Hard-core atomic physics: highly charged ions Jos R R. C Crespo L - - PowerPoint PPT Presentation

Hard-core atomic physics: highly charged ions

José R

• R. C

Crespo L po López-Urr pez-Urrutia tia Max-Planck-Inst x-Planck-Instit itut fü für Ke r Kernph rnphysik ysik Heid Heidelberg rg

• Gamma-ray bubbles extend 50,000 light-years.
• Hints first observed in X-rays (blue) by ROSAT
• Gamma rays mapped by Fermi (magenta)

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1869: Harkness & Young collect spectra of the solar corona

Which element is so light that it

• vercomes the Sun‘s gravity?

Coronium was postulated for the green coronal line at 530.3 nm which was found Edlén and Grotrian explained it in the 1940‘s

• B. Edlén, Z. Astrophys. 22

22, 30 (1942)

What are highly charged ions?

• Atoms loose many electrons at high

temperatures < 100000 K due to collisions

• The incomplete electronic shell does not

compensate the positive nuclear charge

• The electronic structure of such positive ions

with few electrons behaves like that of an atom

Example: Fe XXV = Fe24+ ion From 26 electrons to only two electrons: Helium-like 1s2

Atom:

• size: 100 pm,
• outer electrons weakly bound (10 eV)

HCI:

• size: few pm,
• positive charge
• few strongly

bound electrons (keV)

• strong electron-

nucleus overlap

Highly charged ions (HCI)

• Relevant and precise experimental data

needed for theory tests

• Fundamental phenomena become accessible

to observation:

• simpler electronic structure
• scaling with high powers of Z

Need for experimental data

The classic ideal: H-like ions Two-b Two-body dy-Coulomb-Pr

• Coulomb-Problem

blem  analytical solutio analytical solution

Scaling factors Scaling factors from H from H to to U91+

91+ :

• Level energy

Level energy En ~ Z ~ Z2

2

´ 8 ´ 810 103 Transiti Transition

• n probabi

probabilit ity Aik

ik :

• E1

E1 ~ ~ Z4 a factor a factor of

• f

´ 710 107

• 2E1 ~

2E1 ~ Z6 ´ 6 ´ 610 1011

11

• M1

M1 ~ ~ Z Z10

10

´ 4 ´ 410 1019

19

• M2

M2 ~ ~ Z Z8

8

´ 5 ´ 510 1015

15

• hyperfin

hyperfine splittin e splitting g ~ ~ Z3

• nuclear size

nuclear size effects effects ~ ~ Z6

• QED contrib

QED contribution tions s ~ ~ Z4

• PNC contrib

PNC contribution tions s ~ ~ Z5

„forbidden“ lines „forbidden“ lines (Sun) (Sun)/(H atom) (H atom)

Why highly charged ions? Sch Schrödi ödinger nger Dirac Dirac QED ED

n=1 n=1 p3/2

3/2

s1/2

1/2, p

, p1/2

1/2

n=2 n=2 p1/2

1/2

s1/2

1/2

p3/2

3/2

115 115 keV keV 132 132.3 .3 keV keV 131 131.8 .8 keV keV +radi +radiation fiel field En = R = Ry

. Z2/n

/n2

1s Lamb 1s Lamb shift shift

n=3 n=3 s1/2

1/2

+ r relati tivi vity ty

for U for U92+

92+ 468 eV

468 eV Lamb shift Lamb shift

Li: 0.002% of 1.85 eV Fe23+ : 1% of 48.6 eV U89+ : 15% of 280 eV

Li-like

» QED

QED

Lamb shift Lamb shift

H-like Lamb shift in hydrogen- and lithium-like ions

QED contributions:

1 H 2 He 3 Li 4 Be 5 B 6 C 7 N 8 O 9 F 10 Ne 11 Na 12 Mg 13 Al 14 Si 15 P 16 S 17 Cl 18 Ar 19 K 20 Ca 21 Sc 22 Ti 23 V 24 Cr 25 Mn 26 Fe 27 Co 28 Ni 29 Cu 30 Zn 31 Ga 32 Ge 33 As 34 Se 35 Br 36 Kr 37 Rb 38 Sr 39 Y 40 Zr 41 Nb 42 Mo 43 Tc 44 Ru 45 Rh 46 Pd 47 Ag 48 Cd 49 In 50 Sn 51 Sb 52 Te 53 I 54 Xe 55 Cs 56 Ba * 71 Lu 72 Hf 73 Ta 74 W 75 Re 76 Os 77 Ir 78 Pt 79 Au 80 Hg 81 Tl 82 Pb 83 Bi 84 Po 85 At 86 Rn 87 Fr 88 Ra * * 103 Lr 104 Rf 105 Db 106 Sg 107 Bh 108 Hs 109 Mt 110 Ds 111 Rg 112 Cn 113 Uut 114 Uuq 115 Uup 116 Uuh 117 Uus 118 Uuo

