The Primordial Lithium Problem Can We Avoid New Physics ? Nachiketa - - PowerPoint PPT Presentation

▶
the primordial lithium problem can we avoid new physics
SMART_READER_LITE
LIVE PREVIEW

The Primordial Lithium Problem Can We Avoid New Physics ? Nachiketa - - PowerPoint PPT Presentation

Jun 07, 2023 274 likes •1.43k views

The Primordial Lithium Problem Can We Avoid New Physics ? Nachiketa Chakraborty, Prof. Brian D. Fields Prof. Keith A. Olive New Perspectives 2011 Whats the problem ? Light elemental abundances constrain Big Bang cosmology (Wagoner, Fowler

slide-1
SLIDE 1

The Primordial Lithium Problem Can We Avoid New Physics ?

Nachiketa Chakraborty, Prof. Brian D. Fields

  • Prof. Keith A. Olive

New Perspectives 2011

slide-2
SLIDE 2

What’s the problem ?

Light elemental abundances constrain Big Bang cosmology

(Wagoner, Fowler and Hoyle, 1967 ; Steigman, Schramm and Gunn, 1977 ; Schramm and Turner, 1998)

Abundances set by

nb/nγ = η α Ωb

WMAP gives η Discrepancy between theory (Cyburt, Fields and Olive, 2008) and

  • bservation of 7Li (Spite and Spite, 1982 ;

Smith et al., 1998)

“Law of trichotomy”

  • Theory wrong
  • Observation wrong (Richards et al.,

2005 ; Melendez et al., 2010)

  • Both wrong

Cyburt, Fields and Olive, 2008

WMAP

slide-3
SLIDE 3

What’s the problem ?

Light elemental abundances constrain Big Bang cosmology

(Wagoner, Fowler and Hoyle, 1967 ; Steigman, Schramm and Gunn, 1977 ; Schramm and Turner, 1998)

Abundances set by

nb/nγ = η α Ωb

WMAP gives η Discrepancy between theory (Cyburt, Fields and Olive, 2008) and

  • bservation of 7Li (Spite and Spite, 1982 ;

Smith et al., 1998)

“Law of trichotomy”

  • Theory wrong
  • Observation wrong (Richards et al.,

2005 ; Melendez et al., 2010)

  • Both wrong

Cyburt, Fields and Olive, 2008

WMAP

slide-4
SLIDE 4

What’s the problem ?

Light elemental abundances constrain Big Bang cosmology

(Wagoner, Fowler and Hoyle, 1967 ; Steigman, Schramm and Gunn, 1977 ; Schramm and Turner, 1998)

Abundances set by

nb/nγ = η α Ωb

WMAP gives η Discrepancy between theory (Cyburt, Fields and Olive, 2008) and

  • bservation of 7Li (Spite and Spite, 1982 ;

Smith et al., 1998)

“Law of trichotomy”

  • Theory wrong
  • Observation wrong (Richards et al.,

2005 ; Melendez et al., 2010)

  • Both wrong

Cyburt, Fields and Olive, 2008

WMAP

?

Observation Theory

slide-5
SLIDE 5

What’s the problem ?

Light elemental abundances constrain Big Bang cosmology

(Wagoner, Fowler and Hoyle, 1967 ; Steigman, Schramm and Gunn, 1977 ; Schramm and Turner, 1998)

Abundances set by

nb/nγ = η α Ωb

WMAP gives η Discrepancy between theory (Cyburt, Fields and Olive, 2008) and

  • bservation of 7Li (Spite and Spite, 1982 ;

Smith et al., 1998)

“Law of trichotomy”

  • Theory wrong
  • Observation wrong (Richards et al.,

2005 ; Melendez et al., 2010)

  • Both wrong

Cyburt, Fields and Olive, 2008

WMAP

?

Observation Theory

slide-6
SLIDE 6

What’s the problem ?

