Chapter 6: Stellar Evolution (Part 2): Stellar End-Products

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Chapter 6: Stellar Evolution (part 2): Stellar end-products

Final evolution stages of high-mass stars

Stellar end-products White dwarfs Neutron stars and black holes

Supernovae Core-collapsed SNe Pair-Instability Supernovae (PISNe) Type Ia SNe

Review Outline

Final evolution stages of high-mass stars

Stellar end-products White dwarfs Neutron stars and black holes

Supernovae Core-collapsed SNe Pair-Instability Supernovae (PISNe) Type Ia SNe

Review Final evolution stages of high-mass stars

I What do stars in the mass range of ∼ 8 − 11M eventually evolve to is still somewhat uncertain; they may just develop degenerate O-Ne cores.

I A star with mass above ∼ 11M will ignite and burn fuels heavier than carbon until an Fe core is formed which collapses and causes a supernova explosion. I For a star with mass & 15M , mass loss by the stellar wind becomes important during all evolution phases, including the MS. Kippenhahn Diagram When the degenerate core’s mass surpasses the Chandrasekhar limit (or close to it), the core contracts rapidly. No further source of nuclear energy in the iron core, the temperature rises from the contraction, but not fast enough. It collapses on a time scale of seconds!

Mass-loss of high-mass stars

For stars with masses & 30M , I The mass loss time scale is shorter than the MS timescale. The MS evolutionary paths of such stars converge toward that of a 30M star. I Mass-loss from Wolf-Rayet stars leads to CNO products (helium and nitrogen) exposed. I The evolutionary track in the H-R diagram becomes nearly horizontal, since the luminosity is already close to the Eddington limit. I Electrons do not become degenerate until the core consists of iron. When the degenerate core’s mass surpasses the Chandrasekhar limit (or close to it), the core contracts rapidly. No further source of nuclear energy in the iron core, the temperature rises from the contraction, but not fast enough. It collapses on a time scale of seconds! ˙ I How could M and vw be measured? I In general, mass-loss rates during all evolution phases increase with stellar mass, resulting in timescales for mass loss that are less that the nuclear Kippenhahn diagram of the evolution of

timescale for M & 30M . As a result, a 60 M star at Z = 0.02 with mass there is a convergence of the ﬁnal loss. Cross-hatched areas indicate (pre-supernova) masses to ∼ 5 − 10M . where nuclear burning occurs, and I However, this effect is much diminished curly symbols indicate convective for metal-poor stars because the regions. See text for details. Figure mass-loss rates are generally lower at from Maeder & Meynet (1987). low metallicity.

Mass loss of high-mass stars Mass loss plays an essential role in regulating the evolution of very massive stars.

I WR stars are examples, following the ˙ 1/2 correlation: log[Mv∞R ] ∝ log[L]. I In general, mass-loss rates during all evolution phases increase with stellar mass, resulting in timescales for mass loss that are less that the nuclear Kippenhahn diagram of the evolution of

Mass loss of high-mass stars Mass loss plays an essential role in regulating the evolution of very massive stars.

I WR stars are examples, following the ˙ 1/2 correlation: log[Mv∞R ] ∝ log[L]. ˙ I How could M and vw be measured? Mass loss of high-mass stars Mass loss plays an essential role in regulating the evolution of very massive stars.

I WR stars are examples, following the ˙ 1/2 correlation: log[Mv∞R ] ∝ log[L]. ˙ I How could M and vw be measured? I In general, mass-loss rates during all evolution phases increase with stellar mass, resulting in timescales for mass loss that are less that the nuclear Kippenhahn diagram of the evolution of

Final evolution stages of high-mass stars

Stellar end-products White dwarfs Neutron stars and black holes

Supernovae Core-collapsed SNe Pair-Instability Supernovae (PISNe) Type Ia SNe

Review Stellar end-products

It is primarily the mass of a star that decides the outcome at the end of the stellar evolution. The radii of WDs are not too different from the −2 Earth’s (about 10 R ). Thus, the average density is near 106 g cm−3.

White dwarfs WDs are the stellar end-products of relatively low-mass stars. Observations show two peaks in the mass distribution of WDs:

I (Isolated) stars normally undergo the AGB phase, accounting for most of the WDs observed with their mass peaking at 0.67 ± 0.21 M (Zorotovic et al. 2011). I A helium white dwarf can theoretically be made by mass transfer in a binary. But, many He white dwarfs apparently single, puzzlingly. I But, mean white dwarf mass in CVs is high (∼ 0.83 ± 0.24 M ; Zorotovic et al. 2011), which cannot be explained by selection effects. We still don’t understand how CVs evolve. They may contribute to the single-degenerate progenitors of type Ia SNe. White dwarfs WDs are the stellar end-products of relatively low-mass stars. Observations show two peaks in the mass distribution of WDs:

