Toy model black holes per galaxy average number...

[Orion1]

Planck satellite baryonic cosmological composition parameter: (ref. 1, pg. 11, ref. 2, pg. 3)
[math]\Omega_{b} = 0.0495[/math]
[math]\;[/math]
Black holes cosmological composition parameter: {ref. 2, pg. 3)
[math]\Omega_{bh} = 0.00007[/math]
[math]\;[/math]
Solar mass: (ref. 3)
[math]M_{\odot} = 1.9885 \cdot 10^{30} \; \text{kg}[/math]
[math]\;[/math]
Milky Way galaxy mass: (ref. 4, pg. 1)
[math]M_{mw} = 1.260 \cdot 10^{12} \cdot M_{\odot} = 2.506 \cdot 10^{42} \; \text{kg}[/math]
[math]\boxed{M_{mw} = 2.506 \cdot 10^{42} \; \text{kg}}[/math]
[math]\;[/math]
PSR J2215+5135 pulsar Tolman-Oppenheimer-Volkoff observational lower mass limit: (ref. 5)
[math]\boxed{M_{bh} \geq 2.27 \cdot M_{\odot}}[/math]
[math]\boxed{M_{bh} \geq 4.514 \cdot 10^{30} \; \text{kg}}[/math]
[math]\;[/math]
Stellar class O upper mass limit: (ref. 6)
[math]\boxed{M_{bh} \geq 16 \cdot M_{\odot}}[/math]
[math]\boxed{M_{bh} \geq 3.182 \cdot 10^{31} \; \text{kg}}[/math]
[math]\;[/math]
Toy model black holes per galaxy average number:
[math]\frac{N_{bh}}{N_g} = \frac{\Omega_{bh} M_{mw}}{\Omega_b M_{bh}} = \left(1.114 \cdot 10^{8} \rightarrow 7.851 \cdot 10^{8} \right) \; \frac{\text{black holes}}{\text{galaxy}}[/math]
[math]\boxed{\frac{N_{bh}}{N_g} = \frac{\Omega_{bh} M_{mw}}{\Omega_b M_{bh}}}[/math]
[math]\boxed{\frac{N_{bh}}{N_g} = \left(1.114 \cdot 10^{8} \rightarrow 7.851 \cdot 10^{8} \right) \; \frac{\text{black holes}}{\text{galaxy}}}[/math]
[math]\;[/math]
Synthetic catalog black holes per galaxy average number: (ref. 7, pg. 1)
[math]\frac{N_{bh}}{N_g} = 1.693 \cdot 10^{8} \; \frac{\text{black holes}}{\text{galaxy}}[/math]
[math]\;[/math]
Any discussions and/or peer reviews about this specific topic thread?
[math]\;[/math]
Reference:
Planck 2013 results. XVI. Cosmological parameters: (ref. 1)
http://planck.caltech.edu/pub/2013results/Planck_2013_results_16.pdf
The Cosmic Energy Inventory: (ref. 2)
http://arxiv.org/pdf/astro-ph/0406095v2.pdf
Wikipedia - Sun Sol: (ref. 3)
https://en.wikipedia.org/wiki/Sun
Mass models of the Milky Way: (ref. 4)
http://arxiv.org/pdf/1102.4340v1
Wikipedia - Tolman-Oppenheimer-Volkoff limit: (ref. 5)
https://en.wikipedia.org/wiki/Tolman-Oppenheimer-Volkoff_limit
Wikipedia - Stellar classification - Harvard spectral classification: (ref. 6)
https://en.wikipedia.org/wiki/Stellar_classification#Harvard_spectral_classification
Synthetic catalog of black holes in the Milky Way: (ref. 7)
https://arxiv.org/pdf/1908.08775.pdf

Edited September 5, 2019 by Orion1
source code correction...

[Orion1]

[math]\color{blue}{\text{Total stellar class number: (ref. 1)}}[/math]
[math]n_c = 7[/math]
[math]\;[/math]
[math]\color{blue}{\text{key: 1 O, 2 B, 3 A, 4 F, 5 G, 6 K, 7 M}}[/math]
[math]\Omega_f - \text{main sequence stars stellar class fraction}[/math]
[math]N_s - \text{total observable stellar number}[/math]
[math]M_s - \text{main sequence stellar mass}[/math]
[math]\;[/math]
[math]\color{blue}{\text{Toy model average stellar mass: (ref. 1)}}[/math]
[math]M_{as} = \frac{1}{N_s} \sum_{n = 1}^{n_c} \Omega_f\left(n \right) N_s M_s\left(n \right) = \sum_{n = 1}^{n_c} \Omega_f\left(n \right) M_s\left(n \right) = 0.219 \cdot M_{\odot} \rightarrow 0.595 \cdot M_{\odot}[/math]
[math]\boxed{M_{as} = \sum_{n = 1}^{n_c} \Omega_f\left(n \right) M_s\left(n \right)} \; \; \; n_c = 7[/math]
[math]\boxed{M_{as} = \left(0.219 \rightarrow 0.595 \right) \cdot M_{\odot}}[/math]
[math]\;[/math]
[math]\color{blue}{\text{Toy model average stellar mass upper bound limit:}}[/math]
[math]\boxed{M_{as} = 1.184 \cdot 10^{30} \; \text{kg}}[/math]
[math]\;[/math]
[math]\color{blue}{\text{Observabe universe average stellar mass: (ref. 2, pg. 20)}}[/math]
[math]M_{as} = 0.6 \cdot M_{\odot} = 1.193 \cdot 10^{30} \; \text{kg}[/math]
[math]M_{as} = 1.193 \cdot 10^{30} \; \text{kg}[/math]
[math]\;[/math]
[math]\color{blue}{\text{Synthetic catalog black holes per galaxy average number: (ref. 3, pg. 1)}}[/math]
[math]\frac{N_{bh}}{N_g} = 1.693 \cdot 10^{8} \; \frac{\text{black holes}}{\text{galaxy}}[/math]
[math]\;[/math]
[math]\color{blue}{\text{Synthetic catalog Milky Way galaxy average black hole mass:}}[/math]
[math]\boxed{M_{bh} = \frac{\Omega_{bh} M_{mw}}{\Omega_{b}} \left(\frac{N_{g}}{N_{bh}} \right)}[/math]
[math]\boxed{M_{bh} = 2.093 \cdot 10^{31} \; \text{kg}}[/math]
[math]\boxed{M_{bh} = 10.527 \cdot M_{\odot}}[/math]
[math]\;[/math]
[math]\color{blue}{\text{Black hole mass spectrum domain: (ref. 4), (ref. 5)}}[/math]
[math]\boxed{2.27 \cdot M_{\odot} \leq M_{bh} \leq 36 \cdot M_{\odot}}[/math]
[math]\color{blue}{\text{Synthetic catalog Milky Way galaxy average black hole mass:}}[/math]
[math]\boxed{M_{bh} = 10.527 \cdot M_{\odot}}[/math]
[math]\color{blue}{\text{Toy model average stellar mass:}}[/math]
[math]\boxed{M_{as} = \left(0.219 \rightarrow 0.595 \right) \cdot M_{\odot}}[/math]
[math]\;[/math]
[math]\color{blue}{\text{Any discussions and/or peer reviews about this specific topic thread?}}[/math]
[math]\;[/math]
Reference:
Wikipedia - Stellar classification - Harvard spectral classification: (ref. 1)
https://en.wikipedia.org/wiki/Stellar_classification#Harvard_spectral_classification
On The Mass Distribution Of Stars...: (ref. 2)
http://www.doiserbia.nb.rs/img/doi/1450-698X/2006/1450-698X0672017N.pdf
Synthetic catalog of black holes in the Milky Way: (ref. 3)
https://arxiv.org/pdf/1908.08775.pdf
Wikipedia - Tolman-Oppenheimer-Volkoff limit: (ref. 4)
https://en.wikipedia.org/wiki/Tolman-Oppenheimer-Volkoff_limit
Wikipedia - Black hole - Detection of gravitation waves from merging black holes: (ref. 5)
https://en.wikipedia.org/wiki/Black_hole#Detection_of_gravitational_waves_from_merging_black_holes

