Starship Asterisk*

Several APODs over the past few months have shown dramatic images of galaxies in collision. More than one of the accompanying narratives has stated that it is unlikely that stars in those galaxies will actually collide.

Okay, I can accept that it is statistically 'unlikely' that stars in those galaxies will collide, but I suspect that one could make an equally strong case that, statistically, a few collisions of stars almost certainly would occur!

Has anyone thought and/or written (hopefully the thinking would precede the writing!) about exactly what would happen if two stars did have a head on collision at great velocities? I'd suspect that it might set off some rather spectacular cosmic fireworks!

http://apod.nasa.gov/apod/ap080506.html
I wonder if they would merge or become a nova. Anyway it would be an interesting observation. I don't recall reading of such an occurrence being recorded

orin stepanek wrote:http://apod.nasa.gov/apod/ap080506.html
I wonder if they would merge or become a nova. Anyway it would be an interesting observation. I don't recall reading of such an occurrence being recorded

http://www.ifa.hawaii.edu/hitchhiker/ma ... ision.html
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Was brightest supernova fuelled by stellar collision?
* 17 November 2007
* NewScientist.com news service

<<IT WAS one of the brightest stellar explosions ever seen - the brilliance of 50 billion suns. Now two astronomers think they know what lit the fuse.
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In September 2006, astronomers spotted a supernova 240 million light years away. Known as 2006gy, it had exploded with a force a hundred times as powerful as a typical supernova. Since then several groups have attempted to explain what led to such a large blast, but none could explain why it appeared to be so rich in hydrogen.
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Now Simon Portegies Zwart and Edward van den Heuvel of the University of Amsterdam in the Netherlands suggest that dozens of massive stars - some hydrogen-rich - might have crashed into each other to form a dense cluster. This would have produced a monstrous heavyweight star with the mass of more than 100 suns, they say.
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Unable to support its own weight after a few million years, this star would have exploded into a supernova that outshone its galaxy. If their theory is right, the dense star cluster should become visible once the supernova has faded a few years from now, say the researchers.>>
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Brightest supernova discovery hints at stellar collision
* 19:37 03 January 2007
* NewScientist.com news service
* David Shiga
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http://space.newscientist.com/data/imag ... -1_320.jpg
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<<A supernova intrinsically two to three times brighter than any previously recorded has been observed, and its characteristics suggest it did not form like others of its class. It appears to have been forged in a collision between two stars, adding fuel to a long-running debate about what causes the type Ia explosions that are a crucial tool in cosmology.

The prevailing view of type Ia supernovae is that they result from a dense stellar corpse called a white dwarf that slowly collects matter from an ordinary companion star. Eventually the white dwarf reaches a mass threshold called the Chandrasekhar limit, triggering an explosion that completely destroys it.

This mass cut-off is thought to make all such supernovae explode with about the same intrinsic brightness, allowing astronomers to calculate their distance based on how bright they appear through telescopes. In fact, it was observations of type Ia supernovae that led to the surprising discovery in 1998 that some mysterious entity, dubbed dark energy, was causing the universe's expansion to speed up.

But some astronomers have argued that type Ia's are actually due to two white dwarfs merging. The combined mass of the two objects is above the Chandrasekhar limit, leading to the explosion.

Evidence for this hypothesis came in 2002 from a supernova called 2002ic. It had some characteristics of type Ia's, but unlike others of its type, it also showed clear signs of hydrogen in its light spectrum. Some researchers said that could be explained by a white dwarf colliding with the core of a red giant star – a dying, Sun-like star that bloats up and starts expelling its outer layers before becoming a white dwarf itself.

But other astronomers countered that 2002ic was a disguised type II supernova. These explosions occur when a massive ordinary star collapses to form a neutron star or a black hole.

Since then, three other supernovae with similar characteristics to 2002ic have been found. Now, a fourth has been detected, and it offers the best evidence yet for the merger scenario – at least for some type Ia's, according to a new study led by Eran Ofek of Caltech in Pasadena, US.

The supernova was discovered on 18 September 2006, and was named 2006gy. After correcting for light absorbed by dust between Earth and the supernova, it appears to have been about three times brighter than any previously observed stellar explosion.

