1

Nuclear reactions Nuclear reactions in the Sunin the Sun

• A first look at the SunA first look at the Sun• A deeper look: A deeper look:

helioseismologyhelioseismology

• Neutrino: the spy of the Neutrino: the spy of the innermost suninnermost sun

• Nuclear reactions in the Nuclear reactions in the Sun, after SNO and Sun, after SNO and KamLANDKamLAND

Gianni Fiorentini @Santa Tecla 2003Gianni Fiorentini @Santa Tecla 2003

2

3

A first look at the SunA first look at the Sun

• Observables: Observables:

--MMass ass

--LLuminosityuminosity

- - RRadius, adius,

- Metal content of the photosphere- Metal content of the photosphere

- - AAgege

• Inferences on the typical scales of the Inferences on the typical scales of the solar interior (solar interior (, P, T), P, T)

M= 2 1030 Kg R=7 108m Np=M/mp=1057

L=4 1026W

4

Who measured the solar mass?

Galileo

Cavendish

Kelvin

Rolfs

5

Solar massSolar mass• Astronomy only deals with the Astronomy only deals with the

extremely extremely well well determined Gaussian constant: determined Gaussian constant: GGNNMMoo=(132 712 438 =(132 712 438 5) 105) 1012 12 mm33/s/s22

• Astrophysics needs MAstrophysics needs Moo, since:, since:- opacity is determined by - opacity is determined by NNe e N Np p M Moo/m/mp p 10 105757

- energy content/production of the star - energy content/production of the star depends on Ndepends on Npp..

• Cavendish by determining GCavendish by determining GNN provided a provided a

measurement of Mmeasurement of Moo

• The (poor) accuracy on GThe (poor) accuracy on GNN (0.15%)reflects on M (0.15%)reflects on Moo

MMoo= 1.989 (1 = 1.989 (1 0.15%) 100.15%) 1033 33 gr gr 10 105757mmpp

1erro

r

sM= 2 1030 Kg

6

Solar LuminositySolar Luminosity

• Derived from measurements of the solar Derived from measurements of the solar constant constant KKoo: the : the amount of energy per unit time amount of energy per unit time

and unit area, impinging from the Sun onto Earth.and unit area, impinging from the Sun onto Earth.

• Not precisely a constant, it varies with time Not precisely a constant, it varies with time (0.1% in a solar cycle). The average over 12 (0.1% in a solar cycle). The average over 12 years of solar irradiance (and over different years of solar irradiance (and over different satellite radiometers) multiplied by Sun Earth satellite radiometers) multiplied by Sun Earth distance, gives the solar luminosity:distance, gives the solar luminosity:

LLoo=4=4dd22KKoo =3.844(1 =3.844(1 0.4%) 100.4%) 1033 33 erg/serg/s

(Lo= 10 17 nuclear power plants)

L=4 1026W

7

Solar RadiusSolar Radius

• The distance from the center of the The distance from the center of the sun to its visible surface (the sun to its visible surface (the photosphere) photosphere)

• Difficult to define the edge of the sunDifficult to define the edge of the sun

• Different methods and different Different methods and different experiments:experiments:

RRoo=6.9598(1=6.9598(1 0.04%) 100.04%) 1010 10 cmcm

R=7 108m

8

Solar AgeSolar Age• Method: radioactive dating of oldest Method: radioactive dating of oldest

objects in the solar system objects in the solar system

(chondritic meteorites)(chondritic meteorites)• Problems: Problems:

– relationship between the relationship between the

age of the meteorite and theage of the meteorite and the

age of the sunage of the sun– what is the the zero time what is the the zero time

for the sun?for the sun?• The age of the sun referred to The age of the sun referred to

Zero Age Main SequenceZero Age Main Sequence

t=4.57(1 t=4.57(1 0.4%) Gyr 0.4%) Gyr

9

Solar Metal abundanceSolar Metal abundance• Spectroscopic measurements of the solar Spectroscopic measurements of the solar

photosphere yield the relative abundances photosphere yield the relative abundances (in mass) of “metals“ to H (in mass) of “metals“ to H (Z/X)(Z/X)photophoto=0.0233(1 =0.0233(1 6%) 6%)

• Most abundant metals: O, C, N, FeMost abundant metals: O, C, N, Fe• Results are generally consistent with Results are generally consistent with

the meteoritic abundancesthe meteoritic abundances• A remarkable exception: the solar Li content A remarkable exception: the solar Li content

is depleted by 100 with respect to is depleted by 100 with respect to meteoritesmeteorites

Note: Hydrogen abundance X0.75

10

A remark: Helium abundanceA remark: Helium abundance

• Helium was discovered in the Sun (1895), Helium was discovered in the Sun (1895), but its abundance cannot be accurately but its abundance cannot be accurately measured theremeasured there

• Until a few years ago, estimate of the Until a few years ago, estimate of the photospheric He abundance was taken the photospheric He abundance was taken the result of solar modelsresult of solar models

• Helioseismology provides now an indirect Helioseismology provides now an indirect measurement….. measurement…..