Edited November 13, 2021 by Orion1

[Orion1]

[math]\color{blue}{\text{Planck satellite baryonic cosmological composition parameter:} \; (\text{ref. 1, pg. 11, ref. 2, pg. 3})}[/math]
[math]\Omega_{b} = 0.0495[/math]
[math]\;[/math]
[math]\color{blue}{\text{Black holes cosmological composition parameter:} \; (\text{ref. 2, pg. 3})}[/math]
[math]\Omega_{bh} = 0.00007[/math]
[math]\;[/math]
[math]\color{blue}{\text{Solar mass:} \; (\text{ref. 3})}[/math]
[math]M_{\odot} = 1.9885 \cdot 10^{30} \; \text{kg}[/math]
[math]\;[/math]
[math]\color{blue}{\text{Milky Way galaxy mass:} \; (\text{ref. 4, pg. 1})}[/math]
[math]M_{mw} = 1.260 \cdot 10^{12} \cdot M_{\odot} = 2.506 \cdot 10^{42} \; \text{kg}[/math]
[math]\boxed{M_{mw} = 2.506 \cdot 10^{42} \; \text{kg}}[/math]
[math]\;[/math]
[math]\color{blue}{\text{Toy model stellar baryon composition:} \; (\text{ref. 2, pg. 3})}[/math]
[math]\Omega_s = \left(\Omega_{ms} + \Omega_{wd} + \Omega_{ns} \right) = 2.460 \cdot 10^{-3}[/math]
[math]\boxed{\Omega_s = 2.460 \cdot 10^{-3}}[/math]
[math]\;[/math]
[math]\color{blue}{\text{Total stellar class number:} \; (\text{ref. 5})}[/math]
[math]n_c = 7[/math]
[math]\color{blue}{\text{key: 1 O, 2 B, 3 A, 4 F, 5 G, 6 K, 7 M}}[/math]
[math]\Omega_f - \text{main sequence stars stellar class fraction}[/math]
[math]N_s - \text{total observable stellar number}[/math]
[math]M_s - \text{main sequence stellar mass}[/math]
[math]\;[/math]
[math]\color{blue}{\text{Toy model average stellar mass:} \; (\text{ref. 5})}[/math]
[math]M_{as} = \frac{1}{N_s} \sum_{n = 1}^{n_c} \Omega_f\left(n \right) N_s M_s\left(n \right) = \sum_{n = 1}^{n_c} \Omega_f\left(n \right) M_s\left(n \right) = 0.219 \cdot M_{\odot} \rightarrow 0.595 \cdot M_{\odot}[/math]
[math]\boxed{M_{as} = \sum_{n = 1}^{n_c} \Omega_f\left(n \right) M_s\left(n \right)} \; \; \; n_c = 7[/math]
[math]\boxed{M_{as} = \left(0.219 \rightarrow 0.595 \right) \cdot M_{\odot}}[/math]
[math]\color{blue}{\text{Toy model average stellar mass upper bound limit:}}[/math]
[math]\boxed{M_{as} = 1.184 \cdot 10^{30} \; \text{kg}}[/math]
[math]\color{blue}{\text{Observabe universe average stellar mass:} \; (\text{ref. 6, pg. 20})}[/math]
[math]M_{as} = 0.6 \cdot M_{\odot} = 1.193 \cdot 10^{30} \; \text{kg}[/math]
[math]M_{as} = 1.193 \cdot 10^{30} \; \text{kg}[/math]
[math]\;[/math]
[math]\color{blue}{\text{Toy model Milky Way stars per galaxy average number:}}[/math]
[math]\frac{N_s}{N_g} = \frac{\Omega_s M_{mw}}{\Omega_b M_{as}} = 1.053 \cdot 10^{11} \; \frac{\text{stars}}{\text{galaxy}}[/math]
[math]\boxed{\frac{N_s}{N_g} = \frac{\Omega_s M_{mw}}{\Omega_b M_{as}}}[/math]
[math]\boxed{\frac{N_s}{N_g} = 1.053 \cdot 10^{11} \; \frac{\text{stars}}{\text{galaxy}}}[/math]
[math]\;[/math]
[math]\color{blue}{\text{Observable universe stars per galaxy average number:} \; (\text{ref. 7, ref. 8})}[/math]
[math]\frac{N_s}{N_g} = 1.500 \cdot 10^{11} \; \frac{\text{stars}}{\text{galaxy}}[/math]
[math]\;[/math]
[math]\color{blue}{\text{Observable universe Milky Way galaxy total stellar number:} \; (\text{ref. 8})}[/math]
[math]\frac{N_s}{N_g} = 2.500 \cdot 10^{11} \pm 1.500 \cdot 10^{11} \; \frac{\text{stars}}{\text{galaxy}} \; \; \; \; \; \frac{N_s}{N_g} = \left(1.000 \cdot 10^{11} \rightarrow 4.000 \cdot 10^{11} \right) \; \frac{\text{stars}}{\text{galaxy}}[/math]
[math]\;[/math]
[math]\color{blue}{\text{Toy model Milky Way black holes per galaxy average number integration via substitution:}}[/math]
[math]\frac{N_{bh}}{N_{g}} = \frac{\Omega_{bh}}{\Omega_{b}} \left(\frac{N_{s}}{N_{g}} \right) = \frac{\Omega_{bh}}{\Omega_{b}} \left(\frac{\Omega_s M_{mw}}{\Omega_b M_{as}} \right) = \frac{\Omega_{bh} \Omega_s M_{mw}}{\Omega_{b}^{2} M_{as}} = 1.489 \cdot 10^{8} \; \frac{\text{black holes}}{\text{galaxy}}[/math]
[math]\;[/math]
[math]\color{blue}{\text{Toy model Milky Way black holes per galaxy average number:}}[/math]
[math]\boxed{\frac{N_{bh}}{N_{g}} = \frac{\Omega_{bh} \Omega_s M_{mw}}{\Omega_{b}^{2} M_{as}}}[/math]
[math]\boxed{\frac{N_{bh}}{N_{g}} = 1.489 \cdot 10^{8} \; \frac{\text{black holes}}{\text{galaxy}}}[/math]
[math]\;[/math]
[math]\color{blue}{\text{Synthetic catalog black holes per galaxy average number:} \; (\text{ref. 9, pg. 1})}[/math]
[math]\frac{N_{bh}}{N_g} = 1.693 \cdot 10^{8} \; \frac{\text{black holes}}{\text{galaxy}}[/math]
[math]\;[/math]
[math]\color{blue}{\text{Observable universe Milky Way black holes per galaxy average number:}}[/math]
[math]\boxed{\frac{N_{bh}}{N_{g}} = \frac{\Omega_{bh}}{\Omega_{b}} \left(\frac{N_{s}}{N_{g}} \right)}[/math]
[math]\boxed{\frac{N_{bh}}{N_g} = \left(1.414 \cdot 10^{8} \rightarrow 5.657 \cdot 10^{8} \right) \; \frac{\text{black holes}}{\text{galaxy}}}[/math]
[math]\;[/math]
