Final stages of intermediate mass
stars
INTERMEDIATE MASS STARS (2.3≤ M/ Msun≤8)
END THEIR LIFE AS COOLING WHITE
DWARFS…. BUT SOMETHING
DIFFERENT MAY OCCUR…
THE CHANDRASEKHAR MASS VALUE IS
THE KEY PARAMETER OF THE STORY….
DEFINE THE CHANDRASEKHAR
MASS
Stars exist thanks to the pressure gradient
In “normal” stars the free particle pressure
dominates and the standard EOS is at work
In Dwarf Stars it is the pressure of the degenerate
electrons to dominate
The mass of Degenerate Stars cannot exceed the
Chandrasekhar limiting mass.
CHANDRASEKHAR MASS
M ch = (9 / 32π ) (ch / G)
2 0.5
M ch ≅ 5.6 Y
3/ 2
2
e
−2 2
n e
m Y
limiting masses in standard
conditions
H dominated matter
M ch ≈ 5.6 M Sun
Helium, Carbon, Oxygen
M ch ≈ 1.4 M Sun
Iron
M ch ≈ 1.1 M Sun
IMS evolving to a Chandra core
INTERMEDIATE MASS STARS:
2.3 ≤ M / Msun ≤ 8
He is ignited at central H exhaustion and burned in a convective
core.
A degenerate CO core is finally produced
LOW MASS STARS:
0.5 ≤ M / M sun ≤ 2.3
A degenerate He core is at first produced. This accretes by mass
up to 0.5 Msun then He is ignited in a flash and a degenerate CO
core is finally produced
ORIGINAL SYSTEM
M1 = 7 Msun
M2 = 5 Msun
A binary system with two intermediate mass stars.
Say: 7 and 5 solar masses and original separation A
DEGENERATE
CO CORE
CONVECTIVE
EXPANDED
ENVELOPE
After the end of central He burning the primary
develops a degenerate CO core and the envelope
expands to red giant conditions
FIRST COMMON ENVELOPE EPISODE
A Common Envelope phase ensues. The convective
envelope of the primary expands and engulfs the
secondary. While the envelope matter becomes lost
from the external lagrangian points the separation
is reduced.
FIRST INTERMEDIATE PHASE
A = AM 1R M 2/M
'
2
1
The outcome of the first CE episode is a bare CO
white dwarf and a normal star almost unaffected by
the CE stage.
ONE POSSIBLE EVOLUTIONARY CHANNEL
(depending on mass and separation)
LOW
M&
STEADY MASS TRANSFER AT LOW RATE,
NOVA LIKE PHENOMENA
A DIFFERENT EVOLUTIONARY CHANNEL
(depending on mass and separation)
DEGENERATE
CORE
CONVECTIVE EXPANDED
ENVELOPE
IF SEPARATION IS RATHER LARGE THE SECONDARY EVOLVES UP
TO RED GIANT DIMENSION BEFORE STARTING INTERACION
EVOLUTION ALONG THE SECOND CHANNEL
SECOND COMMON ENVELOPE PHASE
THE INTERACTION OF THE EXPANDED
CONVECTIVE ENVELOPE WITH THE REMNANT OF
THE PRIMARY GIVES RISE TO A SECOND CE
EPISODE. ONCE AGAIN THE ENVELOPE BECOMES
LOST.
FINAL OUTCOME
Ω
GWR
A f = A M 2RM 1R / M
'
GWR
A SYSTEM OF TWO VERY CLOSE WDs
SEPARATION SHRINKS BECAUSE OF
GRAVITATIONAL WAVE EMISSION
2
1R
MERGING TIME
τ merg = 1.5 10 A /(M1R M 2R (M1R + M 2 R )) yrs
8
4
f
A f OF THE ORDER OF THE SOLAR RADIUS
FOR
AND M OF THE ORDER OF
THE SOLAR MASS THE MERGING TIME IS ONLY
8
10 yrs
(BUT IT CAN BE ALSO SEVERAL BILLION
YEARS)