11GeV1eV1

mcE

GeV1MeV1

mcE

2chem

chem

2nuc

nuc

• density: =3M =3Moo/(4/(4RRoo33) ) 1.5 g/cm1.5 g/cm33

• pressurepressure P P GM GMoo22/R/Roo

44 10 101616 dine/cm dine/cm22

• Sound speed vSound speed vss (P/(P/) ) 1/21/2 800 Km/s 800 Km/s

• photon mean free path*: photon mean free path*: =1/(n=1/(nee ThTh))

1/(101/(1024 24 cmcm-3-3 10 10-24 -24 cmcm22) ) 1 cm 1 cm

(photon escape time (photon escape time 2 102 1044 yr) yr)

• Cumulated energy productionCumulated energy production• =L=Loot t 10 10-4 -4 M Moocc22 typical nuclear energy scaletypical nuclear energy scale

Typical scalesTypical scales

*astrophyscists use “opacity” =1/()

12

Sun energy inventorySun energy inventory

• The present heat flow L can be sustained by an energy source U The present heat flow L can be sustained by an energy source U for an age t provided that U>Lt :for an age t provided that U>Lt :

[yr][yr]a)chemistry: a)chemistry: UU (1eV)N (1eV)Npp -> t-> tchch=2 10=2 1044

b)gravitation b)gravitation U U GM GM 22/R/R -> t-> tgrgr=3 10=3 1077

c)nuclear c)nuclear U U (1MeV)N(1MeV)Npp -> t-> tnunu=2 10=2 101010

OnlyOnly nuclear energy can sustain the Solar luminosity over the sun nuclear energy can sustain the Solar luminosity over the sun age, t=4.5 10age, t=4.5 1099 y y

Can we prove that actually the Sun shines due to Can we prove that actually the Sun shines due to nuclear energy?nuclear energy?

13

A digression:A digression:The Earth energy inventoryThe Earth energy inventoryIt is not at all easy to understand the dominant contribution to the Earth energy production.

• The present heat flow HE=40 TW can be sustained by an energy source U for a time t=U/HE :

•a)”chemistry”*): U=(0.1 eV)Np=6 1031J ->tch=5 1010 y

•b)gravitation U=GM 2/R=4 1032J ->tgr=3 1011y

•c)nuclear **) U=(1MeV)Np,rad =6 1030J -> tgr=5 109 y

•-> Thus all energy sources seem capable to sustain HE on geological times.

*)actually it means the solidification (latent) heat**)the amount of radioactive material is taken as Mrad 10-8 MEarth

M= 6 1024 Kg R=6 106m Np=M/mp=1051

HE=4 1013W

14

What is the source of What is the source of terrestrial heat?terrestrial heat?

J Verhoogen, in “Energetics of Earth” (1980) N.A.S.:•“What emerges from this morass of fragmentary and uncertain data is that radioactivityradioactivity itself could possibly account for at least 60 per cent if not 10060 per cent if not 100 per cent of the Earth’s heat output”.•“If one adds the greater rate of radiogenic heat production in the past, possible release of gravitational energy (original heat, separation of the core…) tidal friction … and possible meteoritic impact … the total supplytotal supply of energy may seem embarassingly largeembarassingly large…”•Determination of the radiogenic component is thus importantDetermination of the radiogenic component is thus important.

15

The birth of Nuclear The birth of Nuclear AstrophysicsAstrophysics

Eddington: Nature (1920)

“Certain physical investigations in the past year make it probable to my mind that some portion of sub-atomic energy is actually being set free in a star. … If five per cent of a star's mass consists initially of hydrogen atoms, which are gradually being combined to form more complex elements, the total heat liberated will more than suffice for our demands, and we need look no further for the source of a star's energy…”

•In the same paper: “If indeed the sub-atomic energy in the stars is being freely used to maintain their great furnaces, it seems to bring a little nearer to fulfillment our dream of controlling this latent power for the well-being of the human race - or for its suicide”

=Lot 10-4

Moc2

16

Nuclear reactions in the sun?Nuclear reactions in the sun?The tThe temperature scaleemperature scale

