Lithium Update - Berkeley Cosmology Groupcosmology.berkeley.edu/inpac/CDMSCE_Jun06/Talks/irvine_olive2.pdf · Lithium Update • 2 Lithium ... R e a p p ra isin g th e S p ite L ith

Lithium Update

Lithium Update

• 2 Lithium Problems

Lithium Update

• 2 Lithium Problems- BBN overproduction of 7Li

Lithium Update

• 2 Lithium Problems- BBN overproduction of 7Li- GCRN underproduction of 6Li

Lithium Update


Lithium Update


• Lithium Solutions?

Lithium Update


• Lithium Solutions?- Post BBN Particle Decay

Lithium Update


• Lithium Solutions?- Post BBN Particle Decay . claims to solve both problems

Lithium Update


• Lithium Solutions?- Post BBN Particle Decay . claims to solve both problems- Cosmological Cosmic Rays

Lithium Update


• Lithium Solutions?- Post BBN Particle Decay . claims to solve both problems- Cosmological Cosmic Rays. massive Pop III CR production of 6Li

• Production of the Light Elements: D, 3He, 4He, 7Li

• 4He observed in extragalctic HII regions: abundance by mass = 25%

• 7Li observed in the atmospheres of dwarf halo stars:

abundance by number = 10-10

• D observed in quasar absorption systems (and locally):

abundance by number = 3 x 10-5

• 3He in solar wind, in meteorites, and in the ISM:

abundance by number = 10-5

Big Bang Nucleosynthesis

WMAP best fit (WMAPext + 2dFGRS +

Lyman α +running sp. index )

!Bh2 = 0.0224 ± 0.0009

!10 = 6.14 ± 0.25

Q2206-199

Q0347-3819Q1243+3047

PKS1937-1009

D/H abundances inQuasar apsorption

systems

4HeMeasured in low metallicity extragalactic HII

regions (~100) together with O/H and N/H

YP = Y(O/H → 0)

0.00

0.20

0.40

0.60

0.80

1.00

Y

0 50 100 150 200

10 6 O/H

4He is Primordial!

0. .2 .4 .6 .8! ! 1.22

.23

.24

.25

.26

.27

O/H x 104

Y

IT 98

OS 04

Yp

Yp = 0.2495 ± 0.0092

Li/HMeasured in low metallicity dwarf halo stars (over 100 observed)

0.0

1.0

2.0

3.0

[Li]

5000 5500 6000 6500

T (K)

4.0

3.0

2.0

1.0

0.0-4.0 -3.0 -2.0 -1.0 -0.0 1.0

[Li]

[Fe/H]

Li Woes

• Observations based on

- “old”: Li/H = 1.2 x 10-10 Spite & Spite + - Balmer: Li/H = 1.7 x 10-10 Molaro, Primas & Bonifacio- IRFM: Li/H = 1.6 x 10-10 Bonifacio & Molaro- IRFM: Li/H = 1.2 x 10-10 Ryan, Beers, KAO, Fields, Norris

- Hα (globular cluster): Li/H = 2.2 x 10-10 Bonifacio et al.

- Hα (globular cluster): Li/H = 2.3 x 10-10 Bonifacio

- λ6104: Li/H ~ 3.2 x 10-10 Ford et al.

• Li depends on T, ln g, [Fe/H], depletion, post BBN-processing, ...

• Strong systematics

Problem 1: BBN 7Li too high

Possible sources for the discrepancy

• Stellar Depletion- lack of dispersion in the data, 6Li abundance- standard models (< .05 dex), models (0.2 - 0.4 dex)

• Nuclear Rates

- Restricted by solar neutrino flux

• Stellar parameters

Vauclaire & CharbonnelPinsonneault et al.

dLi

dlng=

.09

.5

dLi

dT=

.08

100K

Coc et al.Cyburt, Fields, KAO

arX

iv:a

stro

-ph

/04

09

38

3 v

1

15

Sep

20

04

Submitted to the The Astrophysical Journal

Reappraising the Spite Lithium Plateau: Extremely Thin and

Marginally Consistent with WMAP

Jorge Melendez1 and Ivan Ramırez2

ABSTRACT

The lithium abundance in 62 halo dwarfs is determined from accurate equiv-

alent widths reported in the literature and an improved infrared flux method(IRFM) temperature scale. The Li abundance of 41 plateau stars (those with

Te! > 6000 K) is found to be independent of temperature and metallicity, witha star-to-star scatter of only 0.06 dex over a broad range of temperatures (6000K < Te! < 6800 K) and metallicities (!3.4 < [Fe/H] < !1), thus imposing

stringent constraints on depletion by mixing and production by Galactic chemi-cal evolution. We find a mean Li plateau abundance of ALi = 2.37 dex (7Li/H

= 2.34 "10!10), which, considering errors of the order of 0.1 dex in the absoluteabundance scale, is just in borderline agreement with the constraints imposed

by the theory of primordial nucleosynthesis and WMAP data (2.51 < AWMAPLi <

2.66 dex).

Subject headings: cosmology: observations - stars: abundances - stars: Popula-tion II

1. Introduction

The Li plateau was discovered by Spite & Spite (1982), who showed that the 7Li abun-dance obtained from the Li doublet at 6708 A in F and early G halo dwarfs is independent

of temperature and metallicity, suggesting that the Li abundance determined in halo starsrepresents the primordial abundance from Big Bang nucleosynthesis (BBN). The standard

1Department of Astronomy, Caltech, M/C 105-24, 1200 E. California Blvd, Pasadena, CA 91125;[email protected]

2Department of Astronomy, University of Texas at Austin, RLM 15.306, TX 78712-1083;[email protected]

New evaluation of surface temperaturesin 41 halo stars with systematically highertemperatures (100-300 K)

[Li] = 2.37 ± 0.1Li/H = 2.34 ± 0.54 x 10-10

– 11 –

Fig. 2.— Temperatures obtained in this work minus the temperatures from R01 (for starsin common with the present sample) as a function of the metallicities adopted in the present

work. Filled circles: plateau stars (Te! > 6000 K); open circles: stars with Te! < 6000 K.

– 10 –

Fig. 1.— Upper panel: ALi of the Spite plateau stars (Te! > 6000 K) as a function of

[Fe/H]. Dotted lines indicate the mean Li abundance of the plateau stars, and the solidline represents the lower limit imposed by the WMAP constraint. The error bars are thepredicted error, !pred (= 0.05 dex), and 3!pred (= 0.15 dex). Lower panel: ALi as a function

of Te! for stars with [Fe/H] ! "1.5 (filled triangles) and [Fe/H] > "1.5 (open triangles).The star (HD 106038) with the highest Li abundance (open triangle inside the open circle)

is a star with peculiar abundances (Nissen & Schuster 1997).