[math]\color{blue}{\text{Toy model Milky Way galaxy average black hole mass integration via substitution:}}[/math]
[math]M_{bh} = \frac{\Omega_{bh} M_{mw}}{\Omega_{b}} \left(\frac{N_{g}}{N_{bh}} \right) = \frac{\Omega_{bh} M_{mw}}{\Omega_{b}} \left[\frac{\Omega_{b}^{2} M_{as}}{\Omega_{bh} \Omega_s M_{mw}} \right] = \left(\frac{\Omega_{b}}{\Omega_{s}} \right) M_{as} = 2.379 \cdot 10^{31} \; \text{kg}[/math]
[math]\;[/math]
[math]\color{blue}{\text{Toy model Milky Way galaxy average black hole mass:}}[/math]
[math]\boxed{M_{bh} = \left(\frac{\Omega_{b}}{\Omega_{s}} \right) M_{as}}[/math]
[math]\boxed{M_{bh} = 2.382 \cdot 10^{31} \; \text{kg}}[/math]
[math]\boxed{M_{bh} = 11.979\cdot M_{\odot}}[/math]
[math]\;[/math]
[math]\color{blue}{\text{Synthetic catalog Milky Way galaxy average black hole mass:}}[/math]
[math]\boxed{M_{bh} = \frac{\Omega_{bh} M_{mw}}{\Omega_{b}} \left(\frac{N_{g}}{N_{bh}} \right)}[/math]
[math]\boxed{M_{bh} = 2.093 \cdot 10^{31} \; \text{kg}}[/math]
[math]\boxed{M_{bh} = 10.527 \cdot M_{\odot}}[/math]
[math]\;[/math]
[math]\color{blue}{\text{Observable universe Milky Way galaxy average black hole mass integration via substitution:}}[/math]
[math]M_{bh} = \frac{\Omega_{bh} M_{mw}}{\Omega_{b}} \left(\frac{N_{g}}{N_{bh}} \right) = \frac{\Omega_{bh} M_{mw}}{\Omega_{b}} \left[\frac{\Omega_{b}}{\Omega_{bh}} \left(\frac{N_{g}}{N_{s}} \right) \right] = M_{mw} \left(\frac{N_{g}}{N_{s}} \right) = 6.265 \cdot 10^{30} \; \text{kg} \rightarrow 2.506 \cdot 10^{31} \; \text{kg}[/math]
[math]\;[/math]
[math]\color{blue}{\text{Observable universe Milky Way galaxy average black hole mass:}}[/math]
[math]\boxed{M_{bh} = M_{mw} \left(\frac{N_{g}}{N_{s}} \right)}[/math]
[math]\boxed{M_{bh} = \left(6.265 \cdot 10^{30} \; \text{kg} \rightarrow 2.506 \cdot 10^{31} \; \text{kg} \right)}[/math]
[math]\boxed{M_{bh} = \left(3.151 \rightarrow 12.603 \right) \cdot M_{\odot}}[/math]
[math]\;[/math]
[math]\color{blue}{\text{Black hole mass spectrum domain:} \; (\text{ref. 10, ref. 11})}[/math]
[math]\boxed{2.27 \cdot M_{\odot} \leq M_{bh} \leq 36 \cdot M_{\odot}}[/math]
[math]\;[/math]
[math]\color{blue}{\text{Calculation results summary:}}[/math]
[math]\color{blue}{\text{Toy model Milky Way black holes per galaxy average number:}}[/math]
[math]\boxed{\frac{N_{bh}}{N_{g}} = 1.489 \cdot 10^{8} \; \frac{\text{black holes}}{\text{galaxy}}}[/math]
[math]\color{blue}{\text{Synthetic catalog black holes per galaxy average number:}}[/math]
[math]\frac{N_{bh}}{N_g} = 1.693 \cdot 10^{8} \; \frac{\text{black holes}}{\text{galaxy}}[/math]
[math]\color{blue}{\text{Observable universe Milky Way black holes per galaxy average number:}}[/math]
[math]\boxed{\frac{N_{bh}}{N_g} = \left(1.414 \cdot 10^{8} \rightarrow 5.657 \cdot 10^{8} \right) \; \frac{\text{black holes}}{\text{galaxy}}}[/math]
[math]\color{blue}{\text{Toy model Milky Way galaxy average black hole mass:}}[/math]
[math]\boxed{M_{bh} = 11.979 \cdot M_{\odot}}[/math]
[math]\color{blue}{\text{Synthetic catalog Milky Way galaxy average black hole mass:}}[/math]
[math]\boxed{M_{bh} = 10.527 \cdot M_{\odot}}[/math]
[math]\color{blue}{\text{Observable universe Milky Way galaxy average black hole mass:}}[/math]
[math]\boxed{M_{bh} = \left(3.151 \rightarrow 12.603 \right) \cdot M_{\odot}}[/math]
[math]\color{blue}{\text{Toy model average stellar mass:}}[/math]
[math]\boxed{M_{as} = \left(0.219 \rightarrow 0.595 \right) \cdot M_{\odot}}[/math]
[math]\;[/math]
[math]\color{blue}{\text{Any discussions and/or peer reviews about this specific topic thread?}}[/math]
[math]\;[/math]
Reference:
Planck 2013 results. XVI. Cosmological parameters: (ref. 1)
https://arxiv.org/pdf/1303.5076.pdf
The Cosmic Energy Inventory: (ref. 2)
http://arxiv.org/pdf/astro-ph/0406095v2.pdf
Wikipedia - Sun Sol: (ref. 3)
https://en.wikipedia.org/wiki/Sun
Mass models of the Milky Way: (ref. 4)
http://arxiv.org/pdf/1102.4340v1
Wikipedia - Stellar classification - Harvard spectral classification: (ref. 5)
https://en.wikipedia.org/wiki/Stellar_classification#Harvard_spectral_classification
On The Mass Distribution Of Stars...: (ref. 6)
http://www.doiserbia.nb.rs/img/doi/1450-698X/2006/1450-698X0672017N.pdf
Wikipedia - Observable universe total stellar number: (ref. 7)
https://en.wikipedia.org/wiki/Star#Distribution
Wikipedia - Milky Way Galaxy: (ref. 8)
https://en.wikipedia.org/wiki/Milky_Way
Synthetic catalog of black holes in the Milky Way: (ref. 9)
https://arxiv.org/pdf/1908.08775.pdf
Wikipedia - Tolman-Oppenheimer-Volkoff limit: (ref. 10)
https://en.wikipedia.org/wiki/Tolman-Oppenheimer-Volkoff_limit
Wikipedia - Black hole: (ref. 11)
https://en.wikipedia.org/wiki/Black_hole#Detection_of_gravitational_waves_from_merging_black_holes