I (Isolated) stars normally undergo the AGB phase, accounting for most of the WDs observed with their mass peaking at 0.67 ± 0.21 M (Zorotovic et al. 2011). I A helium white dwarf can theoretically be made by mass transfer in a binary. But, many He white dwarfs apparently single, puzzlingly. I But, mean white dwarf mass in CVs is high (∼ 0.83 ± 0.24 M ; Zorotovic et al. 2011), which cannot be explained by selection effects. We still don’t understand how CVs evolve. They may contribute to the single-degenerate progenitors of type Ia SNe. The radii of WDs are not too different from the −2 Earth’s (about 10 R ). Thus, the average density is near 106 g cm−3. WD structure and cooling

The structure of a WD approximately consists of two parts: I an isothermal degenerate electron core. Why is this a reasonable assumption? I a thermal radiative envelope with negligible mass and energy source. The internal energy source is primarily the thermal energy stored by the ions (as the heat capacity of the electrons is negligible). Neglecting the mass and energy in the envelope, the total thermal energy is 3MkTc UI = , (1) 2µI mA

where Tc is the temperature of the core. The luminosity can be expressed as dU L = − I (2) dt

and is determined by Tc and the WD mass M. This expression is to be found. In the radiative envelope,

dT 3 κρ L = − , dr 4ac T 3 4πr 2 Replacing dr with the hydrostatic equation, using the Kramers’ opacity, and integrate the equation from the surface, where P = T = 0, inward, we have

M 1/2 P ∝ T 17/4. L

Reversing back to the density,

M 1/2 ρ ∝ T 13/4, L which holds down to Rc, where the ideal electron pressure and the degenerate electron pressure are the same:

ρ 5/3 kT = K (ρ/µe) µemA where K is just a constant. We further assume that there is no sudden jump in both density and temperature across the radius. Eliminating ρ between the above two equations, obtain

L/L −3 7 7/2 ≈ 9 × 10 (Tc/10 K ) M/M

Placing the above in Eq. 2 and then integrating it, we get

5/2 5/2 τcool ∝ (1/Tc − 1/Tc,0 )

For Tc Tc,0, we have

5/7 6 M/M τcool = 2.5 × 10 yr L/L

For example, about 2 × 109 yrs would be required for the luminosity of −4 a 1M WD to drop to 10 L . Afterward, the cooling can be accelerated by crystallization. The WD quickly becomes invisible. Neutron stars and black holes

What end-product a massive star produces probably depends on many factors (e.g., rotation, magnetic ﬁeld, etc.). But its initial mass and metallicity may play a major role:

Neutron stars are the stellar remnants of massive stars, with initial mass mostly in the range of ∼ 10 − 25M . The alternative stellar end-products of such massive stars are black holes.

A. Heger et al. 2003, ApJ, 591, 288 Why don’t neutrons decay in a neutron star?

Neutron stars

I The neutron degeneracy pressure balances the gravity. I Neutron stars, determined by the stellar evolution modeling, are generally in the mass range of ∼ 1.2 − 2.5M . I Observationally, the average mass of neutron stars in binary systems is of about 1.4M . A neutron star has a radius of ∼ 10 km, depending on the assumed exact equation of state, an issue of still much interest. The density is ∼ 3 × 1014 g cm−3, comparable to the nuclear matter density. Neutron stars

A newly born neutron star is expected to have fast rotation and strong magnetic ﬁeld. Such magnetized and fast rotating neutron stars explain the presence of pulsars.

The life time of a pulsar is typically on the order of 107 years, depending on the magnetic field, which determines the spin-down rate. The exact evolution of the magnetic field in a young neutron star is still very uncertain. But the magnetic field eventually decays. Accretion neutron stars

A “dead” neutron star may become “alive” again in a binary system. The star may accrete matter from its companion and can be observed as an X-ray binary.

I The accretion leads to the angular momentum transfer and the spin-up of the neutron star. I As a result, the neutron star may become a pulsar again, typically with a period of a few to a few tens of ms. I Because of the weakness of such an old neutron star, the spin rate is extremely stable and decreases very slowly. Outline

Final evolution stages of high-mass stars

Stellar end-products White dwarfs Neutron stars and black holes

Supernovae Core-collapsed SNe Pair-Instability Supernovae (PISNe) Type Ia SNe

Review Supernovae (SNe)

Basic types: I Type Ia: only metal lines; no hydrogen lines in its spectrum; observed in all kinds of galaxies and regions inside a galaxy; rather uniform light curves. I The spectra of Type II supernovae are dominated by H lines, while lines of Ca, O and Mg are also present. SNe II are nearly always found in recent massive star formation regions. I Type Ib,c: Type Ib SNe have strong He lines in their spectra, which are lacking in Type Ic SNe. Similar to SNe II, they are found in star-forming regions, and their late-time spectra are also similar to Type II. A subclass of very bright Type Ic supernovae, known as hypernovae, may be associated with gamma-ray bursts. More physically, Type II and Type Ib,c together are called “core-collapsed” SNe. Core-collapsed SNe Take the Fe core as an example. As the core collapses, instabilities occur: I Because of the high electron degeneracy of the gas, the temperature rises unrestrained. In time, it becomes sufﬁciently high for the photo-disintegration of iron nuclei: e.g.,

56 4 100MeV +26 Fe → 132He + 4n.

