MASSIVE STARS: PRESUPERNOVA EVOLUTION, EXPLOSION AND

NUCLEOSYNTHESIS

Marco LimongiINAF – Osservatorio Astronomico di Roma, ITALY

andCentre for Stellar and Planetary Astrophysics

Monash University – AUSTRALIAEmail: marco@oa-roma.inaf.it

What is a Massive star ?

It is a star that goes through all the hydrostatic burnings in a quiescent way

from H to Si and eventually explodes as a core collapse supernova

Mup’ MPISN < Massive stars <

8 - 10 >120

Why are Massive stars important in the global evolution of our Universe?

Light up regions of stellar birth induce star formation

Production of most of the elements (those necessary to life)

Mixing (winds and radiation) of the ISM

Production of neutron stars and black holes

Cosmology (PopIII):

Reionization of the Universe at z>5

Massive Remnants (Black Holes) AGN progenitors

Pregalactic Chemical Enrichment

High Energy Astrophysics:

GRB progenitors

The understanding of these stars, is crucial for the interpretation of many astrophysical objects

Production of long-lived radioactive isotopes: (26Al, 56Co, 57Co, 44Ti, 60Fe)

-12-11-10

-9-8-7-6-5-4-3-2-1012

0 20 40 60 80 100 120 140 160 180 200

Atomic Weight

Lo

g M

as

s F

rac

tio

n

BB CR neut.Novae IMS SNIISNIa s-r

Le SNII contribuiscono in maniera rilevante all’evoluzione chimica della Galassia. Responsabili per la nucleosintesi degli elementi con 16<A<50 and 60<A<90

BB = Big Bang; CR = Cosmic Rays; neut. = n induced reactions in SNII;IMS = Intermediate Mass Stars; SNII = Core collapse supernovae;SNIa = Termonuclear supernovae; s-r = slow-rapid neutron captures

Computation of the Presupernova Evolution of Massive Stars 64Zn 66Zn 67Zn 68Zn65Zn

63Cu 65Cu

58Ni 59Ni 60Ni 61Ni 62Ni 63Ni 64Ni

54Fe 55Fe 56Fe 57Fe 58Fe 59Fe 60Fe

64Cu

58Co 59Co 60Co 61Co

54Mn 55Mn 56Mn

50Cr 51Cr 52Cr 53Cr 54Cr

49V 50V 51V

47Ti 48Ti 49Ti 50Ti 51Ti46Ti45Ti44Ti

51Mn 52Mn 53Mn

44Sc 45Sc 46Sc 47Sc 48Sc 49Sc41Sc 42Sc 43Sc

42Ca 43Ca 44Ca 45Ca 46Ca 47Ca 48Ca40Ca 41Ca

38K 39K 40K 41K 42K

48Cr 49Cr

37K

49Ca

38Ar 39Ar 40Ar 41Ar35Ar 36Ar 37Ar

38Cl35Cl 36Cl 37Cl33Cl 34Cl

58Cu 59Cu 60Cu 61Cu 62Cu

35S 36S 37S33S 34S32S31S

33P 34P32P31P30P

27Mg

27Si 33Si32Si31Si30Si28Si 29Si

27Al

26Mg24Mg 25Mg

23Na

22Ne20Ne 21Ne

19F

18O16O 17O

16N14N 15N

14C12C 13C

19O

17F 18F

13N

15O

20F

21Na 22Na

23Ne

24Na

25Al 26Al 28Al

47V 48V46V

52Fe 53Fe

54Co 55Co 56Co 57Co

29P

56Ni 57Ni

63Zn60Zn 61Zn 62Zn

65Ni

66Cu

52V

55Cr

61Fe

67Cu

22Na

26Al

44Ti

60Fe

60Co

44Sc

23Mg

45V

57Mn

50Sc

62Co

57Cu

11B10B

10Be8Be 9Be7Be

7Li6Li

4He3He

3H2H1H

n

(p,)

(,n) (,)

(,p)(p,n)

(p,)

(n,)

(n,p)

(n,)

(n)

(p)

()

1. Extended Network

Including a large number of isotopes and reactions(captures of light partcles, e± captures, β± decays)

