Above you see a graphic which presents the main phases of the typical
evolution of a binary systems which leads to the formation of Extreme
Ultraluminous X-ray Source.

We start on ZAMS. These acronym stands for Zero Age Main Sequence. Speaking
shortly, this means the beginning of the thermonuclear reactions in the
stellar core. The ZAMS is the time in which the star produces its first light.
The mass and matter composition on ZAMS, in absence of interactions with other
objects, totally determines the further evolution of the star.

In our case on ZAMS we have two massive stars. One is 33 times heavier than
Sun and the second "just" 11 times. 'a' stands for semi-major axis (i.e., mean
distance between stars), which is quite moderate: 5500 solar radii (nearly the
distance from Sun to Neptune). 'e', on the other hand, is the eccentricity,
which describes how strongly the orbit is ellipsoidal (e=0 is equivalent to
circular orbit). Value e=0.56 means that the orbit is highly ellipsoidal and
the stars during one orbital period approach and move away from one another
significantly changing the separation.

The heavier star in a binary is usually called the 'primary'. The heavier the
star, the faster it evolves. Primary quickly burns out all the Hydrogen (the
thermonuclear fuel), in its core, and starts to expand. Meanwhile its core
shrinks and worms up. At some point the temperature becomes high enough to
start the synthesis of helium. The phase is called Core Helium Burning (CHeB).
The continuous expansion leads to the situation in which the envelope of the
primary starts to engulf the secondary. We reach the Common Envelope (CE)
phase after 5.5 million years of evolution.

Common envelope is a highly important phase in the evolution of binaries,
because it is responsible for shrinking of the orbit, which allows for
interaction between stars. In our case it decreases the semi-major axis 100
times. After CE the primary is just the naked core composed mainly by elements
heavier then hydrogen, because its envelope was repelled from the system.
Afterwards, it quickly evolves to supernova explosion (SN).

Supernova (pl. supernovae) is second most important step on our way. The
massive evolved star ejects its outer layers in a very energetic way. The
release of energy is comparable with the luminosity of the whole galaxy. It
lefts the compact remnant (a neutron star (NS) or a black hole (BH)) or
possibly can destroy the star completely. In our case the BH is formed. The
orbit is slightly altered due to explosion but the companion is nearly
unaffected.

If not the secondary, the BH will be the final step in the life of primary.
However, it is not in our case. The second star evolves slower and comes on
the stage several million years after the primary's SN. It runs out of
hydrogen and starts to expand. This phases is called Hertzsprung Gap (HG). It
is very short and is characterised by a very dynamic expansion of outer
layers, which become only slightly bound with the central parts of the star.

At some point the gravitation of the BH will overcome the gravitation of the
HG star and the matter will start to fall on the compact star. We will obtain
the mass transfer between the stars. Due to the fact that the black hole is a
very small object (about several kilometres in diameter) and the infalling
matter possesses a significant amount of angular momentum, an accretion disk
(AD) forms around the BH.

In the AD happens the most important phenomena for our case. Due to the
viscosity of matter, the kinetic energy is transformed to thermal energy. Gas
warms up and approaches the BH. Near the centre of the disk the temperature
reaches millions of Kelvins and is therefore a source of X-ray radiation. We
obtain the X-ray Binary.

In EULXs the mass transfer rate is so strong that the amount of X-ray
radiation exceeds predictions of all hitherto used model. Nevertheless, the
phase is very short (10,000 yr) in the comparison with the stellar evolution
scales. However, our results showed, that the models are not in contradiction
with observations and we are able to explain what we see.

---

Grzegorz Wiktorowicz
National Astronomical Observatories,
Chinese Academy of Sciences

Thank you for your explanation Grzegorz. If I understood it well, models shows that, IMBHs are not needed to create so bright sources. It also seems that in case of NS brightness can be even higher, but they will last a very short time (on a cosmic scale), which may hinder observation of such objects. I also have question, what exactly are the times in the charts 3 and 4? Is this the age of the galaxy model, the age of the system, or the time since ZAMS?

