KITP: neutron stars in globulars

Phil tutors us today on neutron star formation and retention in globulars.

So we expect neutron stars to be made in globular clusters.
Massive metal poor stars should undergo supernovae and make neutron stars for a mass range of ~ 8-15-or-20 solar masses, maybe more or less, and depending a little bit on whether they are in a tight binary.

More massive stars may, or may not, make stellar mass black holes. But we are not here to talk about black holes, at least not this part of this morning.

So, when type II supernovae go bang (and we're not totally sure yet of the details of how that works, embarrassingly enough, yet there they are...), a lot of energy is released, like about 10⁴⁴ J (yes, Joules, this is an Institute of Therotical Physics, dammit).

So they live fast, die young and leave behind a beautiful degenerate remnant.
An iron core with a baryon mass of ~ 1.55 - 1.65 solar masses.
Core collapse releases most of the binding energy in neutrinos, but if you intercept ~ 1% of the neutrinos in the inner fall back material, then you can drive a reverse shock and blow up the star. Except it is hard to get to work in detail, neutrinos are kinda slippery; so maybe it is (very high) magnetic fields and (very high) rotation etc and so forth.
Or we're missing out on some physics.

Some, (most? all?) type II supernovae are asymmetric, so there is an asymmetric outward momentum flux, and the remnant core "squirts out" (technical term) with a speed of order 200-300 km/sec - with a tail to higher velocities, but maybe not so many with much lower velocities.
The squirted out bit is the neutron star, the ~ 10 km radius superdense core collapsed until it is supported by neutron degeneracy pressure, with a mean density about that of nuclear density. The net gravitational mass is 10-20% lower than the original baryonic mass, due to release of binding energy, the exact difference depends on what the equation of state of matter is at densities higher than nuclear - whether it is "soft" or "hard".
The most soft of the soft postulated equations of state are probably ruled out by data already.

We expect to make few thousand +/- neutron stars in a typical globular, but since escape speeds for even young globulars are tens of km/sec, we conclude most, if not all, the neutron stars escape ballistically at formation...

Yet some globulars have shitloads (technical term) of pulsars.
Consistent with maybe 10-15% of all the neutron stars formed being retained.
Hmmm.

So, either some neutron stars have low natal velocities;
or, some are tied into binaries such that the companions can keep them in the cluster - which pretty much requires companions massive enough to soak up the delta v but not so massive that they will make neutron stars, so like 5-8 solar mass stars, maybe;
or, we make some neutron stars some other way, like through accretion induced collapseelectron capture supernovae! (video, podcast, slides - from '07 KITP SNe meeting)
or, read Nomoto's original paper

e^--capture SNe are kinda interesting, as single stars they seem to maybe occur for 8-10 solar mass stars (of what Z we wonder) with 2-2.5 solar mass He cores.
These are O/Ne/Mg core burning, and there is e^- capture onto Ne20 and Mg24 which leads to drastic loss of pressure support and the core collapses suddenly, driving a fast supernova.
We are relatively sure that these actually work, theoretically, even given the vagaries of high temperature, high pressure 3D hydrodynamic codes with radiation transfer, neutrino transport and full nuclear reaction networks.
The explosion time scale is short, so there is reason to believe non-axisymmetric instabiities don't have time to develop, so explosion is quite symmetric, so these neutron stars may have natal kicks with characteristic speeds <~ 50-100 km/sec
Which gives them reasonable probabiltiies of leaving pulsars in globulars in significant numbers.

But... for single stars, there is a problem, namely second dredge up!
Yes, we finally got there. Will we make it for first dredge up before the workshop ends...

second dredge up for intermediate mass stars mixed core material up into the envelope, so leaves too little mass for ECS SNe - core mass is to small and star fizzles to ONeMg white dwarf, a little bit higher mass you are too hot, no 2nd dredge up and you burn all the way to iron

So... how to you avoid second dredge up?
You remove the AGB envelope, at just the right time, and then there can be no dredge up, merely naked He core...

Hoffman et al 2008

Those would be kinda interesting, we may have seen such systems in the field, and they might plausibly have low δ v
Maybe

the gory details from ORNL (click to embiggen)

can you do it also with CO-CO WD merger?
Maybe, but then how do you make type Ia SNe?

'course there could be other channels for Ia...

Needs to be sorted.

What about black holes?
Yer vanilla stellar black hole ought not to have natal kicks.
But, some do... or, rather Nova Sco does.
So Nova Sco, and one or two others (like XTEJ1118), have high spatial momenta (relative to
the local standard of rest), consistent with similar change in momentum you see for normal
neutron stars.

So maybe Nova Sco is a delayed black hole formation system, possibly a hypernova,
so the neutrinos got out, maybe a GRB, but then a black hole formed after the SNe but
already moving ballistically.

I am rather fond of this scenario

Cole says - what about gravitational radiation from lumpy fallback?
Good question...
Maybe essential answer is in Colpi & Wasserman.

Oh, and binarity and metallicity also matter, a lot, but the general concept is
robust to changes in f_b and Z, just the detailed numbers matter.