# Massive objects in the immediate solar neighbourhood

1. Apr 15, 2005

### Nereid

Staff Emeritus
In a recent thread, here in GA&C, turbo-1 posted this: if there was a massive black hole slinging around out there [beyond the EKB, but closer than Alpha Cen], how do you think we would have been able to detect it apart from some transient lensing effects?

If there were a (OOM) Msol BH somewhere in a MACHO or OGLE pieces of sky, what regions in parameter space (distance, space velocity, mass) would the null results (neither MACHO nor OGLE found any such BH) still allow such a ('nearby') BH to be lurking, undetected (by MACHO and OGLE)?

PS: If Gokul would like to make this into an Astronomy Q&A Game ...
: scratch that; while I would love to have PF members get more enthusiastic about the observational side of astronomy, I realise (today) this isn't a suitable topic for an Astronomy Q&A Game ...

Last edited: Apr 16, 2005
2. Apr 17, 2005

### SpaceTiger

Staff Emeritus
How massive are we talking? The detection method would depend sensitively on that.

Neither one of those experiments could rule out an individual black hole in the immediate vicinity, not just because they don't observe the whole sky, but also because a BH may not produce a lensing event during the course of these experiments. Rather, they are are better for putting statistical constraints on the total number of compact objects (black holes, planets, etc.) that aren't emitting any light, as well as making lucky detections of interesting objects. Such surveys could never be said to be "complete" in any sense of the word.

3. Apr 18, 2005

### turbo

After giving this some more thought, we might miss such a beast completely when looking for transient lensing events, but if it is accreting from the ISM, it should look like a fairly energetic EM source with relatively large (by galactic scale standards) proper motion. Also, if the ISM is non-homogenous on small scales, it's luminosity ought to be variable as it sweeps through denser and more rarified regions of the neighborhood. Maybe it could be detected in long-term x-ray surveys as a point source with too much motion...actually, if the proper motion is high, that could be tough, too, because it might show up over here in one survey and show up 'way over there in another with a different spectrum and luminosity.

4. Apr 18, 2005

### ohwilleke

Indirectly observed black holes have been fairly large. We know of no mechanism for producing a black hole other than the collapse of a star. Even a very modest (say 1% of the Sun) gravitational effect, ought to be detectable as an oscillation of the solar system against the stellar background.

Also, assuming that it isn't hanging out in some sort of orbital system with Alpha Centuri, given its mass, we ought to be able to pin it in some sort of envelope between Sol and AC. At the near to Sol end of the envelope, at least, oscillation effects ought to be noticable with good equipment.

5. Apr 27, 2005

### wstevenbrown

The only requirement for BH formation is (matter or energy) density. During the initial picosecond or so of the BB, local density knots could have failed to participate in the general expansion/inflation, giving rise to a spectrum of Primordial BH's. Strictly speaking, they were never composed of matter, and did not accrete. The accreted version with which we are familiar is required, at the lower end of the mass range, to evaporate 'quickly'. A PBH of lunar mass should be undergoing its final explosive decompression right about now. Those smaller than that are already gone, unless for some reason, accretion exceeded evaporation, which is highly plausible in the early dense universe. For the purpose of your discussion tho, PBH's from Jupiter-mass to Solar-mass are a distinct possibility. See arxiv.org/astro-ph/0504034 .

On a more speculative note, even in the range from atomic-mass to lunar-mass, there may be stable relics. Ultramassive particles (probably electrically neutral) which are stable, but which can no longer be produced because the required energy density does not exist anywhere in the universe.

If they're out there, we'll eventually see them, either 'feeding' or evaporating. Orbits in the Oort cloud take a long time-- interstellar trajectories are not required to be periodic. I doubt we will recognize their gravitational signatures in the mass range from Luna to Jupiter. Higher than that, anyone with a lot of patience could find them. Bear in mind, tho, that their orbits are in no way constrained to be in the plane of the ecliptic. Interactions might be ... sporadic and infrequent.