Light elemental abundances constrain Big Bang cosmology

(Wagoner, Fowler and Hoyle, 1967 ; Steigman, Schramm and Gunn, 1977 ; Schramm and Turner, 1998)

Abundances set by

nb/nγ = η α Ωb

WMAP gives η Discrepancy between theory (Cyburt, Fields and Olive, 2008) and

  • bservation of 7Li (Spite and Spite, 1982 ;

Smith et al., 1998)

“Law of trichotomy”

  • Theory wrong
  • Observation wrong (Richards et al.,

2005 ; Melendez et al., 2010)

  • Both wrong

Cyburt, Fields and Olive, 2008

WMAP

slide-7
SLIDE 7

Theory Solutions

Assume observations right ⇒ Reduce 7Li or 7Be Beyond Standard Model

  • Dark matter decay (Bailly et al., 2009 and others)
  • Bound states (Jittoh et al., 2010, Cyburt et al., 2006 and
  • thers)
  • Varying fundamental constants (Berengut et

al.,2010),....) etc.

slide-8
SLIDE 8

Theory Solutions

Assume observations right ⇒ Reduce 7Li or 7Be Beyond Standard Model

  • Dark matter decay (Bailly et al., 2009 and others)
  • Bound states (Jittoh et al., 2010, Cyburt et al., 2006 and
  • thers)
  • Varying fundamental constants (Berengut et

al.,2010),....) etc.

CERN

slide-9
SLIDE 9

Theory Solutions

Assume observations right ⇒ Reduce 7Li or 7Be Beyond Standard Model

  • Dark matter decay (Bailly et al., 2009 and others)
  • Bound states (Jittoh et al., 2010, Cyburt et al., 2006 and
  • thers)
  • Varying fundamental constants (Berengut et

al.,2010),....) etc.

CERN

Fermilab

slide-10
SLIDE 10

Theory Solutions

Assume observations right ⇒ Reduce 7Li or 7Be Beyond Standard Model

  • Dark matter decay (Bailly et al., 2009 and others)
  • Bound states (Jittoh et al., 2010, Cyburt et al., 2006 and
  • thers)
  • Varying fundamental constants (Berengut et

al.,2010),....) etc.

Within Standard Model

  • Enhance nuclear reactions

(Cyburt and Pospelov, 2009), Chakraborty, Fields and Olive (2011)

OR

CERN

Fermilab

slide-11
SLIDE 11
slide-12
SLIDE 12

Resonances

slide-13
SLIDE 13

Resonances

  • A + B --> C + D vs A + B --> X* --> C + D

Compound nucleus

slide-14
SLIDE 14

Resonance parameters

slide-15
SLIDE 15

Resonance parameters

Energy

Cross-Section

slide-16
SLIDE 16

Resonance parameters

Energy

Cross-Section

2 1 1 2 3 4 0.2 0.4 0.6 0.8 1.0

slide-17
SLIDE 17

Strength

Γeff

Resonance parameters

Energy

Cross-Section

2 1 1 2 3 4 0.2 0.4 0.6 0.8 1.0

slide-18
SLIDE 18

Width

Γtot

Strength

Γeff

Resonance parameters

Energy

Cross-Section

2 1 1 2 3 4 0.2 0.4 0.6 0.8 1.0

slide-19
SLIDE 19

Width

Γtot Resonance Energy

Eres

Strength

Γeff

Resonance parameters

Energy

Cross-Section

2 1 1 2 3 4 0.2 0.4 0.6 0.8 1.0

slide-20
SLIDE 20

Width

Γtot Resonance Energy

Eres

Strength

Γeff

Resonance parameters

Energy

Cross-Section

2 1 1 2 3 4 0.2 0.4 0.6 0.8 1.0

σ ∝ Γ1Γ2 (E − ER)2 + (Γtot/2)2

slide-21
SLIDE 21

Width

Γtot Resonance Energy

Eres

Strength

Γeff

Resonance parameters

Energy

Cross-Section

2 1 1 2 3 4 0.2 0.4 0.6 0.8 1.0

slide-22
SLIDE 22

Narrow Resonance Approximation

Width

Γtot Resonance Energy

Eres

Strength

Γeff

Resonance parameters

Energy

Cross-Section

2 1 1 2 3 4 0.2 0.4 0.6 0.8 1.0

slide-23
SLIDE 23

Narrow Resonance Approximation Resonance Energy

Eres

Strength

Γeff

Resonance parameters

Energy

Cross-Section

2 1 1 2 3 4 0.2 0.4 0.6 0.8 1.0

slide-24
SLIDE 24

Narrow Resonance Approximation Resonance Energy

Eres

Strength

Γeff

Resonance parameters

Energy

Cross-Section

slide-25
SLIDE 25

Narrow Resonance Approximation Resonance Energy

Eres

Strength

Γeff

Resonance parameters

Energy

Cross-Section

2 1 1 2 3 4 0.2 0.4 0.6 0.8 1.0

slide-26
SLIDE 26

Narrow Resonance Approximation Resonance Energy

Eres

Strength

Γeff

Resonance parameters

Energy

Cross-Section

2 1 1 2 3 4 0.2 0.4 0.6 0.8 1.0

a (channel radius )

slide-27
SLIDE 27

Cyburt and Pospelov

Cyburt and Pospelov, (2009)

