Wednesday, 1 July 2020

Mind the Gap - A High Mass Neutron Star or Low Mass Black Hole?


Mind the Gap - A High Mass Neutron Star or Low Mass Black Hole?

This month’s Astrophysical Journal published a discovery of a binary black hole merger/collision of two highly dissimilar objects, as identified by the LIGO and VIRGO gravitational telescopes (GW190814: Gravitational Waves from the Coalescence of a 23 Solar Mass Black Hole with a 2.6 Solar Mass Compact Object, The Astrophysical Journal Letters, 896:L44 (20pp), 2020 June 20).  This is actually quite a big deal, both in terms of the mass of the objects detected (one object was a about 24 times the mass of the sun and the other was about 2.6 solar masses) and its possible impact on astrophysical theory and even nuclear physics.  That’s because the smaller object is in the gap between the highest mass neutron stars so far confidently discovered and the lowest mass black holes discovered.



To quote the Astrophysical Journal paper:

“The highly unequal mass ratio of -0.112 +0.009 or -0.008 and unusual secondary mass of -2.59 +0.09 or -0.08 Solar mass make the source of GW190814 unlike any other compact binary coalescence observed so far. The average mass ratio for BBH (binary black hole) coalescences detected by the LVC during O1 and O2 is 0.9 (Roulet & Zaldarriaga 2019), and an inference of the underlying population predicted that 99% of detectable BBHs have mass ratios q>=0.5 (Fishbach & Holz 2020). However, the paucity of events from O1 and O2 means that this picture is limited. Indeed, the discovery of GW190412 has already changed the picture substantially (Abbott et al. 2020d).”

When stars reach the end of their main sequence life (when most of their nuclear fuel has been exhausted) they will undergo a collapse, due to the intrinsic high gravitational field created by their mass.  Nuclear burning (note that people often say burning, though it is actually nuclear fusion) prevents this from occurring during their time on the main sequence as the outward pressure from the energy caused by the fusion reaction counterbalances the inward pressure of gravity.  But when that stops, something has to give.

What the end point of that collapse is, depends on a number of parameters, with the most important one being the mass of the original star. 

·       It is thought that the smallest stars, red dwarfs, can last for extremely long periods (on the order of a trillion years) of time, as they burn their nuclear fuel relatively slowly.  They eventually probably collapse into white dwarf stars.

·       Smaller stars, like the sun, eventually go nova (after billions of years), expanding outward, but not explosively, losing some mass.  In time the core of the star contracts to a “white dwarf”, about the size of the Earth, a highly compressed object.  The contraction is stopped by something called electron degeneracy, which puts a brake on the gravitational collapse.

·       Larger stars also burn through their nuclear fuel, though at a much faster rate (tens of millions of years).  After a series of stages of nuclear fusion, which create the various different lighter elements (iron and lighter), they run out of fusional fuel and a supernova results.  This is a massive explosion, truly astronomical.  These last moments also create the elements that are heavier than iron, and it is thought that all of these elements that we see in the universe ultimately came from supernovae.

·       It is these large stars which leave behind either a neutron star or a black hole as supernova remnants.  Depending on the mass of the originating large star, the result may be a neutron star (the smaller massive stars) or a black hole (really big massive stars).

o   If a star is not too large, the neutron star is formed, as the collapse is stayed by neutron degeneracy.  An over-simplified way to think of this is as one mass of huge nuclear material, where the nuclear matter is so close together (“touching” so to speak) that only nuclear repulsion (quantum neutron degeneracy) stays the collapse.  Up until this discovery, the largest neutron stars that had been discovered were thought to be about 2 solar masses or a bit over.

o   However, for really massive stars even nuclear repulsive forces won’t stop the collapse.  It is thought that the collapse continues until a singularity is reached, a strange object of “infinite density” (again over-simplifying), where the laws of physics as we understand them don’t apply.  Up until this discovery, the smallest black holes that had been discovered were thought to be about 5 solar masses or a bit under.

It is possible that this recently discovered object could be a “heavy” neutron star or a “light” black hole.  The authors of the paper are inclined to the latter explanation, though the mechanism through which such a relatively small black hole could form is not well established.



On the other hand, it could be a “heavy” neutron star.  If so, it might have significant implications for our understanding of the atom itself (i.e. the “standard model”).  Most currently plausible theories of the neutron stars don’t allow for a neutron star of this size (i.e. the currently accepted neutron star equations of state don’t predict this).  Since the equation of state relies on evidence and extrapolations from evidence of investigations of nuclear reactions here on Earth, it throws in some doubt our understanding of those fundamental atomic interactions.  Thus, the standard model itself might require some significant alterations.

