APOD: The Medusa Nebula (2021 Mar 26)

[Chris Peterson]

I think of it like this. A white dwarf is made of prime fuel. Well, not prime fuel, because only hydrogen is prime fuel, and most white dwarfs are made of helium, carbon and oxygen. (I think.)

So a white dwarf is not made of prime fuel, but "good enough fuel".

Weigh a white dwarf down more than its electron degeneracy can bear, and it will ignite. And then, all that good enough fuel will go ka-poof!!!!

Ann

Hey, I like the number of this post. I missed my 11111th post, but a post number 11211 is not bad, either.

Is it a prime number?

It is easily seen as not prime since all of its digits sum to a multiple of three.

[johnnydeep]

I think of it like this. A white dwarf is made of prime fuel. Well, not prime fuel, because only hydrogen is prime fuel, and most white dwarfs are made of helium, carbon and oxygen. (I think.)

So a white dwarf is not made of prime fuel, but "good enough fuel".

Weigh a white dwarf down more than its electron degeneracy can bear, and it will ignite. And then, all that good enough fuel will go ka-poof!!!!

Ann

Hey, I like the number of this post. I missed my 11111th post, but a post number 11211 is not bad, either.

Is it a prime number?

In short: less massive white dwarfs blow off their outer layers in repeated novas as a result of accretion, whereas more massive white dwarfs accumulate enough to collapse under degeneracy pressure and become supernovas, but somehow avoid becoming mere novas. Why can't they also become novas? Why must they wait for more mass and thereby become supernovas?

[Ann]

I think of it like this. A white dwarf is made of prime fuel. Well, not prime fuel, because only hydrogen is prime fuel, and most white dwarfs are made of helium, carbon and oxygen. (I think.)

So a white dwarf is not made of prime fuel, but "good enough fuel".

Weigh a white dwarf down more than its electron degeneracy can bear, and it will ignite. And then, all that good enough fuel will go ka-poof!!!!

Ann

Hey, I like the number of this post. I missed my 11111th post, but a post number 11211 is not bad, either.

Is it a prime number?

In short: less massive white dwarfs blow off their outer layers in repeated novas as a result of accretion, whereas more massive white dwarfs accumulate enough to collapse under degeneracy pressure and become supernovas, but somehow avoid becoming mere novas. Why can't they also become novas? Why must they wait for more mass and thereby become supernovas?

Wish I knew, Johnny. So let me speculate.

The surface gravity of a white dwarf is very high indeed. So when a gob of gas from a red giant crashes down onto the surface of a white dwarf, it's going to make a big crash indeed. Move over, asteroid that killed the dinosaurs.

Perhaps, if the crash that happens when a gob of gas slams onto the surface of the white dwarf is sufficiently big, maybe the gas that falls onto the surface of the white dwarf will just explode? Like a nova, you know?

Click to play embedded YouTube video.

But if a white dwarf is massive enough to be close to its Chandrasekhar limit, then maybe the entire white dwarf gets sufficiently unsettled to blow itself to smithereens, if just one more gob of gas falls onto it? Like when the obese and sickeningly full Mr. Creosote of Monty Python's The Meaning of Life is persuaded to eat just one after dinner mint and starts vomiting rivers of puke on all and sundry around him.

Ann

[johnnydeep]

I think of it like this. A white dwarf is made of prime fuel. Well, not prime fuel, because only hydrogen is prime fuel, and most white dwarfs are made of helium, carbon and oxygen. (I think.)

So a white dwarf is not made of prime fuel, but "good enough fuel".

Weigh a white dwarf down more than its electron degeneracy can bear, and it will ignite. And then, all that good enough fuel will go ka-poof!!!!

Ann

Hey, I like the number of this post. I missed my 11111th post, but a post number 11211 is not bad, either.

Is it a prime number?

In short: less massive white dwarfs blow off their outer layers in repeated novas as a result of accretion, whereas more massive white dwarfs accumulate enough to collapse under degeneracy pressure and become supernovas, but somehow avoid becoming mere novas. Why can't they also become novas? Why must they wait for more mass and thereby become supernovas?

Wish I knew, Johnny. So let me speculate.

The surface gravity of a white dwarf is very high indeed. So when a gob of gas from a red giant crashes down onto the surface of a white dwarf, it's going to make a big crash indeed. Move over, asteroid that killed the dinosaurs.

Perhaps, if the crash that happens when a gob of gas slams onto the surface of the white dwarf is sufficiently big, maybe the gas that falls onto the surface of the white dwarf will just explode? Like a nova, you know?

Click to play embedded YouTube video.

But if a white dwarf is massive enough to be close to its Chandrasekhar limit, then maybe the entire white dwarf gets sufficiently unsettled to blow itself to smithereens, if just one more gob of gas falls onto it? Like when the obese and sickeningly full Mr. Creosote of Monty Python's The Meaning of Life is persuaded to eat just one after dinner mint and starts vomiting rivers of puke on all and sundry around him.

