## APOD: The Doubly Warped World of Binary... (2021 Apr 16)

alter-ego
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### Re: APOD: The Doubly Warped World of Binary... (2021 Apr 16)

johnnydeep wrote:
Fri Apr 16, 2021 4:55 pm
There are at least two statements here I don't quite understand:

1. "...material orbiting smaller black holes experiences stronger gravitational effects that produce higher temperatures."

Is this due to the tidal effects being greater for smaller black holes? Meaning that the gravity gradient is steeper around a smaller black hole and thereby tears at orbiting matter more greatly?
Yes, although I did not see direct reference to "tidal force". Heating is caused by gas migrating from outer radii to inner radii (loss of angular momentum), and the released energy over a small change in orbital radius (dr) is expressed as as the derivative of gravitational potential energy wrt radius. Only considering black-body accretion disk luminosity (i.e. no jets), the temperature proportionality to BH mass, M, can be found. Bottom line: Temperature increases with larger velocity change and larger accretion rate:
Accretion Disk Lecture wrote: Suppose that as each fluid element moves inward that it releases its energy locally, and that its energy is all gravitational. How much energy would an element of mass, m, release in going from a circular orbit at radius r + dr to one at radius r?
Gravitational potential energy is Eg = -GMm/2r, so the energy released is GMmdr/2r2.
...
However, let us now focus on just the radial dependence, writing [release of gravitational potential energy over dr] dEg ∼ GMmdr/r2. That means that the luminosity of this annulus, for an accretion rate [m → dm/dt], is dL ∼ GM[dm/dt]dr/r2
and assuming black-body radiation, the temperature can be related to Luminosity:
Accretion Disk Lecture wrote:For a blackbody, L = σAT4. The area of the annulus is 2πrdr, and since dL ∼ M[dm/dt]dr/r2 we have T4 ∼ M[dm/dt]/r3, or T ∼ {M[dm/dt]/r3}1/4
Rewriting the parameters in terms of the BH mass, M, and assuming a stead-state accretion rate (dm/dt =constant)then T ∝ M−1/4.
Accretion Disk Lecture wrote: This shows that as black holes get bigger, emission from their accretion disks get cooler, all else being equal. For example, a stellar-mass black hole accreting at nearly the Eddington rate has an inner disk temperature near 107 K, but a supermassive 108 M☉ black hole accreting near Eddington has only a 105 K temperature.
FYI: Given the conditions of no jets, Eddington accretion rate yields the Eddington luminosity = Maximum luminosity a body (such as a star) can achieve when there is balance between the force of radiation acting outward and the gravitational force acting inward. When there are jets, the BH luminosity can exceed the Eddington limit because that radiation does not encounter the accretion disk, therefore it does not contribute to hydrostatic equilibrium.
johnnydeep wrote:
Fri Apr 16, 2021 4:55 pm
2. "...relativity causes the black holes to appear smaller and brighter as they approach the camera and larger and fainter as they recede."

This I don't get at all. Does it matter which BH is closer to the camera and/or whether they are eclipsing each other or not? And either way, I still don't get it
Though I don't necessarily question Art's description about brightness, I don't think it clearly addresses your question.
First, the question is about relativistic aberration, and second, the visual aspects mentioned can apply to single, moving BH. Relativistic Aberration not only acts differentially on the accretion disk, but also acts on the entire black hole (the photon ring and the accretion disk). In this visualization, there are two BHs orbiting each other which leads to a periodic, relativistic aberration. To see the largest aberration, the observer needs view the orbital plane edge on, and when the BHs are at maximum separation. There, one recedes when the other advances directly toward the observer; the velocity difference is maximum so the apparent size differences are a maximum. The noted aberration does not occur when they are eclipsing, or when viewed from above. For the latter two cases, the orbital velocities are perpendicular to the line of sight.

Referring the first APOD link and the visualization:
Light rays from accretion disks wrote:The visualization also shows a more subtle phenomenon called relativistic aberration. The black holes appear smaller as they approach the viewer and larger when moving away.
Relativistic Aberration - Orbiting Black Holes.jpg
This effect doesn't rely on gravity bending light. It's behavior is rooted in both Newtonian physics (stellar aberration, velocity << c), and accurately described in Special Relativity. For a moving source, it comes down to the changing propagating cone angles - narrowing toward the observer, widening away from the observer. The following SR visualizations demonstrate this for a moving observer. Keep in mind the moving observer's narrowing field of view demonstrates the same behavior as a narrowing light-propagation cone-angle of relativistic star moving towards a stationary observer. I.e. the observers FoV doesn't change, but the apparent size of the star is brighter and smaller.

The first is a 6-min video demonstrating all SR doppler and aberration effects. The brightening and narrowing sky FoV is shown around 2.5 minutes into the visualization.
Click to play embedded YouTube video.

The second shows how a 360°FoV collapses (quantifying the view vs velocity).
Click to play embedded YouTube video.