The finding also upsets some astrophysical expectations.  Basically, it was thought that a merger/collision of very high mass stars, where one star was so much larger than the other, would be a rather rare occurrence.  The fact that this one showed up relatively early in the observing history of the LIGO-type gravitational telescopes upsets that assumption.  To use Bayesian-speak, this will definitely result in updating some priors.

From the Astrophysical Journal paper:

“GW190814ʼs secondary mass lies in the hypothesized lower mass gap of 2.5–5Me (Bailyn et al. 1998; Özel et al. 2010; Farr et al. 2011; Özel et al. 2012) between known NSs and BHs. It is heavier than the most massive pulsar in the Galaxy (Cromartie et al. 2019), and almost certainly exceeds the mass of the 1.61–2.52 solar mass primary component of GW190425, which is itself an outlier relative to the Galactic population of BNSs (Abbott et al. 2020a). On the other hand, it is comparable in mass to two BH candidates: the 2.7 solar mass merger remnant of GW170817(Abbott et al. 2019b) and the 2.6–6.1solar mass compact object (95% confidence interval) discovered by Thompson et al. (2019).  It is also comparable to the millisecond pulsar PSR J17482021B (Freire et al. 2008), whose mass is claimed as 2.74+/- 0.21 solar mass at 68% confidence. However, this estimate, obtained via measurement of the periastron advance, could be inaccurate if the system inclination is low or the pulsar’s companion is rapidly rotating (Freire et al. 2008). In sum, it is not clear if GW190814ʼs secondary is a BH or an NS.”

It  is also worth noting that what I called a “LIGO-type telescope” isn’t a telescope in the usual sense of the word.  It actually detects the effect of gravitational waves on space-time, via careful measurements of distances, which indicate a perturbation in local space-time as the gravitational waves pass by.  But, since it’s purpose is to detect a form of radiation (gravitational radiation in this case), the term telescope seems fair.



It is also worth noting that this merger/collision is thought to have occurred in a galaxy about 240 million parsecs from Earth (or about a billion light years).


Note: The BBC website had a good article on this, which is where the images in this blog originated.


So, that was interesting, but you should think about reading a nice SF book that features a neutron star:

The Witches’ Stones Book 1: Rescue from the Planet of the Amartos

 So, go on a romantic science fiction adventure with an agent of Earth’s Terra Federation’s counter-intelligence group “The Agency”, to prevent the mystical and powerful Witches’ Stones from falling into the hands of the shadowy power-mad developing galactic empire, known to Earthlings only as The Organization.  Key to this mission is the rescue of an apparently unassuming Earth girl, who holds the key to the galactic balance of power, via her ability (unknown to her) to psychically unlock the energies of the Witches’ Stones. 
Amazon U.S:  https://www.amazon.com/dp/B008PNIRP4

Witches’ Stones Book One – Rescue from the Planet of the Amartos

Sarah Mackenzie had trained as a space ship mechanic at the Space Port of her home city on Earth. She left Earth to explore the galaxy, and, some months later, landed a dream assignment, to become the ship mechanic of an Explorer ship, the Beth 117.

The Beth was on its way to a planet at the edge of the galaxy, where its crewmembers were to search for the Witches’ Stones, or amartos, the mysterious crystals, which the Witches of the world, Kordea, use to channel and augment their psychic energies.

Sarah has no idea that she, herself, happens to be Stone-sensitive, just like the Witches are. Under perilous circumstances, she comes across the cache of the Stones which the Explorers are looking for, and, unwittingly, “keys” them, igniting a psychic blaze that attracts the attention of The Organization, the implacable foe of the Terra Confederation, the centuries-old star-spanning government of most of the human race, and its non-human allies. To make use of amarto-energy, The Organization needs, not just the Stones, but also amarto-sensitive individuals whom they enslave to the devices which they have developed in their pursuit of galactic domination. Thus, they want not just the cache of Stones; they also want Sarah.

To forestall galactic war, rescuers, from a counter-intelligence group, known as The Agency, are sent to the Planet of the Amartos. A fast scoutship, manned by an Agent and a Pilot, must try to fetch Sarah and the amartos, bringing them to a safe haven among the Kordean Witches.

Sarah, herself, has to deal with serious conflicts. In the psychic realm she must choose between The Organization and the Kordean Witches, while retaining mastery over her own mind. In the physical reality, she has become the centre of an armed battle between the Terran scoutship and a military task force sent by The Organization to capture her and the Stones. Her determination to keep control of her own self sends her into unexplored mental realities, while exciting but dangerous physical events swirl around her and the crew of the scoutship, Camin.

To further complicate things, she senses within herself, the beginnings of an attraction to the handsome Agent sent to rescue her. However, she’s merely a naive young woman from Earth; surely, her hopes are beyond realization....

The novel is about 100,000 words, or 250 pages. It is the first book in the Witches' Stones series, which explores the struggle for power among the Terra Confederation, the Kordean Witches and The Organization, as well as the personal and romantic entanglements of the characters. Book 2  and Book 3 complete the series.