Figure 7: As in Figure 6, including the constraints from 4He - medium (pink) shading and7Li - medium-light (green) shading.

23

D, He and Li

Cyburt, Ellis, Fields, KAO

“All”

Figure 8: As in Figures 6 and 7 including the constraints from 6Li (dark red).

Our results agree quite well with previous studies [11, 12, 13]. When comparing to [11, 13],one has to take into account that they have taken the relic abundance as the abundance beforeelectron/positron annihilation, therefore a factor of 11/4 should be applied to our results tocompensate. One should note that [11] did not include secondary production reactions. Theremaining di!erences are most likely due to assumed cross section fits. Since the previousstudies do not present their photodissociation cross sections we cannot compare directly.

There is a significant di!erence in the predicted 6Li abundance, however. Besides crosssection di!erences, the center-of-mass thresholds were used by [12, 13] rather than the labframe thresholds we use. In this scenario, the lab frame is the appropriate frame. Thismistake alone causes 6Li to be overproduced by almost an order of magnitude. Had thesecondary cross sections we adopted not been significantly larger than those used by [12, 13],our constraint would be noticeably weaker.

One might be concerned that uncertainties from nuclear reactions propagate into ourresults. BBN uncertainties have been taken into account. The photodistruction cross sec-tions, however, are weighted by steep functions of energy, which puts all of the cross sec-tion dependence very close to the threshold energy. The remaining uncertanties from thephotodissociation and secondary cross sections are of the order of 10%, thus weakening our-constraints only slightly. The dominant uncertainties arise from the BBN predictions of thelight element abundances.

As already noted, if the observed light-element abundances retain their current central

24

Cyburt, Ellis, Fields, KAO

-5

-10

-15

4 5 6 7 8 9 10 11 12

Lo

g [!x

(G

eV)]

Log ["x (sec)]

6Li

4He

D

D

6Li/

7Li

7Li

JedamzikFeng et al.

Ellis, KAO, Vangioni

100 1000 2000

0

100

200

300

400

500

100 1000 2000

0

100

200

300

400

500

!NSP < 104 sm0 (

GeV

)

m1/2 (GeV)

m3/2 = 10 GeV , tan " = 10 , µ > 0

r < 1

100 1000 2000

0

100

200

300

400

500

100 1000 2000

0

100

200

300

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m0 (

GeV

)

m1/2 (GeV)

m3/2 = 100 GeV , tan " = 10 , µ > 0

r < 1

100 1000 2000

0

100

200

300

400

500

100 1000 2000

0

100

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300

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500

!NSP < 104 s

m0 (

GeV

)

m1/2 (GeV)

m3/2 = 0.2 m0 , tan " = 10 , µ > 0

r < 1

100 1000 2000

0

100

200

300

400

500

100 1000 2000

0

100

200

300

400

500

!NSP < 104 s

m0 (

GeV

)

m1/2 (GeV)

m3/2 = m0 , tan " = 10 , µ > 0

r < 1

Figure 3: The (m1/2, m0) planes for µ > 0, tan! = 10 and (a) m3/2 = 10 GeV, (b)m3/2 = 100 GeV, (c) m3/2 = 0.2m0 and (d) m3/2 = m0. We restrict our attention to theregions between the solid black lines, where the gravitino is the LSP and the NSP lifetimeexceeds 104 s. In each panel, the near-vertical dashed black (dash-dotted red) line is theconstraint m!± > 104 GeV (mh > 114 GeV), the upper (purple) dashed line is the constraint!3/2h2 < 0.129, and the light green shaded region is that where the NSP would have had0.094 ! !h2 ! 0.129 if it had not decayed. The solid red (dashed grey-green) line is theregion now (previously) allowed by the light-element abundances: r < 1 as described in thetext. The red (blue) shaded region is that where the 7Li abundance could have been improvedby NSP decays, but which is now excluded by the 3He (D) constraint.

10

100 1000 2000

0

100

200

300

400

500

100 1000 2000

0

100

200

300

400

500

!NSP < 104 sm0 (

GeV

)

m1/2 (GeV)

m3/2 = 10 GeV , tan " = 10 , µ > 0

r < 1

100 1000 2000

0

100

200

300

400

500

100 1000 2000

0

100

200

300

400

500

m0 (

GeV

)

m1/2 (GeV)

m3/2 = 100 GeV , tan " = 10 , µ > 0

r < 1

100 1000 2000

0

100

200

300

400

500

100 1000 2000

0

100

200

300

400

500

!NSP < 104 s

m0 (

GeV

)

m1/2 (GeV)

m3/2 = 0.2 m0 , tan " = 10 , µ > 0

r < 1

100 1000 2000

0

100

200

300

400

500

100 1000 2000

0

100

200

300

400

500

!NSP < 104 s

m0 (

GeV

)

m1/2 (GeV)

m3/2 = m0 , tan " = 10 , µ > 0

r < 1

Figure 3: The (m1/2, m0) planes for µ > 0, tan! = 10 and (a) m3/2 = 10 GeV, (b)m3/2 = 100 GeV, (c) m3/2 = 0.2m0 and (d) m3/2 = m0. We restrict our attention to theregions between the solid black lines, where the gravitino is the LSP and the NSP lifetimeexceeds 104 s. In each panel, the near-vertical dashed black (dash-dotted red) line is theconstraint m!± > 104 GeV (mh > 114 GeV), the upper (purple) dashed line is the constraint!3/2h2 < 0.129, and the light green shaded region is that where the NSP would have had0.094 ! !h2 ! 0.129 if it had not decayed. The solid red (dashed grey-green) line is theregion now (previously) allowed by the light-element abundances: r < 1 as described in thetext. The red (blue) shaded region is that where the 7Li abundance could have been improvedby NSP decays, but which is now excluded by the 3He (D) constraint.

10

Regions in the plane with Li/H < 3 x 10-10

Blue: D/H > 1.3 x 10-5

Red: D/H > 2.2 x 10-5


Regions in the plane with Li/H < 3 x 10-10

Blue: D/H > 1.3 x 10-5

Red: D/H > 2.2 x 10-5


100 1000 2000

0

100

200

300

400

500

100 1000 2000

0

100

200

300

400

500

m0 (

GeV

)

m1/2 (GeV)

A = 3 - ˆ3; µ > 0^

r < 130

2520

15

30

25

20

15

100 1000 2000

0

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200

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500

100 1000 2000

0

100

200

300

400

500

m0 (

GeV

)

m1/2 (GeV)

A = 2; µ > 0^

r < 1

Figure 5: As in Fig. 3, but now for very constrained models motivated by mSUGRA. Thevalue of tan ! is fixed by the vacuum conditions, and varies across the (m1/2, m0) planes withvalues indicated by the steep black contours. These models are specified by the choices ofA ! Am3/2: (a) A = (3 "

#3), the Polonyi model, and (b) A = 2.

lines: above the higher one, the gravitino is no longer the LSP, and below the lower onethe lifetime falls below 104 s. In addition to the constraints discussed earlier, panel (b) alsodisplays a small green shaded region at low m1/2 that is excluded by b $ s" decay.