Unlike the other unusual type Ia's, such as 2002ic, the September supernova has been traced to a galaxy dominated by old stars. This suggests it was not a type II event, which requires a massive star that has a very short lifetime, the researchers argue.

Study co-author Avishay Gal-Yam, also of Caltech, says most type Ia supernovae may originate in such mergers. To explain why typical type Ia's do not show hydrogen in their spectra, he argues the white dwarfs manage to eject the red giants' hydrogen as they spiral into them.
Small fraction

But he admits that there is still room for doubt about the merger model. "When you have one example, you are always a little cautious," he told New Scientist. The merger model would receive a boost "if we have another one like this and it also happens in a galaxy made of old stars", he says.

Mario Livio of Johns Hopkins University in Baltimore, Maryland, US, who has studied both the merger and accretion models, agrees that the September supernova "looks as if it might have come from some sort of a merger".

But he says this scenario probably accounts for only a very small fraction of type Ia supernovae. Calculations of white dwarf mergers suggest that such catastrophic events would convert carbon in the two objects into heavier elements. That would theoretically lead to the creation of a black hole or a neutron star rather than a type Ia supernova, he says.

Because merger-generated explosions are likely so rare, they should not affect the interpretation of cosmological studies that rely on type Ia supernovae – including measurements of dark energy, he says.>>

Rare stellar mergers may be the cause behind the appearance of "blue straggler" stars in globular clusters, as well.

Qev wrote:Rare stellar mergers may be the cause behind the appearance of "blue straggler" stars in globular clusters, as well.

What puzzles me is why are some sources mentioning supernove explosions, while others mention Blue Stragllers? After some simple thinking i came up with the following idea.

When stars are merging, it must be more like a pursuit: the direction of the velocity vector of the stars must be roughly in the same direction. The time for interaction between the two stellar atmospheres is much longer than when stars collide: opposite directions of the velocity vector. So stars in pursuit will lead to Blue stragglers, while a head on collision might trigger a supernova explosion.

The why. The velocity of a star is of the order of 0.001 times c. The distance between stars in a closely packed area is of the order of lightmonths. Although the actual process of collision is of the order of 1000 months, which is long compared to the lifespan of a human being, the time for interaction of the stellar atmospheres is short compared to the time for stellar formation. IMHO when stars are still far apart from each other, e.g. lighthours or lightdays, the relative gravitational pull in a stellar atmosphere is very much in favour for its own star. As an indicator: at the stellar surface there is an equilibrium between the thermal (outbound) pressure of the gas and the gravitational (inward) pull. A star is typically a few lightseconds in diameter. That means that the gravitational pull at e.g. a light minute away is two orders of magnitude less than the gravitational pull at the stellar surface. So in order to rip a stellar atmosphere away, the approaching star must be quite close for having a considerable effect. That, in combination with the relative velocity of 0.001c makes a significant interaction between mutual atmospheres during a head on collision a very short phenomenon, of the order of a day. Such a collision will destabilise the nuclearly active cores of the stars. An implosion of the star is IMHO more likely. However, that might trigger other nuclear reactions and ultimatedly a supernova explosion.

When the stars are in pursuit of each other, a real merger is likely to occur. The process might last thousands of years, in which period the stars have sufficient time to adapt their nucleosynthesis to the new situation: a blue straggler.

Strange to see: the ideas of sir James Jeans, i.e. the planets in our solar system were generated by a passing star, were dismissed as obsolete later in 1930-1950: too improbable. Nowadays the same interaction between stars leads to a new type of stars.

henk21cm wrote:What puzzles me is why are some sources mentioning supernove explosions, while others mention Blue Stragllers?

I think that the difference comes from the types of stars that are merging. Blue stragglers, I believe, are the result of mergers between relatively low-mass main sequence stars, whereas the merger of a white dwarf with a main sequence star or another white dwarf would lead to a somewhat exotic sort of Type Ia supernova.