Saturday, 27 June 2020

What is the difference between a representative sample and a random sample?


What is the difference between a representative sample and a random sample?

In principle, a large enough random sample will be a representative sample, the majority of the time. This is based on scientific and mathematical principles, ultimately derived from probability theory.

However, this assumes that the sample is large enough, is drawn from a representative sample frame, and is properly randomized. It also assumes that there isn’t any bias introduced by the tendency of some groups to be more or less willing to be surveyed than other groups and that there is no systematic reason to think that some groups were missed in the sampling. Quite a few qualifiers there, especially in this era of sample fatigue (i.e. people get tired of being surveyed due to the large number of surveys being done, since it now relatively cheap and easy).
When you hear the term, “a representative sample”, that generally means some testing has been done on the survey results, to confirm that the survey respondents have similar proportions of members from critical groups as the population at large, or at least the population that is considered relevant to the survey’s overall purpose.

It can also mean that special efforts have been made to ensure that the survey will be representative of the relevant population, in some particularly important way, via survey design (e.g. cluster sampling, stratified sampling). In those cases, the phrase “representative” might actually mean “non-representative” (e.g. if you want to ensure that certain smaller but important groups are over-sampled).
In either case, the checking for representative proportions can either be informal (it looks like we got about as many males as females) or a rigorous formal inferential statistical process (in a respondent group of this size, from a sample of some other size, we should expect between x1 and x2 females, 19 times out of 20).
Since there are dozens of ways to measure whether a respondent group is representative (gender, age, ethnic background, educational background, socioeconomic status, language, religion, etc.) these post-survey checks can never really be certain of guaranteeing a representative sample.
That’s why a large, randomly drawn, high response rate survey is the gold standard for survey research, but it is very difficult to achieve in practice.

But note that random sampling is not appropriate for many endeavors in life:
  

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And, as always, you should think about taking a break and reading an adventure/romance story (or the entire series). 

The Witches’ Stones Book 1: Rescue from the Planet of the Amartos

 So, go on a romantic science fiction adventure with an agent of Earth’s Terra Federation’s counter-intelligence group “The Agency”, to prevent the mystical and powerful Witches’ Stones from falling into the hands of the shadowy power-mad developing galactic empire, known to Earthlings only as The Organization.  Key to this mission is the rescue of an apparently unassuming Earth girl, who holds the key to the galactic balance of power, via her ability (unknown to her) to psychically unlock the energies of the Witches’ Stones. 




Witches’ Stones Book One – Rescue from the Planet of the Amartos

Sarah Mackenzie had trained as a space ship mechanic at the Space Port of her home city on Earth. She left Earth to explore the galaxy, and, some months later, landed a dream assignment, to become the ship mechanic of an Explorer ship, the Beth 117.
The Beth was on its way to a planet at the edge of the galaxy, where its crewmembers were to search for the Witches’ Stones, or amartos, the mysterious crystals, which the Witches of the world, Kordea, use to channel and augment their psychic energies.
Sarah has no idea that she, herself, happens to be Stone-sensitive, just like the Witches are. Under perilous circumstances, she comes across the cache of the Stones which the Explorers are looking for, and, unwittingly, “keys” them, igniting a psychic blaze that attracts the attention of The Organization, the implacable foe of the Terra Confederation, the centuries-old star-spanning government of most of the human race, and its non-human allies. To make use of amarto-energy, The Organization needs, not just the Stones, but also amarto-sensitive individuals whom they enslave to the devices which they have developed in their pursuit of galactic domination. Thus, they want not just the cache of Stones; they also want Sarah.
To forestall galactic war, rescuers, from a counter-intelligence group, known as The Agency, are sent to the Planet of the Amartos. A fast scoutship, manned by an Agent and a Pilot, must try to fetch Sarah and the amartos, bringing them to a safe haven among the Kordean Witches.
Sarah, herself, has to deal with serious conflicts. In the psychic realm she must choose between The Organization and the Kordean Witches, while retaining mastery over her own mind. In the physical reality, she has become the centre of an armed battle between the Terran scoutship and a military task force sent by The Organization to capture her and the Stones. Her determination to keep control of her own self sends her into unexplored mental realities, while exciting but dangerous physical events swirl around her and the crew of the scoutship, Camin.
To further complicate things, she senses within herself, the beginnings of an attraction to the handsome Agent sent to rescue her. However, she’s merely a naive young woman from Earth; surely, her hopes are beyond realization....
The novel is about 100,000 words, or 250 pages. It is the first book in the Witches' Stones series, which explores the struggle for power among the Terra Confederation, the Kordean Witches and The Organization, as well as the personal and romantic entanglements of the characters. Book 2  and Book 3 complete the series.