Black Holes: Some Recent Observations

[lpetrich]

Let's consider alternatives to quadrupole sources:

Monopole:
+
Dipole:
+ -
Quadrupole:
+ -
- +

G-wave size: h ~ f*m*(w*a)^p/D ~ f*m*M^p/2*a^-p/2/D

Energy loss: dE/dt ~ (w*D*h)² ~ f²*m²*M^p+1*a^-p-3

Energy: E ~ M*m/a

t ~ a^p+2 / (f²*m*M^p)

giving T ~ t^3/(2*(p+2))

• Monopole: p = 0 -- exponent = 3/4
• Dipole: p = 1 -- exponent = 1/2
• Quadrupole: p = 2 -- exponent = 3/8

So one can distinguish GR and other theories from the inspiral G-wave emission.

 

[lpetrich]

The 4 big black hole frontiers for gravitational waves - Big Think - "So far, gravitational waves have revealed stellar mass black holes and neutron stars, plus a cosmic background. So much more is coming."

1.) The most massive black holes of all.

2.) Supermassive black holes and extreme mass-ratio mergers.

3.) Intermediate mass black holes and black holes beyond stellar production.

4.) The lightest black holes of all and the so-called “mass gap.”

 List of black holes and  List of most massive black holes and  Tolman–Oppenheimer–Volkoff limit

If there are two black holes, each of a billion solar masses or more, orbiting one another at very close distances (where they may merge in the next few million years) almost anywhere within the observable Universe, pulsar timing measurements should be able to pick out these individual objects at some point in the next decade or two.

...
Although the ultramassive black holes in the Universe — the most massive black holes of all, in the billions to tens of billions of solar masses — might be far and away the most impressive, they don’t represent the majority of supermassive black holes. At the centers of nearly all known galaxies lie supermassive black holes that are relatively more modest: possessing millions, tens of millions, or perhaps hundreds of millions of solar masses, such as the black holes at the centers of the Milky Way, Andromeda, and the majority of known, large galaxies. Because of their lower masses, however, pulsar timing is likely a very long way away from being sensitive to their presence, even if they’re in a binary system, possessing another orbiting black hole companion.

Meanwhile, we cannot hope to detect these objects using ground-based detectors, as objects orbiting a ~million solar mass black hole will emit gravitational waves with a characteristic period of about 100-to-1000 seconds, whereas LIGO and other terrestrial detectors can only detect gravitational waves emitted with a period between milliseconds and a few tenths of a second.

 

[lpetrich]

 Laser Interferometer Space Antenna - "It aims to measure gravitational waves directly by using laser interferometry. The LISA concept has a constellation of three spacecraft arranged in an equilateral triangle with sides 2.5 million kilometres long, flying along an Earth-like heliocentric orbit. The distance between the satellites is precisely monitored to detect a passing gravitational wave." - LISA - Laser Interferometer Space Antenna -NASA Home Page - ESA - LISA factsheet - should launch around 2030 - 2035.

It will be most sensitive to G-wave periods around 100 - 1000 seconds, and it can do 1 to 100,000 seconds.

Out to billions of light-years away, LISA will be sensitive to:

• binary black holes (of comparable masses) weighing in from around 10,000 to tens of millions of solar masses,
• extreme mass ratio inspirals, where objects of only ~1-100 solar masses fall into a typical supermassive black hole,
• and the types of black holes that LIGO and other ground-based detectors are sensitive to, except during a very early stage of the inspiral phase, enabling us to predict when (and, quite possibly, where) a stellar mass binary black hole merger will occur.

Intermediate-mass ones?

Even when LISA is operating in space and advanced LIGO (plus Virgo, KAGRA, and LIGO India) operate on the ground, there’s still going to be a gap between the highest-mass black hole that ground-based detectors can see, capping out at around ~200 solar masses, and the lowest-mass black hole that a space-based detector can see, down to about ~10,000 solar masses.

One can build a large G-wave observatory on our planet, a much larger version of LIGO and Virgo.

