Radioactivity

Lecture 10 The radioactive Universe

Universe, Galaxy, Solar System, Earth

The Radioactive Universe

The Planck map of the Universe showing the temperature distribution in the background radiation from the Big Bang cooled down to an average temperature of 2.73 K. The small temperature fluctuations are in the 0.01% range and indicate slight inhomogeneities in the early universe

Other signals from the Big Bang relic neutrinos

The Cosmic Microwave Background decoupled from matter 400,000 years after the Big Bang. The Cosmic Neutrino Background decoupled after 1 second leaving relic neutrinos as direct signal from the nuclear particle processes in the first second. They have cooled now with the expansion of the universe to 1.95K which translates into an energy of about 100-200µeV. All other neutrinos from stellar nuclear reaction and decay processes have higher energies! The relic neutrino flux (number of neutrinos penetrating every square centimeter of our body per second) is up to 20 trillion/cm2⋅sec. About 10 million share the volume of your and my bodies at any time. But there is no harm, the probability for damage is exceedingly small.

Infrared radiation range

Gamma radiation range

Distribution of heat sources (stars) along the galactic plane

Distribution of radioactive sources along the galactic plane

Our Radioactive Galaxy

Specific decay processes

511 keV γ radiation associated with the positron β+ decay of neutron deficient radioactive elements in our universe. The positron annihilates interacting with an electron and converting its mass into 511keV γ radiation through annihilation.

1809 keV γ radiation is associated with the positron β+ decay of 26Al to the first excited state in 26Mg followed by the decay of this level to the ground state under emission of 1809 keV γ radiation.

Inter=

The Observers

INTEGRAL

COMPTON RHESSI

26Al and 60Fe as long-lived isotopes 26Al is a neutron deficient Aluminum isotope (27Al is stable) with a half-life of 716,000 years. It is produced by proton induced reactions on stable 25Mg isotopes during the last phases of stellar burning in massive stars and during the shock-front expansion of supernovae. 60Fe has a lifetime of 2.6⋅106 years and is produced by neutron capture on the stable 58Fe isotope. The decay lines of both isotopes are observed by satellite based gamma detectors like INTEGRAL and RHESSI.

The estimated steady state production rates are 2.0±1.0 M/Myr for 26Al and 0.75± 0.4 M /Myr for 60Fe. This corresponds to 2.2±1.1 M of 26Al and 1.7±0.9 M of 60Fe in the present interstellar medium. Predictions for the 60Fe mass distribution, total mass, and flux map are given, in particular a 60Fe/26Al flux ratio of 0.16 ± 0.12.

The galactic activity from 26Al and 60Fe

Bqs

FeNT

FeNFeA

nucleiFeMkg

FeMA

NFeN

kgkgMFeM

Bqs

AlNT

AlNAlA

nucleiAlMkg

AlMA

NAlN

kgkgMAlM

A

A

415576

60

2/1

6060

55603

236060

303060

425675

26

2/1

2626

56263

232626

303026

1087.2104.31014.3106.2

69.0)(2ln)()(

104.3)(1060

10022.6)()(

1038.310989.17.17.1)(

1011.3101014.31016.7

69.0)(2ln)()(

10)(1026

10022.6)()(

1038.410989.12.22.2)(

⋅=⋅⋅⋅⋅⋅

=⋅=⋅λ=

⋅=⋅⋅

⋅=⋅=

⋅=⋅⋅=⋅=

⋅=⋅⋅⋅⋅

=⋅=⋅λ=

=⋅⋅

⋅=⋅=

⋅=⋅⋅=⋅=

−

⊕

−

⊕

The solar mass M=1.989⋅1030 kg

Radioactive decay patters of 26Al, 44Ti, and 60Fe

2.6

Emission of the 1.8 MeV γ ray from the ground-state transition in the daughter nucleus 26Mg.

Emission of the 1.17 MeV and the 1.33 MeV γ lines from the subsequent 60Co decay to 60Ni.

β+ decay γ 1.809 MeV

Emission of the 1.157 MeV γ line from the subsequent 44Sc decay to 44Ca.

The radioactivity of 44Ti in Cassiopeia A

A core collapse supernova such as Cassiopeia A (Cas A) that exploded 336 years ago ejects up to 10-4⋅M on 44Ti into interstellar space. The ejected 44Ti can easily be calculated:

BqeBqeTiATiA

Bqs

TiNT

TiNTiA

particlesTiMkg

TiMA

NTiN

kgkgMTiM

yyt

ADnow

A

40336

5969.0

421680

4444

42567

44

2/1

4444

51443

234444

26304444

1021001.1)()(

1001.1101014.359

69.0)(2ln)()(

107.2)(1044

10022.6)()(

10210989.11010)(

⋅=⋅⋅=⋅=

⋅=⋅⋅⋅

=⋅=⋅λ=

⋅=⋅⋅

⋅=⋅=

⋅=⋅⋅=⋅=

⋅−⋅λ−

−

−⊕

−

What is the 44Ti activity emitting γ radiation today?

