Black Holes: Some Recent Observations

[lpetrich]

Testing General Relativity with Pulsars - AAS Nova
noting
The Orbital-decay Test of General Relativity to the 2% Level with 6 yr VLBA Astrometry of the Double Neutron Star PSR J1537+1155 - IOPscience

Earlier measurements of the inspiral rate had a 9% difference with GR. But it was difficult to model what kind of galactic orbit this pulsar has. Lao Ding and his colleagues decided to resolve this issue by finding the parallax of this pulsar using the Very Large Baseline Array (VLBA), a set of radio telescopes with outputs combined to make them act like a single Earth-sized radio telescope. With the VLBA, they found a very precise position for this pulsar, and the watched it change over a year to measure its parallax. They found its distance to be 0.94 kiloparsecs (3,066 light years). This enabled them to model its galactic orbit much better, and to get that 2% of agreement.

List of pulsars in binary systems
The two neutron stars in PSR J1537+1155 have masses 1.333 and 1.345 Msun.


Gravitational-wave detection

I'd mentioned the detection of G-wave events earlier, events caused by inspiraling black holes and/or neutron stars.

 GW170817 - two neutron stars merging. They made a gamma-ray burst that arrived 1.3 seconds after the G-wave event, thus constraining differences in their speeds to around 10^-15.

A different sort of detection was recently made by correlating pulsar timings: Physics - Researchers Capture Gravitational-Wave Background with Pulsar “Antennae” - pulsars in different directions have correlations that vary like what one expects of a random collection of G-waves with GR-like polarizations.

Remarkable how well GR has held up.

 

[lpetrich]

The cheap wristwatch provided by my employer runs fast by about 15 sec/week. This is comprised of:

50 mcsec/d time dilatation effect from the Earth's nearby gravitational field, + 2.143 s/d from the Chinese manufacturer not giving a shit.

I don't know where that first number comes from, so I decided to calculate it.

For 1 meter difference in elevation on our planet, time dilation is 1.09*10^-16 or 3.44 nanoseconds per year.

For 1 kilometer, that is 1.09*10^-13 or 3.44 microseconds per year.

Most of Australia's cities are on the coast, with the largest exception being Canberra at about 578 meters. That means 6.3*10^-14 or 1.99 mcsec/year faster than sea level.

Several of China's cities are also on the coast, though it has some inland ones with elevations around 400 meters, like Chengdu and Xi'an.

How accurate is a quartz clock? - Quora

A few seconds to tens of seconds per year, about 10^-7 to 10^-6.

 

[Loren Pechtel]

The cheap wristwatch provided by my employer runs fast by about 15 sec/week. This is comprised of:

50 mcsec/d time dilatation effect from the Earth's nearby gravitational field, + 2.143 s/d from the Chinese manufacturer not giving a shit.

I don't know where that first number comes from, so I decided to calculate it.

For 1 meter difference in elevation on our planet, time dilation is 1.09*10^-16 or 3.44 nanoseconds per year.

For 1 kilometer, that is 1.09*10^-13 or 3.44 microseconds per year.

Most of Australia's cities are on the coast, with the largest exception being Canberra at about 578 meters. That means 6.3*10^-14 or 1.99 mcsec/year faster than sea level.

Several of China's cities are also on the coast, though it has some inland ones with elevations around 400 meters, like Chengdu and Xi'an.

How accurate is a quartz clock? - Quora

A few seconds to tens of seconds per year, about 10^-7 to 10^-6.

I would think you would need to specify latitude to capture all the effects from relativity.

 

[Tigers!]

The cheap wristwatch provided by my employer runs fast by about 15 sec/week. This is comprised of:

50 mcsec/d time dilatation effect from the Earth's nearby gravitational field, + 2.143 s/d from the Chinese manufacturer not giving a shit.

At least you get a wristwatch.

Our work sundial can't be used at present as it is raining

 

[lpetrich]

Continuum emission from within the plunging region of black hole discs | Monthly Notices of the Royal Astronomical Society | Oxford Academic - 16 May 2024

We show that the X-ray spectrum of MAXI J1820+070 in a soft-state outburst is extremely well described by a full Kerr black hole disc, while conventional models that neglect intra-ISCO emission are unable to reproduce the data. We believe this represents the first robust detection of intra-ISCO emission in the literature, and allows additional constraints to be placed on the MAXI J1820 + 070 black hole spin which must be low a• < 0.5 to allow a detectable intra-ISCO region.

ISCO =  Innermost stable circular orbit
Its radius is outside the black-hole radius, 3 times that radius in the nonrotating case (Schwarzschild), closer for a direct or prograde orbit in the rotating case (Kerr), and farther for a retrograde orbit in that case.

So if material is pushed inside of the ISCO, it will then fall in, because there is no stable circular orbit inside of it.