Computation of the Presupernova Evolution of Massive Stars

),,(4

),,(),,(),,(

),,(4

14

2

2

4

i

igraviinuc

i

YTPPr

GmT

m

T

YTPYTPYTPm

L

YTPrm

rr

Gm

m

P

Ni

YYYvNlkjc

YYvNkjcYjct

Y

lklkj

jlkjAi

kkj

jkjAij

jjii

,........,1

),,(

),()(

,,,,

22

,,

H/He burnings:),( ; ),(

; ),( ; ),( ; ),(

TPTP

TPTPTP

gravgrav

nucnuc

+

Decoupled

Adv. burnings: ),,( inucnuc YTP Coupled

2. Strong coupling between physical and chemical evolution:

Computation of the Presupernova Evolution of Massive Stars

3. Tratment of convection:

tmix

nucmix - Time dependent convection

- Interaction between Mixing and Local Burning

conv

i

nuc

ii

gravnuc

t

Y

t

Y

t

Y

Pr

GmT

m

Tm

L

rm

rr

Gm

m

P

2

2

4

4

4

14

m

YDr

mt

Y i

conv

i 24

D = Diffusion Coefficient

Core H burning

CNO Cycle

Convective Core

TR

MTP

3 4

2

R

MPc

R

MTc

FacTdr

dT

rad34

3

)1(2.0 HTh X

The Convective Core shrinks in mass

Massive Stars powered by the CNO Cycle

(T 3×107 K)

12C + 1H 13N +

13N 13C + e+ +

13C + 1H 14N +

14N + 1H 15O +

15O 15N + e+ +

15N + 1H 12C + 4He (99%)

16O + (1%)

16O + 1H 17F +

17F 17O + e+ +

17O + 1H 14N + 4He

CN-Cycle

C N O

i i

i

i i

i

A

X

A

X 0

CNO Cycle

NO-Cycle

CNO Processed Material

20Ne + 1H 21Na +

21Na 21Ne + e+ +

21Ne + 1H 22Na +

22Na 22Ne + e+ +

22Ne + 1H 23Na +

23Na + 1H 20Ne + 4He

Ne-Na Cycle

24Mg + 1H 25Al +

25Al 25Mg + e+ +

25Mg + 1H 26Al +

26Al 26Mg + e+ +

26Mg + 1H 27Al +

27Al + 1H 24Mg + 4He

Mg-Al Cycle

Ne-Na and Mg-Al Cycles

During Core H Burning the central temperature is high enough (3-7×107 K) that the Ne-Na and Mg-Al cycles

become efficient

21Na e 25Mg destroyed

22Ne slightly burnt

23Na e 26Mg increases

26Al (~10-7) produced

Evolutionary Properties of the Interior

t=6.8 106 yr

Evolutionary Properties of the Surface

Mmin(O) = 14 M

t(O)/t(H burning): 0.15 (14 M ) – 0.79 (120 M)

Core H

Burning

Models

Major Uncertainties in the computation of core H burning models:

Extension of the Convective Core (Overshooting, Semiconvection)

Mass Loss

Both influences the size of the He core that drives the following evolution

He Convective

Core

3+ 12C()16O

H burning shell

H exhausted core (He Core)

Core He burningK 105.1 8cT

4He + 4He 8Be +

8Be 4He + 4He

8Be + 4He 12C +

3 4He 12C +

ad

rad

Bordo iniziale

CC

Core Convettivo

He C,OMix He

The He convective core increases in mass

Nucleosynthesis during Core He burning

3 4He 12C +

12C + 4He 12O +

16O + 4He 20Ne +

20Ne + 4He 24Mg +

Chemical composition at core He exhaustion: mainly C/O

C/O ratio depends on:

1. Treatment of convection (late stages of core He burning)2. 12C()16O cross section

The C/O ratio is one the quantity that mainl affects the advanced evolution of Massive Stars (it determines the

composition of the CO core)

Nucleosynthesis during Core He burning14N, produced by H burning activates the sequence of reactions:

14N + 4He 18F +

18F 18O + e+ +

18O + 4He 22Ne +

22Ne + 4He 25Mg + n

For the CNO cycle:

XCNO(iniziale) X14N

i i

i

i i

i

A

X

A

X 0

For e Solar composition ),,,,,( 1036.9 17161514131240

OONNCCiA

X

i i

i

2414 103.1141036.9 X

For a Solat composition at core H exhaustion: X(14N) ~ ½ Z

In general: ZX2

114

The efficiency of the 14N reactions scales with the metallicity

14N 22Ne during the initial stages of core He burning

ZX

X 21422 10222

14

During core He burning, 22Ne is reduced by a factor of ~2 by the nuclear reaction:

