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Ligo. What happened 1.3 billion years ago.



 
 
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  #1  
Old February 27th 16, 09:11 PM posted to sci.astro.research
Nicolaas Vroom
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Posts: 216
Default Ligo. What happened 1.3 billion years ago.

In Nature of 18 Februari 2016 at page 263 we read:
"Surprisingly Ligo's first detection dit not come from a binary neutron
star system etc but from two large BH's. Both were of the order of 30
times the mass of the Sun. 'They are real astronomical beast'."

My understanding is that BH's 30 times the size of the Sun are extremely
small.See: https://en.wikipedia.org/wiki/List_o..._massive_stars
See: https://en.wikipedia.org/wiki/List_o...ve_black_holes

At page 262 we read:
"Although the two BH's had probably been orbiting each other for
millions of years LIGO began to pick up their waves only when they
reached a a freq of 35 Hz. This frequency rapidly increased to 250 Hz."

This sentence gives the impression that binary systems in general
are stable configurations. So what happened.
Simulations I have performed give the impression that for a binary
system to merge generally speaking at least one object should increase
in mass. For example comets which collide with the Sun will decrease
the size of the solar system.
This brings me to my question: Are we sure that this is really
a binary system and is not a third object involved.
See for example:
http://users.telenet.be/nicvroom/VB%...0operation.htm
Starting point of simulation is a binary star system.
The standard configuration is that the masses are 1000, 1000 and 1.
When you change this configuration to 1000, 500 and 50 you can
investigate the influence the a relative large third object.
In such a simulation you can get a configuration with average
distance (radius) of 200 units, which changes in an elipse which
shortest distance of 100 units.

In the case of the BH you will get something like 36,29 and 3 Solar m.

In this particular case I assume that the third object is rather small
but it also could be a red giant which constantly transmit mass
to the binary BH system

Nicolaas Vroom
  #2  
Old February 28th 16, 08:28 AM posted to sci.astro.research
Phillip Helbig (undress to reply)[_2_]
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Posts: 273
Default Ligo. What happened 1.3 billion years ago.

In article , Nicolaas Vroom
writes:

In Nature of 18 Februari 2016 at page 263 we read:
"Surprisingly Ligo's first detection dit not come from a binary neutron
star system etc but from two large BH's. Both were of the order of 30
times the mass of the Sun. 'They are real astronomical beast'."

My understanding is that BH's 30 times the size of the Sun are extremely
small.See: https://en.wikipedia.org/wiki/List_o..._massive_stars
See: https://en.wikipedia.org/wiki/List_o...ve_black_holes


The term "beast" here means large in mass, not in radius.

At page 262 we read:
"Although the two BH's had probably been orbiting each other for
millions of years LIGO began to pick up their waves only when they
reached a a freq of 35 Hz. This frequency rapidly increased to 250 Hz."

This sentence gives the impression that binary systems in general
are stable configurations.


In general, yes, but they lose energy via gravitational waves.

So what happened.


Due to energy loss via gravitational waves, the orbits decayed until
they merged.

Simulations I have performed give the impression that for a binary
system to merge generally speaking at least one object should increase
in mass. For example comets which collide with the Sun will decrease
the size of the solar system.


Did you include energy loss via gravitational waves?

This brings me to my question: Are we sure that this is really
a binary system and is not a third object involved.


Calculations are done for two merging objects and the comparison with
observations is good. There is no hint of a third object.
  #3  
Old March 3rd 16, 08:44 AM posted to sci.astro.research
Nicolaas Vroom
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Posts: 216
Default Ligo. What happened 1.3 billion years ago.

Op zondag 28 februari 2016 08:28:43 UTC+1 schreef Phillip Helbig:


The term "beast" here means large in mass, not in radius.


IMO the BH in the center of the Milkey Way is a beast,
almight a small one compared with others.


At page 262 we read:
"Although the two BH's had probably been orbiting each other for
millions of years LIGO began to pick up their waves only when they
reached a a freq of 35 Hz. This frequency rapidly increased to 250 Hz."

This sentence gives the impression that binary systems in general
are stable configurations.


In general, yes, but they lose energy via gravitational waves.