We see that there is a large di!erence between the e!ects of implementing the old and newlight-element constraints in panel (a) of Fig. 5 for A = (3"

#3), the Polonyi value, whereas

the e!ect in panel (b) for A = 2 is smaller. In the Polonyi case, there are large 7Li-friendlyregions that are excluded by the 3He and D constraints. This reflects the fact that tan ! isrelatively small in this case, so the model is qualitatively similar to the m3/2 = m0 case fortan ! = 10 shown in panel (d) of Fig. 3. On the other hand, tan! is typically larger forA = 2, and when combined with a smaller stau mass, we find no visible 7Li-friendly region,as a result of small yet significant shifts in the values of both #X and $X .

As noted earlier, the 7Li abundance can be reduced slightly by hadronic decays when thelifetime is approximately 103 s with a density #X % 10!12 [10, 17]. We have have searchedthe parameter spaces of both the CMSSM and mSUGRA models discussed above. Forlifetimes between 300 and 3000 s, we find no models with #X between 10!13 and 10!11 whentan ! = 10, or in any of the mSUGRA models. When tan! = 57, we also find no parametersfor the models described in Figs. 4a, b or d. When m3/2 = 0.2m0, we do find a handful ofcases, all with #X between 4 " 7 & 10!12 and all with m0 ' 20 GeV and m1/2

>% 1.7 TeV. Amore complete treatment of the e!ects of hadronic decays will be given elsewhere.

14

10-10

10-9

10-8

10-7

10-6

104

105

106

107

Log [!x (

GeV

)]

Log ["x (sec)]

0

100

200

300

400

500

600

700

800

0 4 8 12 16 20 24 28 32 36 40 44

Co

un

t

3He/D

Figure 2: (a) The region of the (!X , "X) plane in which a decaying relic particle could havethe desired impact on the 7Li abundance. To derive the blue (darker grey) region, the onlyabundance cuts applied are: 0.9 < 7Li/H ! 1010 < 3.0, 1.3 < D/H ! 105 < 5.3, and 6Li/7Li< 0.15. To obtain the red (lighter grey) region, the lower bound on D/H was increased to2.2 ! 10!5. (b) A histogram of the 3He/D ratios found in scenarios sampling the regiondisplayed in panel (a), with similar colour coding.

found in a dense sample of scenarios in the interesting regions shown in panel (a). SinceDeuterium is more fragile than 3He, whose abundance is thought to have remained roughlyconstant since primordial nucleosynthesis when comparing the BBN value to it proto-solarabundance, one would expect, in principle, the 3He/D ratio to have been increased by stellarprocessing. Indeed, there is considerable uncertainty in the evolution of 3He [32]. Thisuncertainty is largely associated with the degree to which 3He is produced or destroyed instars. Since D is totally destroyed in stars, the ratio of 3He/D can only increase in timeor remain constant if 3He is also completely destroyed in stars. The present or proto-solarvalue of 3He/D can therefore be used to set an upper limit on the primordial value. Fig. 1displays the upper limits

3He

D< 1 or 2 (8)

as solid black lines. Above these contours, the value of 3He/D increases very rapidly, andpoints high in the Deuterium cleft of Fig. 1 have absurdly high values of 3He/D, exceedingthe limit (8) by an order of magnitude or more. These are the red points producing thehigh-end peak of the histogram shown in panel (b) of Fig. 2, whereas the blue points arethose excluded by the lower limit D/H > 2.2!10!5 that is now preferred. We see that thesepoints mostly have acceptably low values of 3He/D, though some large values are found nearthe boundary with the red region in panel (a) of Fig. 2.

It is interesting to note that in the red region which has acceptable D/H and a 7Li/H

7

Blue: D/H > 1.3 x 10-5

Red: D/H > 2.2 x 10-5


10-10

10-9

10-8

10-7

10-6

104

105

106

107

Log [!x (

GeV

)]

Log ["x (sec)]

0

100

200

300

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500

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700

800

0 4 8 12 16 20 24 28 32 36 40 44

Co

un

t

3He/D



3He

D< 1 or 2 (8)



7

10-10

10-9

10-8

10-7

10-6

104

105

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107

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g [!x

(G

eV)]

Log ["x (sec)]

0

100

200

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700

800

0 4 8 12 16 20 24 28 32 36 40 44

Cou

nt

3He/D



3He

D< 1 or 2 (8)



7

Blue: D/H > 1.3 x 10-5

Red: D/H > 2.2 x 10-5


10-10

10-9

10-8

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10-6

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Log [!x (

GeV

)]

Log ["x (sec)]

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Co

un

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3He/D



3He

D< 1 or 2 (8)



7

10-10

10-9

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104

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g [!x

(G

eV)]

Log ["x (sec)]

0

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800

0 4 8 12 16 20 24 28 32 36 40 44

Cou

nt

3He/D



3He

D< 1 or 2 (8)



7

Blue: D/H > 1.3 x 10-5

Red: D/H > 2.2 x 10-5

Require 3He/D < 1Ellis, KAO, Vangioni

-5

-10

-15

4 5 6 7 8 9 10 11 12

Lo

g [!x

(G

eV)]

Log ["x (sec)]

6Li

4He

D

D

6Li/

7Li

7Li


-5

-10

-15

4 5 6 7 8 9 10 11 12

Lo

g [!x

(G

eV)]

Log ["x (sec)]

6Li

4He

D

D

6Li/

7Li

7Li

-5

-10

-15

4 5 6 7 8 9 10 11 12

Lo

g [!x

(G

eV)]

Log ["x (sec)]

6Li

4He

D

D

3He/D

6Li/

7Li

7Li

Figure 1: The constraints imposed by the astophysical observations of 4He (red lines), D/H(green lines), 6Li (yellow line), 6Li/7Li (blue lines), 7Li (blue band) and 3He (black lines).

5


6Li

LiBeB Data

7Li:7Li/H = 1.6 ±0.1 ! 10"10

[Li] = (1.28 ± .43) + (.015 ± .007) T

100

[Li] = (2.17 ± .07) + (-.018 ± .031) [Fe/H]

Dispersion consitent with Observational errors

6Li (@ [Fe/H] # "2.3):

HD 84937: 6Li/Li = 0.054 ± 0.011BD 26o3578: 6Li/Li = 0.05 ± 0.03

SLN

Hobbs & Thorburn

Cayrel etal

1

In the happy but not too distant past:

cf. BBN abundance of about 6Li/H = 10-14 or 6Li/Li < 10-4

SFOSW

These data nicely accounted for by Galactic Cosmic Ray Nucleosynthesis

Fields and OliveVangioni et al.