 

[lpetrich]

The article then gets into the "mass gap" between the most massive known neutron star, at around 2 solar masses, and the least massive known black hole, at around 3 solar masses.

A pulsar in a binary with a compact object in the mass gap between neutron stars and black holes - between 2.09 to 2.71 solar masses

We now have:

• direct images of the event horizons around black holes,
• gravitational wave detections, from pulsar timing, of a stochastic background of gravitational waves permeating the Universe,
• and gravitational wave detections, from inspiraling and merging compact objects, that reveal neutron star and black hole mergers from ~1 up to ~200 solar masses.

There are 40 quintillion black holes in our Universe - Big Think - "For the first time, astronomers have created a data-driven estimate for how many black holes are in our Universe: more than anyone expected." - about 0.04% of the mass of our Universe.

 

[lpetrich]

I'll now consider falling into Sgr A*. Its mass is 4.3 million solar masses, its BH radius is 13 million kilometers or 0.08 AU, and its BH time 42 seconds. That means that the Earth-Moon system could fall into it, though both the Earth and the Moon will get spaghettified. At an hour or two to go, they will be distorted into American-football shape, then they will disintegrate. By the time they reach Sgr A*'s event horizon, they will both be broken up into chunks a few kilometers in size. If the Sun falls in, it also will be pulled apart.

Turning to M87*, it has a mass of 6.5 billion solar masses, a BH radius of 19 billion kilometers or 128 AU, and a BH time of 64,000 seconds or 18 hours. Most of the Solar System could fall into it and its celestial bodies would become spaghettified only well inside its event horizon. However, they would be pulled out of their orbits long before they fell in.

Looking through  List of most massive black holes there are several that are estimated to be more massive, but most of these estimates are from quasar emissions properties. An exception is the central black hole in  Abell 1201 BCG - Brightest Cluster Galaxy - an estimate from gravitational lensing: 30 billion solar masses - 5 times the mass of M87*. The maximum is of Phoenix A - 100 billion solar masses - 15 times the mass of M87* - estimated from quasar emissions.


How big can a black hole grow? | Monthly Notices of the Royal Astronomical Society: Letters | Oxford Academic

• Nonrotating: 42 billion solar masses - 6 * M87*
• Maximally rotating: 270 billion solar masses - 40 * M87*

Reporting on this work: Black holes could grow as large as 50 billion suns before their food crumbles into stars, research shows — University of Leicester

 

[Shadowy Man]

 Laser Interferometer Space Antenna - "It aims to measure gravitational waves directly by using laser interferometry. The LISA concept has a constellation of three spacecraft arranged in an equilateral triangle with sides 2.5 million kilometres long, flying along an Earth-like heliocentric orbit. The distance between the satellites is precisely monitored to detect a passing gravitational wave." - LISA - Laser Interferometer Space Antenna -NASA Home Page - ESA - LISA factsheet - should launch around 2030 - 2035.

It will be most sensitive to G-wave periods around 100 - 1000 seconds, and it can do 1 to 100,000 seconds.

Out to billions of light-years away, LISA will be sensitive to:

• binary black holes (of comparable masses) weighing in from around 10,000 to tens of millions of solar masses,
• extreme mass ratio inspirals, where objects of only ~1-100 solar masses fall into a typical supermassive black hole,
• and the types of black holes that LIGO and other ground-based detectors are sensitive to, except during a very early stage of the inspiral phase, enabling us to predict when (and, quite possibly, where) a stellar mass binary black hole merger will occur.

Intermediate-mass ones?

Even when LISA is operating in space and advanced LIGO (plus Virgo, KAGRA, and LIGO India) operate on the ground, there’s still going to be a gap between the highest-mass black hole that ground-based detectors can see, capping out at around ~200 solar masses, and the lowest-mass black hole that a space-based detector can see, down to about ~10,000 solar masses.

One can build a large G-wave observatory on our planet, a much larger version of LIGO and Virgo.

I recall the first time I saw a presentation on LISA. It was in 1994 during my REU summer program. The general joke was that you have a mission as long as you have an acronym and an artist’s conception. Maybe one day we will see this mission fly.