Consider 3 different configurations:
1. A binary star system of 30 solar masses each.
2. A binary BH system of 30 solar masses each.
3. A one BH system of 60 solar masses.

Consider as part of each system a star of 1 solar mass which rotates
at a certain distance r from the Center of Gravity of each.
Is it true that the speed v and the revolution time in each
of these cases is identical?
That being the case do you agree that the loss in gravitational
energy in each case is the same?
Gravitational energy loss implying gravitons?

So what happened.


This brings me to my question: Are we sure that this is really
a binary system and is not a third object involved.


Calculations are done for two merging objects and the comparison with
observations is good. There is no hint of a third object.


When an ordinary large star approaches a Binary Black Hole system it will
evaporate (as a matter of saying). This process will increase
the mass of the two BH's which will start to merge.

Nicolaas Vroom
  #4  
Old March 5th 16, 10:32 AM posted to sci.astro.research
Jonathan Thornburg [remove -animal to reply][_3_]
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Posts: 137
Default Ligo. What happened 1.3 billion years ago.

Nicolaas Vroom wrote:
Consider 3 different configurations:
1. A binary star system of 30 solar masses each.
2. A binary BH system of 30 solar masses each.
3. A one BH system of 60 solar masses.


Let me first answer your questions for cases 1 and 2; here the issues
are quite clear-cut:
Is it true that the speed v and the revolution time in each
of these cases is identical?
That being the case do you agree that the loss in gravitational
energy in each case is the same?
Gravitational energy loss implying gravitons?


The speed v and the orbital period, and the rate of
gravitational-radiation emission, all depend on the distance between
the two bodies. If that distance is the same between cases 1 and 2,
then apart from tidal effects (which are only important for very
close-in binaries -- they fall off rapidly with orbital separation),
cases 1 and 2 will have identical orbital speeds, periods, and
gravitational-radiation emission.


Consider as part of each system a star of 1 solar mass which rotates
at a certain distance r from the Center of Gravity of each.


If the 1-solar-mass star orbits at a distance that is *not* very much
larger than the distance between the two 30-solar-mass objects (say,
in very round numbers, less than 1000 times the distance between the
two 30-solar-mass objects), then even in Newtonian gravity the 1-solar-mass
star will feel a different gravitational potential between cases 1/2
and 3, which will lead to slightly different long-term orbital evolution
of the 1-solar-mass star. See, for example,
https://en.wikipedia.org/wiki/Kozai_mechanism

But if the 1-solar-mass star orbits at a distance that is much larger
than the distance between the two 30-solar-mass objects, then there will
be relatively little difference in the 1-solar-mass-star's orbit between
cases 1/2 and 3. Again, cases 1 and 2 will be essentially identical, but
case 3 will differ a bit even at the Newtonian level.

Adding relativistic effects doesn't change this picture much.



This brings me to my question: Are we sure that this is really
a binary system and is not a third object involved.


By the customary standards of "proof" in astrophysics, yes, we're sure
that there is not a dynamically-significant 3rd object. That is, we
can model the system very nicely as a binary system, so Occham's razor
(actually Russell's teapot, https://en.wikipedia.org/wiki/Russell%27s_teapot)
argues against hypothesizing a 3rd undetectable object which doesn't
significantly influence the dynamics of the two detectable objects.



The basic binary-system analysis is pretty simple: The observed
gravitational-wave signal is sinusoidal, and it sweeps up ("chirps") in
frequency and amplitude simultaneously. It was first observed above the
detector noise at a frequency of around 35 Hz and ended at a frequency
of around 250 Hz (*not* limited by detector noise, i.e., if it had kept
on chirping up to still-higher frequencies it should have been detectable).
The frequency, frequency-chirp rate (i.e. d frequency/d time), and
amplitude increase rate (i.e., d amplitude/d time) are all measurable.
And they agree exactly with what general relativity predicts for the
decay of a close binary system (in this phase of the analysis, it
doesn't matter whether the objects are black holes or something else),
and there is no other known source which produces such a signal.

For this sort of binary system the gravitational-wave signal is *twice*
the orbital frequency (there are two complete gravitational-wave cycles
per orbit), so the orbital frequency is around 17.5 Hz when the system
is first observed, chirping up to around 125 Hz. Assuming that the
bodies can't orbit faster than the speed of light, an orbital frequency
of 125 orbits/second limits the radius of the orbit to no more than
about 380 km.