Problem 2: There appears to be a 6Li plateau

Li/H

6Li/H

log

(6 Li/H

), lo

g (L

i/H)

[Fe/H] Data from Asplund et al and Inoue

Solution 1: Particle Decays 4

3e-05

D/H

1e-10

7Li/H

1e-02

0.1

1

10

102

103

104

105

106

! (sec)

6Li/

7Li

FIG. 2: Abundance yields of D/H, 7Li/H, and 7Li/6Li inan !bh

2 = 0.026 Universe as function of the hadronic de-cay time ! of a putative primordial relic. The models aredecay of a m! = 10GeV particle (long-dashed), decay of am! = 200GeV particle (solid), decay of a m! = 4TeV par-ticle (dashed-dotted), injection of monoenergetic nucleons ofEkin = 250 MeV (short-dashed), and extended power-law in-jection due to a m! = 200 GeV particle (dotted). Also shownare the two-sigma ranges of the inferred primordial D/H and7Li/H abundances [3, 10] as well as the 6Li/7Li ratio as in-ferred in the low-metallicity star HD84937 [25]. See text forfurther details.

scatterings an interconversion of protons to neutrons oc-curs frequently, such that energetic protons produce sec-ondary neutrons. For example, though the decay of a200 GeV particle generates only about ! 1 neutron perannihilation, around ! 1, 0.6 secondary neutrons resultat T ! 20, 40 keV, respectively [39], and ! 3.5 asymptot-ically at low temperatures T " 0.1#1 keV. Here at highertemperatures the number of secondary neutrons reducesdue to the rapid Coulomb losses of protons. Neutrons,on the other hand, do not possess a significant bias to-wards producing secondary neutrons in np inelastic inter-

actions. Excess neutrons at T ! 40 keV are mostly dueto inelastic processes on 4He, accompanied by the pro-duction of D and 3He (i.e. n+4He $ D+p+2n, ...), witha comparatively smaller amount of neutrons removed inpionic fusion processes (i.e. np $ D!0, ...). One thusobtains approximately a ratio n/D! 3.6 for a 200 GeVparticle at T ! 40 keV, with similar ratios for n/3H andn/3He. As the 3H and 3He are energetic they may yieldthe production of 6Li. Nevertheless, 6Li production (andsurvival) may only be e!cient at somewhat lower temper-atures. Due to Coulomb losses of energetic 3H and 3Heproduction is only e!cient at T <

! 20 keV, whereas sur-vival of the freshly synthesized 6Li against destruction via6Li(p, ")3He is only nearly complete for T <

! 10 keV. Theproduction of 6Li at temperatures T ! 10# 20 keV for a200 GeV particle is found to be approximately 2 % 10"4

per decaying particle, becoming significantly lower atlower temperatures (e.g. 3%10"5 at T ! 1 keV). Cascadeyields are subject to some nuclear physics data uncertain-ties which in the case of 6Li may be of the order of a factortwo. In particular, it may be that 6Li yields are under-estimated due to an experimentally incomplete determi-nation of the high-energy tail of the energy distributionof energetic 3H and 3He produced in 4He spallation.

The developed code allows me to present detailed pre-dictions on the BBN in the presence of decaying parti-cles. Figure 2 shows the light-element yields for a varietyof decaying particles as a function of particle life time# . The panels show, from top-to-bottom, final abun-dances of D/H, 7Li/H, and 6Li/7Li, with the understand-ing that Yp is virtually unchanged when compared toSBBN at the same "bh2. In all models "bh2= 0.026has been assumed. Hadronically decaying particle yields(with the simplifying assumption that $ $ qq yields theproduction of a pair of quarks, the up-quark for definit-ness) are shown for three particle masses: m! = 10 GeVwith "!h2 = 7.5 % 10"5 (long-dashed), m! = 200 GeVwith "!h2 = 1 % 10"4 (solid), and m! = 4 TeV [40]with "!h2 = 6 % 10"4 (dashed-dotted). It is evidentthat for decay times around # ! 103s an e!cient de-struction of 7Li is obtained. For # much shorter than103s the destroyed 7Be is regenerated, whereas for #much longer, incomplete 7Li burning in the reaction chain7Be(n, p)7Li(p, ")4He results in only partial reduction ofthe total 7Li yield. As anticipated, the destruction of 7Liis accompanied by production of D. When compared tothe injection of thermal neutrons, D/H yields are higher.This is due to D generated in the nuclear cascade it-self (i.e. by 4He spallation and pionic fusion). Cascadegenerated deuterium (as well as 3H, 3He, and 6Li) is sub-stantially reduced per injected neutron for sources whichinject nucleons with a soft spectrum. For example, I havealso employed a soft source with monoenergetic nucleonsof 250 MeV. Results for this case are shown by the short-dashed line, assuming "!h2/m! ! 7.5%10"7GeV"1 andthe injection of one np pair per decay [41]. A cascaden/D! 10 ratio at T ! 40 keV is obtained in such scenar-ios. The more pronounced depth of the 7Li dip in Fig.

Figure 35: Contours of constant 6Li/H. Cosmological and model parameters are the sameas Fig. 32. In the SBBN, the theoreical predication is (6Li/H)SBBN = 1.30 ! 10−14.

Figure 36: Contours of constant 7Li/H. Cosmological and model parameters are the sameas Fig. 32. In the SBBN, the theoreical predication of the abundance is (7Li/H)SBBN =3.81 ! 10−10.

57

Figure 35: Contours of constant 6Li/H. Cosmological and model parameters are the sameas Fig. 32. In the SBBN, the theoreical predication is (6Li/H)SBBN = 1.30 ! 10!14.

Figure 36: Contours of constant 7Li/H. Cosmological and model parameters are the sameas Fig. 32. In the SBBN, the theoreical predication of the abundance is (7Li/H)SBBN =3.81 ! 10!10.

57

Jedamzik Kaw

asak

i, K

ohri,

Mor

oi

Solution 1: Particle Decays

Figure 35: Contours of constant 6Li/H. Cosmological and model parameters are the sameas Fig. 32. In the SBBN, the theoreical predication is (6Li/H)SBBN = 1.30 ! 10−14.

Figure 36: Contours of constant 7Li/H. Cosmological and model parameters are the sameas Fig. 32. In the SBBN, the theoreical predication of the abundance is (7Li/H)SBBN =3.81 ! 10−10.