22Ne + 4He 25Mg + n

CNO (~1/2 Z) 14N (~1/2 Z) 22Ne (~Z)H burning He burning

ZX

X n 40

1106.4

222

1 422 Neutron Mass Fraction

s-process nucleosynthesis

Nucleosynthesis during Core He burning

84Se

85Br

86Kr

83As 84As 85As

85Se 86Se

86Br 87Br

87Kr 88Kr

73Ge 74Ge 75Ge 76Ge

74As 75As 76As

72Ga 73Ga

77As

75Se 76Se 77Se 78Se 79Se 80Se 81Se 82Se

76Br 77Br 78Br 79Br 80Br 81Br 82Br 83Br

77Kr 78Kr 79Kr 80Kr 81Kr 82Kr 83Kr 84Kr

80As 81As78As 79As

78Rb 79Rb 80Rb 81Rb 82Rb 83Rb 85Rb84Rb

80Ge77Ge 78Ge 79Ge

79Ga76Ga 77Ga 78Ga74Ga 75Ga

n,

b-

b-

b-

p

s

r

s,r

s-process during Core He burning

Both the neutron mass fraction and the seed nuclei abundances scale with the metallicity

The abundance of the s-process nuclei scales with the metallicity

Evolutionary Properties of the Interior

t=5.3 105 yr

WIND

Evolutionary Properties of the Surface

Core He

Burning

Models

Core He

Burning

Models

M ≤ 30 M RSG

M ≥ 35 M BSG

Major Uncertainties in the computation of core He burning models:

Extension of the Convective Core (Overshooting, Semiconvection)

Central 12C mass fraction (Treatment of Convection + 12C(,)16O cross section)

Mass Loss (determine which stars explode as RSG and which as BSG)

All these uncertainties affect the size of the CO core that drives the following

evolution

22Ne(,n)25Mg (main neutron source for s-process nucleosynthesis)

Advanced burning stages

Neutrino losses play a dominant role in the evolution of a massive star beyond core He burning

At high temperature (T>109 K~0.08 MeV) neutrino emission from pair production start to become very

efficient

eeee

H burning shell

H exhausted core (He Core)

He burning shell

He exhausted core (CO Core)

Core Burning

Advanced burning stages

Mt

EL

nuc

nuc L

MEt nucnuc

Evolutionary times of the advanced burning stages reduce dramatically

Evolutionary Properties of the Surface

M < 30 M Explode as RSG

M ≥ 30 M Explode as BSG

costL

LL 108 1010

After core He burning

Absolute Magnitude increases by ~25

At PreSN stage

Advanced Nuclear Burning Stages: Core C burning

H

He

CO

H burning shell

He burning shell

T~109 K

C-burning K 10~ 9T

Main Products of C burning

20Ne, 23Na, 24Mg, 27Al

MgnNe 2522 ),(

Scondary Products of C burning

s-process nuclesynthesis

Advanced Nuclear Burning Stages: C burning

At high tempreatures a larger number of nuclear reactions are activated

Heavy nuclei start to be produced

H

He

CO

H burning shell

He burning shell

T~1.3×109 K

NeO C burning shell

Advanced Nuclear Burning Stages: Core Ne burning

Ne-burning K 103.1~ 9T

Advanced Nuclear Burning Stages: Ne burning

Main Products of Ne burning

16O, 24Mg, 28Si

Scondary Products of Ne burning

29Si, 30Si, 32S

H

He

CO

H burning shell

He burning shell

T~2×109 K

NeO

C burning shell

Advanced Nuclear Burning Stages: Core O burning

O

Ne burning shell

Advanced Nuclear Burning Stages: O burning

O-burning K 102~ 9T

28Si (~0.55) 32S (~0.24)

38Ar (~0.10)

34S (~0.07)36Ar (~0.02)

40Ca (~0.01)