 

[lpetrich]

If some black hole approached the Solar System, what would we see of it as it approaches?

Its gravitational-lens effect for some source s would have size sqrt(R*Dr) where R is the black-hole radius and Dr is the reduced total distance to the source: Ds*Do/(Ds+Do) where Ds is the distance from the lenser to the source and Do is the distance from the lenser to the observer.

If Ds >> Do, like for a star behind the lenser, then Dr ~= Do, and the effect size is sqrt(R*Do) with observed angular size sqrt(R/Do).

If Ds ~ R, for an object near a BH, then Dr ~= R and the effect size is R with observed angular size R/Do.


Let's look at other celestial objects also.

First, our interstellar spacecraft. They will go only a little bit into interstellar space before becoming derelicts, and some of them have already done so (Pioneer 10, 11). But it is instructive to consider what one could see of them.

Their size scale is roughly the size scale of their antenna dish, and that is:

• Pioneer 10, 11 - 2.74 m / 9 ft
• Voyager 1, 2 - 3.7 m / 12 ft
• New Horizons - 2.1 m / 8.9 ft

nugget_IRTF_2015-TC25_smallest-NEA_Reddy - 2015_smallest-near-earth-asteroid.pdf

Just two days after its discovery on October 11, 2015, asteroid 2015 TC25 made a very close pass by the Earth at a distance of about 69,300 miles (111,000 kilometers), or 29% of the distance to the Moon. Using data obtained at NASA’s Infrared Telescope Facility, scientists supported by the Near Earth Objects Observation Program determined that 2015 TC25 is very similar to a rare class of carbon-rich stony meteorites, called Ureilites, found on Earth. 2015 TC25, which rotates once every 133 seconds, is only about 6 feet (2 meters) in diameter, making it the smallest asteroid ever mineralogically characterized with a ground-based telescope

About as big as those spacecraft, meaning that they would be very hard to observe outside of the distance to the Moon.

 

[lpetrich]

I'll skip over a lot of asteroids, moons, and small planets to the largest rocky planet in the Solar System, one not much smaller than the largest rocky planets elsewhere: the Earth, our home planet.

Its brightness from reflected sunlight would be magnitude -4 + 5*log10(dsp) + 5*log10(dep) for Sun-planet distance dsp and Earth-planet distance dep in AU's (size of Earth orbit). For dsp >> 1 AU, that reduces to -4 + 10*log10(dsp) -- an inverse-fourth-power law.  Absolute magnitude Its angular diameter at 1 AU would be 17.6 seconds of arc, observable in a small telescope.

At Saturn's distance (10 AU), it would be +6 mag, 2" of arc, enough for a comet hunter to easily spot it, and at Eris's distance (100 AU), it would be +16 mag, 0.2" of arc, hard to observe, but likely in the range of asteroid searches.

Gravitational effects? Its effect on a planet's orbit when near that orbit would be about m/M where m is its mass and M the sun's mass. For distance d >> planet distance a, that would be (m/d^3)/(M/a^3) = (m/M)*(a/d)^3. About 1/333,000 when nearby, about a second of arc or 1.5 milliseconds of radio-signal travel time at 1 AU. So such a planet could be detected by spacecraft tracking.

At 1 AU, the lens effect would be 0.05" across, at 10 AU 0.02", and at 100 AU 0.005" across - blocked by the planet's bulk.

-

Redoing for a Jupiter-sized planet, the absolute magnitude gets -5 added, and the size gets multiplied by 11. That gives us -9 and 3' (minutes of arc) at 1 AU, +1 and 19" at 10 AU, and +11 and 2" at 100 AU.

The planet's mass is 1/1047. that of the Sun, meaning that perturbations on the planets' motions will be much easier to observe, and meaning that the gravitational-lens effect will be 30 times larger: 0.9" at 1 AU, 0.3" at 10 AU, and 0.09" at 100 AU.