• We have found scales for We have found scales for PP and and • Need equation of state for deriving Need equation of state for deriving TT. . • Use perfect gas equation assuming the Use perfect gas equation assuming the

Sun consists of fully ionized hydrogenSun consists of fully ionized hydrogen

kT= P/(2nkT= P/(2npp)=P )=P mmpp/(2/(2 1 keV 1 keV

(T (T 1.2 101.2 1077 K) K)

• [Remark: kT>> e[Remark: kT>> e22/r /r e e22nn1/31/3 implies implies perfect gas reasonable]perfect gas reasonable]

• However: kT<< eHowever: kT<< e22/r/rnucnuc 1MeV 1MeV

17

The gross solar structureThe gross solar structure• CoreCore

R < 0.1 RR < 0.1 Roo M M 1/3 M 1/3 Moo

(the site of nuclear reactions) (the site of nuclear reactions)

• Radiative zoneRadiative zone

(0.1 (0.1 0.7) R 0.7) Ro o M M 2/3 M 2/3 Moo

• Convective zoneConvective zone (0.7 (0.7 1) R 1) Roo M M 2% M 2% Moo ((As temperature drops, opacity As temperature drops, opacity increases and radiation is not increases and radiation is not efficient for energy transport)efficient for energy transport)

• PhotospherePhotospherethe very tiny layer of the Sun that the very tiny layer of the Sun that we can observe directlywe can observe directly

18

How can we look at the solar How can we look at the solar interior?interior?

• “If there are more things in heaven and Earth than are dreamt of in our natural philosphy, it is partly because electromagnetic detection alone is inadequate”

• We have two probes:

Sound waves and Neutrinos

19

HelioseismologyHelioseismology

•Birth: in 1960 it was found that the solar surface vibrates with a period T 5 min,

•Plan: reconstruct the properties of the solar interior by studying how the solar surface vibrates

(as one studies the deep Earth ’s structure through hearthquakes or just like you can tell something about a material by listening to the sounds that it makes when something hits it)

20

MethodMethod• By means of Doppler effect on By means of Doppler effect on

the emitted radiation, one can the emitted radiation, one can measure oscillations of the solar measure oscillations of the solar surface with a very high surface with a very high accuracyaccuracy

• Most recent measurements Most recent measurements performed with SOHO satellite performed with SOHO satellite (SOlar and Heliospheric (SOlar and Heliospheric Observatory) Observatory)

tsincv

cv o

http://sohowww.nascom.nasa.gov/

21

The modesThe modes

• The observed oscillations are The observed oscillations are decomposed into discrete decomposed into discrete modes.modes.

• Some 10Some 1044 modes are available modes are available• Their frequencies are Their frequencies are

accurately determined accurately determined

((// 10 10-3 -3 - 10- 10-4-4))• So far, only p-modes have So far, only p-modes have

been observed, i.e. pressure been observed, i.e. pressure driven oscillations.driven oscillations.

22

Helioseismic inferencesHelioseismic inferences

• The sound speed profile The sound speed profile (with accuracy of order (with accuracy of order 0.5%…see later)0.5%…see later)

• Locate the transition Locate the transition between radiative transport between radiative transport and convection: and convection:

RRbb =0.711 (1 ± 0.14%) R =0.711 (1 ± 0.14%) R • The photospheric He The photospheric He

abundance: Yabundance: Yphotophoto= 0.249 = 0.249 (1± 1.4%) (1± 1.4%)

By comparing the measured frequencies with the By comparing the measured frequencies with the calculated ones (inversion method) one can calculated ones (inversion method) one can determine:determine:

23

Standard Solar Model (SSM)Standard Solar Model (SSM)

• Bahcall (1995): “A SSM is one which Bahcall (1995): “A SSM is one which reproduces, within uncertainties, the reproduces, within uncertainties, the observedobserved properties of the Sun, by properties of the Sun, by adopting a set of physical and chemical adopting a set of physical and chemical inputs chosen within the range of their inputs chosen within the range of their uncertainties”.uncertainties”.

24

SSM before Helioseismology: SSM before Helioseismology: 3 data and 3 parameters3 data and 3 parameters

• In order to produce a SSM one In order to produce a SSM one had to shad to studtudyy the the evolution of an initially homogeneous solar mass evolution of an initially homogeneous solar mass MMoo up up

to the sun ageto the sun age t t so as to reproduce so as to reproduce LLoo, R, Ro o andand ( (Z/X)Z/X)photophoto

• OOne can tune 3 parameters:ne can tune 3 parameters:

--the initial Helium abundance Ythe initial Helium abundance Yinin

--the initial metal abundance(s) Zthe initial metal abundance(s) Zinin

--“the mixing length“the mixing length”” parameter parameter • Up to here, the SSM is not such a big success….Up to here, the SSM is not such a big success….