I daresay the majority of stellar mergers aren't headlong collisions, but rather the result of orbital decay causing the participants to spiral together. The odds against two unbound stars just randomly smacking into each other would be... I can't help it... astronomical.

henk21cm wrote: Strange to see: the ideas of sir James Jeans, i.e. the planets in our solar system were generated by a passing star, were dismissed as obsolete later in 1930-1950: too improbable. Nowadays the same interaction between stars leads to a new type of stars.

Strange indeed. I remembered seeing this in an illustration in the Life magazine in the 1950s when I was a young lad. Many years later, when I learned more about stars and planetary formations, I wondered why this idea ever got off the ground in the first place. Didn't astronomers already know that most stars have hydrogen envelope as evidenced in spectrograph? There is no way you could get solid planets like the inner planets of the Solar System condensed from a blob of hydrogen pulled from the Sun by a passing star!

starnut wrote: I remembered seeing this in an illustration in the Life magazine in the 1950s when I was a young lad. Many years later, when I learned more about stars and planetary formations, I wondered why this idea ever got off the ground in the first place.

I read his book on stars, written in ?1920? as a youngster as well, one decade later than you. At the same time his idea was discussed at the national amateur association 'as very unlikely'.

Didn't astronomers already know that most stars have hydrogen envelope as evidenced in spectrograph?

That was known in the 19th century by the work of Fraunhofer and Kirchhoff, in a similar way as they detected an odd substance in our suns atmosphere, unknown on earth: Helium.

Qev wrote:I think that the difference comes from the types of stars that are merging. Blue stragglers, I believe, are the result of mergers between relatively low-mass main sequence stars, whereas the merger of a white dwarf with a main sequence star or another white dwarf would lead to a somewhat exotic sort of Type Ia supernova.

van den Heuvel described the latter process in a lecture which was distributed by our amateur association. A neutron star or a white dwarf could be 'revitalised' by canibalising a red giant or a star with a relative low gravity. However he did not mention supernovae. It must have been 20 maybe 30 years ago, so what he exactly said, i do not remember.

Qev wrote:I daresay the majority of stellar mergers aren't headlong collisions, but rather the result of orbital decay causing the participants to spiral together.

I am not blessed with your intuition for this process. Would not it depend on the relative velocity and the nearest distance between the stars, or in other words: its kinetic energy compared to the potential energy pit of the stars? As an example, lets inject a planet in the solar system. If this planet -without any interaction- would approach the sun to 1 AU as the nearest point, and if its velocity is less than the earth velocity (30 km/s), i guess it will fall closer to the sun and maybe sprial down to it. If this planet would have had a velocity of 45 km/s, it will escape. The same laws are valid for stars or am i missing something?

henk21cm wrote: . . . Would not it depend on the relative velocity and the nearest distance between the stars, or in other words: its kinetic energy compared to the potential energy pit of the stars? As an example, lets inject a planet in the solar system. If this planet -without any interaction- would approach the sun to 1 AU as the nearest point, and if its velocity is less than the earth velocity (30 km/s), i guess it will fall closer to the sun and maybe sprial down to it. If this planet would have had a velocity of 45 km/s, it will escape. The same laws are valid for stars or am i missing something?

With a non-gaseous planet, it would seem to be a simple either/or situation: escape or not.

With stars, would there not be a likelihood of losing kinetic energy due to the interactions of the stellar atmospheres which would result in a reduction of the relative velocity? i.e., in this scenario, the star could initially have velocity in excess of the "escape velocity", but after the interactions/perturbations/whatever of the atmospheres, it would, in effect, be captured and there would be a bound star pair.

(No calculations or anything to go with this - just amateurish conjecture.)

Regarding to missing phenomena:

iampete wrote: With a non-gaseous planet, it would seem to be a simple either/or situation: escape or not.

With stars, would there not be a likelihood of losing kinetic energy due to the interactions of the stellar atmospheres which would result in a reduction of the relative velocity?

If mass is exchanged between the stars, there should not be a loss of kinetic or potential energy. The angular momenta will however change. When the gas interacts, heats up or emits radiation, these two phenomena will dissipate energy and thus:

iampete wrote: the star could initially have velocity in excess of the "escape velocity", but after the interactions/perturbations/whatever of the atmospheres, it would, in effect, be captured and there would be a bound star pair.

in which you are right. A similar effect occurs, as Art Neufer mentioned in an earlier discussion, when two galaxies collide: the interaction of the gasses heats them up and thus these systems are rather bright in Spitzers UV images.

iampete wrote:(No calculations or anything to go with this - just amateurish conjecture.)