Best regards-- Steve

Last edited by a moderator: Apr 30, 2005
6. Apr 30, 2005

### Nereid

Staff Emeritus
Hmm, would readers and members mind if I bring this thread back to the question I originally posed?

I'd like to take a 'purely' obsevational approach - IF there were massive objects beyond the EKB but within ~1.5 pc, and IF they were in one of the OGLE or MACHO (or other microlensing survey) fields, THEN given that none of these surveys has (yet) 'seen' such a massive object, what constraints can we put on their existence?

For the purposes of my question, I want us to assume that these massive objects are 'black' - I'm asking only about detection by microlensing, and only microlensing of the OGLE, MACHO, etc kind.

Perhaps a start - what is the size (in arcseconds) of the 'lensing footprint' of a Msol dense object (detectable by an OGLE or MACHO survey)? How does this size (on the sky) vary with mass, density, distance from our solar system?

7. May 1, 2005

### Chronos

Perhaps, it does not exist.

8. May 1, 2005

### SpaceTiger

Staff Emeritus
The crucial number here is the Einstein radius; that is, the angular scale on which significant lensing effects can occur. In general, it's given by:

$$\theta_E=\sqrt{\frac{4GM}{c^2}\frac{D_{LS}}{D_LD_S}}$$

where $$D_L,\ D_S,\ D_{LS}$$ are the distance to the lens, to the source, and between the lens and source, respectively. In the case we're discussing, the lens is much closer than the sources it will be lensing, so

$$D_S \simeq D_{LS}$$

and

$$\theta_E=\sqrt{\frac{4GM}{c^2D_L}}=\sqrt{\frac{2R_g}{D_L}}$$

where $$R_g$$ is the gravitational/Schwartzschild radius. Let's give this equation some units:

$$\theta_E=4.1\ (\frac{M}{M_{sun}})^{1/2}(\frac{100\ AU}{D_L})^{1/2}\ arcseconds$$

This means that a solar mass black hole just beyond the kuiper belt would lens on a scale easily detectable by ground-based telescopes (i.e. it's not microlensing). Of course, a black hole this massive would probably also have noticable gravitational perturbations on the planets, so it may be a moot point anyway. Less massive black holes (say, planet mass) would be in the microlensing regime.

There's a problem, however. Because the BH would be so close, the Earth's motion around the sun would make it move across the sky fairly quickly. The time it will take for an object (say, a star) to cross the Einstein radius would be:

$$t_{cross}=\frac{\theta_E}{\mu}=\frac{\theta_ED_L}{v_{earth}}=\frac{\sqrt{2R_gD_L}}{v_{earth}}$$

$$t_{cross}=10,000\ (\frac{M}{M_{sun}})^{1/2}(\frac{D_L}{100\ AU})^{1/2}\ seconds$$

This means that the microlensing events will be very short. Why is this a problem? Well, in order to detect the event, we need to have enough photons coming in per second that there's a detectable rise in the light curve. The longer the event, the larger the total number of background objects there are that can be lensed in a detectable way. For comparison, most OGLE microlensing events last many days.

I don't think current surveys are well-suited to detect any microlensing events from nearby mini-black holes, but a larger BH (say solar mass) might give detectable multiple images of background objects.

9. May 2, 2005

### Chronos

Or, on the other hand, it may not exist. A simpler solution.

10. May 2, 2005

### Billy T

Very interesting and your knowledge very impressive. Is it correct to infer from this "shot noise problem" that it is actually easier to detect presence of mini BH, via gravitational lens effects, if it is not too close to solar system?

I also wonder about the detection of it by capture of solar wind (weak quasar type luminosity seen in sky survey telescopes) if it were approximately 100 AU from sun or less. (yet far enough away to not make more gravitational "wiggle" of outer planets than Ort cloud objects can. Of course it could be in sector where Pluto and Neptune are not.)