Main Products of O burning

Secondary Products of O burning

Advanced Nuclear Burning Stages: O burning

During core O burning weak interactions become efficient

42Ca 43Ca 44Ca40Ca 41Ca

38K 39K 40K 41K 42K37K

38Ar 39Ar 40Ar 41Ar35Ar 36Ar 37Ar

38Cl35Cl 36Cl 37Cl33Cl 34Cl

35S 36S 37S33S 34S32S31S

33P 34P32P31P30P

27Si 33Si32Si31Si30Si28Si 29Si

27Al26Al 28Al

29P

Pro

ton

Nu

mb

er

(Z)

Neutron Number (N)

31S(+)31P 33S(e-,)33P 30P(e-,)30Si 37Ar(e-,)37Cl

Most efficient processes:

The electron fraction per nucleon 5.0i

ii

ie X

A

ZY

H

He

CONeO

Advanced Nuclear Burning Stages: Core Si burning

OSiS

H burning shell

He burning shell

T~2.5×109 K

C burning shell

Ne burning shell

O burning shell

jlik rr

),max()(

jlik

jlik

rr

rrij

0)( ij

Non equilibrium1)( ij

Full equilibrium

Advanced Nuclear Burning Stages: Si burning

At Oxygen exhaustion

K 105.2~ 9T Balance between forward and reverse (strong

interaction) reactions for increasing number of

processes

i + k j + l

A measure of the degree of equilibrium reached by a couple of forward and reverse processes

At Oxygen exhaustion

K 105.2~ 9T

Si

Sc

Equilibrium

At Si ignition

K 105.3~ 9T

Out of Equilibrium

Equilibrium

Partial Eq.

Out of Eq.

At Si ignition(panel a + panel b)

K 105.3~ 9T

A=44A=45

Eq. Clusters

28Si

56Fe

Advanced Nuclear Burning Stages: Si burning

1.0)( ij

1.0)( ij

01.0)( ij

1.0)(01.0 ij

1.0)( ij

1.0)( ij

Advanced Nuclear Burning Stages: Si burning

K 105.3~ 9T

56,57,58Fe, 52,53,54Cr, 55Mn, 59Co, 62Ni

NSE

1.0)( ijA=44

A=45

Clusters di equilibrio

28Si

56Fe

24Mg20Ne

16O12C

4He

Ca),(K

Sc),(Sc Ti),(Ca

Ti),(Ca Ti),(Sc

Ti),(Ti Ti),(Ca

Ti),(Ca Ca),(Sc

Sc),(Ca Ca),(Ca

4441

45444643

45414544

45444542

46424444

45424443

p

nn

p

nn

pn

pn

1. 28Si is burnt through a sequence of reactions

2. The two QSE clusters reajdust on the new equilibrium abundances of the light particles

3. The matter flows from the lower to the upper cluster through a sequence of non equilibirum reactions

Equilibrium Clusters

4. Ye is continuosuly decreased by the weak interactions (out of equilibrium)

H

He

CONeO

Pre-SuperNova Stage

OSiS

H burning shell

He burning shell

T~4.0×109 K

C burning shell

Ne burning shell

O burning shell

Si burning shell

Fe

Evolutionary Properties of the Interior

H burning shell

He burning shell

C burning shell

Ne burning shell

O burning shell

Si burning shell

Chemical Stratification at PreSN Stage

Each zone keeps track of the various central or shell burnings

14N, 13C, 17O14N, 13C, 17O

12C, 16O

12C, 16O s-proc

20Ne,23Na, 24Mg,25Mg, 27Al,s-proc

16O,24Mg, 28Si,29Si, 30Si

28Si,32S, 36Ar,40Ca, 34S, 38Ar

56,57,58Fe, 52,53,54Cr,

55Mn, 59Co, 62NiNSE

Fase Time (yr)

Lnuc L Mcc Tc c Mshell Fuel Main Prod.

Sec. Prod.

H 5.93(6) 12.8 3.7(7) 7.2 8.7 1H 4He 13C, 14N, 17O

He 6.8(5) 6.02 1.5(8) 4.7(2) 6 4He 12C, 16O 18O, 22Ne, s-proc.

C 9.7(2) 1.0(6)-5.0(7)

4.0(7)-1.0(9)

7.2(8) 1.2(5) 2.39 12C 20Ne, 23Na, 24Mg, 27Al

25Mg, s-proc.

