atomic weight f1 = scattering coeff. r0 = classical electron radius f1 far from the fluorescence edges f1 Z and for heavy elements Z/A 0.5: crit ( arc min) 5.6λ(Å) ρ Riflettività θ reflectivity loss due to scattering: IR I 0 exp 4 n sin = rms microroughness level 2 Angolo di incidenza = 0.5 deg Ni Au Energia dei fotoni (kev) 12 14

24 Other examples: C, Ni, Au 0 10 Dati sperimentali Modello -1 Riflettività z(nickel)=60 nm Angolo di incidenza [arcsec] 6000

25 X-ray mirrors with parabolic profile y x y2 = 2 p x p = 2 * dist. focus-vertex perfect on-axis focusing off-axis images strongly affected by coma

26 The Abbe sine condition to have coma-free focusing mirrors Coma off-axis aberration Coma free mirrors must satisfy the Abbe sine condition: The surface defined by the intersection of each input ray with its corresponding output ray (principal or Abbe surface) must be a sphere around the image, i.e.: h1 h2 const. sin 1 sin 2

27 Parabolic mirrors & the Abbe sine condition The parabolic profile approximately obeys to the Abbe rule only near the vertex, i.e. at normal incidence but not for grazing incidence angles the parabolic geometry is not optimal for X-ray telescopes

28 Wolter s solution to the X-ray imaging H. Wolter, Ann. Der Phys., NY10,94

29 The Wolter I mirror profile for X-ray astronomy applications it guarantees the minimum focal length for a given aperture it allows us to nest together many confocal mirror shells Effective Area: 8 F L 2 Refl.2 F= focal length = R / tan 4 = on-axis incidence angle R = aperture radius L=mirror height

30 The Abbe condition and the Wolter I mirror profile Spherical aberration term rms 0.2 tan tan 2 L 2 4 tan tan F rms = rms blur circle = incidence angle F= focal length = off-axis angle L = mirror height NOTE: 2 L r the optimal focal plane is not flat: flat 2 1 F tan 2 Residual coma term r = focal plane radius

31 Alternative profiles derived from Wolter I Wolter-Schwarzschild profile: it exactly satisfies the Abbe sine condition and it has been adopted for the Einstein mirrors; is coma free but it strongly affected by spherical aberration double-cone profile: it better approximates the Wolter I at small reflection angles: It is utilized for practical reasons (cost + effective area). polynomial profile: parameters have been specifically optimized to maintain the same HEW in a wide field of view (introducing small aberration on-axis the off-axis imaging behavior is improved same principle of the Ritchey-Chretien normal-incidence telescope in the optical band)

32 Kirpatrick-Baez Telescopes parabolic-profile curved mirrors in just one direction to focus a beam in a single point another identical mirror has to be orthogonally placed with respect to the first one; it is possible to nest many confocal mirrors to increase the effective area; compared to a Wolter I system with same focal length and same incidence angle (onaxis), angles are two time larger; imaging capabilities result to be limited by some inherent aberration; NB: by means of a K-B optics was performed the first successful attempt of the focalization of an X-ray beam in total-reflection regime (1948)

33 Lobster-Eye optics system similar to spherical normal-incidence mirrors but, in this case, the beam impinges on the convex part of the entrance pupil; the pupil is formed by a system of channels with square section uniformly distributed around a spherical surface of radius R. To be focused in a single point a collimated beam has to sustain the reflection by two orthogonal walls of a same channel; the photons are focused onto points distributed on a spherical surface of radius R/2; a preferential optical axis does not exist the system field of view can be in principle as large as 4 p with the same Effective Area for every direction

34 Manufacturing techniques utilized so far 1. Classical precision optical polishing and grinding Projects: Einstein, Rosat, Chandra Advantages: superb angular resolution Drawbacks: high mirror walls small number of nested Credits: NASA mirror shells, high mass, high cost process 2. Replication Projects: EXOSAT, SAX, JET-X/Swift, XMM, ABRIXAS ( Credits: ESA examples follow hereafter) Advantages: good angular resolution, high mirror nesting the same mandrels for many modules Drawbacks: relatively high cost process; high mass/geom. area ratio (if Ni is used). 3. Thin foil mirrors Projects: BBXRT, ASCA, SODART, ASTRO-E Advantages: high mirror nesting possibility, low mass/geom. area ratio (the foils are made of Al), cheap process Drawbacks: until now low imaging resolutions (1-3 arcmin) Credits: ISAS

35 Present Astronomical optics technologies: HEW Vs Mass/geometrical area

36 Replication methods Ni electroforming replication (SAX, JET-X/Swift, XMM, ABRIXAS, erosita, SIMBOL-X, SVOM/XIAO) epoxy replication: EXOSAT (Be), WFXT (Alumina & SiC prototypes), EDGE/XENIA?