We show that in general the neglected intra-ISCO emission produces a hot-and-small quasi-blackbody component, but can also produce a weak power-law tail for more extreme parameter regions. A similar hot-and-small blackbody component has been added in by hand in an ad hoc manner to previous analyses of X-ray binary spectra

But why wasn't it modeled earlier? I think that it seemed insignificant. If some material orbits 100 times before falling in, then it will contribute only 1/100 the total luminosity when it falls in.

 

[lpetrich]

 Quasi-periodic oscillation (astronomy)

In X-ray astronomy, quasi-periodic oscillation (QPO) is the manner in which the X-ray light from an astronomical object flickers about certain frequencies.[1] In these situations, the X-rays are emitted near the inner edge of an accretion disk in which gas swirls onto a compact object such as a white dwarf, neutron star, or black hole.[2]

[2001.08758] A review of quasi-periodic oscillations from black hole X-ray binaries: observation and theory
Proposing that some of the black-hole ones are due to precession caused by the BH's rotation.

Under "Measuring black holes",

QPOs can be used to determine the mass of black holes.[6] The technique uses a relationship between black holes and the inner part of their surrounding disks, where gas spirals inward before reaching the event horizon. The hot gas piles up near the black hole and radiates a torrent of X-rays, with an intensity that varies in a pattern that repeats itself over a nearly regular interval. This signal is the QPO. Astronomers have long suspected that a QPO's frequency depends on the black hole's mass. The congestion zone lies close in for small black holes, so the QPO clock ticks quickly. As black holes increase in mass, the congestion zone is pushed farther out, so the QPO clock ticks slower and slower.

 

[bilby]

The cheap wristwatch provided by my employer runs fast by about 15 sec/week. This is comprised of:

50 mcsec/d time dilatation effect from the Earth's nearby gravitational field, + 2.143 s/d from the Chinese manufacturer not giving a shit.

At least you get a wristwatch.

Our work sundial can't be used at present as it is raining

I am directly employed by the city council, and we have a strong union.

Literally the only things I wear to work that are not provided by my employer, are my underpants and my spectacles.

 

[Tigers!]

The cheap wristwatch provided by my employer runs fast by about 15 sec/week. This is comprised of:

50 mcsec/d time dilatation effect from the Earth's nearby gravitational field, + 2.143 s/d from the Chinese manufacturer not giving a shit.

At least you get a wristwatch.

Our work sundial can't be used at present as it is raining

I am directly employed by the city council, and we have a strong union.

Literally the only things I wear to work that are not provided by my employer, are my underpants and my spectacles.

I do hope you are not driving as you reply to these posts.

 

[bilby]

The cheap wristwatch provided by my employer runs fast by about 15 sec/week. This is comprised of:

50 mcsec/d time dilatation effect from the Earth's nearby gravitational field, + 2.143 s/d from the Chinese manufacturer not giving a shit.

At least you get a wristwatch.

Our work sundial can't be used at present as it is raining

I am directly employed by the city council, and we have a strong union.

Literally the only things I wear to work that are not provided by my employer, are my underpants and my spectacles.

I do hope you are not driving as you reply to these posts.

Nah, I can't reply to posts while I am driving; It would interrupt my TV shows.

 

[Tigers!]

Nah, I can't reply to posts while I am driving; It would interrupt my TV shows.

Was he the bloke who crashed the bus we saw earlier in the contest?

 

[bilby]

Nah, I can't reply to posts while I am driving; It would interrupt my TV shows.

Was he the bloke who crashed the bus we saw earlier in the contest?

No. As far as I am aware, the guy watching TV managed to crash his career without actually crashing his bus first.

 

[lpetrich]

What is it like to fall into a black hole? Seen from outside, one gets more and more redshifted, and more and more time dilated, as one approaches the black-hole radius, the event horizon, the radius of no return. So outside observers will watch your time slow to a stop at the time that you cross that radius.

But you yourself won't experience anything out of the ordinary, and you will still be able to see the outside world from there. You won't notice that you crossed the black-hole radius.

What happens as you fall ? Tides. One will be stretched in the radial direction and squeezed in the other two directions, thus becoming "spaghettified".

(Acceleration difference between two points) ~ T . (distance between two points)

where T is the tidal factor GM/r³ * (-2 radial, 1, 1 tangential dimensions)
for gravitational constant G, source mass M, source distance r

For this infall problem, T ~ 1/t²

This force produces pressure P, and over size r and density D,

P ~ D * T * r² ~ D * (r/t)²

giving r ~ t * sqrt(P/D)

So if P is the yield strength of the material, then r is the size of a chunk that remains intact at time t before the end.

 

[steve_bank]

A good way to stretch your back.