Ne 7.7(-1) (280 d)

7.0(9) 2.2(9) 0.62 1.2(9) 2.1(6) 2.39 20Ne 16Ne, 24Mg

29Si, 30Si

O 3.3(-1) (120 d)

5.0(10) 5.9(11)

4.0(10) 1.05 1.8(9) 4.0(6) 1.7 16O 28Si, 32S, 36Ar, 40Ca,

Cl, Ar, K, Ca

Si 2.1(-2) (7 d)

1.1(13) 1.0(12) 1.08 3.1(9) 7.5(7) 1.5 28Si 54Fe, 56Fe, 55Fe

Ti, V, Cr, Mn, Co, Ni

Main Properties of the PreSN Evolution

Evolution of More Massive Stars: Mass Loss

O-Type: 60000 > T(K) > 33000

• WNL: 10-5< Hsup <0.4 (H burning, CNO, products)

• WNE: Hsup<10-5 (No H)

• WN/WC: 0.1 < X(C)/X(N) < 10 (both H and He burning products, N and C)

• WC: X(C)/X(N) > 10 (He burning products)

Wolf-Rayet : Log10(Teff) > 4.0

Final Masses at the PreSN stage

No Mas

s Loss

Final Ma

ss

He-Cor

e Mass

He-CC Mass

CO-Core

Mass

Fe-Core Mass

WNLWNE

WC/WO

RSG

Radius

WIND

HEAVY ELEMENTS

Major Uncertainties in the computation of the advanced burning stages:

Treatment of Convection (interaction between mixing and local burning, stability criterion behavior of convective shells final M-R relation explosive nucleosynthesis)

Computation of Nuclear Energy Generation (minimum size of nuclear network and coupling to physical equations, NSE/QSE approximations)

Weak Interactions (determine Ye hydrostatic and explosive nucleosynthesis behavior of core collapse)

Nuclear Cross Sections (nucleosynthesis of all the heavy elements)

Neutrino Losses

Partition Functions (NSE distribution)

THE EVOLUTION UP TO THE IRON CORE COLLAPSE

The Iron Core is mainly composed by Iron Peak Isotopes at NSE

The following evolution leads to the collapse of the Iron Core:

The Fe core contracts to gain the energy necessary against

gravity

T, increase

nuc lowers becaus the matter is at NSE

The Fe core begins to degenerate

The Chandrasekhar Mass

MCh=5.85×(Ye)2 M is reached

A strong gravitational

contraction begins

The Fermi energy increasesthe electron

captures on both the free and bound protons incease

as well

Tc ~ 1010 K, c ~ 1010 K

Pe ~ 1028 dyne/cm2

Pi ~ 2×1026 dyne/cm2

Prad ~ 3×1025 dyne/cm2

The main source of pressure against gravity (electron

Pressure) lowers

The gravitational collapse begins

3g/cm 103 11

Fe Core

3g/cm 103 12 diffusion

Neutrino Trapping

npe e

3g/cm 1014

Core Bounce and Rebounce

Shock waveFe Core

Stalled ShockEenergy Losses2 x 1051 erg/0.1M

“Prompt”shocks eventually stall!

-sphere

Strong Shock vs Weak Shock

A strong shock propagates.Matter is ejected.

A weak shock stalls.

Matter falls back.

diffusiondiffusionn,p

ee ,p,n

e+,e-

heating

cooling

Gain RadiusRG=100-150 Km

Stalled ShockRS=200-300 Km

NeutrinosphereR=50-700 Km

Neutrino-driven explosions

Energy deposition behind the stalled shock wave due to

neutrino interactions:

eeee

ee ee

Shock Wave reheated

Explosion

Propatagiont of the shock wave through

the envelope

Explosive Nucleosynthesis

Compression and

Heating

Explosive Nucleosynthesi

s

Explosion Mechanism Still Uncertain

The explosive nucleosynthesis calculations for core collapse supernovae are still based on explosions induced by injecting an arbitrary amount of energy in a (also arbitrary) mass location of the presupernova model and then following the development of the blast wave by means of an hydro code.

• Piston

• Thermal Bomb

• Kinetic Bomb

Induced Explosion and Fallback

Injected Energy

Induced Shock

Compression and Heating

Induced Expansion and

Explosion

Initial Remnant

Matter Falling Back

Mass Cut

Initial Remnant

Final Remnant

Matter Ejected into the ISMEkin1051 erg

Composition of the ejecta

The Iron Peak elements are those mostly affected by the properties of the explosion, in particular the amount of

Fallback.