Supernova light curve

Radioactive 56Ni in core collapse supernovae Core collapse supernovae produce up to 1 M on 56Ni, depending on the mass of the progenitor star. The half-life of 56Ni is 6.1 days, it therefore decays faster than the examples discussed before, but releases its energy at a much faster time scale which explains the SN light curve.

BqeBqeCoACoA

BqeBqeNiANiA

Bqs

NiNT

NiNNiA

particlesNiMkg

NiMA

NNiN

kgkgMNiM

ddt

ADnow

ddt

ADnow

A

8105023.7769.0

491987

5656

105021.669.0

491987

5656

49554

56

2/1

5656

55563

235656

303056

1045.51081.2)()(

01081.2)()(

1081.21015.21064.81.6

69.0)(2ln)()(

1015.2)(1056

10022.6)()(

10210989.11)(

⋅=⋅⋅=⋅=

=⋅⋅=⋅=

⋅=⋅⋅⋅⋅

=⋅=⋅λ=

⋅=⋅⋅

⋅=⋅=

⋅=⋅=⋅=

⋅−⋅λ−

⋅−⋅λ−

−

⊕

Today, 29 years (or 10 thousand days) later the 56Ni activity is gone, replaced by the activity of 56Co (T1/2=77.3d) and superseded by the activity of the long-lived 44Ti (T1/2=59 y).

10,000 days

Decay law for longer lived daughter nuclei

10,000 days

1E+25

1E+27

1E+29

1E+31

1E+33

1E+35

1E+37

1E+39

1E+41

1E+43

1E+45

0.01 0.1 1 10 100 1000 10000

56Ni

56Co

( ) ( )

( ) ( )21

21

2/12

2/11

12

102

2ln2lnTT

with

eeNtN tt

=λ=λ

−λ−λ

λ⋅= λ−λ− Daughter nucleus 56Co is formed by the

decay of the 56Ni mother nucleus and maintains the overall level of activity or energy release depending on its lifetime.

My supernova is hundred times more powerful than SN1887a, because of the initial guess of 1 M on 56Ni, with a 56Ni production of 0.01 M good agreement is obtained!

Energy production powering the light curve

Each decay by electron capture generates energy that corresponds to the mass difference between 56Ni and the final decay product 56Fe.

The energy Q is produced by the radioactive decay of the 56Ni to 56Fe, which is facilitated by electron capture as alternative to β+ decay; the energy release for each decay process corresponds to the mass difference

( ) ( ) ( )

radiationasemittedMeVMeVQcMeVuwith

MeVJQsmc

kg.ucuucFemcNimQ -

γ==

=⋅=⋅=

⋅=⋅−=⋅−⋅=

−

8.355.6/502.9311:

55.61005.11099.8

106605411935.55942.55

2

122

2162

272256256

That is the energy released by a single decay event, what is the total energy released in a supernovae?

( ) ( )

serg

sJ

sMeVQ

BqtAtAQQ

total

total

443750

490

1095.21095.21084.1

1081.2

⋅=⋅=⋅=

⋅=⋅=

ergMeVJsmkg :unitsEnergy 712

2

2

101024.611 =⋅==

Uranium Thorium Radioactivities From model predictions and observations supernova produces only a small fraction of very heavy elements above Fe. Average values are:

654 105102102.3 −−− ⋅=⋅=⋅=FeU

FeTh

FePb

Metal poor star elemental abundance observation

( )( ) ( )( ) ( )( ) ( )( )( ) ( )( ) BqUA

yUUA

BqThAy

ThThA

yUTparticlesUNyThTparticlesThN

particlesFeNwith

33238

5079

50238238

33232

51710

51232232

92382/1

50

102322/1

51

56

1044.2

1051014.3105.4

2ln105

1014.3

1021014.3104.1

2ln102

105.4105

104.110210

⋅=

⋅⋅⋅⋅⋅

=⋅⋅λ=

⋅=

⋅⋅⋅⋅⋅

=⋅⋅λ=

⋅=⋅≈

⋅=⋅≈

≈

Comparable activities because of balance between abundance and half-life but only about a billionth of the activity from 26Al and 60Fe observed in our universe!