Ann

Yeah, perhaps it’s still all (and only) about the mass. And perhaps also the accretion rate, since I don’t think of gas accreting in discrete gobs, but in a continual process. I still need to read up on all this stuff, but not today since I’m running on literally zero sleep after an emergency molar tooth extraction late yesterday. Kept fearing I would bleed to death in my sleep, which kept me from falling to it (sleep , that is). TMI?

[Ann]

Yeah, perhaps it’s still all (and only) about the mass. And perhaps also the accretion rate, since I don’t think of gas accreting in discrete gobs, but in a continual process. I still need to read up on all this stuff, but not today since I’m running on literally zero sleep after an emergency molar tooth extraction late yesterday. Kept fearing I would bleed to death in my sleep, which kept me from falling to it (sleep , that is). TMI?

Sounds pretty awful. Hope you'll have a good night's sleep and feel better tomorrow.

Ann

[johnnydeep]

Yeah, perhaps it’s still all (and only) about the mass. And perhaps also the accretion rate, since I don’t think of gas accreting in discrete gobs, but in a continual process. I still need to read up on all this stuff, but not today since I’m running on literally zero sleep after an emergency molar tooth extraction late yesterday. Kept fearing I would bleed to death in my sleep, which kept me from falling to it (sleep , that is). TMI?

Sounds pretty awful. Hope you'll have a good night's sleep and feel better tomorrow.

Ann

Thanks. Feeling much better today, after 10 hours of restful sleep. Now, on to tackle novas and supernovas!

[Ann]

Irregular galaxy UGC 12682. Credit: ESA/Hubble & NASA.

---

Very good to hear that you are feeling better, Johnny! Then you may be up for this: A "failed supernova" that just may have been something in between a classical nova, where only the newly accreted material on the surface of a white dwarf is blown off, and a type Ia supernova, in which the entire white dwarf annihilates itself.

ESA/Hubble wrote:

In November 2008, 14-year-old Caroline Moore from New York discovered a supernova in UGC 12682. This made her the youngest person at the time to have discovered a supernova. Follow-up observations by professional astronomers of the so-called SN 2008ha showed that it was peculiarly interesting in many different ways: its host galaxy UGC 12682 rarely produces supernovae. It is one of the faintest supernovae ever observed and after the explosion it expanded very slowly, suggesting that the explosion did not release copious amounts of energy as usually expected.

Astronomers have now classified SN 2008ha as a subclass of a Type Ia supernova, which is the explosion of a white dwarf that hungrily accretes matter from a companion star. SN 2008ha may have been the result of a partially failed supernova, explaining why the explosion failed to decimate the whole star.

So SN 2008ha may have been an explosion where a part of the white dwarf was destroyed, but not all of it. Very interesting, if you ask me!

Ann

[XgeoX]

I think of it like this. A white dwarf is made of prime fuel. Well, not prime fuel, because only hydrogen is prime fuel, and most white dwarfs are made of helium, carbon and oxygen. (I think.)

So a white dwarf is not made of prime fuel, but "good enough fuel".

Weigh a white dwarf down more than its electron degeneracy can bear, and it will ignite. And then, all that good enough fuel will go ka-poof!!!!

Ann

Hey, I like the number of this post. I missed my 11111th post, but a post number 11211 is not bad, either.

Is it a prime number?

Nope, at least according to the prime number calculator...

11211 is a Composite Number and can be factored by any of the following numbers.

All the factors of 11211 :
1, 3, 37, 101, 111, 303, 3737, 11211

https://www.calculatorsoup.com/calculat ... ulator.php

Warning: it is very addictive!

Eric

[johnnydeep]

Irregular galaxy UGC 12682. Credit: ESA/Hubble & NASA.

---

Very good to hear that you are feeling better, Johnny! Then you may be up for this: A "failed supernova" that just may have been something in between a classical nova, where only the newly accreted material on the surface of a white dwarf is blown off, and a type Ia supernova, in which the entire white dwarf annihilates itself.

ESA/Hubble wrote:

In November 2008, 14-year-old Caroline Moore from New York discovered a supernova in UGC 12682. This made her the youngest person at the time to have discovered a supernova. Follow-up observations by professional astronomers of the so-called SN 2008ha showed that it was peculiarly interesting in many different ways: its host galaxy UGC 12682 rarely produces supernovae. It is one of the faintest supernovae ever observed and after the explosion it expanded very slowly, suggesting that the explosion did not release copious amounts of energy as usually expected.

Astronomers have now classified SN 2008ha as a subclass of a Type Ia supernova, which is the explosion of a white dwarf that hungrily accretes matter from a companion star. SN 2008ha may have been the result of a partially failed supernova, explaining why the explosion failed to decimate the whole star.

So SN 2008ha may have been an explosion where a part of the white dwarf was destroyed, but not all of it. Very interesting, if you ask me!

Ann

Yes, pretty interesting. It seems no matter how unusual the phenomenon, there is always something even more unusual!

[neufer]

11211 is a Composite Number and can be factored by any of the following numbers.

All the factors of 11211 :
1, 3, 37, 101, 111, 303, 3737, 11211

https://www.calculatorsoup.com/calculat ... ulator.php

Warning: it is very addictive!