Edited November 29, 2021 by Orion1

[iNow]

I think you need a blog more than a forum. 

[swansont]

4 hours ago, iNow said:

I think you need a blog more than a forum. 

!

Moderator Note

I'm not going to fault someone for not getting responses on a narrowly-focused topic. There is a clear invitation to discussion, there are calculations and copious references for interested parties, which is in stark contrast to most speculations threads. 

<referee motions for play to continue>

 

[beecee]

12 hours ago, Orion1 said:

 Any discussions or peer reviews about this topic thread?

As a poor old soul, who is not into the complicated mathematics of BH's, could someone tell me, what Orion1 is concluding, and if or how that conclusion differs from the mainstream conclusion.

much appreciated.

[Bufofrog]

As a poor old soul, who is not into the complicated mathematics of BH's, could someone tell me, what Orion1 is concluding, and if or how that conclusion differs from the mainstream conclusion.

His calculations look within the rather large error bars for the estimates of the number of blackholes in a galaxy.  Essentially you estimate the number of large stars (that collapse into blackholes) over the life of the galaxy and estimate the life of such stars and then you have the number of black holes in the galaxy.  There are a lot of errors in the estimates as you can well imagine hence the large variation in the number of black holes estimated. 

Edited November 29, 2021 by Bufofrog

[beecee]

18 minutes ago, Bufofrog said:

 

His calculations look within the rather large error bars for the estimates of the number of blackholes in a galaxy.  Essentially you estimate the number of large stars (that collapse into blackholes) over the life of the galaxy and estimate the life of such stars and then you have the number of black holes in the galaxy.  There are a lot of errors in the estimates as you can well imagine hence the large variation in the number of black holes estimated. 

I was sort of thinking along those lines, thanks anyway. So really not something essentially opposed/alternative to the mainstream picture re BH's? (except perhaps estimate numbers) 

[Bufofrog]

1 hour ago, beecee said:

I was sort of thinking along those lines, thanks anyway. So really not something essentially opposed/alternative to the mainstream picture re BH's? (except perhaps estimate numbers)

I haven't taken time to read much of what he wrote.  He didn't take the time to discuss what he was doing, instead he just sited sources without explanation for his equations.  If he can't take the time to explain what he is doing I am not going to take the time to go through his sources to see why he is doing. [shrug]

[Orion1]

Quote

I think you need a blog more than a forum.

Peer review discussions have proven to be more valuable in improving my research, equations, calculations and solutions than a blog.

Quote

(Time) is one of those concepts that is profoundly resistant to a simple definition. - Carl Sagan

Time: The indefinite continued progress of existence and events in the past, present, and future regarded as a whole.
"travel through space and time"

The definition seems simple enough.

Quote

could someone tell me, what Orion1 is concluding, and if or how that conclusion differs from the mainstream conclusion.

I am attempting to look within the rather large error bars for the estimates of the number of black holes in a galaxy. The calculated solutions are within the parameters of the mainstream conclusion. The difference is that the prior required only a single equation, while the latter required a sophisticated computer algorithm.

Quote

So really not something essentially opposed/alternative to the mainstream picture re BH's? (except perhaps estimate numbers)

Does not oppose but validates the mainstream picture, however, this offers an alternative solution to mainstream physics. In terms of stellar astrophysics, the estimate numbers are equivalent to an arrow hitting a target bulls-eye.

Quote

I haven't taken time to read much of what he wrote. He didn't take the time to discuss what he was doing.

Time is the indefinite continued progress of existence and events in the past, present, and future regarded as a whole.

I am attempting to look within the rather large error bars for the estimates of the number of black holes in a galaxy.

Quote

If he can't take the time to explain what he is doing I am not going to take the time to go through his sources to see why he is doing.

There is no discussion requirement to follow external sources, those external sources exist because the burden of proof is mine.

However, anyone interested in astrophysics would be depleting themselves of interesting information by not researching available resource materials.

"I would rather have questions that can't be answered than answers that can't be questioned." - Richard Feynman
 

Edited November 30, 2021 by Orion1

[StringJunky]

Orion1 wants his work to be analyzed and shot at.... unlike many.

[beecee]

9 hours ago, Orion1 said:

I am attempting to look within the rather large error bars for the estimates of the number of black holes in a galaxy. The calculated solutions are within the parameters of the mainstream conclusion. The difference is that the prior required only a single equation, while the latter required a sophisticated computer algorithm.

Does not oppose but validates the mainstream picture, however, this offers an alternative solution to mainstream physics. In terms of stellar astrophysics, the estimate numbers are equivalent to an arrow hitting a target bulls-eye.

 

I am attempting to look within the rather large error bars for the estimates of the number of black holes in a galaxy.
 

Ahhha thanks for that. I am not qualified to review your estimates nor the methodology you are using, its just that on many occasions, we do have others that even dispute their existence. I hope you get your answer.

My only question would be, if your estimates are correct and there are far more BH's then thought, could that constitute the Dark Matter problem? ( or part thereof) MACHO's come to mind.

How many BH's out there may not have accretion disks? (having been around long enough to consume all matter/energy within its region) is another consideration I think.

PS: If this is detracting from your posts and thread orion1, then ignore it and perhaps a mod may even move.

[Orion1]

Orion1 wants his work to be analyzed and shot at.... unlike many.
Peer review discussions have proven to be more valuable in improving my research, equations, calculations and solutions.

Confucius says: Man with watch always knows the time. Man with two watches is never sure.
And two men each with a watch, and time becomes relative.

I am not qualified to review your estimates nor the methodology you are using, its just that on many occasions, we do have others that even dispute their existence.
The ability to multiply and divide math is the only qualification to review my estimates. I disagree that my equations are incomprehensible. There is observational evidence for the existence of black holes. 
On 10 April 2019 an image was released of a black hole, which is seen in magnified fashion because the light paths near the event horizon are highly bent. The dark shadow in the middle results from light paths absorbed by the black hole. The image is in false color, as the detected light halo in this image is not in the visible spectrum, but radio waves.