• binding energy

 Z2 10 eV  140 keV

• correlation

nearly Z independent

• relativistic fine structure  Z4

eV  keV

• QED

 Z4 eV  300 eV

• hyperfine structure

 Z3 eV  5 eV

• nuclear size effects

 Z5 eV  200 eV

• Forbidden transition probabilites Z10

up to a factor 1018

Scaling laws: Effects grow as powers of atomic number Z The relative weight of these effects can be tuned

Why photon spectroscopy beyond hydrogen?

• Non-perturbative Q
• perturbative QED:

D: co coupling co ling constant tant Zα ≈ 1 1

Bound e und electr ectron

• n expanded:

panded: sum o

• f free e

ee electron p ectron propagators agators Many ny virtual p rtual photons, e

• tons, each i

ch interaction teraction Z t Z times st stronger t ronger than an in H H

• Few-particle QED unexplored
• Theory of (non-perturbative) QED in high fields

still under construction; general scaling law ~Z 4

• Large nuclear size effects

• Interior of the Sun (15 MK)
• Solar corona (2 MK)
• Solar wind (MK)
• Supernova remnants
• Active galactic nuclei (100 MK)
• Warm-hot intergalactic medium (0.1-1 MK)

In the laboratory:

• Fusion machines (50 MK)
• Accelerators, laser produced plasmas (1 MK)
• Electron beam ion traps (e. g. in Heidelberg)

In the Universe, elements are mostly highly ionized: Highly charged ions (HCI)

Compilation of current observational measurements of the low redshift baryon census (Shull, Smith, & Danforth, ApJ 2012)

Warm-hot intergalactic medium at 105 to 108 K

Galaxies consist of: 90% ionized hydrogen 10% stars 0.01% planets

Baryonic matter (“atoms” ) is mostly highly ionized in the intergalactic medium, galaxy clusters and galaxies

Hitomi SXS spectra of the Perseus cluster of galaxies

Solar abundance ratios of the iron-peak elements in the Perseus cluster Hitomi Collaboration, Nature (2017) kT

e = 3.97 ± 0.02 keV

Fe/H= 0.63 ± 0.01 (relative to solar abundance)

X-ray lines from H-like, He-like and Li-like ions

Supernova explosions disperse the elements

Cat‘s Eye Nebula

NASA Image, Hubble ST, Cat's Eye Nebula Nordic Optical Telescope and Romano Corradi (Isaac Newton Group of Telescopes, Spain)

3 light years

Cassiopeia nebula: Remnant of the1680 AD supernova

X-RAY: NASA/CXC/SAO; visible: NASA/STScI; infrared: NASA/JPL-Caltech/Steward/O.Krause et al.

Supernova remnants, hot shocks X rays

X ray telescope XMM

• rbiting Earth

Supernova remnants (Tycho)

Warm-hot intergalactic medium

AAMOP 2011‐2012 2011‐11‐02 24 Date: 11 May 2010, Satellite: XMM-Newton; artist's impression of WHIM in the Sculptor Wall Spectrum: NASA/CXC/Univ. of California Irvine/T. Fang. Illustration: CXC/M. Weiss

Blazar H2356-309: Line-of-sight crosses the Sculptor Wall, a large-scale superstructure of galaxies at z ~ 0.03 Observer

Photoabsorption lines due to warm-hot intergallactic medium are due to highly charged ions

hot, photoionized intergallactic medium

How to detect WHIM

Backlighting quasar

For very tenuous media, measurements in absorption are far more sensitive than those in emission

4.5 3.7

Spectrum shows absorption lines absorbing medium

Total absorption yields column density information

X-ray observatory

HST + Chandra Deep Field South: X-ray View

There are X-ray sources (shown in blue) outshining whole galaxies

• Black hole: Million times the solar mass
• Event horizon 100 times solar radius
• Accretion disk size: light days
• Jets: 105 light years
• 100 light days away: Broad line region
• 100 light years: Molecular torus
• Narrow line region
• Event horizon of central black hole in NGC 3783

has a diameter 100 times that of the Sun

• It produces more radiation than 109 suns

A primer on black holes

Size matters

The first black hole, Cygnus X-1, was

• bserved more than

40 years ago with Aerobee rockets (Bowyer et al., 1965)

Radiotelescopes can interferometrically resolve the near structure

Magnetic spinning in BH jets

Supermassive black holes produce narrow particle jets (orange) and wider streams of gas (blue-gray) which can regulate both gallactic star formation and the growth of the black hole

F . Tombesi et al., ApJ, MNRAS 2010,2011,2012

Ultra-fast outflows (UFOs)

UFOs exist!