If you are on a platform standing up how heavy does your leg became when you lift it?

f = ma
f force in Newtons
a gravitational acceleration

 

[lpetrich]

Let's look at some actual numbers.

One won't feel much tidal force until the last second, and it then increases almost too fast to perceive.

• 1 s - 1 m/s^2 - 0.1 g
• 0.3 s - 10 m/s^2 - 1 g
• 0.1 s - 100 m/s^2 - 10 g
• 0.03 s - 1000 m/s^2 - 100 g

That last time is close to the limit of our consciousness's time perception.

 Yield (engineering) and  Ultimate tensile strength Going further, one can estimate when materials will start to disintegrate from their yield strength P and their density D. One gets a "pressure velocity" v ~ sqrt(P/D), and the time at disintegration for size L is L/v.

The pressure velocity for yield pressure is typically around 100 - 300 m/s, and for a size of 1 meter, that is a time at disintegration of 3 - 10 milliseconds.

 Bond-dissociation energy - typically around 3 eV. That gives a yield-pressure disintegration velocity of roughly 3 - 10 km/s, and a disintegration time of 100 - 300 microseconds for size 1 meter. Scaling down to the size of a small molecule, a few times 10^-10 meter, that gives 10^-14 s. At that time, ordinary matter is reduced to single atoms.

They get stripped of their electrons by this tidal force, a process that is complete by 10^-16 seconds.

 Nuclear binding energy - nuclei disintegrate at around 10^-22 seconds, and nucleons start getting pulled apart at 10^-23 seconds.

The final time is roughly 10^-43 s, the quantum-gravity,  Planck units time. We don't have much of a clue as to what goes on there.

 

[steve_bank]

You are falling feet first into a black hole. Doesn't your heart have to pump blood against the gravity even if you are in free fall?

 

[bilby]

You are falling feet first into a black hole. Doesn't your heart have to pump blood against the gravity even if you are in free fall?

Not according to the figures given by @lpetrich above, if I understand them correctly.

You go from a survivable (even comfortable) 1g of tidal difference between head and feet, to a fatal 10g, in about 0.2 sec (and on to a physically destructive 100g in a further 0.07sec); 0.27 sec is not enough time for your heart to beat once - even if we assume that your heart rate will be quite elevated given the stressful circumstance you are in.

Your heart will be perfectly capable of doing its job, right up to the very last beat.

 

[lpetrich]

You are falling feet first into a black hole. Doesn't your heart have to pump blood against the gravity even if you are in free fall?

This is a tidal force - in the first approximation of it, it pulls the same amount both inward and outward.

If you are falling feet-first or head-first, the object's gravity will pull blood to both your head and to your feet.

 

[lpetrich]

Let's compare these times to actual black holes.

Solar-mass: 10 microseconds. Cygnus X-1*: 200 mcsec, Gaia BH3: 300 mcsec, Sgr A*: 40 seconds, M87*: 18 hours

So one would be pulled apart long before one reaches the event horizon of a stellar-mass black hole. Pulled apart into chunks with size about 0.1 - 1 cm for solar mass, about 1 - 10 cm for Cyg X-1* or GBH3.

For falling onto a neutron star, the chunks would be only a little bigger, while for falling onto a white dwarf, one would reach its surface before that final second.

For galactic-center black holes, however, one would spend that final second well inside them.

 

[Loren Pechtel]

Let's look at some actual numbers.

One won't feel much tidal force until the last second, and it then increases almost too fast to perceive.

• 1 s - 1 m/s^2 - 0.1 g
• 0.3 s - 10 m/s^2 - 1 g
• 0.1 s - 100 m/s^2 - 10 g
• 0.03 s - 1000 m/s^2 - 100 g

That last time is close to the limit of our consciousness's time perception.

I've been saying for a long time that the craziness that everyone loves to portray about black holes simply isn't a factor. Things get mighty wonky for a few radii out, but since you're moving very close to lightspeed you don't spend enough time there to perceive them.

 

[lpetrich]

 Gravitational wave and  Quadrupole formula

I will set c = G = 1 for convenience.

G-wave size: h ~ m*a²*w²/D

For two objects with masses m1 and m2 orbiting each other with distance a and angular velocity w:
Period T ~ 1/w
Total mass M = m1 + m2, reduced mass m = m1*m2/M

Kepler-Newton: a³*w² = M

h ~ (m*M)/(D*a)

Inspiral time: t ~ a⁴/(m*M²)
In terms of the time, the orbit has time behavior a ~ t^1/4, T ~ t^3/8

At coalescence, a ~ M, T ~ M, h ~ m/D, t(inspiral) ~ M²/m with (that time)/ T ~ M/m

The final orbit period gives M, and with it, the inspiral time gives m. With h, one finds the distance D.