The Event Horizon Telescope (EHT), is an active program that directly observes the immediate environment of the event horizon of black holes, such as the black hole at the centre of the Milky Way. In April 2017, The Event Horizon Telescope (EHT) began observation of the black hole in the center of Messier 87.

Prior to this, in 2015, the The Event Horizon Telescope (EHT) detected magnetic fields just outside the event horizon of Sagittarius A*.

On 14 September 2015 the LIGO gravitational wave observatory made the first-ever successful direct observation of gravitational waves. The signal was consistent with theoretical predictions for the gravitational waves produced by the merger of two black holes: one with about 36 solar masses, and the other around 29 solar masses. This observation provides the most concrete evidence for the existence of black holes to date.

if your estimates are correct and there are far more BH's then thought, could that constitute the Dark Matter problem? (or part thereof) MACHO's come to mind.
Negative, in my opinion black holes do not constitute dark matter. Although the population densities and masses seem high, their overall compositional parameter is low compared to the dark matter compositional parameter:
 

Black holes cosmological composition parameter:
[math]\Omega_{bh} = 0.00007[/math]
Dark matter cosmological composition parameter:
[math]\Omega_{dm} = 0.268[/math]
This means that 0.007% of everything is composed of black holes, while 26.8% of everything is composed of dark matter.

Dark energy composition plus dark matter composition plus baryonic matter composition equals one.
[math]\Omega_{\Lambda} + \Omega_{dm} + \Omega_{b} = 1[/math]
68.25% + 26.8% + 4.95% = 100%

In my opinion, the "Bullet Cluster" rules out all candidate theories for dark matter, except for, (and possibly non-baryonic), extremely small mass quantum particles.

Several groups have searched for MACHOs by searching for the microlensing amplification of light. These groups have ruled out dark matter being explained by MACHOs with mass in the range 1×10−8 solar masses (0.3 lunar masses) to 100 solar masses.

These searches have ruled out the possibility that these objects make up a significant fraction of dark matter in our galaxy.

Observations using the Hubble Space Telescope's NICMOS instrument showed that less than one percent of the halo mass is composed of red dwarfs. This corresponds to a negligible fraction of the dark matter halo mass. Therefore, the missing mass problem is not solved by MACHOs.

How many BH's out there may not have accretion disks? (having been around long enough to consume all matter/energy within its region) is another consideration I think.
This is a dynamic question that depends mostly on the environment that the black hole was generated in, its age, and the availability of baryonic matter in that environment as accretion fuel. I would expect newly generated black holes to have a bright accretion disk and polar jets, and as time passes, the disk and jets fade away from fuel exhaustion, with the remaining residual baryonic matter being driven away by the accretion and polar jet radiation. 

However, black holes in binary systems could receive an unstable continuous supply of fuel from their companion star's solar wind, or if within proximity, accreted directly from the companion star's surface, possibly producing intermittent high energy x-ray and gamma radiation bursts.

According to the "Synthetic catalog of black holes in the Milky Way", there are 9.3 million black holes in binary systems:

Black Holes in binary systems:
[math]N_{bhb} = 9.3 \cdot 10^{6} \; \text{black holes}[/math]

"Only when it is dark enough can you see the stars." - Martin Luther King, Jr.

Reference:
Wikipedia - Black hole - Observational evidence/Accretion of matter:
https://en.wikipedia.org/wiki/Black_hole#Observational_evidence
https://en.wikipedia.org/wiki/Black_hole#Accretion_of_matter
Wikipedia - Dark matter
https://en.wikipedia.org/wiki/Dark_matter
Wikipedia - Bullet Cluster:
https://en.wikipedia.org/wiki/Bullet_Cluster
Wikipedia - Massive compact halo object
https://en.wikipedia.org/wiki/Massive_compact_halo_object
Synthetic catalog of black holes in the Milky Way:
https://arxiv.org/pdf/1908.08775.pdf
 

Edited December 1, 2021 by Orion1

[beecee]

3 hours ago, Orion1 said:

On 10 April 2019 an image was released of a black hole, which is seen in magnified fashion because the light paths near the event horizon are highly bent. The dark shadow in the middle results from light paths absorbed by the black hole. The image is in false color, as the detected light halo in this image is not in the visible spectrum, but radio waves.

I hope you have not misunderstood me...I was in no way inferring you doubted the existence of BH's. I also see the evidence for them as conclusive. Question/s I put to any doubters, is to explain the observational data another way.

Thatnks for an informative post and your answers to questions I asked. 

[Orion1]

we do have others that even dispute their existence.

There is no misunderstanding, I was merely responding that there is in fact a long standing dispute if black holes exist or not. Any observational evidence for their existence was not available until Cygnus X-1 was discovered in 1964. For any scientific claim, the burden of proof is on the individual making such a claim. Therefore, absent any observational evidence, the rational default position is that they are merely potentially falsifiable "theoretical artifacts" until experimental observational evidence becomes available.

Even Albert Einstein doubted the existence of black holes.

In a paper written in 1939, Albert Einstein attempted to reject the notion of black holes that his theory of general relativity and gravity, published more than two decades earlier, seemed to predict.

Einstein denied several times that black holes could form. In 1939 he published a paper that argues that a star collapsing would spin faster and faster, spinning at the speed of light with infinite energy well before the point where it is about to collapse into a Schwarzchild singularity, or black hole.

"The essential result of this investigation is a clear understanding as to why the "Schwarzschild singularities" do not exist in physical reality. Although the theory given here treats only clusters whose particles move along circular paths it does not seem to be subject to reasonable doubt that mote general cases will have analogous results. The "Schwarzschild singularity" does not appear for the reason that matter cannot be concentrated arbitrarily. And this is due to the fact that otherwise the constituting particles would reach the velocity of light." - Albert Einstein

Reference:
Wikipedia - Cygnus X-1:
https://en.wikipedia.org/wiki/Cygnus_X-1
Wikipedia - List of black_holes:
https://en.wikipedia.org/wiki/List_of_black_holes
The Racah Institute of Physics - On A Stationary System With Spherical Symmetry Consisting Of Many Gravitating Masses - Albert Einstein - 1939:
http://old.phys.huji.ac.il/~barak_kol/Courses/Black-holes/reading-papers/Einstein1939.pdf
 

Edited December 2, 2021 by Orion1

[Bufofrog]

Reference 1 of the OP can't be found.

[Orion1]

On 12/2/2021 at 7:32 AM, Bufofrog said:

Reference 1 of the OP can't be found.

Affirmative, that OP post 1, reference 1 link has since been broken after it was posted on September 4, 2019.

The updated reference link is still available on post 3, reference 1, and in Reference here.