  • Recognised existing level

(16.7 MeV in 9B)

  • 7Be + d → p + 2 α
  • Strength unknown
  • Big error bars in
  • Potential solution ?
  • We agree

Eres

slide-28
SLIDE 28

Cyburt and Pospelov

Cyburt and Pospelov, (2009)

  • Recognised existing level

(16.7 MeV in 9B)

  • 7Be + d → p + 2 α
  • Strength unknown
  • Big error bars in
  • Potential solution ?
  • We agree

Eres

7Li / H = 1.23e-10 7Li / H = 2.0e-10 7Li / H = 3.0e-10 7Li / H = 4.0e-10 7Li / H = 5.0e-10

slide-29
SLIDE 29

Cyburt and Pospelov

Cyburt and Pospelov, (2009)

  • Recognised existing level

(16.7 MeV in 9B)

  • 7Be + d → p + 2 α
  • Strength unknown
  • Big error bars in
  • Potential solution ?
  • We agree

Eres What if experiment rules this out ?

7Li / H = 1.23e-10 7Li / H = 2.0e-10 7Li / H = 3.0e-10 7Li / H = 4.0e-10 7Li / H = 5.0e-10

slide-30
SLIDE 30

Cyburt and Pospelov

Cyburt and Pospelov, (2009)

  • Recognised existing level

(16.7 MeV in 9B)

  • 7Be + d → p + 2 α
  • Strength unknown
  • Big error bars in
  • Potential solution ?
  • We agree

Eres What if experiment rules this out ?

7Li / H = 1.23e-10 7Li / H = 2.0e-10 7Li / H = 3.0e-10 7Li / H = 4.0e-10 7Li / H = 5.0e-10

Problem solved !!

slide-31
SLIDE 31

There’s more options

slide-32
SLIDE 32

There’s more options

Problem solved ??

slide-33
SLIDE 33

We may be able to avoid new physics

Potentially yes → But nuclear resonances with large channel radii (a > 10 fm)

Fat nuclei or SUSY - take a pick

Testable by current nuclear experiments Complete or partial match

  • 7Be + d → p + 2 α (Cyburt and Pospelov, (2009) and competing channels)
  • 7Be + t → Inelastic (Chakraborty, Fields and Olive, (2011)
  • 7Be + 3He → Inelastic (Chakraborty, Fields and Olive, (2011)
  • Missed resonances / levels
slide-34
SLIDE 34

Thank you !!!

Acknowledgments http://www.tunl.duke.edu/nucldata/ http://www.nndc.bnl.gov/chart/