From the overall amplitude of the gravitational-wave signal we know
the total mass of the system (a bit over 60 solar masses). So... what
sorts of objects which can have a total mass of 60 solar masses and
which can get to within 400 km of each other *without* physically
colliding (which would lead to quite different gravitational-wave
signals that what are observed)? The answer is that the only known
objects which could do this are black holes. [Neutron stars are also
be compact enough to get within 400 km without colliding... but neutron
stars can't exceed about 3 solar masses ("the Chandresekhar limit").]

The "icing on the cake" is that after the gravitational-wave signal
peaks in amplitude, it rises sharply in frequency and decays rapidly
(exponentially) in amplitude. This is (to within the -- sadly rather
large -- experimental errors) precisely the pattern you would expect
from a black hole which has just formed from a black-hole collision,
i.e., a black hole which is not in its equilibrium shape: the newly
formed (deformed) black hole "rings down" and settles into its
equilibrium shape, and these "ringdown" oscillations have specific
frequencies and decay rates. The observed frequency and decay rate
of the final part of the observed gravitational-wave signal nicely
match (to within those error bars I mentioned) the calculated frequency
and decay rate of a distorted black hole ringing down to an equilibrium
state (described by the Kerr metric).

From that final "ringdown" signal we can estimate the mass of the
final black hole (the ringdown frequencies scale as 1/mass), and this
mass comes out to be significantly *less* than the sum of the two
inspiraling black holes -- a bit over 3 solar masses less, in fact.
That's just what you'd expect from merging black holes -- that 3 solar
masses corresponds to just the expected-from-general-relativity energy
radiated in gravitational waves from a black hole collision of this
type.

So overall, this is a pretty well-constrained system, and a model based
purely on general relativity + the known detector noise spectrum fits
the signal beautifully.



Of course, it could be that some other system -- one for which noone
has yet done a detailed (relativistic-gravity) simulation -- would fit
the data equally well. Until these alternatives are simulated in detail
(which probably takes years of research, plus large supercomputer
simulations), we won't know.

What is clear is that this system was observed at a fairly modest
signal-to-noise ratio, and that the observations lasted for only a
short time ( 1 second). Longer and/or higher-signal-to-noise-ratio
observations would (will) allow more stringent tests of whether general
relativity alone (still) suffices to accurately model the observed
signals.



Finally, if you're interested in the details of how the LIGO data is
analyzed (the various steps that lie between the raw detector data and
the curves you see in the published papers), I second Steve Willner's
recommendation

There's a tutorial on LIGO data processing at
https://losc.ligo.org/s/events/GW150..._tutorial.html


From a quick look it seems to be an excellent tutorial.

--
-- "Jonathan Thornburg [remove -animal to reply]"
Dept of Astronomy & IUCSS, Indiana University, Bloomington, Indiana, USA
currently visiting colleagues in Europe (at one of the institutions
closely involved in the LIGO data analysis, in fact)
"There was of course no way of knowing whether you were being watched
at any given moment. How often, or on what system, the Thought Police
plugged in on any individual wire was guesswork. It was even conceivable
that they watched everybody all the time." -- George Orwell, "1984"
  #5  
Old March 5th 16, 10:34 AM posted to sci.astro.research
Jonathan Thornburg [remove -animal to reply][_3_]
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Posts: 137
Default Ligo. What happened 1.3 billion years ago.

Nicolaas Vroom asked:
This brings me to my question: Are we sure that this is really
a binary system and is not a third object involved.


I replied:
By the customary standards of "proof" in astrophysics, yes, we're sure
that there is not a dynamically-significant 3rd object. [[...]]

The basic binary-system analysis is pretty simple: The observed
gravitational-wave signal is sinusoidal, and it sweeps up ("chirps") in
frequency and amplitude simultaneously. [[...]]
The frequency, frequency-chirp rate (i.e. d frequency/d time), and
amplitude increase rate (i.e., d amplitude/d time) are all measurable.
And they agree exactly with what general relativity predicts for the
decay of a close binary system [[...]]
and there is no other known source which produces such a signal.