"Once we accept our limits, we go beyond them." - Albert Einstein

Reference:
Planck 2013 results. XVI. Cosmological parameters:
https://arxiv.org/pdf/1303.5076.pdf
Toy model black holes per galaxy average number - post 3 - Orion1:
https://www.scienceforums.net/topic/120012-toy-model-black-holes-per-galaxy-average-number/?do=findComment&comment=1192794
 

Edited December 4, 2021 by Orion1

[Orion1]

I am attempting to look within the rather large error bars for the estimates of the number of black holes in a galaxy. The calculated solutions are within the parameters of the mainstream conclusion.

Revision complete for year 2020 data...  

[math]\color{blue}{\text{Planck satellite baryonic cosmological composition parameter:} \; (\text{ref. 1, pg. 11, ref. 2, pg. 3})}[/math]
[math]\Omega_{b} = 0.0495[/math]
[math]\;[/math]
[math]\color{blue}{\text{Black holes cosmological composition parameter:} \; (\text{ref. 2, pg. 3})}[/math]
[math]\Omega_{bh} = 0.00007[/math]
[math]\;[/math]
[math]\color{blue}{\text{Solar mass:} \; (\text{ref. 3})}[/math]
[math]M_{\odot} = 1.9885 \cdot 10^{30} \; \text{kg}[/math]
[math]\;[/math]
[math]\color{blue}{\text{Milky Way galaxy mass:} \; (\text{ref. 4, pg. 1})}[/math]
[math]M_{mw} = 1.260 \cdot 10^{12} \cdot M_{\odot} = 2.506 \cdot 10^{42} \; \text{kg}[/math]
[math]\boxed{M_{mw} = 2.506 \cdot 10^{42} \; \text{kg}}[/math]
[math]\;[/math]
[math]\color{blue}{\text{Toy model stellar baryon composition:} \; (\text{ref. 2, pg. 3})}[/math]
[math]\Omega_s = \left(\Omega_{ms} + \Omega_{wd} + \Omega_{ns} \right) = 2.460 \cdot 10^{-3}[/math]
[math]\boxed{\Omega_s = 2.460 \cdot 10^{-3}}[/math]
[math]\Omega_{ms} - \text{main sequence stars cosmological composition parameter}[/math]
[math]\Omega_{wd} - \text{white dwarf stars cosmological composition parameter}[/math]
[math]\Omega_{ns}- \text{neutron stars cosmological composition parameter}[/math]
[math]\;[/math]
[math]\color{blue}{\text{Total stellar class number:} \; (\text{ref. 5})}[/math]
[math]n_c = 7[/math]
[math]\color{blue}{\text{key: 1 O, 2 B, 3 A, 4 F, 5 G, 6 K, 7 M}}[/math]
[math]\Omega_f - \text{main sequence stars stellar class fraction}[/math]
[math]N_s - \text{total observable stellar number}[/math]
[math]M_s - \text{main sequence stellar mass}[/math]
[math]\;[/math]
[math]\color{blue}{\text{Toy model average stellar mass:} \; (\text{ref. 5})}[/math]
[math]M_{as} = \frac{1}{N_s} \sum_{n = 1}^{n_c} \Omega_f\left(n \right) N_s M_s\left(n \right) = \sum_{n = 1}^{n_c} \Omega_f\left(n \right) M_s\left(n \right) = 0.219 \cdot M_{\odot} \rightarrow 0.595 \cdot M_{\odot}[/math]
[math]\boxed{M_{as} = \sum_{n = 1}^{n_c} \Omega_f\left(n \right) M_s\left(n \right)} \; \; \; n_c = 7[/math]
[math]\boxed{M_{as} = \left(0.219 \rightarrow 0.595 \right) \cdot M_{\odot}}[/math]
[math]\color{blue}{\text{Toy model average stellar mass upper bound limit:}}[/math]
[math]\boxed{M_{as} = 1.184 \cdot 10^{30} \; \text{kg}}[/math]
[math]\color{blue}{\text{Observabe universe average stellar mass:} \; (\text{ref. 6, pg. 20})}[/math]
[math]M_{as} = 0.6 \cdot M_{\odot} = 1.193 \cdot 10^{30} \; \text{kg}[/math]
[math]M_{as} = 1.193 \cdot 10^{30} \; \text{kg}[/math]
[math]\;[/math]
[math]\color{blue}{\text{Toy model Milky Way stars per galaxy average number:}}[/math]
[math]\frac{N_s}{N_g} = \frac{\Omega_s M_{mw}}{\Omega_b M_{as}} = 1.053 \cdot 10^{11} \; \frac{\text{stars}}{\text{galaxy}}[/math]
[math]\boxed{\frac{N_s}{N_g} = \frac{\Omega_s M_{mw}}{\Omega_b M_{as}}}[/math]
[math]\boxed{\frac{N_s}{N_g} = 1.053 \cdot 10^{11} \; \frac{\text{stars}}{\text{galaxy}}}[/math]
[math]\;[/math]
[math]\color{blue}{\text{Observable universe stars per galaxy average number:} \; (\text{ref. 7, ref. 8})}[/math]
[math]\frac{N_s}{N_g} = 1.500 \cdot 10^{11} \; \frac{\text{stars}}{\text{galaxy}}[/math]
[math]\;[/math]
[math]\color{blue}{\text{Observable universe Milky Way galaxy total stellar number:} \; (\text{ref. 8})}[/math]
[math]\frac{N_s}{N_g} = 2.500 \cdot 10^{11} \pm 1.500 \cdot 10^{11} \; \frac{\text{stars}}{\text{galaxy}} \; \; \; \; \; \frac{N_s}{N_g} = \left(1.000 \cdot 10^{11} \rightarrow 4.000 \cdot 10^{11} \right) \; \frac{\text{stars}}{\text{galaxy}}[/math]
[math]\;[/math]
[math]\color{blue}{\text{Toy model Milky Way black holes per galaxy average number integration via substitution:}}[/math]
[math]\frac{N_{bh}}{N_{g}} = \frac{\Omega_{bh}}{\Omega_{b}} \left(\frac{N_{s}}{N_{g}} \right) = \frac{\Omega_{bh}}{\Omega_{b}} \left(\frac{\Omega_s M_{mw}}{\Omega_b M_{as}} \right) = \frac{\Omega_{bh} \Omega_s M_{mw}}{\Omega_{b}^{2} M_{as}} = 1.489 \cdot 10^{8} \; \frac{\text{black holes}}{\text{galaxy}}[/math]
[math]\;[/math]
[math]\color{blue}{\text{Toy model Milky Way black holes per galaxy average number:}}[/math]
[math]\boxed{\frac{N_{bh}}{N_{g}} = \frac{\Omega_{bh} \Omega_s M_{mw}}{\Omega_{b}^{2} M_{as}}}[/math]
[math]\boxed{\frac{N_{bh}}{N_{g}} = 1.489 \cdot 10^{8} \; \frac{\text{black holes}}{\text{galaxy}}}[/math]
[math]\;[/math]
[math]\color{blue}{\text{Synthetic catalog black holes per galaxy average number:} \; (\text{ref. 9, pg. 1})}[/math]
[math]\frac{N_{bh}}{N_g} = 1.293 \cdot 10^{8} \; \frac{\text{black holes}}{\text{galaxy}}[/math]
[math]\;[/math]
[math]\color{blue}{\text{Observable universe Milky Way black holes per galaxy average number:}}[/math]
[math]\boxed{\frac{N_{bh}}{N_{g}} = \frac{\Omega_{bh}}{\Omega_{b}} \left(\frac{N_{s}}{N_{g}} \right)}[/math]