(ESA image)

Size matters

Relativistic Doppler shifts

The broad line region (BLR) shows very large Doppler shifts due to high velocity fields

Averaged spectral profile of Lockman hole AGN

MD Trigo et al. Nature 504 504, 260 (2013)

Fe XXVI ions moving at 0.66 c in an AGN

• Ratio of data to model results for two XMM-Newton
• bservations. Dotted lines: rest energy of the transitions of

Fe XXVI (6.97 keV) and Ni XXVII (7.74 keV).

• Flux ratio between blue- and redshifted components of Fe XXVI

is consistent with predicted Doppler boost in a jet.

Relativistically broadened emission lines near BHs

• Dominant feature: Fe Kα at 6.4 keV
• Observed in active galactic nuclei, and galactic

BHs with ASCA, RXTE, XMM, Chandra, Suzaku

Line profiles

• Gravitational red shift
• Radiation from the backside bent towards observer
• Rotation causes red and blue wings
• Intensity depends on distance from center

Line profiles show accretion disk dynamics

• Black hole spin lets accretion disk approach more the

event horizon

• Line profile is modified by space-time frame rotation

around BH

Black hole rotation leaves spectral imprint

Full general relativistic models can explain the lines shapes and the morphology of AGN

From: Thomas Dauser, PhD thesis, Bamberg, Erlangen

• bserver

Around BHs, X rays generated by infalling matter photoionize the surroundings: Photoabsorption lines

• Black holes accretion disks emit X rays
• Fe K-shell radiation ( of Fe24+,25+ )is the last observable

spectral feature since everything else is fully ionized

X-ray spectrum of Sgr A* in quiescence and model fits: central black hole seems starved of infalling matter X-ray-emitting gas around the black hole at the center of our galaxy

• Q. D. Wang et al., Science 2013

Fe XXV = Fe24+ S XV = S14+

Highly charged ions getting closer to us

Astrophysical Journal 92 92, 27 (1940)

HCI survive even at the solar core

naked, no bound-bound transitions excited states embedded in continuum: bound-free transitions excited states still around and working

A small volume (1%) of the Sun at its core generates by fusion of H nuclei thermal energy

Millions of years are necessary for energetic photons to traverse the

• paque “radiation

shield” due to the dense medium

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 10

• 2

10

• 1

10 10

1

10

2

Density (g/cm

3) Temperature (MK)

Total power (10

26 W) Opacity (g/cm 2)

Radius (r/Rsun)

T D

The opacity problem of the solar model: How is energy transferred to the surface?

• Radiation transport determines equilibrium

temperature in the solar core

• Iron ions (Fe16+…24+) control 25% of total opacity

T= 15600000 K T= 5700 K

Transition probabilities Aik scale up steeply

1 10 100 10

8

10

10

10

12

10

14

10

16

10

18 H He Li Be Ne Ar Ca Fe Zn Kr Zr Mo Sn Nd Yb Hg Pb Th U Cf

2p

2P1/2-1s 1S1/2 Transition probability (s

• 1)

Atomic number (Z)

y=k x Z

3.88

1 fs radiative lifetime 1 ns radiative lifetime

×106

Iron atoms can absorb radiation 1 million times faster than hydrogen, each photon being 600 times more energetic than in hydrogen

Radiative dominance of iron

The product of this three parameters boosts the radiative energy flux handled by iron and its ions in the X-ray domain regardless of its low absolute abundance

• Transition

probabilities grow with Z4

• Photon

energy scales with Z2

• Cosmic

abundance (30 ppm)

Hydrogen-1 Helium-4 Oxygen-16 Carbon-12 Nitrogen-14 Neon-20 Silicon-28 Magnesium-24 Iron-56 Sulfur-32

5 10 15 20 25 10

5

10

6

10

7

10

8

10

9

10

10

10

11

10

12

10

13

Photonic energy transfer yield (a. u.) Atomic number Z

Iron rules the X-ray spectrum

Fusion at core delivers: 280 W/m3 power  reptile metabolism… Photons would leave at speed of light, but: 600 Earth masses of iron, or 300 km thick wall at RSun /2 keeps photons trapped… this maintains a Temperature  15.7 MK, or 1.35 keV giving a Radiative energy flux  1021 J/(m2×s) with Peak photon flux at  6 keV

• f

Flux at Fe Kα  4×1031 photons/(cm2×s×sr) at Resonant cross section  4×10-18 cm2 yielding an Excitation rate by photons  1014 /s →(10% excited)

Some quick estimates for iron in the Sun core