Overall, I'd say the case that this is a binary-something-or-other
decay/merger is very very strong -- the "chirp" signal is very
characteristic of such a system, and I can't think of (and don't
recall ever seeing a published proposal for) any other way to get
such a "chirp".

The case that the two pre-merger objects were (already) both black
holes is somewhat less strong. The data rule out any extended bodies
(they would physically collide much earlier than black holes), but if
you imagine some sort of exotic object (gravastar, boson star, etc etc)
it *might* be possible to fit the data adequately (i.e., to within the
finite signal/noise available).

The case that the post-merger object is a black hole is also moderately
strong. The data are consistent with the "ringing" of a black hole
as it relaxes to an equilibrium state, but the signal/noise of this
part of the data is modest. The challenge for any alternative hypothesis
would be to (quantitative) match the observed frequency and decay rate
of the ringing (which do nicely match those predicted for a black hole).

Overall, as astrophysics observations go, this is pretty watertight.
But of course, observations of more systems and/or observations with
higher signal/noise will more tightly constrain our models.

--
-- "Jonathan Thornburg [remove -animal to reply]"
Dept of Astronomy & IUCSS, Indiana University, Bloomington, Indiana, USA
"There was of course no way of knowing whether you were being watched
at any given moment. How often, or on what system, the Thought Police
plugged in on any individual wire was guesswork. It was even conceivable
that they watched everybody all the time." -- George Orwell, "1984"
  #6  
Old March 7th 16, 10:19 PM posted to sci.astro.research
Jonathan Thornburg [remove -animal to reply][_3_]
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Posts: 137
Default Ligo. What happened 1.3 billion years ago.

Nicolaas Vroom asked:
This brings me to my question: Are we sure that this is really
a binary system and is not a third object involved.


I replied:
By the customary standards of "proof" in astrophysics, yes, we're sure
that there is not a dynamically-significant 3rd object. That is, we
can model the system very nicely as a binary system, so Occham's razor
(actually Russell's teapot, https://en.wikipedia.org/wiki/Russell%27s_teapot)
argues against hypothesizing a 3rd undetectable object which doesn't
significantly influence the dynamics of the two detectable objects.


I should also add that we can only rule out a 3rd object if (roughly
speaking) that 3rd object is massive and close to the binary. If the
3rd object is low-mass enough and/or far enough away from the binary,
its effect wouldn't be detectable.

For *this* system (GW150914), and for almost any other system observed
by a ground-based gravitational-wave detector, our bounds on a possible
3rd object will be very poor, because (roughly speaking) these bounds
scale as the square of the observation time, and for this system the
observation time is very short ( 0.1 seconds).

However, for inspirals observed over multi-year timescales by (future)
pulsar-timing-array or space-based gravitational-wave detectors,
interesting observations of, or constrinats on, supermassive
"3rd-object" black holes are possible. Yunes, Miller, and I analysed
this case a few years ago:

Yunes, Miller, and Thornburg
Phys. Rev. D 83, 044030 (2011)
DOI: 10.1103/PhysRevD.83.044030
arXiv:1010.1721
Abstract:
Extreme mass ratio inspirals, in which a stellar-mass object merges
with a supermassive black hole, are prime sources for space-based
gravitational wave detectors because they will facilitate tests of
strong gravity and probe the spacetime around rotating compact
objects. In the last few years of such inspirals, the total phase
is in the millions of radians and details of the waveforms are
sensitive to small perturbations. We show that one potentially
detectable perturbation is the presence of a second supermassive
black hole within a few tenths of a parsec. The acceleration produced
by the perturber on the extreme mass-ratio system produces a steady
drift that causes the waveform to deviate systematically from that
of an isolated system. If the perturber is a few tenths of a parsec
from the extreme-mass ratio system (plausible in as many as a few
percent of cases) higher derivatives of motion might also be
detectable. In that case, the mass and distance of the perturber
can be derived independently, which would allow a new probe of
merger dynamics.