I The increase of the density forces the degenerate electrons to ever-higher momentum state - hence higher energy states, exceeding the neutron-proton mass difference. Eventually, free protons capture free electrons and turn into neutrons. I Not only does this process absorb energy, but it also reduces the number of particles. I The rapid energy loss from neutrinos further deprives the thermal pressure support. 9 −3 I The star contracting from a density of ∼ 10 g cm and ending up with a neutron star with a size of ∼ 10 km, in which the neutron degeneracy pressure could be sufﬁcient to stop the collapsing. A few observational characteristics of CC SNe: I They are related to Pop I stars. Evidence for the core collapse: pulsars and neutrinos (from SN1987A). I Eject more mass, but at slower speed than Ia SNe. I Slightly fainter. Light-curves are much less uniform. I Relatively easy to be picked up in radio and X-ray, usually at later times than the visible light peak.

Characteristics of CC SNe

The total gravitational energy release from the collapse is ∼ 3 × 1053 ergs, more than enough to dissolve all the synthesized nuclear materials ∼ 2 × 1052. But how a fraction of this energy may be used to drive the explosion is not clear. A few possibilities: 1) bouncing shock wave, 2) trapped neutrinos, and 3) jets. A few observational characteristics of CC SNe: I They are related to Pop I stars. Evidence for the core collapse: pulsars and neutrinos (from SN1987A). I Eject more mass, but at slower speed than Ia SNe. I Slightly fainter. Light-curves are much less uniform. I Relatively easy to be picked up in radio and X-ray, usually at later times than the visible light peak. SN1987A

First observed visually on Feb. 24, 1987 in the LMC. Kind of unique light-curve and intrinsically dimmer, compared with the “normal” Type II SNe. Progenitor: B3 I blue supergiant (16-20 M ).

The key evidence for the core collapse and the formation of a neutron star is the detection of the neutrinos about a quarter of a day before optical discovery. But the neutron star is so far not detected. The explosion leads to the synthesis of heavy elements in the ejecta, chieﬂy 56Ni, which decays into 56Co and then to 56Fe. These decays give the major energy source that keeps the expanding ejecta bright. The pair production decreases the distance that gamma rays travel in the gas, which leads to an instability: as gamma ray travel distance decreases, the temperature at the core increases, and this increases the generation of the nuclear energy and hence the gamma ray energy and further decreases the distance that gammas can travel. The consequence of the instability depends on the mass and metallicity of a star:

Pair-Instability Supernovae (PISNe)

The hotter a star’s core becomes, the higher energy the gamma rays it produces. When the mass of a star exceeds about 100M , the produced gamma rays become so energetic, their interaction with atomic nucleus can lead to the production of electron-position pairs. The pair production decreases the distance that gamma rays travel in the gas, which leads to an instability: as gamma ray travel distance decreases, the temperature at the core increases, and this increases the generation of the nuclear energy and hence the gamma ray energy and further decreases the distance that gammas can travel. Pair-Instability Supernovae (PISNe)

I For a star in the mass range of ∼ 100 − 130M , the instability most likely leads to partial collapse and pressure pulses. This process tends to eject parts of the outer layers of the star until it becomes light enough to collapse in a normal SN. I For a star in the mass range of ∼ 130 − 250M , the collapse caused by the pair instability proceeds to allow runaway oxygen and silicon burning of the star’s core, creating a thermonuclear explosion, or a “hypernova”, a term that used to refer an exceptionally energetic explosion with an inferred energy over 100 SNe. I A PISN may be distinguished from other SNe by its very long duration to peak brightness, together with its brightness due to the production of much more radioactive Ni. I The pair instability tends to happen in low metallicity stars (e.g., Pop III stars, resulting in weak stellar winds and large core masses), with low to moderate rotation rates. I In addition, stars formed by collision mergers having a metallicity Z between 0.02 and 0.001 may also end their lives as PISNe if their mass is in the appropriate range. I For a star in the mass range of & 250M , a different reaction mechanism, photo-disintegration, results after collapse. This endothermic reaction (energy-absorbing) causes the star to continue collapse into a black hole rather than exploding due to thermonuclear reactions. The Progenitor – SN Map

Red Type II-P SN 2003gd, SN 2004A, Supergiant SN 2005cs, SN 2008bk

Blue ? SN 1987A Supergiant SN 1987A (faint, slow)

