Multiplicative character: Difference between revisions
Jump to navigation
Jump to search
en>Michael Hardy mNo edit summary |
en>Addbot m Bot: Migrating 4 interwiki links, now provided by Wikidata on d:q1062934 |
||
| Line 1: | Line 1: | ||
The '''Sołtan argument''' is an [[astrophysics|astrophysical]] theory outlined in 1982 by [[Poland|Polish]] [[astronomer]] Andrzej Sołtan. It maintains that if [[quasar]]s were powered by [[Accretion (astrophysics)|accretion]] onto a [[supermassive black hole]], then such supermassive black holes must exist in our local universe as "dead" quasars. | |||
==History== | |||
As early as 1969, [[Donald Lynden-Bell]] wrote a paper suggesting that "dead quasars" were found at the center of the [[Milky Way]] and nearby galaxies by arguing that given the quasar-number counts, luminosities, distances, and the efficiency of accretion into a "Schwarzschild throat" through the [[Photon sphere|last stable circular orbit]] (note that the term ''[[black hole]]'' had been coined only two years earlier and was still gaining popular usage), roughly 10<sup>10</sup> quasars existed in the [[observable universe]]. This number density of "dead quasars" was attributed by Lynden-Bell to high [[mass-to-light ratio]] objects found at the center of galaxies. This is essentially the Sołtan argument, though the direct connection between black hole masses and quasar [[luminosity function (astronomy)|luminosity function]]s is missing. In the paper, Lynden-Bell also suggests some radical ideas that are now fully integrated into modern understanding of astrophysics including the model that [[accretion disks]] are supported by [[magnetic field]]s, that [[extragalactic cosmic ray]]s are accelerated in them, and he estimates to within an order of magnitude the masses of several of the closest [[supermassive black hole]]s including the ones in the [[Milky Way]], [[Andromeda galaxy|M31]], [[Messier 32|M32]], [[Messier 81|M81]], [[Messier 82|M82]], [[Messier 87|M87]], and [[NGC 4151]].<ref>{{cite journal | |||
| author = Lynden-Bell, D. | |||
| title = Galactic Nuclei as Collapsed Old Quasars | |||
| journal = Nature | |||
|date=August 1969 | |||
| volume = 223 | |||
| issue = 5207 | |||
| pages = 690–694 | |||
| bibcode = 1969Natur.223..690L | |||
| doi = 10.1038/223690a0 | |||
}}</ref> | |||
Thirteen years later, Sołtan explicitly showed that the [[luminosity]] (<math>L</math>) of quasars was due to the accretion rate of mass onto black holes given by: | |||
<math>L = \epsilon \dot{M} c^2</math> | |||
where | |||
*<math>\epsilon</math> is the efficiency factor | |||
*<math>\dot{M}</math> is the [[time rate]] of mass falling into the black hole | |||
*<math>c</math> is the [[speed of light]]<ref name=F&F>{{cite journal | |||
| author = Ferrarese, L. and Ford, H. | |||
| title = Supermassive Black Holes in Galactic Nuclei: Past, Present and Future Research | |||
| journal = Space Science Reviews | |||
|date=February 2005 | |||
| volume = 116 | |||
| issue = 3–4 | |||
| pages = 523–624 | |||
| doi = 10.1007/s11214-005-3947-6 | |||
| bibcode = 2005SSRv..116..523F | |||
|arxiv = astro-ph/0411247 }}</ref> | |||
Given the number of observed quasars at various [[redshift]]s, he was able to derive an [[integral|integrated]] [[energy density]] due to quasar output. Since observers on Earth are [[flux limit]]ed, there are always more quasars that exist than are observed and thus the energy density he derived is a [[lower bound]]. He obtained the value of approximately 10<sup>−10</sup> [[erg]]s per [[cubic meter]].<ref name=Soltan>{{cite journal | |||
| author = Sołtan, A. | |||
| title = Masses of quasars, | |||
| journal = Monthly Notices of the Royal Astronomical Society | |||
|date=July 1982 | |||
| volume = 200 | |||
| pages = 115–122 | |||
| bibcode = 1982MNRAS.200..115S | |||
}}</ref> | |||
Sołtan calculated the mass density of accreted material as it is directly related to the energy density of quasar light. He derived a value of approximately 10<sup>14</sup> [[solar mass]]es per cubic [[Gigaparsec]]. This mass would be [[discrete probability distribution|discretely distributed]] (since quasars are single point sources); given an average mass of approximately ten million solar masses, it would be statistically likely for a "dead quasar" to be within a few [[megaparsec]]s of Earth.<ref name=Soltan /> | |||
At this time, evidence was already accumulating that supermassive black holes were found at the center of large galaxies, which are distributed approximately on the order of a megaparsec apart from each other. This argument therefore made a reasonable case that supermassive black holes were at one time ultraluminous quasars. | |||