slide-35
SLIDE 35
slide-36
SLIDE 36

Nuclear Physics Solution

  • Two main checks
  • 1. Completeness of nuclear database or

missing reactions

  • 2. Improved reaction rates
  • Can’t decrease production rates - well

studied and constrained

  • Increase destruction
  • Resonances ?
slide-37
SLIDE 37

Let’s try resonances

http://pntpm3.ulb.ac.be/Nacre/barre_database.htm

http://en.wikipedia.org/wiki/ Nuclear_reaction

  • A + B --> C + D vs A + B --> X* --> C + D
slide-38
SLIDE 38

Let’s try resonances

http://pntpm3.ulb.ac.be/Nacre/barre_database.htm

http://en.wikipedia.org/wiki/ Nuclear_reaction

  • A + B --> C + D vs A + B --> X* --> C + D
slide-39
SLIDE 39

Let’s try resonances

http://pntpm3.ulb.ac.be/Nacre/barre_database.htm

http://en.wikipedia.org/wiki/ Nuclear_reaction

  • A + B --> C + D vs A + B --> X* --> C + D
slide-40
SLIDE 40

Let’s try resonances

http://pntpm3.ulb.ac.be/Nacre/barre_database.htm

http://en.wikipedia.org/wiki/ Nuclear_reaction

  • A + B --> C + D vs A + B --> X* --> C + D
slide-41
SLIDE 41

Let’s try resonances

http://pntpm3.ulb.ac.be/Nacre/barre_database.htm

http://en.wikipedia.org/wiki/ Nuclear_reaction

  • A + B --> C + D vs A + B --> X* --> C + D
slide-42
SLIDE 42

Let’s try resonances

http://en.wikipedia.org/wiki/ Nuclear_reaction

  • A + B --> C + D vs A + B --> X* --> C + D
slide-43
SLIDE 43

Let’s try resonances

  • A + B --> C + D vs A + B --> X* --> C + D
slide-44
SLIDE 44

Let’s try resonances

slide-45
SLIDE 45

Let’s try resonances

http:// www.tunl.duke.edu/ nucldata/figures/09figs/ 09_05_2004.gif

slide-46
SLIDE 46

Resonant Cross-section

  • In nuclear physics,
  • (Breit-Wigner single level formula)
  • Rate of reaction ~ nA nB < σ v >

Width Resonance energy

σ ∝ Γ1Γ2 (E − ER)2 + (Γtot/2)2

2 1 1 2 3 4 0.2 0.4 0.6 0.8 1.0

Strength

slide-47
SLIDE 47

Resonant Cross-section

  • In nuclear physics,
  • (Breit-Wigner single level formula)
  • Rate of reaction ~ nA nB < σ v >

Width Resonance energy

σ ∝ Γ1Γ2 (E − ER)2 + (Γtot/2)2

T Not position of the energy

level in the compound nucleus, but extra energy required by reactants to get there over Q-value

2 1 1 2 3 4 0.2 0.4 0.6 0.8 1.0

Strength

slide-48
SLIDE 48

Resonant Cross-section

  • In nuclear physics,
  • (Breit-Wigner single level formula)
  • Rate of reaction ~ nA nB < σ v >

Width Resonance energy

σ ∝ Γ1Γ2 (E − ER)2 + (Γtot/2)2

T Not position of the energy

level in the compound nucleus, but extra energy required by reactants to get there over Q-value

2 1 1 2 3 4 0.2 0.4 0.6 0.8 1.0

Strength

Energy

Cross-Section

slide-49
SLIDE 49

Equilibrium Rates

  • The rate eqn for abundances
  • At equilibrium, production =

destruction

  • New rates must compare with old

important rates

dYi dt = nbΣ(YkYlσvkl − YiYjσvij)

ΣYkYlσvkl = ΣYiYjσvij

Yi = ΣYkYlσvkl (ΣYjσvij)old + (Ypσvip)new = (Yi)old 1 +

Yp vip)new (ΣYj vij)old

Yi = ni nH

slide-50
SLIDE 50

Fred Hoyle set a famous precedent

slide-51
SLIDE 51

Fred Hoyle set a famous precedent

4He + 4He -> 8Be 8Be + 4He -> 12C

slide-52
SLIDE 52

Fred Hoyle set a famous precedent

4He + 4He -> 8Be 8Be + 4He -> 12C

slide-53
SLIDE 53

Fred Hoyle set a famous precedent

4He + 4He -> 8Be 8Be + 4He -> 12C

There it is

slide-54
SLIDE 54

Cyburt and Pospelov

  • Identified a narrow level in

9B at 16.7 MeV

  • Width of energy level

unknown

  • Enhancement of reaction

7Be(d,γ )9B and 7Be(d,p)αα

  • (ER,Γd) ~ (170-220,10-40)

keV ,

7Li/H = (2.5 - 6) x 10-10

  • Needs experimental

verification

slide-55
SLIDE 55

Cyburt and Pospelov

  • Identified a narrow level in

9B at 16.7 MeV

  • Width of energy level

unknown

  • Enhancement of reaction

7Be(d,γ )9B and 7Be(d,p)αα

  • (ER,Γd) ~ (170-220,10-40)

keV ,

7Li/H = (2.5 - 6) x 10-10

  • Needs experimental

verification

slide-56
SLIDE 56

Cyburt and Pospelov

  • Identified a narrow level in

9B at 16.7 MeV

  • Width of energy level

unknown

  • Enhancement of reaction

7Be(d,γ )9B and 7Be(d,p)αα

  • (ER,Γd) ~ (170-220,10-40)

keV ,

7Li/H = (2.5 - 6) x 10-10

  • Needs experimental

verification

slide-57
SLIDE 57

Cyburt and Pospelov

  • Identified a narrow level in

9B at 16.7 MeV

  • Width of energy level

unknown

  • Enhancement of reaction

7Be(d,γ )9B and 7Be(d,p)αα

  • (ER,Γd) ~ (170-220,10-40)