<<Sexy primes are prime numbers that differ from each other by 6.

• Sexy primes below 500 are:
  
  (5,11), (7,13), (11,17), (13,19), (17,23), (23,29), (31,37), (37,43), (41,47), (47,53), (53,59), (61,67), (67,73), (73,79), (83,89), (97,103), (101,107), (103,109), (107,113), (131,137), (151,157), (157,163), (167,173), (173,179), (191,197), (193,199), (223,229), (227,233), (233,239), (251,257), (257,263), (263,269), (271,277), (277,283), (307,313), (311,317), (331,337), (347,353), (353,359), (367,373), (373,379), (383,389), (433,439), (443,449), (457,463), (461,467).

As of October 2019, the largest-known pair of sexy primes was found by P. Kaiser and has 50,539 digits. The primes are:

• p = (520461 × 2⁵⁵⁹³¹+1) × (98569639289 × (520461 × 2⁵⁵⁹³¹-1)²-3)-1
  
  p+6 = (520461 × 2⁵⁵⁹³¹+1) × (98569639289 × (520461 × 2⁵⁵⁹³¹-1)²-3)+5

...............................................................
Sexy primes can be extended to larger constellations.

E.g., triplets of primes (p, p+6, p+12) such that p+18 is composite are called sexy prime triplets.

• Sexy prime triplets below 1,000 are:
  
  (7,13,19), (17,23,29), (31,37,43), (47,53,59), (67,73,79), (97,103,109), (101,107,113), (151,157,163), (167,173,179), (227,233,239), (257,263,269), (271,277,283), (347,353,359), (367,373,379), (557,563,569), (587,593,599), (607,613,619), (647,653,659), (727,733,739), (941,947,953), (971,977,983).

in December Norman Luhn & Gerd Lamprecht & Norman Luhn set a record for the largest-known sexy prime triplet with 10,602 digits:

• p = 2683143625525 x 2³⁵¹⁷⁶+1.
  p+6 = 2683143625525 x 2³⁵¹⁷⁶+7.
  p+12 = 2683143625525 x 2³⁵¹⁷⁶+13.

>>

[johnnydeep]

11211 is a Composite Number and can be factored by any of the following numbers.

All the factors of 11211 :
1, 3, 37, 101, 111, 303, 3737, 11211

https://www.calculatorsoup.com/calculat ... ulator.php

Warning: it is very addictive!

<<Sexy primes are prime numbers that differ from each other by 6.

• Sexy primes below 500 are:
  
  (5,11), (7,13), (11,17), (13,19), (17,23), (23,29), (31,37), (37,43), (41,47), (47,53), (53,59), (61,67), (67,73), (73,79), (83,89), (97,103), (101,107), (103,109), (107,113), (131,137), (151,157), (157,163), (167,173), (173,179), (191,197), (193,199), (223,229), (227,233), (233,239), (251,257), (257,263), (263,269), (271,277), (277,283), (307,313), (311,317), (331,337), (347,353), (353,359), (367,373), (373,379), (383,389), (433,439), (443,449), (457,463), (461,467).

As of October 2019, the largest-known pair of sexy primes was found by P. Kaiser and has 50,539 digits. The primes are:

• p = (520461 × 2⁵⁵⁹³¹+1) × (98569639289 × (520461 × 2⁵⁵⁹³¹-1)²-3)-1
  
  p+6 = (520461 × 2⁵⁵⁹³¹+1) × (98569639289 × (520461 × 2⁵⁵⁹³¹-1)²-3)+5

...............................................................
Sexy primes can be extended to larger constellations.

E.g., triplets of primes (p, p+6, p+12) such that p+18 is composite are called sexy prime triplets.

• Sexy prime triplets below 1,000 are:
  
  (7,13,19), (17,23,29), (31,37,43), (47,53,59), (67,73,79), (97,103,109), (101,107,113), (151,157,163), (167,173,179), (227,233,239), (257,263,269), (271,277,283), (347,353,359), (367,373,379), (557,563,569), (587,593,599), (607,613,619), (647,653,659), (727,733,739), (941,947,953), (971,977,983).

in December Norman Luhn & Gerd Lamprecht & Norman Luhn set a record for the largest-known sexy prime triplet with 10,602 digits:

• p = 2683143625525 x 2³⁵¹⁷⁶+1.
  p+6 = 2683143625525 x 2³⁵¹⁷⁶+7.
  p+12 = 2683143625525 x 2³⁵¹⁷⁶+13.

>>

Sometimes mathematicians appear to have too much time on their hands. Sexy Primes seem particularly useless to me, let alone "sexy", and not really even very interesting. Same for "sexy prime triples". Perhaps that's why I abandoned the idea of becoming a professional mathematician after getting an MS in math. Now, consecutive primes {p,p+6} (that is, with no intervening primes), or consecuting primes {p,p+n} for various values of n do seem interesting. And even more interesting is the "primorial" function, which extends the idea of the factorial to the multiplication of all primes up to and including n. See https://en.wikipedia.org/wiki/Primorial