25

The impact of helioseismology on SSMThe impact of helioseismology on SSM

Agreement of SSM with helioseismic data within very tiny errors (for u as well as Yph Rb..)

3

1

* Dziembowki et al. Astrop. Phys. 7 (1997) 77

U/U

= (

SS

M-s

un

)/S

SM

26

List of applications of helioseismologyList of applications of helioseismologyBy means of helioseismology one can constrain:By means of helioseismology one can constrain:• rotation in the solar interiorrotation in the solar interior• p+p cross sectionp+p cross section• screening effectscreening effect• solar agesolar age [A&A 343 (1999) 990][A&A 343 (1999) 990]

• diffusion efficiencydiffusion efficiency [A&A 342 (1999) 492][A&A 342 (1999) 492]

• existence of a mixed core existence of a mixed core [Astr. Phys. 8(1998) 293][Astr. Phys. 8(1998) 293]

• Axion production in the sunAxion production in the sun• WIMPs-matter interaction WIMPs-matter interaction [hep-ph/0206211][hep-ph/0206211]

• Existence of extra-dimensions Existence of extra-dimensions [PLB 481(2000)291][PLB 481(2000)291]

• Possible deviations from standard Maxwell-Possible deviations from standard Maxwell-Boltzmann distribution Boltzmann distribution [PLB 441(1998)291][PLB 441(1998)291]

S

UN

EX

OTIC

27

Solar rotation• Solar surface does not rotate uniformely:

T=24 days (30 days) at equator (poles). And the solar interior?

• Helioseismology (after 6 years of data taking) shows that below the convective region the sun rotates in a uniform way

• Note: Erot =1/2 m rotR2 0.02 eV Erot << KT

28

An example: the helioseismic determination of p+p cross section (Spp)

•Remind: SRemind: Spppp is not measured is not measured. .

•The value used in SSM The value used in SSM SSpppp(SSM)=4(1 ± 2%)(SSM)=4(1 ± 2%)

xx 1010-22-22KeVbKeVb

is derived from theory.is derived from theory.

•Build solar models with Build solar models with different Sdifferent Spppp

•Consistency with Consistency with

helioseismology requires:helioseismology requires:

SSpppp=S=Spppp (SSM)(1 ± 2%) (SSM)(1 ± 2%)

•This accuracy is comparable This accuracy is comparable to the to the theoretical theoretical uncertainty:uncertainty:

U/U

(m

od

-SS

M)/

SS

M

Degli Innocenti et al. PLB 416 (1998) 365

29

Can helioseismogy probe the Can helioseismogy probe the core of the Sun? core of the Sun?

• Accuracy degrades Accuracy degrades from 0.1 % to 1% as from 0.1 % to 1% as moving towards the moving towards the solar center.solar center.

• This follows form the This follows form the fact that p modes do fact that p modes do not propagate in the not propagate in the innermost part of the innermost part of the SunSun

=mp/[2x+3/4 Y+1/2 Z]mean molecular weight

core

energy radiative convectivegener. transport transport

30

Can helioseismogy measure Can helioseismogy measure the solar temperature?the solar temperature?

• NO : to go from sound speed to NO : to go from sound speed to temperature one needs the chemical temperature one needs the chemical compositioncomposition

• e.g, for a perfect gas:e.g, for a perfect gas:

kT=P/n=(P/kT=P/n=(P/))• The abundances of elements (and EOS) is The abundances of elements (and EOS) is

needed for translating sound speed into needed for translating sound speed into temperature.temperature.

=mp/[2x+3/4 Y+1/2 Z]mean molecular weight

31

Can helioseismogy prove that Can helioseismogy prove that the Sun is shining by nuclear the Sun is shining by nuclear

reactions? reactions?

• Just indirectly : Standard Solar Models, Just indirectly : Standard Solar Models, which assume that solar energy is which assume that solar energy is generated by means of H-fusion into generated by means of H-fusion into Helium are consistent with Helium are consistent with helioseismology.helioseismology.

32

A first summary A first summary • The knowledge of M, R, L and age immediately

determine the physical scales (T, P,) of the solar interior and show that nuclear reactions are the only sufficient source of solar power.

• Helioseismology provides an accurate picture of the solar interior, in excellent agreement with SSM calculations

• The accuracy of helioseismology degrades in the solar core.

• Helioseismology does not measure the temperature profile.

• We need a proof that nuclear energy sustains the Sun

33