Most of us -including me- are amateur astronomers: in the real sense of the word amateur, i.e. we like the stars.

You remark triggered my curiosity: what would be the results? A simple argument. The core of the stars are very dense. The bulk of the mass of a star is concentrated in the star itself. Only a relatively small part of the mass is concentrated in its atsmosphere, as an order of magnitude: 1%. So i write down a balance between kinetic energy and (internal) thermal energy: kinetic energy equals the energy needed for a rise in temperature:

0.5 m v^2 = 0.01 * m * C * ΔT (eq. 1)

with C the specific heat of the atmosphere. C is of the order of 10 kJ/kg/K. The 0.01 is the fraction of the mass of the atmosphere with respect to the total stellar mass.

Suppose the relative velocity is 40 km/s, so we can loose 40 km/s. Equation (1) calculates the temperature rise -adiabatic- of the atmosphere when all kinetic energy is converted into heat. That leads to:

ΔT = 50 v^2 / C = 50 * 4E4 * 4E4/1E4 = 800E4 = 8E6 K

The atmosphere will heat up 8 million kelvin, hotter than the corona of our sun. So, my assumptions may not be correct. The process will not be adiabatic, the atmosphere will emit radiation thus cooling down.

The balance shows however that your assumption: "one has to stretch the limiting velocities for capture", is correct. Good point Pete!

henk21cm wrote:

Qev wrote:I daresay the majority of stellar mergers aren't headlong collisions, but rather the result of orbital decay causing the participants to spiral together.

I am not blessed with your intuition for this process. Would not it depend on the relative velocity and the nearest distance between the stars, or in other words: its kinetic energy compared to the potential energy pit of the stars? As an example, lets inject a planet in the solar system. If this planet -without any interaction- would approach the sun to 1 AU as the nearest point, and if its velocity is less than the earth velocity (30 km/s), i guess it will fall closer to the sun and maybe sprial down to it. If this planet would have had a velocity of 45 km/s, it will escape. The same laws are valid for stars or am i missing something?

I kind of look at it this way: if you assume every one of the two hundred billion or so stars in our galaxy are about the size of the Sun (which is being generous), and do not overlap each other if you flatten the galaxy down to a 2D projection (maximizing the area the stars take up), there's still greater than two trillion times more empty space than there is space taken up by stars.

Obviously there are going to be regions of higher density (eg. galactic cores), but it just comes down to the fact that, on the scale of a whole galaxy, stars are utterly mindbogglingly small little things. To actually collide head-on, they'd need to be lined up pretty much perfectly.

Hello QEV,

Quick question: wether these objects collide or not do they travel on their vectors more like frisbees or do they appear sort of skewed in different angles with regard to their direction of travel. Just curious as the deep field pix show them in such a variety of attitudes with respect to our line of sight. Maybe the answer lies with the guys running the VBLA

Oh, as in... do galaxies tend to move through space edge-on? I'm pretty sure their orientation and their direction of motion are unrelated. There'd certainly exist galaxies that are traveling edge-on, but it'd be coincidental. At least, I've never read anything that would suggest otherwise.

[quote= Obviously there are going to be regions of higher density (eg. galactic cores), but it just comes down to the fact that, on the scale of a whole galaxy, stars are utterly mindbogglingly small little things. To actually collide head-on, they'd need to be lined up pretty much perfectly.[/quote]

I'm certainly not hypothesizing that head-on stellar collisions would be commonplace; quite the contrary. But from a purely statistical point of view, the likelihood that such events will occur occasionally still is greater than zero, especially when two galaxies are colliding. (In much the same way that the statistical probability of there being intelligent life elsewhere in the universe probably is greater than zero, imo.)

Qev wrote: I kind of look at it this way: if you assume every one of the two hundred billion or so stars in our galaxy are about the size of the Sun (which is being generous), and do not overlap each other if you flatten the galaxy down to a 2D projection (maximizing the area the stars take up), there's still greater than two trillion times more empty space than there is space taken up by stars.