This one is for an observer falling into a black hole. When his visible aberrated world blinks out, the screen goes black.
I'll admit, I find this a bit unsettling.
Click to play embedded YouTube video.

Hope all this helps.
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johnnydeep
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### Re: APOD: The Doubly Warped World of Binary... (2021 Apr 16)

Thanks for that, alter-ego! I'll have to read it a few more times before I can claim to understand it.
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### Mergers of Black Holes with Neutron Stars

https://www.ligo.caltech.edu/news/ligo20210629 wrote:
LIGO-Virgo-KAGRA Finds Elusive Mergers of Black Holes with Neutron Stars
LIGO Caltech: News Release • June 29, 2021

<<For the first time, researchers have confirmed the detection of a collision between a black hole and a neutron star. In fact, the scientists detected not one but two such events occurring just 10 days apart in January 2020. The extreme events made splashes in space that sent gravitational waves rippling across at least 900 million light-years to reach Earth. In each case, the neutron star was likely swallowed whole by its black hole partner.

The gravitational waves were detected by the National Science Foundation's (NSF's) Laser Interferometer Gravitational-Wave Observatory (LIGO) in the United States and by the Virgo detector in Italy. The KAGRA detector in Japan, joined the LIGO-Virgo network in 2020, but was not online during these detections.

The first merger, detected on January 5, 2020, involved a black hole about 9 times the mass of our sun, or 9 solar masses, and a 1.9-solar-mass neutron star. The second merger was detected on January 15, and involved a 6-solar-mass black hole and a 1.5-solar-mass neutron star. The results were published today, June 29, in The Astrophysical Journal Letters.

"With this new discovery of neutron star- black hole mergers outside our galaxy, we have found the missing type of binary. We can finally begin to understand how many of these systems exist, how often they merge, and why we have not yet seen examples in the Milky Way," says Astrid Lamberts, a researcher at Observatoire de la Côte d'Azur, in Nice, France.

The first of the two events, GW200105, was observed by the LIGO Livingston and Virgo detectors. It produced a strong signal in the LIGO detector but had a small signal-to-noise in the Virgo detector. The other LIGO detector, located in Hanford, Washington, was temporarily offline. Given the nature of the gravitational waves, the team inferred that the signal was caused by a black hole colliding with a 1.9-solar-mass compact object, later identified as a neutron star. This merger took place 900 million light-years away.

"Even though we see a strong signal in only one detector, we conclude that it is real and not just detector noise. It passes all our stringent quality checks and sticks out from all noise events we see in the third observing run," says Harald Pfeiffer, group leader in the Astrophysical and Cosmological Relativity department at Max Planck Institute for Gravitational Physics (AEI) in Potsdam, Germany.

Because the signal was strong in only one detector, the location of the merger on the sky remains uncertain, lying somewhere in an area that is 34,000 times the size of a full moon.

"While the gravitational waves alone don't reveal the structure of the lighter object, we can infer its maximum mass. By combining this information with theoretical predictions of expected neutron star masses in such a binary system, we conclude that a neutron star is the most likely explanation," says Bhooshan Gadre, a postdoctoral researcher at the AEI.

The second event, GW200115, was detected by both LIGO detectors and the Virgo detector. GW200115 comes from the merger of a black hole with a 1.5-solar mass neutron star that took place roughly 1 billion light-years from Earth. Using information from all three instruments, scientists were better able to narrow down the part of the sky where this event occurred. Nevertheless, the localized area is almost 3,000 times the size of a full moon.

Astronomers were alerted to both events soon after they were detected in gravitational waves and subsequently searched the skies for associated flashes of light. None were found. This is not surprising due to the very large distance to these mergers, which means that any light coming from them, no matter what the wavelength, would be very dim and hard to detect with even the most powerful telescopes. Additionally, the mergers likely did not give off a light show in any case because their black holes were big enough that they swallowed the neutron stars whole.

"These were not events where the black holes munched on the neutron stars like the cookie monster and flung bits and pieces about. That 'flinging about' is what would produce light, and we don't think that happened in these cases," says Patrick Brady, a professor at University of Wisconsin-Milwaukee and Spokesperson of the LIGO Scientific Collaboration.

Previously, the LIGO-Virgo network found two other candidate neutron star-black hole mergers. One event called GW190814, detected August 14, 2019, involved a collision of a 23-solar-mass black hole with an object of about 2.6 solar masses, which could be either the heaviest known neutron star or the lightest known black hole. Another candidate event, called GW190426, and detected on April 26, 2019, was thought to possibly be a neutron star-black hole merger, but could also simply be the result of detector noise.

Having confidently observed two examples of gravitational waves from black holes merging with neutron stars, researchers now estimate that, within one billion light-years of Earth, roughly one such merger happens per month.

"The detector groups at LIGO, Virgo, and KAGRA are improving their detectors in preparation for the next observing run scheduled to begin in summer 2022," says Brady. "With the improved sensitivity, we hope to detect merger waves up to once per day and to better measure the properties of black holes and super-dense matter that makes up neutron stars.">>
Art Neuendorffer