--
-- "Jonathan Thornburg [remove -animal to reply]"
Dept of Astronomy & IUCSS, Indiana University, Bloomington, Indiana, USA
"There was of course no way of knowing whether you were being watched
at any given moment. How often, or on what system, the Thought Police
plugged in on any individual wire was guesswork. It was even conceivable
that they watched everybody all the time." -- George Orwell, "1984"
  #7  
Old March 8th 16, 09:18 AM posted to sci.astro.research
Steve Willner
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Posts: 1,172
Default Ligo. What happened 1.3 billion years ago.

In article ,
"Jonathan Thornburg [remove -animal to reply]"
writes:
From the overall amplitude of the gravitational-wave signal we know
the total mass of the system (a bit over 60 solar masses).


How is that possible without knowing the distance? I thought the
masses came from detailed fitting to the waveform, but I am no expert
in this business.

--
Help keep our newsgroup healthy; please don't feed the trolls.
Steve Willner Phone 617-495-7123
Cambridge, MA 02138 USA
  #8  
Old March 8th 16, 04:20 PM posted to sci.astro.research,sci.physics.research
Jonathan Thornburg [remove -animal to reply][_3_]
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Posts: 137
Default Ligo. What happened 1.3 billion years ago.

I wrote:
From the overall amplitude of the gravitational-wave signal we know
the total mass of the system (a bit over 60 solar masses).


Steve Willner asked:
How is that possible without knowing the distance? I thought the
masses came from detailed fitting to the waveform, but I am no expert
in this business.


In fact, fitting the waveform gives both the masses *and* the distance
(and the orbital inclination too)!

I think this was first realised by

@article{Schutz-1986,
author = "Bernard F. Schutz",
title = "Determining the {H}ubble constant
from gravitational wave observations",
journal = "Nature",
year = 1986, month = "September 25",
volume = 323, pages = "310--311",
doi = "10.1038/323310a0",
ADScite = "http://adsabs.harvard.edu/abs/1986Natur.323..310S",
}

The basic idea is pretty simple:

Suppose we have a "compact" binary system, i.e., one where the two bodies
can be approximated as point masses (i.e., tidal effects are negligible).
In practice, this is an excellent approximation for black holes or neutron
stars until shortly before the actual merger. And let's also assume that
the binary orbit is roughly circular (we expect gravitational wave
emission to damp out any significant eccentricity well before the system
is observable by LIGO et al, so this is a reasonable assumption).

The observed gravitational-wave (GW) signal is a "chirp", a sinusoid
which sweeps up in frequency and amplitude as the binary spirals closer
together. To lowest post-Newtonian order, the "chirp rate"
$\dot{f} := df/dt$
(where $f$ is the instantaneous GW frequency) turns out to depend on
the binary masses $m_1$ and $m_2$ only through a particular combination,
known as the "chirp mass",
$\mathcal{M} := (m_1 m_2)^{3/5} / (m_1 + m_2)^{1/5}$.
So, measuring $f$ and $\dot{f}$ (which -- apart from cosmological
redshifts -- can be done without knowing the source's distance) suffices
to determine the chirp mass.

[The orbital inclination can be determined from the
linear-vs-circular polarization of the GW signal; a
more detailed analysis is needed to get the individual
masses $m_1$ and $m_2$.]

But -- and this is the remarkable part -- it turns out that the total
GW "absolute magnitude" (signal amplitude at some fidicual frequency as
measured at some fiducial luminosity distance) depends on $m_1$ and $m_2$
only through that *same* combination, the chirp mass. So knowing the
chirp mass lets us calculate the GW "absolute magnitude".

In other words, compact-binary GW signals are "standard candles" in the
usual astronomical sense. (We often say "standard sirens" because (for
ground-based detectors like LIGO) the frequencies involved are in the
audio band.)

Combining this with the observed signal amplitude then lets us calculate
the (luminosity) distance to the source, in the usual astronomical way.

[Note that GW detectors measure signal *amplitude*, not
power, so there's a 1/r falloff with luminosity distance,
not a 1/r^2. This is good because it means a fractor-of-10
reduction in detector noise gives a factor-of-10 increase
in the maximum distance at which a given source can be
detected, i.e., and factor-of-1000 increase in the volume
of space within which we can detect such sources.

This (a factor of 10 reduction in detector noise) is roughly
the improvement between the initial LIGO/Virgo detectors and
their current "advanced" versions.]