I can reproduce your factor 2E12. Since there is so much open space, the odds that you randomly locate two stars at the same location, creating an overlap, is very small: 5E-13. These are the odss for the initial condition. Thereafter stars start moving. In a galaxy the drift of the stars is predominantly in the same direction. The frequency (probability per unit of time) of collisions is very low. So i agree with your "daresay". However, when two galaxies meet each other, -which obviously seems to happen-, the direction of the stars is no longer so precisely aligned in the same direction as in an isolated galaxy. Still space is sparsely populated by stars, since doubling the number of stars per unit volume or surfcae will not tip the scales. Even when visualising the trajectories of the stars as solid 'cables' like a fine web of wires, these wires will hardly touch or cross. The area where each star might be, is however enhanced, increasing the odds for a collision.

Unfortunatedly the mathematical knowledge to estimate the odds for collisions of randomly moving stars fails me, so i can not quantify this argument. Maybe i should run a few Monte Carlo simulations with exceedingly large stars and extrapolate to smaller stars. A nice job for the long weekend.

Hello QEV,

Thank you for the response, I haven't come across anything either. I know lateral forces can be a factor in angle vs. trajectory which, as you say, is probably unrelated. It can be quite a complicated affair I imagine.

Hi all! I'm new to the forums and I have a related question to this topic. I see it was partially touched on but I wanted to be more direct.

If you had atmosphere or life bearing planets orbiting stars in colliding galaxies, what usually happens to the planets? Are they lost from the stars because of velocity change? Would they usually be kept? Would a species survive? Would most of the stars still not interact close enough to put most of them at risk? How often would a star, on average (based on typical galactic density) pass by other stars from the other galaxy in any given time period, if it was a head-to-head collision? What angle of interaction is more typical for the collision? Or is it more of a rotation thing usually?

Also, which forums is appropriate for asking questions not exactly about the image of the day, but that we just think about when we see the image? Because I have lots of starry-eyed questions.

Thanks,

Lewis

There are many dependancies in this question like depending on the mass and gravity of the passing star, depending on the distance between your parent star and the passing menace, and where the planet is in ots orbit at the time of the near miss (I use near miss because it is the most likely scenereo).
The passing star could tug at the planet's host star enough to tweak the orbital velocity/eccrenticity of a planetary body and pull it into a farther orbit or alter its orbital plane.
If the menace star passed slightly closer than the parent star, the planet could be pulled away from the parent and become a stepchild of the menace, though the new orbit would likely be so elyptical that life might be extinguished during the forst new orbit (too hot or too cold).
Or if the vectors are correct, a planet could be ejected into space.

Hello All,

I have been mulling over this thing about galaxy inclination vs. it's direction of travel and maybe the idea of "travelling" is where my mental gymnastics go awry. I recall the concept that galaxies don't move (unless attracted), space expands. So objects can be inclined because their not moving THROUGH something. Generally speaking, of course, and disregarding the exceptions for the sake of oversimplifying the point.

Qev wrote: Obviously there are going to be regions of higher density (eg. galactic cores), but it just comes down to the fact that, on the scale of a whole galaxy, stars are utterly mindbogglingly small little things. To actually collide head-on, they'd need to be lined up pretty much perfectly.

I finished writing the collision simulation program. It is now in its testing phase. I'll describe the basics of the model. Results will follow later this week or next weekend in this forum (if you are still interested).

1. The model is 2D. The z coordinate is always 0.
2. There are two galaxies. One is fixed in the origin, the other can be located anywhere in the XY plane. It can move in both X and Y direction. The velocity in X and Y direction is constant.
3. The galaxies have a radius R of 50 000 lightyears (50 kly).
4. Each galaxy is populated with N stars.
5. The stars are randomly placed within the galaxy. This leads to a uniform distribution of stars. The seed of random number generator is changed for each calculation.
6. The stars obey the observed shape of the rotation curve. If the distance, r, from the center is less than 0.1 of the radius of the galaxy, the velocity increases with distance from the center linearly from 0 to v_max @ r=0.1R. If the distance from the center is larger than 0.1R, the velocity is constant: v_max.
7. The position of the stars is calculated by assuming circular orbits. Since stars in the second galaxy have a circular movement superimposed on the linear movement of the center of the galaxy, the position of each star is recalculated after each time step.
8. The path between two adjacent positions of stars is assumed to be linear.
9. If the path of a star from galaxy 1 crosses the path of a star from galaxy 2, the point of closest approach is calculated. This value is stored in a file.
10. There is no gravitational interaction between the stars.
11. Crossings of stars within the population of the same galaxy are neglected.
12. The unit in which everything is expressed, is ly.