[math]\boxed{\frac{N_{bh}}{N_g} = \left(1.414 \cdot 10^{8} \rightarrow 5.657 \cdot 10^{8} \right) \; \frac{\text{black holes}}{\text{galaxy}}}[/math]
[math]\;[/math]
[math]\color{blue}{\text{Toy model Milky Way galaxy average black hole mass integration via substitution:}}[/math]
[math]M_{bh} = \frac{\Omega_{bh} M_{mw}}{\Omega_{b}} \left(\frac{N_{g}}{N_{bh}} \right) = \frac{\Omega_{bh} M_{mw}}{\Omega_{b}} \left[\frac{\Omega_{b}^{2} M_{as}}{\Omega_{bh} \Omega_s M_{mw}} \right] = \left(\frac{\Omega_{b}}{\Omega_{s}} \right) M_{as} = 2.379 \cdot 10^{31} \; \text{kg}[/math]
[math]\;[/math]
[math]\color{blue}{\text{Toy model Milky Way galaxy average black hole mass:}}[/math]
[math]\boxed{M_{bh} = \left(\frac{\Omega_{b}}{\Omega_{s}} \right) M_{as}}[/math]
[math]\boxed{M_{bh} = 2.382 \cdot 10^{31} \; \text{kg}}[/math]
[math]\boxed{M_{bh} = 11.979\cdot M_{\odot}}[/math]
[math]\;[/math]
[math]\color{blue}{\text{Calculated synthetic catalog Milky Way galaxy average black hole mass:}}[/math]
[math]\boxed{M_{bh} = \frac{\Omega_{bh} M_{mw}}{\Omega_{b}} \left(\frac{N_{g}}{N_{bh}} \right)}[/math]
[math]\boxed{M_{bh} = 2.741 \cdot 10^{31} \; \text{kg}}[/math]
[math]\boxed{M_{bh} = 13.783 \cdot M_{\odot}}[/math]
[math]\;[/math]
[math]\color{blue}{\text{Synthetic catalog Milky Way galaxy average black hole mass:} \; (\text{ref. 9, pg. 1})}[/math]
[math]M_{bh} = 2.784 \cdot 10^{31} \; \text{kg}[/math]
[math]M_{bh} = 14.000 \cdot M_{\odot}[/math]
[math]\;[/math]
[math]\color{blue}{\text{Observable universe Milky Way galaxy average black hole mass integration via substitution:}}[/math]
[math]M_{bh} = \frac{\Omega_{bh} M_{mw}}{\Omega_{b}} \left(\frac{N_{g}}{N_{bh}} \right) = \frac{\Omega_{bh} M_{mw}}{\Omega_{b}} \left[\frac{\Omega_{b}}{\Omega_{bh}} \left(\frac{N_{g}}{N_{s}} \right) \right] = M_{mw} \left(\frac{N_{g}}{N_{s}} \right) = 6.265 \cdot 10^{30} \; \text{kg} \rightarrow 2.506 \cdot 10^{31} \; \text{kg}[/math]
[math]\;[/math]
[math]\color{blue}{\text{Observable universe Milky Way galaxy average black hole mass:}}[/math]
[math]\boxed{M_{bh} = M_{mw} \left(\frac{N_{g}}{N_{s}} \right)}[/math]
[math]\boxed{M_{bh} = \left(6.265 \cdot 10^{30} \; \text{kg} \rightarrow 2.506 \cdot 10^{31} \; \text{kg} \right)}[/math]
[math]\boxed{M_{bh} = \left(3.151 \rightarrow 12.603 \right) \cdot M_{\odot}}[/math]
[math]\;[/math]
[math]\color{blue}{\text{Black hole mass spectrum domain:} \; (\text{ref. 10, ref. 11})}[/math]
[math]\boxed{2.27 \cdot M_{\odot} \leq M_{bh} \leq 36 \cdot M_{\odot}}[/math]
[math]\;[/math]
[math]\color{blue}{\text{Calculation results summary:}}[/math]
[math]\color{blue}{\text{Toy model Milky Way black holes per galaxy average number:}}[/math]
[math]\boxed{\frac{N_{bh}}{N_{g}} = 1.489 \cdot 10^{8} \; \frac{\text{black holes}}{\text{galaxy}}}[/math]
[math]\color{blue}{\text{Synthetic catalog black holes per galaxy average number:}}[/math]
[math]\frac{N_{bh}}{N_g} = 1.293 \cdot 10^{8} \; \frac{\text{black holes}}{\text{galaxy}}[/math]
[math]\color{blue}{\text{Observable universe Milky Way black holes per galaxy average number:}}[/math]
[math]\boxed{\frac{N_{bh}}{N_g} = \left(1.414 \cdot 10^{8} \rightarrow 5.657 \cdot 10^{8} \right) \; \frac{\text{black holes}}{\text{galaxy}}}[/math]
[math]\color{blue}{\text{Toy model Milky Way galaxy average black hole mass:}}[/math]
[math]\boxed{M_{bh} = 11.979 \cdot M_{\odot}}[/math]
[math]\color{blue}{\text{Calculated synthetic catalog Milky Way galaxy average black hole mass:}}[/math]
[math]\boxed{M_{bh} = 13.783 \cdot M_{\odot}}[/math]
[math]\color{blue}{\text{Synthetic catalog Milky Way galaxy average black hole mass:}}[/math]
[math]M_{bh} = 14.000 \cdot M_{\odot}[/math]
[math]\color{blue}{\text{Observable universe Milky Way galaxy average black hole mass:}}[/math]
[math]\boxed{M_{bh} = \left(3.151 \rightarrow 12.603 \right) \cdot M_{\odot}}[/math]
[math]\color{blue}{\text{Toy model average stellar mass:}}[/math]
[math]\boxed{M_{as} = \left(0.219 \rightarrow 0.595 \right) \cdot M_{\odot}}[/math]
[math]\;[/math]
[math]\color{blue}{\text{Any discussions and/or peer reviews about this specific topic thread?}}[/math]
[math]\;[/math]
"This above all: to thine own self be true, And it must follow, as the night the day, Thou canst not then be false to any man." - Polonius
[math]\;[/math]
Reference:
Planck 2013 results. XVI. Cosmological parameters: (ref. 1)
https://arxiv.org/pdf/1303.5076.pdf
The Cosmic Energy Inventory: (ref. 2)
http://arxiv.org/pdf/astro-ph/0406095v2.pdf
Wikipedia - Sun Sol: (ref. 3)
https://en.wikipedia.org/wiki/Sun
Mass models of the Milky Way: (ref. 4)
http://arxiv.org/pdf/1102.4340v1
Wikipedia - Stellar classification - Harvard spectral classification: (ref. 5)
https://en.wikipedia.org/wiki/Stellar_classification#Harvard_spectral_classification
On The Mass Distribution Of Stars...: (ref. 6)
http://www.doiserbia.nb.rs/img/doi/1450-698X/2006/1450-698X0672017N.pdf
Wikipedia - Observable universe total stellar number: (ref. 7)
https://en.wikipedia.org/wiki/Star Distribution
Wikipedia - Milky Way Galaxy: (ref. 8)
https://en.wikipedia.org/wiki/Milky Way
Synthetic catalog of black holes in the Milky Way (2020): (ref. 9)
https://arxiv.org/pdf/1908.08775.pdf
Wikipedia - Tolman-Oppenheimer-Volkoff limit: (ref. 10)
https://en.wikipedia.org/wiki/Tolman-Oppenheimer-Volkoff_limit
Wikipedia - Black hole: (ref. 11)
https://en.wikipedia.org/wiki/Black_hole#Detection_of_gravitational_waves_from_merging_black_holes

