18-19 Settembre 2006

Dottorato in Astronomia Università di Bologna

The Virial Theorem

g

M

rrR

R

dMr

GMPrPdV

0

03

0

43

02 gE

UdVE

UP3

2

R

rR

drrr

GMdPr

0

32

0

3 44 2r

GM

dr

dP r

log

log

P

5/3

4/3

M1

M2

Non-degenerate

Non-relativistic

relativisticCollapse or ig

nition

Stellar core evolution

5.1

3

1

0

2

0

M

Md

M

R

r

Mq

VPR

GMq

r

dMMG

rr

Mrr

g

3

2

3

442 MRMP

457.15.0

83.5 2

Che

eCh

MYif

YM

Degenerate Fermi gas

Stellar evolution

M<0.8 M

0.8<M/M<8

8<M/M<11

11<M/M<100

M>100 M

GyrMyr 0.5<Mf /M<1.1 CO WD

Myr Mf

=1.2-1.3 M ONeMg WD

<10 Myr Mf =1.2-2.5 M Fe (Ye0.45) collapse NS or BHfew Myr O (pair jnstability) (Ye=0.5) may or may not explode

Thermonuclear SNe Progenitors

Core Collapse SNe

Progenitors

Summary:

• Age of simple (stellar clusters) and complex (disk, bulge, halo) stellar populations.

• Properties of nowadays extinct stellar populations.

• Nature of barionic dark matter

• Physics of high density matter

• Amount of C/O in the He-exhausted core: hints for nuclear physics and theory of turbulent convection, as well as constraints for massive stars evolution and any type of SNe

47 tuc (Zoccali et al 2001)

M4 (Bedin et al. 2001)

NGC 6397 (King et al. 1998)

Data obtained with the WFPC2 on board the HST (Hansen et al. 2002, Richer et al. 2002).

The target is a region located 5’ E of the center of M4

andhas been imaged through

the:

F606W (98 orbits x 1300 sec)F814W (148 orbits x 1300

sec)

M4: the deepest WD cooling sequence

12.70.7 Gyr.

Cooling sequence

Age from luminosity Age from luminosity functionfunctionss

Crystallization phase

Debye cooling

Convective couplingWD

cooling

Different colors > different WD masses

WD Age from the CM-diagram:WD Age from the CM-diagram: Collision Induced Abortion Collision Induced Abortion (CIA) (CIA) and and the blue hockthe blue hock

Isochrones for DA WD

Simulated WD sequence in Simulated WD sequence in NGC639NGC6397 with ACS7 with ACS

NGC 6397

Good match between theory and observation

Good descriptionof the high density matter behavior

Bad: only a lower limit for the age can be set: 9 Gyr

The observed WD Luminosity function

Good: smaller dependence on the distance

WDs are relicts of an extinct WDs are relicts of an extinct population: progenitors mass population: progenitors mass

function: function:

Synthetic NGC 6397 13 Gyr - Salpeter mass function

98% C-O core (0.5-1.1 M)

2% He mantel (<10-2 M)

0.01% H envelope (<10-4 M)

no conduction

e- highly degenerate isothermal

envelope

coreC-O ions main energy reservoirenergy reservoir

e- non-degenerate

thermal insulatorthermal insulator

DA White Dwarf

Thermal conductivity by degenerate electrons

From Prada Moroni & Straniero 2002

C/O Core

He-rich Mantel

WD progenitorsWD progenitors

Case B no-AGB

Case B1 Post-AGB with final thermal pulse

Case B2 classical Post-AGB

Case C Post RGB

4He

16O

12C

5 M

Z=0.02 Y=0.28

He-burning: the competition between He-burning: the competition between

33 ->-> 1212C and C and 1212C+C+ ->->1616O+O+

Ex (keV) J

10957

10367

9847 9580

8872

7117 6917

6130

6049

0

0-

4+

2+

1-

2-

1-

2+

3-

0+

0+

1212C+C+44HeHe

2418

2685 3195

ECM (keV)

Gamow peack energies Gamow peack energies

-45

-245

1616O O level schemelevel scheme

Q = 7.162 MeV

Low Adop. high

Kunz et al 2001

5.25 7.58 10.2

Buchmann 1996

3.04 7.04 13.04

NACRE 5.44 9.11 12.8

CF88 4.74

CF85 11.3

Na<,v> (10-15 cm3mol-1s-

1) for T9=0.2

White Dwarf interior: C and O profiles

12C()16

O

High rate

Low rate

cooling is affected by the internal

chemical stratification

high rate

low rate

4 models for convection

same nuclear reaction rates

different convective scheme

WD internal composition is affected by core He burning

convection

MD

16O

At the onset of the core collapse

18.145.0 Che MY

• e-+p n+e (10 MeV)

• 56Fe+ 13+4n (124 MeV)

SNe Ia:Theoretical

Light Curves