 

[lpetrich]

A Sunlike star would make itself very obvious once it reaches the distance of the nearest stars to the Solar System - it would be one of the brightest stars in the sky.  List of nearest stars - Alpha Centauri: 1.33 pc, 4.34 ly, mag -0.27, Sirius: 2.67 pc, 8.71 ly, mag -1.46. At 1 pc, the Sun would have visual magnitude -0.17, and at 1 ly, -0.68.

So I'll consider white dwarf stars.  White dwarf and  List of white dwarfs

• Sirius B - mass 1.018 Msun, radius 0.0084 Rsun, age 0.1 Gyr, temp 25,000 K, mag at 1 pc: +6.31
• Procyon B - mass 0.602 Msun, radius 0.01234 Rsun, age 1.37 Gyr, temp 7,740 K, mag at 1 pc: +8.0
• WD 0343+247 - mass 0.553 Msun, radius 0.011 Rsun, age 11.49 Gyr, temp 4,197 K, mag at 1 pc: +11.80

Gravitational-lens size for 1 solar mass at 1 parsec: 0.064". It will be about 1 second of arc at 845 AU, well into the Oort cloud. At that distance, the full range of white dwarfs will be easily visible, with these ones having mag -5.6, -3.9, -0.1.

 

[lpetrich]

Next is neutron stars. RADIO EFFICIENCY OF PULSARS

It states that the radio luminosities of pulsars range from 10^27 to 10^31 ergs/s, or 10^20 to 10^24 watts. The Sun's luminosity is 3.827*10^(26) watts.

(PDF) Distances and other parameters for 1328 radio pulsars and  Pulsar - pulsars are often observed over sizable fractions of our Galaxy's side, with the closest known ones being some 150 parsecs (500 light years) away.

That will make a pulsar easy to observe. In fact, if a pulsar gets into the inner Solar System, it will be about as bright as our radio transmitters, thus making it a big source of radio noise. Though if a pulsar does so, it will disrupt the planets' orbits, and we may end up in a bad orbit for us - too hot much of the time, too cold much of the time, or alternating between these states.

When a pulsar spins down enough, it will no longer emit radio-wave pulses. [2207.04723] Pulsar death line revisited -- II. 'The death valley'

Pulsars' masses are typically 1.2 to 1.6 solar masses, at least those in binary systems. Study of measured pulsar masses and their possible conclusions | Astronomy & Astrophysics (A&A) and Pulsar mass measurements and tests of general relativity

 

[lpetrich]

A dead pulsar will be hard to observe with nongravitational effects, so I consider gravitational effects. These will have similar sizes for active pulsars and for white dwarfs, I must note, though those objects are easily observed nongravitationally.

At 1000 AU distance, its gravitational-lens size scale is about 1", and at 10 AU, 10". Let's see how likely it is for some stars to be near the lens effect.

Average number of stars brighter than the given magnitude per per square degree | Download Table - also the average separation in degrees, then minutes - all for (Galactic pole), (sky average), (Galactic plane)

• 5.0 - 0.04, 0.05, 0.08 - 5.0, 4.5, 3.5
• 9.0 - 1,99, 4.10, 12.8 - 0.71, 0.49, 0.28 - 43, 30, 17
• 14.0 - 91.2, 297, 968 - 0.105, 0.058, 0.032 - 6.3, 3.5, 1.9

So lensing a star will be very improbable unless it is a very faint one.

if this object gets to around 10 AU from the Sun, it will disrupt the outer planets' orbits, though it may take some decades to be very noticeable.

Getting to 1 AU means disrupting the inner planets' orbits, including our homeworld's orbit.

 

[lpetrich]

At 1000 AU, the gravitational-lens effect sizes: Neutron star: 1", Cygnus X-1: 4", Gaia BH3: 5", Sgr A*: 32', M87* 21d.

At 1000 AU, the amount of perturbation of the Earth's orbit over a year: NS: ~ 10^(-9), Cyg X-1, GBH3: 3*10^(-8), Sgr A*: 4*10^(-3), M87*: (disruption)

So it would be hard to observe a stellar-mass black hole at that distance, but easy to observe galactic-center supermassive black holes, even the smaller ones.