keV ,

7Li/H = (2.5 - 6) x 10-10

  • Needs experimental

verification

slide-58
SLIDE 58

Cyburt and Pospelov

  • Identified a narrow level in

9B at 16.7 MeV

  • Width of energy level

unknown

  • Enhancement of reaction

7Be(d,γ )9B and 7Be(d,p)αα

  • (ER,Γd) ~ (170-220,10-40)

keV ,

7Li/H = (2.5 - 6) x 10-10

  • Needs experimental

verification

slide-59
SLIDE 59

Cyburt and Pospelov

  • Identified a narrow level in

9B at 16.7 MeV

  • Width of energy level

unknown

  • Enhancement of reaction

7Be(d,γ )9B and 7Be(d,p)αα

  • (ER,Γd) ~ (170-220,10-40)

keV ,

7Li/H = (2.5 - 6) x 10-10

  • Needs experimental

verification

slide-60
SLIDE 60

Cyburt and Pospelov

  • Identified a narrow level in

9B at 16.7 MeV

  • Width of energy level

unknown

  • Enhancement of reaction

7Be(d,γ )9B and 7Be(d,p)αα

  • (ER,Γd) ~ (170-220,10-40)

keV ,

7Li/H = (2.5 - 6) x 10-10

  • Needs experimental

verification

Observations

1.23e-10

2.0e-10

3.0e-10 4.0e-10

slide-61
SLIDE 61
  • Need other options ready
  • Want to try all conceivable resonances
  • Not infinite choices !!
  • Lock on to our targets
  • 7Li, 7Be
  • Ready our projectiles
  • n,p,t, 3He, 4He, and photons
  • Destroy !!!

Systematic Search for the “Hoyle” State

slide-62
SLIDE 62

Candidate resonance selection

  • Compound nuclei of masses 8 to 11
  • Obey selection rules
  • 2 body - 2 body reactions
  • Existing resonances not included in

BBN estimates

  • New or missed resonances
slide-63
SLIDE 63

data mining

slide-64
SLIDE 64

data mining

slide-65
SLIDE 65

data mining

slide-66
SLIDE 66

LIST(S) of Candidates

slide-67
SLIDE 67

some more

slide-68
SLIDE 68

And more

slide-69
SLIDE 69

You get the point !!!

slide-70
SLIDE 70

Final Candidates

slide-71
SLIDE 71

Final Candidates

slide-72
SLIDE 72

Final Candidates

slide-73
SLIDE 73

Final Candidates

http://www.tunl.duke.edu/ nucldata/figures/10figs/

slide-74
SLIDE 74

Final Candidates

http://www.tunl.duke.edu/ nucldata/figures/10figs/

slide-75
SLIDE 75

Final Candidates

http://www.tunl.duke.edu/ nucldata/figures/10figs/

slide-76
SLIDE 76
slide-77
SLIDE 77

Resonance parameters

slide-78
SLIDE 78

Resonance parameters

2 1 1 2 3 4 0.2 0.4 0.6 0.8 1.0

slide-79
SLIDE 79

Resonance parameters

Energy

Cross-Section

2 1 1 2 3 4 0.2 0.4 0.6 0.8 1.0

slide-80
SLIDE 80

Resonance Energy

Eres

Strength

Γeff

Resonance parameters

Energy

Cross-Section

2 1 1 2 3 4 0.2 0.4 0.6 0.8 1.0

slide-81
SLIDE 81

Width

Γtot

Resonance Energy

Eres

Strength

Γeff

Resonance parameters

Energy

Cross-Section

2 1 1 2 3 4 0.2 0.4 0.6 0.8 1.0

slide-82
SLIDE 82

Narrow Resonance Approximation

Width

Γtot

Resonance Energy

Eres

Strength

Γeff

Resonance parameters

Energy

Cross-Section

2 1 1 2 3 4 0.2 0.4 0.6 0.8 1.0

slide-83
SLIDE 83

Narrow Resonance Approximation

Width

Γtot

Resonance Energy

Eres

Strength

Γeff

Resonance parameters

Energy

Cross-Section

slide-84
SLIDE 84

Narrow Resonance Approximation

Width

Γtot

Resonance Energy

Eres

Strength

Γeff

Resonance parameters

Energy

Cross-Section

2 1 1 2 3 4 0.2 0.4 0.6 0.8 1.0

slide-85
SLIDE 85

Narrow Resonance Approximation Resonance Energy

Eres

Strength

Γeff

Resonance parameters

Energy

Cross-Section

2 1 1 2 3 4 0.2 0.4 0.6 0.8 1.0

slide-86
SLIDE 86

Our bets

slide-87
SLIDE 87

Our bets

slide-88
SLIDE 88

Our bets

slide-89
SLIDE 89

Our bets

Problem solved !!

