Question regarding the future of galaxies within a group of clusters

[Buzz Bloom]

TL;DR

In today's APOD,
https://apod.nasa.gov/apod/ap200515.html
two galaxies are shown. The accompanying text says:
These two galaxies are far far away, 12 million light-years distant toward the northern constellation of the Great Bear.
. . .
In the next few billion years, their continuing gravitational encounters will result in a merger, and a single galaxy will remain.

My question is below in the main text of this post.

Given that the galaxies within a cluster of galaxies are generally gravitationally bound, and not affected by the expanding universe, would it not also be expected that after some large number of billions of years, all of the individual galaxies would merge together to become one single very large galaxy? If this is so, is there a way to approximately calculate how long it would take?

See https://en.wikipedia.org/wiki/Galaxy_cluster .

 

[phyzguy]

Not necessarily. Jupiter and the sun are gravitationally bound, but we don't expect them to merge, even many billions of years from now.

 

[Buzz Bloom]

Jupiter and the sun are gravitationally bound, but we don't expect them to merge, even many billions of years from now.

Hi phyz:

My question was specifically about galaxies merging.

Regarding Jupiter and the sun, eventually all planets fall into their sun due to the loss of orbital energy from the the effect of gravitational waves being generated from the planet. I have seen this discussed several places, but the only convenient reference I have handy is:

https://en.wikipedia.org/wiki/Gravitational_wave .​

Sources:​

Two objects orbiting each other, as a planet would orbit the Sun, will radiate.​

Binaries:​

Gravitational waves carry energy away from their sources and, in the case of orbiting bodies, this is associated with an in-spiral or decrease in orbit.​

Regards,
Buzz

 

[phyzguy]

You're right of course. I suggest you try calculating how long it will take for Jupiter to spiral into the sun due to the emission of gravitational waves.

 

[Buzz Bloom]

Hi phyz:

As I remember it, an equation for calculating the time for a planetary orbit to decay from gravitational waves is well known, and somewhere in my random notes, I have that information, but it will take some time for me to find it.

The phenomena of galaxy merging has an entirely different cause. As I remember it (possibly incorrectly), some orbital energy between two galaxies is converted to heat as the galactic material interacts during a passage in which some of the contents of one galaxy interacts (chemically and electro-dynamically) directly with the contents of the other galaxy.

ADDED

I found something relevant regarding gravitational waves.

https://www.physicsforums.com/threads/qs-re-gravitational-waves.918313​

Post #29 from @PAllen.​

The following link covers orbital decay from GW. As an exercise, they compute that Earth would spiral into the sun in 10²³ years, only 10 trillion times the current age of the universe.​

http://www.tapir.caltech.edu/~chirata/ph236/2011-12/lec15.pdf​

You will want to took at Equation 44 on page 5.

Regards,
Buzz

 

[stefan r]

You're right of course. I suggest you try calculating how long it will take for Jupiter to spiral into the sun due to the emission of gravitational waves.

Stellar mass objects should pass between Jupiter and the Sun much sooner. Tidal effect should increase Jupiter's orbit until rotation slows. The Sun losing mass will also increase Jupiter's orbit.

Wikipedia says 10¹⁵ years for planets to be ejected or dropped in from orbit. Similarly 10²⁰ years for 90+% of stars to be ejected from the galaxy.

I would like the number though. How long would it take for a Jupiter mass black hole orbiting a solar mass black hole?

 

[Buzz Bloom]

I would like the number though. How long would it take for a Jupiter mass black hole orbiting a solar mass black hole?

Hi stefan:

I have done the math, and Equation 45 (page 6) appears in the reference to have reasonable hints about constants, unlike Equation 44. I present (with some simplifying edits) Equation 45 below.

t_GW = 3.3x10¹⁷ yr x a⁴ / (M_sun x M_earth x (M_sun+M_earth))​

t_GW is the time in years it will take for the Earth to fall into the sun.​

a is the distance between the Sun and Earth in AU units.​

the M variables are in Solar masses.​

The result is given as

t_GW = 10²³ yrs​

with a = 1, M_sun = 1, and M_earth = 3x10^-6.​

To calculate for Jupiter instead of Earth, the numerator value becomes the current distance between Jupiter and the Sun raised to the 4th power. The denominator will increase approximately by the ratio of Jupiter's mass to the Earth's mass.

​

Using the following approximations

(a_jupiter)⁴ = 5.2⁴ = 731​

M_jupiter / M_earth = 218​

I get for Jupiter,

t_GW = 3.4 x 10²³ yrs.​

So the difference between the time to fall into the sun for Jupiter is only 3.4 times that of the time for the Earth. Omitted from the calculations is the factor

M_sun+M_earth​

because a planet's mass is so much smaller than the sun's mass.

Regards,
Buzz

 

[phyzguy]

@Buzz Bloom OK, thanks. So you see that for an orbit like Jupiter and the sun, the time for the orbit to decay due to gravitational waves is hugely longer than the current age of the universe, which is about 10^10 years. You're right that galaxy orbits can decay much faster due to energy loss due to interaction between the gas streams of the two galaxies. But this requires that the two galaxies are close enough for their gas streams or dark matter halos to to interact. The point of my post was to show that your statement in the OP:

would it not also be expected that after some large number of billions of years, all of the individual galaxies would merge together to become one single very large galaxy?

is not to always to be expected. Two galaxies in a cluster that are orbiting at a large distance will happily continue orbiting for a very long time, and will not be expected to merge unless something changes, like a third galaxy coming in and colliding with them

 

[snorkack]

is not to always to be expected. Two galaxies in a cluster that are orbiting at a large distance will happily continue orbiting for a very long time, and will not be expected to merge unless something changes, like a third galaxy coming in and colliding with them

Each galaxy by itself will be slowly evaporating stars.
How is the internal dynamics of a galaxy affected by tidal forces from a nearby galaxy that orbits with a periapse safely outside merger?