The current setup is that the center of the second galaxy passes right through the center of the first galaxy. The relative velocity of the 2nd galaxy is 180 km/s. The time step, dt, is 100 000 years. With v_max = 180 km/s, i.e. 6E-4 c, stars move in each time step at most 60 ly. With N=5000 stars in each galaxy a typical run on a fast PC takes 2 hours. On my own PC it takes 6 hours. Preliminary results show that a few encounters between two stars of 1E-3 ly have been found, that is 9 light hours, i.e. 70 AU.

Currently a test is running with a time step 1/5 of the normal time step, i.e. 20 000 y, and the same seed, to check that a time step of 1E5 y is not too large.

Advice, corrections or recommendations are appreciated.

henk21cm:

Wow ! Either you have way too much spare time on your hands, or (hopefully) this is a labor of love for a passionate avocation.

I have two suggestions (Please don't take these as criticism of your efforts to date.)

A. for item 5. - On the surface, it seems that it would be fairly easy to bias the distribution of stars such that their population density falls off as a function of radial distance from the center of the galaxy. It would seem that the complication to the model would be virtually negligible, while showing more interesting/realistic results.


B. (This one probably introduces a very large complication, and may not be worth the effort.) It would be most interesting if, when a close approach between two stars of less than TBD ly occurs, the program could start modeling the gravitational interactions of ONLY those stars that are in close approach and drop dt to a much smaller value for the duration that such close approaches exist.

In any event, I am looking forward to reading about your results.

iampete wrote:Wow ! Either you have way too much spare time on your hands, or (hopefully) this is a labor of love for a passionate avocation.

Your last suggestion: love for the hobby, the drive to understand what might happen and a quest for mental nourishment are the main drive. Doing optical astronomy in a light poluted -usually clouded- area is nearly impossible.

iampete wrote:A. for item 5. - On the surface, it seems that it would be fairly easy to bias the distribution of stars such that their population density falls off as a function of radial distance from the center of the galaxy. It would seem that the complication to the model would be virtually negligible, while showing more interesting/realistic results.

That is a good suggestion. Assuming that the density of stars decreases inversely proportional with the distance from the center, the probability density function (pdf) must be something like:

pdf(r) = a / (r+b) (Eq. 1)

Lets assume that the density of stars in the center of the galaxy is C times larger than at the edge (r=R). Substitution this assumption in eq. 1 leads to:

C = (R+b)/b

so :

b = R/(C-1).

The constant C has nothing to do with the speed of light! A further demand (normalisation) is that when we integrate the pdf between 0 and R, the result must be 1.

∫ {a/(r+b)} dr = a ln(R+b) - aln(b) = a ln((R+b)/b)) = a ln(C) = 1.

So a = 1/ln(C). To find the shape of the cumulative distribution, we integrate the pdf from 0 to r:

F= ∫ {a/(r+b)} dr = a ln((r+b)/b) = ln(((C-1)r+R)/R) / ln(C)

So F is the function which transforms a flat distribution into a distribution, which has the following properties:

1. The density of stars in the center of the galaxy is C times larger than at the edge (r=R)
2. The density of stars is inversely proportional with r

Since the pdf of my random number generator is flat, it can now be transformed into the required random number generator, which create a more likely distribution of stars within a galaxy.

iampete wrote: B. (This one probably introduces a very large complication, and may not be worth the effort.) It would be most interesting if, when a close approach between two stars of less than TBD ly occurs, the program could start modeling the gravitational interactions of ONLY those stars that are in close approach and drop dt to a much smaller value for the duration that such close approaches exist.