LBV ? Type IIn (η Car) SN 2005gl (dense CSM) Late W-R Type IIL/IIb (WN) (little H) SN 1993J, SN 2008ax? Early W-R ? Type Ib (WC/WO) (H, He) ? Massive SN 2002ap, SN 2004gt, Type Ic (He) Binaries SN 2007gr (upper limits) GRB/XRF Based on Gal-Yam et al. 2007; updated http://www.weizmann.ac.il/home/galyam/progenitors.html The fuel must be degenerate at ignition, as in a “He-ﬂash”. I Where do we expect to ﬁnd this amount of carbon and oxygen? A WD. But a WD with mass smaller than the Chandrasekhar limiting mass will just sit and cool off for the age of the Universe.

Type Ia SNe

I The lack of hydrogens in the spectra of such SNe strongly indicates that they result from the collapse of “undressed” cores (e.g., due to strong stellar winds and/or by transferring to companions).

I Energy source of Ia SN: explosive fusion of close to 1 M carbon and oxygen to iron-peak elements, especially 56Ni. The formation of each 56Ni from Carbon generates ∼ 8 × 10−5 erg. 52 Thus 1 M would generate about 10 erg, with a pretty to spare for a SN. I What causes this explosive burning? A WD. But a WD with mass smaller than the Chandrasekhar limiting mass will just sit and cool off for the age of the Universe.

Type Ia SNe

I Energy source of Ia SN: explosive fusion of close to 1 M carbon and oxygen to iron-peak elements, especially 56Ni. The formation of each 56Ni from Carbon generates ∼ 8 × 10−5 erg. 52 Thus 1 M would generate about 10 erg, with a pretty to spare for a SN. I What causes this explosive burning? The fuel must be degenerate at ignition, as in a “He-ﬂash”. I Where do we expect to ﬁnd this amount of carbon and oxygen? Type Ia SNe

I Energy source of Ia SN: explosive fusion of close to 1 M carbon and oxygen to iron-peak elements, especially 56Ni. The formation of each 56Ni from Carbon generates ∼ 8 × 10−5 erg. 52 Thus 1 M would generate about 10 erg, with a pretty to spare for a SN. I What causes this explosive burning? The fuel must be degenerate at ignition, as in a “He-ﬂash”. I Where do we expect to ﬁnd this amount of carbon and oxygen? A WD. But a WD with mass smaller than the Chandrasekhar limiting mass will just sit and cool off for the age of the Universe. I Accretion (single-degenerate scenario):

I A natural process that leads to an explosion at the Chandrasekhar limit. I But, physically most of the accreted materials is fused to carbon and oxygen during nova and possibly ejected. So all these need to lead to the increase of the WD mass. I The accumulated X-ray emission from such accreting sources, as observed from nearby galaxies, seems to be far less than required by this scenario. I The missing of the running-away companion stars in Ia SN remnants also casts doubts on the the scenario.

Is a neutron star expected? Typically not. But a leftover WD is a possibility, if the explosion is only partial and off-center.

How to make a WD add mass?

I Merging two WDs (double degenerate scenario):

I accounting for the absence of hydrogen. I But there may not be enough of them with enough masses and tight enough to merge over the age of the Universe. I Also how could the explosion of a WD merger be a standard candle? Is a neutron star expected? Typically not. But a leftover WD is a possibility, if the explosion is only partial and off-center.

How to make a WD add mass?

I Merging two WDs (double degenerate scenario):

Is a neutron star expected? Typically not. But a leftover WD is a possibility, if the explosion is only partial and off-center. Outline

Final evolution stages of high-mass stars

Stellar end-products White dwarfs Neutron stars and black holes

Supernovae Core-collapsed SNe Pair-Instability Supernovae (PISNe) Type Ia SNe

Review Review

1. What is the internal energy source of a white dwarf that keeps it bright? Why is the interior close to be isothermal? 2. What are the main differences of the post-MS evolution of massive stars (≥ 10M ) from that of lower mass ones? 3. In an HR diagram, name the nuclear burning states along the evolutionary tracks for low and high mass stars, separately. 4. How do massive stars end their lives? Why do the cores eventually collapse? 5. How do neutron stars form? Why don’t the neutrons decay in neutron stars? 6. What are the key observational signatures that distinguish Type I and Type II supernovae? Why are Type Ib,c supernovae also believed to arise from the collapse of massive stars? 7. What is a pair-instability supernova? Why is it proposed to be related to Pop III stars? Review (cont.)

9. What is the energy source that keeps a supernova bright for ∼ 102 days or longer? 10. Why do most stars show absorption lines? What kinds of stars tend to have emission lines? 11. How might one estimate the rate of supernova explosions in a galaxy? 12. Can you roughly estimate the “waiting time” for a supernova explosion within, say, 50 light-years of the Sun?