slide-90
SLIDE 90

Our bets

slide-91
SLIDE 91

Our bets

slide-92
SLIDE 92

Our bets

slide-93
SLIDE 93

Our bets

slide-94
SLIDE 94

Our bets

slide-95
SLIDE 95

Our bets

slide-96
SLIDE 96

Our bets

slide-97
SLIDE 97

Do we have any Standard Model solutions ?

  • Potentially yes → Nuclear resonances
  • Complete or partial match
  • 7Be + d → p + 2 α (Cyburt and Pospelov, (2009) and competing

channels)

  • 7Be + t → Inelastic (Chakraborty, Fields and Olive, 2010)
  • 7Be + 3He → Inelastic (Chakraborty, Fields and Olive, 2010)
  • Missed resonances / levels
  • Testable by current nuclear experiments
  • We may be able to avoid new physics
slide-98
SLIDE 98

We know reactions pretty well

Cyburt, Fields and Olive (2008)

slide-99
SLIDE 99

Resonant rate

λ = NA 2π µK 2ω Γ1Γ2 Γtot T −3/2 exp(−ER/KT)

slide-100
SLIDE 100

t ∝ T-2 Radiation dominated

History of the elements

slide-101
SLIDE 101

t ∝ T-2 Radiation dominated

History of the elements

slide-102
SLIDE 102

t ∝ T-2 Radiation dominated

History of the elements

slide-103
SLIDE 103

t ∝ T-2 Radiation dominated

t History of the elements

slide-104
SLIDE 104

t ∝ T-2 Radiation dominated

t History of the elements

slide-105
SLIDE 105

t ∝ T-2 Radiation dominated

t History of the elements

slide-106
SLIDE 106

t ∝ T-2 Radiation dominated

t History of the elements

slide-107
SLIDE 107

t ∝ T-2 Radiation dominated

t History of the elements

slide-108
SLIDE 108

Effect on abundances

CFO (2008)

slide-109
SLIDE 109

Theory vs Observations - The Lithium problem

Cyburt, Fields and Olive, 2008

Observations Theory

Observations

slide-110
SLIDE 110

New physics

  • Decays of NLSP => 7Li destruction
  • Hadronic showers due to longer lifetime of

NLSP

  • Formation of bound states reducing

Coloumb barrier

  • Quark mass variation -> Changes in BE
slide-111
SLIDE 111

Lithium Observations

Observed in metal-poor, halo stars (Spite and Spite, 1982 ; Bonifacio and Molaro, 1997 ; Pinsonnealt et al., 1992) The resonance line at 6707 Ao is

  • bserved.

Equivalent widths -> primordial abundance Sources of uncertainty include

  • 1. Galactic chemical evolution of Li
  • 2. Depletion of initial surface

abundance

  • 3. Derivation of abundance
  • 4. Stellar scatter

Most promising - Stellar transport (Melendez et al.,2010 and others)

Ryan et al., (2000)

Low Metallicity Plateau

Solar Metallicity

slide-112
SLIDE 112

Caveats to Li depletion

Low metallicities stars -> Lower

  • pacity -> Reduction in Convection ->

Harder to convect 7Li to places where T > 2*10^6 Lithium - Small scatter, within error bars There is 6Li which is much more fragile

slide-113
SLIDE 113

Equivalent width

The shape of an absorption line depends on the number of photons that are absorbed at a particular wavelength. In order to compare the strengths of different absorption lines from a source, or the same absorption line from several different sources, we can use the equivalent width. To obtain the equivalent width, first we measure the area, A, of the spectral line below the continuum intensity level, as shown in the diagram below: The area, A, of a spectral line measured below the continuum level is related to a rectangular line profile with the same area, and equivalent width, b. We then replace the spectral line profile by a rectangle with the same area such that where I is the intensity level of the continuum and b is the equivalent width of the absorption line.

slide-114
SLIDE 114

Solar Abundances