57

Figure 35: Contours of constant 6Li/H. Cosmological and model parameters are the sameas Fig. 32. In the SBBN, the theoreical predication is (6Li/H)SBBN = 1.30 ! 10!14.

Figure 36: Contours of constant 7Li/H. Cosmological and model parameters are the sameas Fig. 32. In the SBBN, the theoreical predication of the abundance is (7Li/H)SBBN =3.81 ! 10!10.

57

Kaw

asak

i, K

ohri,

Mor

oi

Figure 32: Contours of constant D/H on the !X vs. EvisYX plane for mX = 1 TeV. Herewe take Bh = 1, Evis = mX , and X is assume to decay into two hadronic jets with2Ejet = mX . Here, we take " = 6.1 ! 10!10. In the SBBN, the theoreical predication is(D/H)SBBN = 2.78 ! 10!5.

For 6Li, we include the non-thermal secondary production process discussed in the previoussection and hence we obtain

dn6Li

dt=

!

dn6Li

dt

"

SBBN

+

!

dn6Li

dt

"

photodis

+

!

dn6Li

dt

"

!+"BG"T/3He+···

+ BhnX!X#(T,3He)6Li .

(9.5)

Here, the terms with the subscript “SBBN” represent the SBBN contributions to theBoltzmann equations (including the e"ect of the cosmic expansion).

In order to solve these equations, as we mentioned, we have modified the KawanoCode (Version 4.1, with the nuclear cross sections being updated), including the new sub-routines which take account of photodissociation, inter-conversion, and hadrodissociationprocesses. The photodissociation and hadrodissociation processes included in our analysisare summarized in Tables 2, 3, and 4. In addition, our treatments of the inter-conversionand non-thermal production of Li are discussed in Sections 6 and 8, respectively.

9.2 Predicted light-element abundances

To see how the abundances of the light elements behave, we estimated the light-elementabundances using the center values of the cross sections and model parameters. In Figs.32, 33, 34, 35 and 36, we plot contours of D/H, 3He/D, Yp, 6Li/H, and 7Li/H, in (!X ,

55

4

FIG. 1: Parameter space in the GUT–scale unified supersym-metric scalar mass m0 – gaugino mass m1/2 plane (all in GeV)where NLSP decay into gravitinos may resolve one or both ofthe lithium problems. The parameters of the CMSSM pointemployed are tan! = 10, µ > 0, and A0 = 0 and a num-ber of di!erent gravitino mass m !G choices as explained inthe text. The origin of the 6Li in low–metallicity stars maybe explained (criterium (a), see text) in the area indicatedby green (light grey). The discrepancy between observation-ally inferred– and standard BBN predicted primordial 7Li/Habundance may be resolved (criterium (b), see text) in thearea shown in red (darker grey). Both lithium problems maybe solved at the same time (criterium (c), see text) in thearea shown by blue (darkest grey). When additional stellar6Li depletion (see text) occurs, both lithium problems maybe resolved (criterum (d), see text) in the small area shownby pink (grey shading between the shading of green and red).

yond the standard model each point is also subjected tothe following observationally inferred limits on the light–element abundances: 2.2 ! 10!5 <

"2H/H <

" 5.3 ! 10!5

derived from the 2H/H abundance in the local interstel-lar medium and in high–redshift Lyman–! absorbers,3He/2H <

" 1.72 derived from the presolar nebula and,Yp

<" 0.258, where Yp is the helium mass fraction.

For the lithium isotopes we examine three concep-tually di!erent possibilities: The 6Li is due to relicparticle decay with the primordial 7Li abundance notmuch changed. The discrepancy between the standardBBN predicted and observationally inferred 7Li/H ratiois solved by stellar depletion. A 7Li destruction factor of2.5 implies generically [20, 25] a 6Li destruction of 10"40.Therefore we apply:

(a) 7Li/H >" 2.5 ! 10!10 and 0.015 <

"6Li/7Li <

" 3.

FIG. 2: Present day gravitino abundance "Gh2 as a func-tion of NLSP decay time in the points shown in Fig. 1. Thecolor coding is that of Fig. 1. Here only the gravitino abun-dance generated during NLSP decay (the NTP component)is shown. An additional contribution to the gravitino abun-dance could result for a su#ciently high cosmic reheat tem-perature T ! 109GeV after inflation.

FIG. 3: Gravitino mass m !G as a function of NLSP massmNLSP (all in GeV) for those points shown in Fig. 1 and 2.The color coding is that of Fig. 1.

Jedamzik et al.

2 10-5

4 10-5

6 10-5

8 10-5

1 10-4

1.2 10-4

0 1000 2000 3000 4000 5000 6000

brianem

DE

D

A

10-14

10-13

10-12

10-11

10-10

10-9

10-8

10-7

10-6

0 1000 2000 3000 4000 5000 6000

brianem

FG

F

Am1/2 m1/2

7Li

6Li D

3HePr

elimina

ry

Cyburt, Ellis, Fields, Olive, Spanos

Solution 1 plagued by the overproduction of D/H.

Solution 2: Cosmological Cosmic Rays(to Problem 2 only)

• Cosmic Chemical Evolution• Early Reionization and Massive Stars• Cosmic Ray Production and Propagation in an expanding Universe

3

al. (2004) have developed models that include an early burstof massive stars with several possible mass ranges, capableof reionizing the intergalactic medium, while satisfying ob-servational constraints on cosmic chemical evolution in pre-galactic structures and in the intergalacticmedium. In particu-lar, Daigne et al. (2004) have demonstrated that the presenceof massive stars (M! 40-100M") is required at high redshift(z>

! 15!20). This early population of stars (pop III) is able toreionize the intergalactic medium and generate a prompt ini-tial enrichment (PIE) in metals. It is likely that particles willbe accelerated within the same process.Gamma-ray emission, as well as cosmic rays, may also

come from active (Stecker & Salamon 1993; Mukherjee &Chiang 1999) and normal (Pavlidou & Fields 2002) galax-ies (see also Lemoine 2002). Depending on the strengh ofthe magnetic fields in those structures, cosmic rays will beconfined or will propagate into the intergalactic medium (e.g.Berezinsky, Blasi & Ptuskin 1997; Zweibel 2003). In addi-tion, recent numerical simulations have shown that the forma-tion of large scale structures leads to accretion shocks in thebaryonic gas, and thus to particle acceleration directly in theintergalactic medium (Kang & Jones 2002; Miniati 2002;Keshet et al. 2003; Ryu et al. 2003). Finally, at ultra-high energies, more exotic sources of cosmic rays have alsobeen studied (Bhattacharjee, Hill & Schramm 1992; Sigl etal. 1999). Clearly, there are several viable mechanisms forthe production of CCRs and just as clearly, there is a greatdeal of uncertainty surrounding their production.In this paper, CCRs are assumed to be produced in a single

burst correlated to a very early generation of pop III stars asdiscussed in Daigne et al. (2004) at a given redshift zs. Notethat very little is known about the cosmic ray injection spectraat these energies. Here, our formalism is directly derived fromthe work of Montmerle (1977a), hereafter M77. We brieflysummarize this formalism and note explicitly our differenceswith this model. A power-law distribution in particle energyis adopted for the CR injection spectrum,