Interesting indeed. The main issue, which Art Neufer in an earlier discussion raised is, that the dynamics of stars within a galaxy is complicated. As one is likely to believe is that simple Newtonian physics might rule the stars. If so, the rotation curve would display a steady decrease in velocity of the stars with increasing r, whereas observations lead to a constant velocity if r > 0.1R. Since multiple observations confirm this phenomenon, an observational error can be excluded. An explanation for this phenomenon is dark matter, Halo etc. These are things which i do not grasp, have a grip on, in such a way that i can make a mathematical model for it.

In the current model all stars with r>0.1R have a constant velocity, v_max. The angular velocity is v_max/r. The stars itself are mathematical points and thus massless, but adding mass to their properties is a piece of cake. A possible solution is the following:

1. Make an estimate of the gravitational pull of the center of the galaxy on a star. Kepplers laws will provide a handle for the estimate of the 'effective mass'. (M_gal+m_star) = r^3/P^2. Since v_max is known and r_star is known, P is known as well.
2. Give all stars the same mass, being equal to twice the solar mass.
3. Calculate the distance between two stars where their mutual attraction is 10% of the pull of the center of the galaxy.
4. From that point solve the equations of motion for the two stars. The time step must be quite somewhat smaller than now: 100 ky.
5. If -after the point of closest approach- the mutual attraction has decreased to below 10% of the pull of the galaxy center, resume bussiness as usual

Maybe it is better to study the effects of the interaction first in a separate programm than to integrate it in the galaxy simulation. If there is any noticeble difference between the 'non-interaction' path and the path in which interaction takes place, it must be integrated in the galaxy simulation programm as well.

Your first suggestion about the density of stars i will happily integrate in my program. For C i'll take 100: there are 100 times as many stars per unit of volume in the center of the galaxy as at the edge.

Your last suggestion is on the whish list, postponed untill somebody (or a accessible article) gives me a good insight how to model the mass of the galaxy and the equation of motion for the non-Newtoninan/non-Kepplerian physics of star dynamics in a galaxy.

Keep you posted!

Henk,

Really like your monte carlo approach to the problem, and I look forward to reading the results. What exactly are you planning to measure? Frequency of hits, or just yes/no there was a hit? Might be more appropriate to report the median closest approach, but that really doesn't address the likelihood of collision that's been discussed. I've also tried a similar, but conceptually much more trivial approach. It'd be interesting to compare results.

Just a thought for you. Physical chemists spend a lot of time worrying about things like how often atoms collide. For example, if I have a cloud of cesium atoms at 500K in a vacuum of xx torr, how often will the average atom experience a collision. The equation is:

z=sqrt(2) * pi * d^2 * v * N

z-collisional frequency
d is distance we will consider a "hit"
v is mean velocity
N is the number density (particles per volume)
the root 2 term comes from the assumption that all particles are moving with the same relative velocity, leading to a concept of "reduced mass".

Many assumptions here, some acceptable for your problem, others not. Biggest assumption we break with this equation is that particle interactions are slow relative to mean velocity.

I'm not savvy enough to plug in the right numbers for an astronomy application, but if I use your mean velocity (6e-4*C), radius of 1 light min (anything coming within 1 lm of a star is a "hit"?), and a density of one star(particle) per cubic ly, I get a frequency of one hit per 10e14 years. Multiply that by the number of stars in your galaxy, and you have a guess of the frequency of collisions. I'd be interested to have someone plug better numbers into this equation. Also like to hear how this deviates from your simulations.

ne0357 wrote: Really like your monte carlo approach to the problem, and I look forward to reading the results. What exactly are you planning to measure? Frequency of hits, or just yes/no there was a hit? Might be more appropriate to report the median closest approach, but that really doesn't address the likelihood of collision that's been discussed.

Neo,
That what i was planning to do: calculate the distribution of closest approach. Since the number of stars is rather large, simple approximations between the probability and the number of stars will do a reasonable job.

neo0357 wrote:I've also tried a similar, but conceptually much more trivial approach. It'd be interesting to compare results.