P.S. Is it possible that predicted difference, about factor of 10 (NS: ~10^44 vs. BH: ~10^43), in maximum luminosity between systems with NS in relation to systems with BH, is a consequence of that most of the energy is absorbed by the BH?

You are right Sebastian. We showed that regular compact objects are adequate to obtain EULXs and we do not need to introduce IMBH, which are still hypothetical objects.

The times on this chart are the time since ZAMS or the age of the system, which we defined to be the same. The ZAMS is the moment when the object starts to fulfil the definition of the star, so it is a best place to be marked as zero age.

As far as this difference in maximum luminosity is concerned, there appeared a small confusion. These are only typical(!) routes and it is not obvious if the inferred characteristics apply to the whole population of objects. For example BH accretors acquire higher luminosities in spite of the fact that comparing typical systems we may come up with different conclusion. On the other hand, you are right that BHs have lower mass-to-energy conversion efficiency due to the lack of solid surface.

---

Grzegorz Wiktorowicz
National Astronomical Observatories,
Chinese Academy of Sciences

Thank you Grzegorz!

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"I should bring one important point to the attention of the authors and that is, the world is not the United States..."

Above you may find the schematic evolution of a binary system leading to the
formation of Extreme Ultraluminous X-ray sources (EULX) with neutron star (NS)
accretors. I assume that you have read the post about BH EULX. A lot of
definitions and processes are similar, so I tried to avoid the repetitions
except if they are practical.

We start with far lighter stars than in the case of BH EULX. The primary on
ZAMS is 10 times larger than the Sun whereas the secondary is 5.6 times
larger. The semi-major axis is also smaller in this case. The only similarity
is the significant eccentricity of the orbit.

Lighter stars evolve slower. The primary runs out of hydrogen in the core
after about 24 million years. It expands and the matter from its outer layers
becomes unbound and falls on the secondary. We acquire the mass transfer. Due
to the tidal interactions the orbit becomes circular (e=0) and therefore
smaller, but the loss of mass leads to orbit expansion. Parallelly, masses of
the stars change strongly.

The primary, which is now only 2 times the mass of the Sun, becomes the
subject of a very specific type of supernova explosion, the so called
Electron-Capture Supernova (ECS). The outcome is the NS with a mass of 1.26
solar masses (very typical mass for NS).

Neutron stars, in contrast to BH, born with a significant natal kick. This
means that they obtain additional velocity due to the asymmetry of the SN
explosion. This results in a slight distortion of the orbit.

Just like in the case of BH, in absence of a companion, a neutron star will
not change. However, evolving companion starts to expand (due to the lack of
thermonuclear fuel), enters the Giant Branch phase (more long lasting and
stable phase than HG which it proceeds) and engulf the NS with its envelope.
We acquire the Common Envelope (CE) phase which strongly shortens the
separation between stars and lowers the mass of the secondary.

Afterwards we are left with an unaffected NS and a companion which is
consisted of helium and heavier elements. The secondary commences the helium
burning in its core in thermonuclear reactions producing carbon. However,
after a few million years, the star runs out of this fuel also and, just like
in the case of hydrogen, starts to expand. The phase is known as Helium
Hertzsprung Gap (HeHG).

In the end, the mass transfer starts due to the strong gravitational field of
NS which strips the outer layers from the secondary star. Just like in the
case of the BH, NS is very small, whereas the infalling gas possesses a lot of
angular momentum. Therefore, the accretion disk (AD) forms, which is the
source of X-ray radiation. Such a stellar configuration provides an extremely
large mass transfer rate, but on a very short timescale (~100 years). Such a
situation may occur in a large number of systems, thus we are able to observe
them.

---

Grzegorz Wiktorowicz
National Astronomical Observatories,
Chinese Academy of Sciences

This was excellent. Thank you very much. I enjoyed reading through the life cycles of these binary systems and I'm now much more knowledgeable. :-)