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40 The focusing problem in the hard X-ray region (> 10 kev) Wolter I geometry Aeff F2 x c2 x R2 At photon energies > 10 kev the cut-off angles for total reflection are F = focal length R = reflectivity very small also for heavy metals L = mirror height = incidence angle the geometrical areas with usual focal lengths (~ 10 m) are in general negligible but crit E

41 Focal Length Vs. Diameters for SIMBOL-X and other X-ray telescopes F n o i at m r Fo es! e Th scop tele tu c e t chi r a t il gh Aeff F2 x c2 x R2 nit u t or p p eo h t rs e f f re o FL g lon Multilayers t n 0.6 o me e l p m i y to crit E

42 The formation flight contribution

43 Wide band multilayers Optical supermirrors in a beetle skin X-ray supermirrors a) b) Beetle Aspidomorpha Tecta; 1

44 Multilayers Bragg s law satisfy mλ = 2d sinθ Varying d-spacing allow us to achieve high reflectivity over a range of E and W/Si, W/C, Ni/C, and Pt/C

45 X-ray Pore Optics System Double-Cone approximation N.B.:concept introduced by D. Willingale et al, Capri 1994

46 Silicon Pore Optics technology Credits: ESA & Cosine

47 Hard X-ray Focusing by mosaic crystals Bragg diffraction from a crystal lattice reflectivity peaks at: 2 d sin = n d typical value of a few Angstroms mosaic crystals: at microscopic level a structure of microcrystals almostparallel to the external crystal surface. The distribution of the crystallites normals is described by a Gaussian law each crystallite reflects in an independent way (without any interferometric coupling with the beams reflected from the other crystallites) the integrated reflectivity results to be much larger (>100) than for a perfect crystal case

48 Bragg & Laue Configurations Bragg 2 F 31 Re f int eg FWHM Gauss V Laue 2 T F 3 T FWHM Gauss e sin Re f int eg sin V Bragg kev F = Structure Factor V = Volume of the lattice element = lin. absorb. coeff Laue kev

49 Why crystal diffraction for high energy telescopes Focusing optics in the hard X-/soft gammaray band is crucial for a significant leap The hard X-ray band (E<80 kev) can be covered with multilayer mirrors (NuStar, NeXT, Simbol-X). The higher energy band (>80 kev) can be efficiently covered with Laue lenses. GRI concept

50 Focusing Gamma-Rays - how? (511 kev) = Å Bragg condition 2dsin = d[220] = arcsin( /2d) n Å = Laue-type Gamma-ray lens 2 = ex. radius [220] = 10.1 cm => focal length = 8.2 m PvB, CESR, 19 avril 2004

51 FRESNEL : principle real part of the refraction index for gamma-rays : = 1 where ρ δ= g cm2 9 ( )( E 1 MeV 2 ) 1 ρ λ t 2 π = =0.6 3 δ 10 g cm ( PvB, CESR, 19 avril )( E mm 1 MeV ) 1 kev-10 MeV Focal length 106 km!

52 Compton Telescopes measured parameters : x1,y1 E1 x2,y2 E2 : : : : interaction location in D1 energy deposit in D1 interaction location in D2 energy deposit in D2 t, t : arrival time, TOF D1-D2 derived parameters : x1,y1,x2,y2 =>, E1,E2 => cos - = 1 - mec2/e2 + mec2/(e1+e2) encoding of the two dimensional source distribution into a 3-D dataspace ( ) - PvB, CESR, 19 avril -

53 Dataspace of classical Compton telescopes Eventcircles from a single pointsource at (35, 0 ) PvB, CESR, 19 avril events from same point source lie on a cone with apex at (35, 0 ) grayscale -> probability density (for 1.8 MeV photons, max. at O(j,_) = 23,7 )