I suspect that the ISM density is so low that a mini BH would not pull in enough H atoms (or ions) to have them collide and make excited states that radiate, before crossing the event horizon. It also seems to me that as they are pulled in and get close to the event horizon, they would be "streached" further apart in the direction of infall and this might more than compensate for the convergence of their trajectories. I.e the mean distance between the atoms/ions being eaten by BH might actually be increasing as they are captured by its gravity. I know so little that I request your comment on this means of detecting them also. Perhaps the very close ones, if any, in denser solar wind could be detected as "very weak quasars" and the more distant one by gravitational lens effect. Also perhaps there is a distance and BH size range in which they are undetectable? Thanks in advance for any comments you can make on these questions.

Last edited: May 2, 2005
11. May 2, 2005

### Nereid

Staff Emeritus
Thank you SpaceTiger!

Let's simplify things a bit; let the mass of our BH be Msun, and let's write our distances as multiples of 100au. At a distance of 16 (= 1600 au), our BH would have an Einstein radius of 1" (and a crossing time of 40ks, ~11 hours).

If there were such a BH, in the direction of one of the OGLE or MACHO fields, would it have been detected? Could this BH have a motion (wrt the solar system baricentre) that would make it extremely unlikely to be detected?

If our BH were at a distance of 1600 (approx 2.5 lightyears), the footprint would be 0.1" and the crossing time nearly a (working) week. Would this have been detected?

12. May 3, 2005

### SpaceTiger

Staff Emeritus
It depends on the limiting factors. If you're looking for a population of objects that is really numerous, then you can afford to have a smaller Einstein radius, so you'll want to observe at larger distances so that the event lasts longer (note the dependences of the equations above). If the objects are rare (or you're looking for one particular object), then you don't want to look too far away because they'll present a very small cross section on the sky. All sorts of other things come into play, including your observing strategy, your telescope quality, obscuration, etc. This is part of what makes observational astronomy so hard. We can't tweak the universe to make it easier to observe.

I could easily give an accretion rate for the ISM or solar wind, but I wouldn't know offhand how to calculate the associated luminosity. Mass accretion efficiency is still a big question mark in quasar/BH theory.

13. May 3, 2005

### Billy T

From context, I assume that "baricenter" is the center of the star being lensed, but since any star seen from Earth (other than sun) is a "point" I am not sure.

Again from context, it seems clear to me that the motion of the BH that is important is the component of its motion that is perpendicular to the line joining the star being lensed and the Earth (or sun as these lines are essentially the same). If some one could define "baricenter" from us non astrophysicists I, at least, would appreciate it. Thanks in advance.

14. May 3, 2005

### SpaceTiger

Staff Emeritus
I believe so. This will be very difficult to ascertain precisely because the projects were designed to look for variability on day timscales, so it's not clear whether they even check for the microlensing signature from a nearby black hole. It would be more likely to come up in galactic searches for pulsating stars.

15. May 3, 2005

### Billy T

OK, I would like to know that rate. I think someone can make correct OOM estimate of the luminosity by following approach: Try to compute the collision rate and assume each collision between atoms (even with an ion) but not ion/ion collisions produces one visible photon (detectable in Earth based telescopes -but only our solid angle fraction of the 4pi steradians come to Earth.) It has been a long time since I did collision rate calculations, so if you think there is merit in this OOM approach please try it, your calculations would be more reliable than mine, I'm sure.

First I would try to understand the "streached compression" as atoms approach the event horizon, recognizing that it is not a radial infall, but conserves (until collision occurs) the angular momentum of each approaching atom - some "death spiral" idea for the trajectory might work. I.e. all the gravitational energy converts to velocity and the distance from the BH decreases to conserve the atoms angular momentum, but the distance between two atoms on the same trajectory is increasing as the "front" one always has greater in track acceleration. (transtrack "compression" in "death spiral" and in track "elongation" of the unit volume.) need to estimate the original thermal velocity and it permits collisions with in this shape changing "unit volume" - I sure you have better Ideas, but just wanted to give indication as to How I would approach the problem.