--
-- "Jonathan Thornburg [remove -animal to reply]"
Dept of Astronomy & IUCSS, Indiana University, Bloomington, Indiana, USA
"There was of course no way of knowing whether you were being watched
at any given moment. How often, or on what system, the Thought Police
plugged in on any individual wire was guesswork. It was even conceivable
that they watched everybody all the time." -- George Orwell, "1984"
  #9  
Old March 10th 16, 09:33 AM posted to sci.astro.research
Nicolaas Vroom
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Posts: 216
Default Ligo. What happened 1.3 billion years ago.

Op zaterdag 5 maart 2016 10:32:33 UTC+1 schreef Jonathan Thornburg:
Nicolaas Vroom wrote:
Consider 3 different configurations:
1. A binary star system of 30 solar masses each.
2. A binary BH system of 30 solar masses each.
3. A one BH system of 60 solar masses.



But if the 1-solar-mass star orbits at a distance that is much larger
than the distance between the two 30-solar-mass objects, then there will
be relatively little difference in the 1-solar-mass-star's orbit between
cases 1/2 and 3. Again, cases 1 and 2 will be essentially identical, but
case 3 will differ a bit even at the Newtonian level.


Thanks for all your time and efforts
There exists also a fourth case: a one star system of 60 solar masses.
What you are saying if the 1-solar-mass object is at a far enough
distance it is very difficult to distinquish between the 4 cases.
The issue is how you distinquish between 3 and 4. (one BH versus 1 star)

To study what the influence of a third object could be I have written
a program in VB 5.0.
See http://users.telenet.be/nicvroom/VB%...0operation.htm
In this program (Newton's Law) I make a difference between three cases:
1 BH and a light ray, 2 BH's and 3 BH's.
With 3 BH's I mean: a binary BH system and a third large star.
The idea behind the simulation is that the 2 BH's revolve around each
other and that the initial angle varies. BH#3 always enters from the right.

What the url shows are the results of 36 simulations with the mass
of BH #3 resp 5 and 10 solar masses.
The idea behind the simulation is that when the speed of BH#3 becomes
larger than 300000 km/sec the BH "evaporates" and slowly merges with
either BH1 or BH2.
The result will be that the two BH will start to spiral together.
But in none of these cases the 2 BH's will also merge.

When you use mass of BH3 = 12 and Phi = 40 the speed of BH2
will increase also above 300000 km/sec implying more or less
the same as what LIGO has detected.
The frequency change is from 33 to 88 Hz.
Unfortunate the url does not work well on a ipad.

Nicolaas Vroom
  #10  
Old April 20th 16, 04:26 AM posted to sci.astro.research
Nicolaas Vroom
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Posts: 216
Default Ligo. What happened 1.3 billion years ago.

Op donderdag 10 maart 2016 09:33:32 UTC+1 schreef Nicolaas Vroom:
Op zaterdag 5 maart 2016 10:32:33 UTC+1 schreef Jonathan Thornburg:
Nicolaas Vroom wrote:
Consider 3 different configurations:
1. A binary star system of 30 solar masses each.
2. A binary BH system of 30 solar masses each.
3. A one BH system of 60 solar masses.



The following is an interesting article:
https://astronomynow.com/2016/03/11/...ve-black-hole/
"Clocking the rotation rate of a supermassive black hole"
The article discusses a Binary Blackhole system of two large BH's
The primary BH is 18 billion sm. The second a mere 150 million sm.
(Also see Scientific American May 2016:
"the orbital period is getting shorter because the the system is
losing energy as it emits gravitational waves")
The articles are interesting because the primary BH also contains
a massive accretion disc. The secondary BH goes through
this accretion disc at intervals of 12 years.
My understanding is that as a result of this passing through
the secondary BH will increase in mass and thereby comming
closer to the primary BH. The final result will be that the two
could merge.
The accretion disc of the primary BH is also interesting
because be this could be left overs of previous encounters
with stars or small BH's which collided with the primary BH.
These collisions will increase the mass of the primary BH
which can also be a reason why the secondary BH closely
approaches the primary BH.

Nicolaas Vroom
 




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