!α(E)=F 12.5Kαp(E +E0){E(E +2E0)}!(γ+1)/2

cm!2s!1(GeV per nucleon)!1 , (1)

which is the form expected from standard shock accelerationtheory (Blandford & Eichler 1987). F is a normalizationfactor which is fixed by the value of the injection spectral in-dex, chosen to be " = 3 (Suzuki & Inoue 2002), and by zs. Itwill ultimately be constrained by the observed abundance of6Li in the MPHS (see Section 4). E is the kinetic energy pernucleon, E0 = 939 MeV is the nucleon rest mass energy andKαp = 0.08 is the abundance by number of 4He/H. Lithiumproduction is sensitive to ##s with energy E $ 10 MeV/n.

3.2. Transport function in an expanding universe

The initial burst of cosmological cosmic rays evolves in theframework of an expanding universe with a cosmological con-stant.If Ni(E,z) is the comoving number density per (GeV/n) of

a given species at a given time or redshift, and energy, wedefine Ni,H(E,z) % N(E,z)/nH(z), the abundance by num-ber with respect to the ambient gaseous hydrogen (in unitsof (Gev/n)!1). The evolution of Ni,H is defined through thetransport function

$Ni,H$t

+$

$E(bNi,H)+

Ni,H

TD= Qi,H . (2)

Q is a source function which accounts for different sourcesof particle production while TD is the lifetime against de-struction. b describes the energy losses due to expansion orionization processes ((Gev/n) s!1). The energy and time de-pendencies can be separated as b(E,z) = !B(E) f (z). Wecan distinguish two cases depending on whether losses aredominated by expansion or by ionization. The general formfor the redshift dependence, when expansion dominates isfE(z) = (1 + z)!1|dz/dt|H!1

0 (e.g. Wick, Dermer & Atoyan2004). Other contributions to B or f , do not depend on theassumed cosmology and are given explicitly in M77.

Two important quantities, z%(E,E #,z) and E#

s(E,z) are usedin this formalism. Given a particle (# or lithium) with anenergy E at a redshift z, z%(E,E #,z) corresponds to the red-shift at which this particle had an energy E #. E

#

s(E,z) isthe initial energy required if this particle was produced at

the redshift of the burst, zs. In particular, z%(E,E

#

s,z) = zs.The equation that defines z% (Eq. A5, M77) is $z%/$E =! [B(E) f (z) |dz/dt|]!1 ($z%/$z). M77 gives analytical solu-tions for z% when !! = 0. When !! &= 0, it cannot be solvedanalytically when ionization dominates. Integration of this

equation shows that z%(E,E#

s,z) is the solution of

! z%

zdz## f (z##) (|dz/dt|)z## =

! E #s

E

dE ##

B(E ##)(3)

We solve this relation for z% numerically whenever analyticalsolutions are not available.

3.3. The CCR flux and the lithium abundance

The evolution of the CCR # energy spectrum is derived,using Eq. A8 of M77 and the single burst properties, as

"α,H(E,z) =!α(E)

n0H

&

&#

!α(E#

s)

!α(E)

"

"

"

"

dz

dt

"

"

"

"

zs

exp(!')

|b(E,zs)|

1

|$z%/$E #|E #s

(4)where "α,H(E,z) % "α(E,z)/nH(z) is the flux of #’s per co-moving volume

"α,H(E,z) = &Nα,H(E,z) (5)

and & (&#) is the velocity corresponding to energy E (E#

s); 'accounts for the destruction term (Eq. A9, M77).

The abundance by number of lithium (l = 6Li or 7Li) of en-ergy E , produced at a given redshift z, is computed from

$Nl,H(E,z)

$t=

!

(αα'l(E,E #)nHe(z)"α ,H(E #,z)dE #

=(l(E)Kαp"α(4E,z) [(Gev/n)!1 s!1] , (6)

where (αα'l(E,E #) = (l(E))(E !E #/4). The cross sectionsused have been discussed in Section 2. Note that this equationdoes not take into account the destruction of lithium in theintergalacticmedium. We show below that this is a reasonableapproximation.Furthermore, we want to compute the abundance of lithium

in the gas that is present at the redshift of the formationof the Galaxy (see below). We assume that all the lithiumproduced will be thermalized in the protogalaxy before stars

3





!!(E)=F 12.5K!p(E +E0){E(E +2E0)}!("+1)/2


which is the form expected from standard shock accelerationtheory (Blandford & Eichler 1987). F is a normalizationfactor which is fixed by the value of the injection spectral in-dex, chosen to be " = 3 (Suzuki & Inoue 2002), and by zs. Itwill ultimately be constrained by the observed abundance of6Li in the MPHS (see Section 4). E is the kinetic energy pernucleon, E0 = 939 MeV is the nucleon rest mass energy andK!p = 0.08 is the abundance by number of 4He/H. Lithiumproduction is sensitive to ##s with energy E $ 10 MeV/n.




$Ni,H$t

+$

$E(bNi,H)+

Ni,H

TD= Qi,H . (2)





#



#




∫ z%

zdz## f (z##) (|dz/dt|)z## =

∫ E #s

E

dE ##

B(E ##)(3)




"!,H(E,z) =!!(E)

n0H

&

&#

!!(E#

s)

!!(E)

∣

∣

∣

∣

dz

dt

∣

∣

∣

∣

zs

exp(!')

|b(E,zs)|

1

|$z%/$E #|E #s

(4)where "!,H(E,z) % "!(E,z)/nH(z) is the flux of #’s per co-moving volume

"!,H(E,z) = &N!,H(E,z) (5)




$Nl,H(E,z)

$t=

∫

(!!'l(E,E #)nHe(z)"! ,H(E #,z)dE #

=(l(E)K!p"!(4E,z) [(Gev/n)!1 s!1] , (6)

where (!!'l(E,E #) = (l(E))(E !E #/4). The cross sectionsused have been discussed in Section 2. Note that this equationdoes not take into account the destruction of lithium in theintergalacticmedium. We show below that this is a reasonableapproximation.Furthermore, we want to compute the abundance of lithium


3





!!(E)=F 12.5K!p(E +E0){E(E +2E0)}!("+1)/2


which is the form expected from standard shock accelerationtheory (Blandford & Eichler 1987). F is a normalizationfactor which is fixed by the value of the injection spectral in-dex, chosen to be " = 3 (Suzuki & Inoue 2002), and by zs. Itwill ultimately be constrained by the observed abundance of6Li in the MPHS (see Section 4). E is the kinetic energy pernucleon, E0 = 939 MeV is the nucleon rest mass energy andK!p = 0.08 is the abundance by number of 4He/H. Lithiumproduction is sensitive to ##s with energy E $ 10 MeV/n.