Edited December 6, 2021 by Orion1

[Orion1]

Broken Reference links repaired.

Wikipedia - Observable universe total stellar number: (ref. 7)
https://en.wikipedia.org/wiki/Star#Distribution
Wikipedia - Milky Way Galaxy: (ref. 8)
https://en.wikipedia.org/wiki/Milky_Way
 

[Orion1]

[math]\color{blue}{\text{Neutron stars cosmological composition parameter:} \; (\text{ref. 1, pg. 3})}[/math]
[math]\Omega_{ns} = 5 \cdot 10^{-5}[/math]
[math]\;[/math]
[math]\color{blue}{\text{Black holes cosmological composition parameter:} \; (\text{ref. 1, pg. 3})}[/math]
[math]\Omega_{bh} = 7 \cdot 10^{-5}[/math]
[math]\;[/math]
[math]\color{blue}{\text{Toy model Milky Way neutron stars per galaxy average number:}}[/math]
[math]\frac{N_{ns}}{N_g} = \frac{\Omega_{ns} M_{mw}}{\Omega_b M_{as}} = 2.138 \cdot 10^{9} \; \frac{\text{neutron stars}}{\text{galaxy}}[/math]
[math]\boxed{\frac{N_{ns}}{N_g} = \frac{\Omega_{ns} M_{mw}}{\Omega_b M_{as}}}[/math]
[math]\boxed{\frac{N_{ns}}{N_g} = 2.138 \cdot 10^{9} \; \frac{\text{neutron stars}}{\text{galaxy}}}[/math]
[math]\;[/math]
[math]\color{blue}{\text{Toy model Milky Way black holes per galaxy average number:}}[/math]
[math]\boxed{\frac{N_{bh}}{N_{g}} = \frac{\Omega_{bh} \Omega_s M_{mw}}{\Omega_{b}^{2} M_{as}}}[/math]
[math]\boxed{\frac{N_{bh}}{N_{g}} = 1.489 \cdot 10^{8} \; \frac{\text{black holes}}{\text{galaxy}}}[/math]
[math]\;[/math]
[math]\color{blue}{\text{Toy model Milky Way total supernovae per galaxy average number:}}[/math]
[math]\frac{N_{sn}}{N_g} = \left(\frac{N_{ns}}{N_g} + \frac{N_{bh}}{N_{g}} \right) = 2.287 \cdot 10^{9} \; \frac{\text{supernovae}}{\text{galaxy}}[/math]
[math]\boxed{\frac{N_{sn}}{N_g} = 2.287 \cdot 10^{9} \; \frac{\text{supernovae}}{\text{galaxy}}}[/math]
[math]\;[/math]
[math]\color{blue}{\text{Milky Way galaxy oldest Population II star age - HD 140283:} \; (\text{ref. 2})}[/math]
[math]t_{s} = 13.761 \cdot 10^{9} \; \text{years}[/math]
[math]\;[/math]
[math]\color{blue}{\text{Toy model Milky Way galaxy supernovae average rate per year:}}[/math]
[math]\Gamma_{sn} \geq \frac{N_{sn}}{N_g t_{s}} \geq \frac{}{t_{s}} \left(\frac{N_{ns}}{N_g} + \frac{N_{bh}}{N_{g}} \right) \geq 0.166 \; \frac{\text{supernovae}}{\text{galaxy year}}[/math]
[math]\boxed{\Gamma_{sn} \geq \frac{}{t_{s}} \left(\frac{N_{ns}}{N_g} + \frac{N_{bh}}{N_{g}} \right)}[/math]
[math]\boxed{\Gamma_{sn} \geq 0.166 \; \frac{\text{supernovae}}{\text{galaxy year}}}[/math]
[math]\;[/math]
[math]\color{blue}{\text{Toy model Milky Way galaxy years per supernova average rate:}}[/math]
[math]\boxed{\Gamma_{sn}^{-1} \leq t_{s} \left(\frac{N_{ns}}{N_g} + \frac{N_{bh}}{N_{g}} \right)^{-1}}[/math]
[math]\boxed{\Gamma_{sn}^{-1} \leq 6.017 \; \frac{\text{galaxy years}}{\text{supernova}}}[/math]
[math]\;[/math]
[math]\color{blue}{\text{What is the peak luminosity for a supernova capable of producing a neutron star within this mass domain?}}[/math]
[math]\boxed{0.595 \cdot M_{\odot} \leq M_{ns} \leq 2.27 \cdot M_{\odot}}[/math]
[math]\;[/math]
[math]\color{blue}{\text{What is the peak luminosity for a supernova capable of producing a black hole within this mass domain?}}[/math]
[math]\boxed{11.979 \cdot M_{\odot} \leq M_{bh} \leq 13.783 \cdot M_{\odot}}[/math]
[math]\;[/math]
[math]\color{blue}{\text{Any discussions and/or peer reviews about this specific topic thread?}}[/math]
[math]\;[/math]
"Stars, too, were time travelers. How many of those ancient points of light were the last echoes of suns now dead?" - Ransom Riggs
[math]\;[/math]
Reference:
The Cosmic Energy Inventory: (ref. 1)
http://arxiv.org/pdf/astro-ph/0406095v2.pdf
Wikipedia - Oldest Known Star in Milky Way Galaxy - HD 140283: (ref. 2)
https://en.wikipedia.org/wiki/HD_140283
Wikipedia - Supernova: (ref. 3)
https://en.wikipedia.org/wiki/Supernova
 

Edited January 4, 2022 by Orion1