That would be nice. Combining results is an operation of the type: "1+1 > 2", always more info than just the sum of both. .

neo0357 wrote:z=sqrt(2) * pi * d^2 * v * N
I get a frequency of one hit per 10e14 years. Multiply that by the number of stars in your galaxy, and you have a guess of the frequency of collisions.

With 2E11 stars in a galaxy one would come to 'once per millenium'. I'm afraid this approach is not valid, for a few reasons.

1. Kinetic theory of gasses assumes a random movement of the particles. In a galaxy there are preferential paths: more ore less circular orbits around the center of the galaxy.
2. Kinetic theory assumes rather high densities. The densities as found for stars in a galaxy are quite low. The stars do bear a resemblence to a Knudsen gas, in which other processes than many collision between particles might be more important.

You might object to the first argument that when galaxies collide, the densitiy rises and the orbits are no longer regular and preferential, since two populations of stars mingle like traffic on a junction.

For d you assume 1 lm. This is a reasonable assumption. The earth is 8 lm from the sun. An approach of two stars at Jovian distance (40 lm) is imho too far, the actual diameter of the sun (5 ls) is too small. "Some lightminutes", which basically gets a result of the same order of magnitude as yours. A better estimate will hopefully follow slightly later, when i'll try to simulate an approach between two stars, taking gravity into account. Iampete has suggested the latter approach, making a shortcut through excessively long calculation times.

Keep you posted!

ne0357 and iampete wrote: Really like your monte carlo approach to the problem, and I look forward to reading the results.

In the mean while i did about 10 runs. The density is still assumed to be constant. The last run (with 15000 stars in each galaxy) took about 50000 seconds, more than half a day. The purpose of these runs was to get a feeling for the results and do some simple checks. As a result of these checks the algorithm for the calculation of the 'closest approach' between two stars had to be changed. That involved a lot of math regarding local linearization of non-linear equations, which took a lot of time to figure out.

In the calculations only points with a closest approach less than 1 lightyear (ly) are counted and written.

The calculations with 10000 stars in each galaxy will be used as a base. Analysis of the data showed that the normalised number of closest encounters less than x ly {N'(x)} can be expressed in a formula:

10log(N'(x)) ≅ 0.95 * 10log(x) - 0.35

with 10log the logarithm based on 10, N'(x) the number of encounters less than x ly divided by the number of stars N in each galaxy.

To get a grip on the numbers: suppose we want to know the number of encounters smaller than 1E-6 ly, i.e. of the order of 10 million km. For N'(1E-6) you will find 1E-6. There are 2E11 stars in our galaxy, so the number of encounters adds up to 2E5: 200 000. The number of closest encounters less than 1 million km (diameter of our sun) is 10 times smaller: 20 000.

That is not 'astronomically small'. Nevertheless the time it took for the two galaxies to move through each other, is long: more than 0.3 Gy, so encounters are not a frequent phenomenon: "once a millenium".

I am fully aware that this result is not the absolute truth. It is just a simulation, with all of its shortcomings and over-simplifications. Nevertheless it may give you a feeling for the order of magnitude of close encounters between two stars.

Shortcomings:

1. Only 1E4 stars were used in stead of 2E11 stars in our galaxy
2. All stars are located within a 2-dimensional plane.
3. The density of stars is assumed to be constant in the galaxy
4. The relation between N'(x) and x is extrapolated to 1E-7 ly. The closest encounter calculated is just 4E-5 ly (≅ 2.5 AU)
5. There is no gravitational interaction between the stars

Initial conditions, properties:

• There are 2 galaxies, each 1E5 ly in diameter
  The first galaxy is at rest, the other is moving with 6E-4 c
  The observed rotation curve of stars is assumed for the velocities.
  The maximum rotation velocity of the stars is 6E-4 c
  There are 10000 stars in each galaxy.
  The initial position of the second galaxy is fully outside the first galaxy.

As a cynical note: the calculation time it will take to do the same simulation with all stars in our galaxy is 277 Gy, i.e. 20 times as long as the current age of our universe. "Rather unpractical".

For those that want to play with or improve this simulation software, send me a personal message with your e-mail address and i'll send you the C source of the program. It is gcc complient, it will run under Linux, IRIX and Windows.