$Ni,H$t

+$

$E(bNi,H)+

Ni,H

TD= Qi,H . (2)





#



#




! z%

zdz## f (z##) (|dz/dt|)z## =

! E #s

E

dE ##

B(E ##)(3)




"!,H(E,z) =!!(E)

n0H

&

&#

!!(E#

s)

!!(E)

"

"

"

"

dz

dt

"

"

"

"

zs

exp(!')

|b(E,zs)|

1

|$z%/$E #|E #s

(4)where "!,H(E,z) % "!(E,z)/nH(z) is the flux of #’s per co-moving volume

"!,H(E,z) = &N!,H(E,z) (5)




$Nl,H(E,z)

$t=

!

(!!'l(E,E #)nHe(z)"! ,H(E #,z)dE #

=(l(E)K!p"!(4E,z) [(Gev/n)!1 s!1] , (6)

where (!!'l(E,E #) = (l(E))(E !E #/4). The cross sectionsused have been discussed in Section 2. Note that this equationdoes not take into account the destruction of lithium in theintergalacticmedium. We show below that this is a reasonableapproximation.Furthermore, we want to compute the abundance of lithium


Rollinde. Vangioni, Olive

Montemerle

Montemerle

Daigne, Olive, Silk, Stoehr, Vangioni

[number / Mpc3 / yr]

Model 1(Pop III)

Model 1(Pop II)

Model 1 (total)

Model 1e

0 10 20 30 3 2 1 0 1

[ergs / Mpc3 / yr]

50

55

redshift, z

SNR

log(

CR p

)

3

collapse will be a neutron star of m ! 1.5 M". Stars with 30M" < m < 100 M" become black holes with mass approxi-mately that of the star’s helium core before collapse (Heger etal. 2003). We take the mass of the Helium core to be

MHe =13

24· (m!20M") (7)

for a star with main sequence mass m (Heger & Woosley2002). The supernova rate ultimately determines the metalenrichment of the ISM and when coupled with the model ofoutflow also determines the metal enrichment of the IGM.

The energy emitted in each core collapse, Ecc correspondsto the change in gravitational energy, 99% of which is emittedas neutrinos. In the cases where collapse results in a neu-

tron star, Ecc = 3#1053 ergs. For stars that collapse to blackholes, Ecc is proportional to the mass of the black hole. Formasses less than 100 M", we take Ecc = 0.3MHe . We willparametrize the energy injected in cosmic rays per supernovaas

ECR(m) =!Ecc(m)

100, (8)

where ! is the fraction of energy in the remaining 1% (i.e. en-ergy not in neutrinos) deposited into cosmic rays. Given theIMF described above, the massive mode is dominated by 40M" stars for which the total energy per SN in CRs is EIII =1052.8!III ergs. In contrast, the normal mode associated withPop II, is dominated by lower mass stars for which the energy

per SN in CRs is EII = 1051.5!II ergs. While it is quite plausi-ble that !II and !III differ (indeed we would expect !II < !III ),we will for simplicity assume !II = !III = ! = 0.01!0.30 as abroad and conservative range.

The SNR derived from eq. 6 is shown for both Pop III Mod-els 1 and 1e in Fig. 2 (lower panel). In the upper panel ofFig. 2, we show the energy density in CRs injected per year.The CR production rate in Model 1e (shown by the dot-dashedcurves) is similar to that Model 1 (shown by the solid curves)below a redshift of about 10, as would be expected from theSFRs shown in Fig. 1. The total integrated value is slightlylarger in Model 1e. This will explain the similarity betweenthe two models that arise later. Dashed lines show the ratesof CRs generated by massive PopIII SNe alone, while dottedlines correspond to PopII SNe ejection. Although the SNRof the two populations are quite similar, the energy density incosmic rays is clearly dominated at large redshift by PopIIISNe due to the corresponding IMFs and mass range associ-ated with the two modes and the dependence of Ecc on theprogenitor mass.

The metallicity evolution in both the IGM and the ISM hasbeen derived by Daigne et al. (2005) and is shown in Fig. 3.For Model 1e, the metallicity in the ISM rises very quicklyto [Fe/H] $ !2.5, whereas in Model 1, the initial enrichmentoccurs rapidly only to [Fe/H] $ !4. The IGM abundance areseveral thousand times smaller. Again, both models have thesame metallicity as a function of redshift below z$ 15.

3. PRODUCTION OF LITHIUM IN THE IGM

In RVOI, we considered a single burst of CRs whose totalenergy was fixed in an ad hoc way so as to reproduce the ob-

served 6Li abundance. We now relate the production of CRsto the detailed model of cosmic chemical evolution in whichthe SN history is completely determined by the SFR and IMFof the model and are constrained to reionize the IGM at aredshift z % 12, match the observed SFR at z < 6, as well as


Model 1(Pop III)

Model 1(Pop II)

Model 1 (total)

Model 1e

0 10 20 30!3

!2

!1

0

1

[ergs / Mpc3 / yr]

50

55

redshift, z

SN

Rlo

g(C

R p

)

FIG. 2.— CR history predicted by Daigne et al. (2005). The SNR (lowerpanel) and energy density in cosmic rays (upper panel) are shown in the caseof Model 1 for PopIII (dashed), PopII (dotted) and all SN (solid) and in thecase of the model 1e (dot-dashed).

IGM

ISM

0 10 20 30!10

!5

0

redshift, z

[Fe/H

]FIG. 3.— Evolution of metallicity in ISM and IGM versus redshift in Model

1 (dashed curves) and in Model 1e (solid curves).

chemical abundances at z< 3. As a consequence, the energydensity in cosmic rays is determined by the model and wecan derive the abundance of Lithium produced in the IGM asdescribed below.

3.1. Formalism of Cosmological Cosmic Rays

3.1.1. Ejection of CCR into the IGM

The total kinetic energy given initially to CRs by the SN is

ESN(z) = (1+z)3! msup

max(8M",mmin(t))dm"(m)#(t !$(m))ECR(m).