The Final Fate of a Massive Star

No Mas

s Loss

Final Ma

ss

He-Cor

e Mass

He-CC Mass

CO-Core Mass

Fe-Core Mass

WNLWNE

WC/WO

Remnant Mass

Neutron Star

Black Hole

SNII SNIb/c

Fallback

RSG

Z=Z

E=1051 erg

Initial Mass (M)

Mass (M)

Major Uncertainties in the simulation of the explosion (remnant mass – nucleosynyhesis):

Prompt vs Delayed Explosion (this may alter both the M-R relation and Ye of the presupernova model)

How to kick the blast wave:

Thermal Bomb – Kinetic Bomb – Piston

Mass Location where the energy is injected

How much energy to inject:

Thermal Bomb (Internal Energy)

Kinetic Bomb (Initial Velocity)

Piston (Initial velocity and trajectory)

How much kinetic energy at infinity (typically ~1051 erg)

Nuclear Cross Sections and Partition Functions

Chemical Enrichment due to Massive Stars

Mtot

Mcut

Suni

Mtot

Mcut

i

i

dmX

dmX

PF Different chemical composition of the ejecta for different masses

Chemical Enrichment due to Massive Stars

Yields of Massive Stars used for the interepretation of the chemical composition of the Galaxy

We can have information on the contribution of massive stars to the solar composition by looking at the PFs of solar

metallicity massive star models.

ASSUMPTIONS

The average metallicity Z grows slowly and continuously with respect to the evolutionary timescales of the stars

that contribute to the environment enrichment

Most of the solar system distribution is the result (as a first approximation) of the ejecta of ‘‘quasi ’’–solar-metallicity

stars.The PF of the chemical composition provided by a generation of solar metallicity stars should be flat

Chemical Enrichment due to Massive Stars

Mup

Mlow

itot

i dmmYY )( 2.35 kmm )(Yields averaged over a Salpeter IMF

Oxygen is produced predominantly by the core-collapse supernovae and is also the most abundant element

produced by these stars

Use PF(O) to represents the overall increase of the average ‘‘metallicity ’’ and to verify if the other nuclei follow or not its

behavior

Chemical Enrichment due to Massive Stars

Elements above the compatibility range may constitute a problem

Elements below the compatibility range produced by other sources

Secondary

Isotopes?

No room for other sources (AGB) Type Ia AGB

No room for AGB

process. Other sources

uncertain

Explosion?

Chemical Enrichment due to Massive Stars

Global Properties:

Initial Composition (Mass Fraction)

X=0.695Y=0.285Z=0.020

Final Composition (Mass Fraction)

X=0.444 (f=0.64)Y=0.420 (f=1.47)Z=0.136 (f=6.84)

NO DilutionMrem=0.186

1 M1 M

IMF: Salpeter

Averaged Yields: Relative Contributions

Stars with M>35 M (SNIb/c) contribute for ~20% at maximum (large fallback)

with few exceptions

(H,He burning)

CONCLUSIONS

Stars with M<30 M explode as RSG Stars with M≥30 M explode as BSG

The minimum masses for the formation of the various kind of Wolf-Rayet stars are:

WNL: 25-30 M

WNE: 30-35 M

WNC: 35-40 M

The final Fe core Masses range between:

MFe=1.20-1.45 M for M ≤ 40 M

MFe=1.45-1.80 M for M > 40 M

The limiting mass between SNII and SNIb/c is :

30-35 M

SNII SNIb/c

22.0/

SNII

cSNIbSalpeter IMF

The limiting mass between NS and BH formation is:

25-30 M

NS BH

(uncertainties on mass loss, simulated explosion, etc.)

CONCLUSIONS

Assuming a Salpeted IMF the efficiency of enriching the ISM with heavy elements is:

H: decreased by f=0.64He: increased by f=1.47Metals: increased by f=6.84

For each solar mass of gas

returned to the ISM

Massive Stars are responsible for producing elements with 4<Z<38

SNIb/c contribute for ~20% to the majority of the elements (large fallback)

SNIb/c contribute for ~40% to the elements produced by H and He burning that survive to fallback

Depends on:Simulated expl.Mass LossBinary Systems..............

Pre/Post SN models and explosive yields available at http://www.mporzio.astro.it/~limongi