16. May 3, 2005

### Nereid

Staff Emeritus
The solar system baricentre (or barycenter, to those who live in the US) is its centre of mass.
How about you do a simple calculation for us, BillyT? Assume the only massive objects in the solar system are the Sun and Jupiter, that the mass ratio is 1:1000, and that the distance between the centres of these two objects is 800 million km. Where would the 'solar system baricentre' be?

17. May 5, 2005

### Billy T

Thanks for the definition.
Because of the 1:1000 ratio, the distance from the sun, I'll call it X, is approximately 0.8 Million Km along the line joining them, and dos ont move as both orbit it. More accurately, 1000X = (800 - X) is sovled to find the distance from the sun.

I have been away for three days. I want to return to ideas about how to determine the "weak quasar" radiation of a black hole but have other Emails etc to do first. Do you have any ideas useful for estimating the luminosity, if any, of solar wind or ISM approaching the event horizon of a small black hole? One thing that would help me get started, is to have some idea about the relative amount of hydrogen that is ionized, neutral and molecular in the ISM and the solar wind at 100 AU.

Your question was easy compared to this "weak quasar" radiation problem. I note that in the two only object case you gave, the Baricenter does not "wobble" because these two are orbiting it, but has velocity relative to fixed stars as our solar system "orbits" the the galaxy center (Orbits in quotes as there must be very slight perturbations as other near by stars distrube this orbit.) If there were three (or more) objects it would bve rare that the baricenter was on the line joining any two, and never if the orbit planes were not the same.

18. May 6, 2005

### Nereid

Staff Emeritus
Thanks BillyT.

Several posters have suggested what *other* effects a nearby, massive compact object might have, and how (or whether) these could be detected. These are interesting, and if anyone would like to start a thread on any, I'd be pleased to join in.
Indeed; the baricentre does not 'wobble', by definition!
To an OOM, if the BH had zero proper motion, its apparent motion across the sky would be an ellipse (ranging from a circle at the celestial pole, to a line at the ecliptic); if the BH were 1 parsec distant, the major axis of the ellipse would be 1".

So, if there were an Msol BH in an OGLE or MACHO field, what (proper motion, distance) parameters would it need to have, in order for it to have not been detected (by either OGLE or MACHO, to date)? We can make some simplifying assumptions about the searches - but let's not deviate too much, shall we?

*If there were a (OOM) Msol BH somewhere in a MACHO or OGLE pieces of sky, what regions in parameter space (distance, space velocity, mass) would the null results (neither MACHO nor OGLE found any such BH) still allow such a ('nearby') BH to be lurking, undetected (by MACHO and OGLE)?

19. May 6, 2005

### Billy T

Either I don't understand you or you are wrong on this, assuming "baricenter" is just a new (to me) term for "center of mass."

For example, in your two body case (Sun and Jupiter only), the baricenter is always in the plane of Jupiter's orbit; but now let us add Pluto, which is rarely in this plain. When Pluto is "above" (North or what ever is the correct term), then the baricenter is also slightly above (North) of the "Jupiter ecliptic." Conversely when Pluto is "below" (South), then the baricenter is also slightly South of the "Jupiter ecliptic." - This oscillation above and below the "Jupiter ecliptic" is what I was referring to as "wobble." Any third body, not in "Jupiter's ecliptic," will cause this wobble, Mercury with the shortest oscillatory period and the passing of a near by star, with such a long one that only a few oscillations have occurred in the history of the universe.

I don't see how you can define away this real effect and yet keep the meaning of the "baricenter" the same as the "center of mass."

20. May 6, 2005

### Nereid

Staff Emeritus
I've started a new thread, in Celestial Mechanics, on the baricentre, and whether it wobbles or not. Please continue discussion on that there.
Er, BillyT, did you take the trouble to find out what http://bulge.astro.princeton.edu/~ogle/ [Broken] are?

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