(9)where it is understood that the appropriate IMF is used forcomputing CR energy density due to Pop II or Pop III SN.For example, using eq. 9 we can estimate from Fig. 1, thePop III contribution to the CR energy density. In Model 1,if we take # % 0.02 M" yr!1 Mpc!3 from z = 10 ! 30, andapproximate " by a delta function at m = 40 M", we obtainESN(10)% 7.8#10!13! ergs/cm3. For ! = 0.15, this is slightlylower than our estimates of the necessary energy density to

produce sufficient 6Li in RVOI. Note that the result of thefull calculation of eq. 9 gives a result a factor of about 5larger than this, because the contributions of more massivestars (more massive than 40 M") can not be neglected. ForModel 1, we find ESN % 5.4# 10!13 ergs/cm3, which is stillslightly lower than the estimate in RVOI for a burst at z = 30

and very similar to the one needed at z= 10 to produce the 6Liplateau. For Model 1e, we see that the burst is very intense,

3

collapse will be a neutron star of m ! 1.5 M". Stars with 30M" < m < 100 M" become black holes with mass approxi-mately that of the star’s helium core before collapse (Heger etal. 2003). We take the mass of the Helium core to be

MHe =13

24· (m!20M") (7)

for a star with main sequence mass m (Heger & Woosley2002). The supernova rate ultimately determines the metalenrichment of the ISM and when coupled with the model ofoutflow also determines the metal enrichment of the IGM.

The energy emitted in each core collapse, Ecc correspondsto the change in gravitational energy, 99% of which is emittedas neutrinos. In the cases where collapse results in a neu-

tron star, Ecc = 3#1053 ergs. For stars that collapse to blackholes, Ecc is proportional to the mass of the black hole. Formasses less than 100 M", we take Ecc = 0.3MHe . We willparametrize the energy injected in cosmic rays per supernovaas

ECR(m) =!Ecc(m)

100, (8)

where ! is the fraction of energy in the remaining 1% (i.e. en-ergy not in neutrinos) deposited into cosmic rays. Given theIMF described above, the massive mode is dominated by 40M" stars for which the total energy per SN in CRs is EIII =1052.8!III ergs. In contrast, the normal mode associated withPop II, is dominated by lower mass stars for which the energy

per SN in CRs is EII = 1051.5!II ergs. While it is quite plausi-ble that !II and !III differ (indeed we would expect !II < !III ),we will for simplicity assume !II = !III = ! = 0.01!0.30 as abroad and conservative range.

The SNR derived from eq. 6 is shown for both Pop III Mod-els 1 and 1e in Fig. 2 (lower panel). In the upper panel ofFig. 2, we show the energy density in CRs injected per year.The CR production rate in Model 1e (shown by the dot-dashedcurves) is similar to that Model 1 (shown by the solid curves)below a redshift of about 10, as would be expected from theSFRs shown in Fig. 1. The total integrated value is slightlylarger in Model 1e. This will explain the similarity betweenthe two models that arise later. Dashed lines show the ratesof CRs generated by massive PopIII SNe alone, while dottedlines correspond to PopII SNe ejection. Although the SNRof the two populations are quite similar, the energy density incosmic rays is clearly dominated at large redshift by PopIIISNe due to the corresponding IMFs and mass range associ-ated with the two modes and the dependence of Ecc on theprogenitor mass.

The metallicity evolution in both the IGM and the ISM hasbeen derived by Daigne et al. (2005) and is shown in Fig. 3.For Model 1e, the metallicity in the ISM rises very quicklyto [Fe/H] $ !2.5, whereas in Model 1, the initial enrichmentoccurs rapidly only to [Fe/H] $ !4. The IGM abundance areseveral thousand times smaller. Again, both models have thesame metallicity as a function of redshift below z$ 15.

3. PRODUCTION OF LITHIUM IN THE IGM

In RVOI, we considered a single burst of CRs whose totalenergy was fixed in an ad hoc way so as to reproduce the ob-

served 6Li abundance. We now relate the production of CRsto the detailed model of cosmic chemical evolution in whichthe SN history is completely determined by the SFR and IMFof the model and are constrained to reionize the IGM at aredshift z % 12, match the observed SFR at z < 6, as well as


Model 1(Pop III)

Model 1(Pop II)

Model 1 (total)

Model 1e

0 10 20 30!3

!2

!1

0

1

[ergs / Mpc3 / yr]

50

55

redshift, z

SN

Rlo

g(C

R p

)

FIG. 2.— CR history predicted by Daigne et al. (2005). The SNR (lowerpanel) and energy density in cosmic rays (upper panel) are shown in the caseof Model 1 for PopIII (dashed), PopII (dotted) and all SN (solid) and in thecase of the model 1e (dot-dashed).

IGM

ISM

0 10 20 30!10

!5

0

redshift, z

[Fe/H

]

FIG. 3.— Evolution of metallicity in ISM and IGM versus redshift in Model1 (dashed curves) and in Model 1e (solid curves).

chemical abundances at z< 3. As a consequence, the energydensity in cosmic rays is determined by the model and wecan derive the abundance of Lithium produced in the IGM asdescribed below.

3.1. Formalism of Cosmological Cosmic Rays

3.1.1. Ejection of CCR into the IGM

The total kinetic energy given initially to CRs by the SN is

ESN(z) = (1+z)3! msup

max(8M",mmin(t))dm"(m)#(t !$(m))ECR(m).

(9)where it is understood that the appropriate IMF is used forcomputing CR energy density due to Pop II or Pop III SN.For example, using eq. 9 we can estimate from Fig. 1, thePop III contribution to the CR energy density. In Model 1,if we take # % 0.02 M" yr!1 Mpc!3 from z = 10 ! 30, andapproximate " by a delta function at m = 40 M", we obtainESN(10)% 7.8#10!13! ergs/cm3. For ! = 0.15, this is slightlylower than our estimates of the necessary energy density to

produce sufficient 6Li in RVOI. Note that the result of thefull calculation of eq. 9 gives a result a factor of about 5larger than this, because the contributions of more massivestars (more massive than 40 M") can not be neglected. ForModel 1, we find ESN % 5.4# 10!13 ergs/cm3, which is stillslightly lower than the estimate in RVOI for a burst at z = 30

and very similar to the one needed at z= 10 to produce the 6Liplateau. For Model 1e, we see that the burst is very intense,

! = 0.04 ! 0.15Rollinde. Vangioni, Olive

log

(6 Li/H

), lo

g (L

i/H)

Li/H

6Li/H

[Fe/H]

Rollinde. Vangioni, Olive

Summary

• D, He are ok -- issues to be resolved

• Li: 2 Problems- BBN 7Li high compared to observations- BBN 6Li low compared to observations

6Li plateau?• Important to consider:- Depletion- Li Systematics - T scale- Particle Decays? - PreGalactic production of 6Li

Documents

Lithium Update - Berkeley Cosmology Groupcosmology.berkeley.edu/inpac/CDMSCE_Jun06/Talks/irvine_olive2.pdf · Lithium Update • 2 Lithium ... R e a p p ra isin g th e S p ite L ith