The first quantitative estimates of the mass density in supermassive black holes were 5-10 times higher than Soltan's estimate.<ref>Magorrian, J. et al. (1998), [http://adsabs.harvard.edu/abs/1998AJ....115.2285M The Demography of Massive Dark Objects in Galaxy Centers], ''The Astronomical Journal'', '''115''', 2285-2305</ref> This discrepancy was resolved in 2000 via the discovery of the [[M-sigma relation]], which showed that most of the previously-published black hole masses were in error.<ref name=DEGN>{{cite book|last=Merritt|first=David|author-link=David Merritt|title=Dynamics and Evolution of Galactic Nuclei|year=2013|publisher=Princeton University Press|location=Princeton, NJ|url=http://openlibrary.org/works/OL16802359W/Dynamics_and_Evolution_of_Galactic_Nuclei}}</ref> | |||
==Present constraints== | |||
As of 2008, the best constraints for the supermassive black hole mass per cubic megaparsec in the local universe derived from the Sołtan argument is between 2 - 5 x 10<sup>5</sup> solar masses. This value is consistent with observations of the mass of local supermassive black holes.<ref>[[David Merritt|Merritt, D.]] and Ferrarese, L. (January 2001). [http://adsabs.harvard.edu/abs/2001MNRAS.320L..30M "Black Hole Demographics from the M-sigma Relation"]. ''Monthly Notices of the Royal Astronomical Society'' '''320''': L30-L34</ref> | |||
== See also == | |||
# [[Supermassive black holes]] | |||
# [[M-sigma relation]] | |||
==References== | |||
{{reflist}} | |||
{{DEFAULTSORT:Soltan Argument}} | |||
[[Category:Quasars|*]] | |||
[[Category:Supermassive black holes]] | |||
[[Category:Astrophysics]] | |||
[[Category:Extragalactic astronomy]] | |||
Latest revision as of 08:00, 1 March 2013
The Sołtan argument is an astrophysical theory outlined in 1982 by Polish astronomer Andrzej Sołtan. It maintains that if quasars were powered by accretion onto a supermassive black hole, then such supermassive black holes must exist in our local universe as "dead" quasars.
History
As early as 1969, Donald Lynden-Bell wrote a paper suggesting that "dead quasars" were found at the center of the Milky Way and nearby galaxies by arguing that given the quasar-number counts, luminosities, distances, and the efficiency of accretion into a "Schwarzschild throat" through the last stable circular orbit (note that the term black hole had been coined only two years earlier and was still gaining popular usage), roughly 1010 quasars existed in the observable universe. This number density of "dead quasars" was attributed by Lynden-Bell to high mass-to-light ratio objects found at the center of galaxies. This is essentially the Sołtan argument, though the direct connection between black hole masses and quasar luminosity functions is missing. In the paper, Lynden-Bell also suggests some radical ideas that are now fully integrated into modern understanding of astrophysics including the model that accretion disks are supported by magnetic fields, that extragalactic cosmic rays are accelerated in them, and he estimates to within an order of magnitude the masses of several of the closest supermassive black holes including the ones in the Milky Way, M31, M32, M81, M82, M87, and NGC 4151.[1]
Thirteen years later, Sołtan explicitly showed that the luminosity () of quasars was due to the accretion rate of mass onto black holes given by:
where
- is the efficiency factor
- is the time rate of mass falling into the black hole
- is the speed of light[2]
Given the number of observed quasars at various redshifts, he was able to derive an integrated energy density due to quasar output. Since observers on Earth are flux limited, there are always more quasars that exist than are observed and thus the energy density he derived is a lower bound. He obtained the value of approximately 10−10 ergs per cubic meter.[3]
Sołtan calculated the mass density of accreted material as it is directly related to the energy density of quasar light. He derived a value of approximately 1014 solar masses per cubic Gigaparsec. This mass would be discretely distributed (since quasars are single point sources); given an average mass of approximately ten million solar masses, it would be statistically likely for a "dead quasar" to be within a few megaparsecs of Earth.[3]
At this time, evidence was already accumulating that supermassive black holes were found at the center of large galaxies, which are distributed approximately on the order of a megaparsec apart from each other. This argument therefore made a reasonable case that supermassive black holes were at one time ultraluminous quasars.
The first quantitative estimates of the mass density in supermassive black holes were 5-10 times higher than Soltan's estimate.[4] This discrepancy was resolved in 2000 via the discovery of the M-sigma relation, which showed that most of the previously-published black hole masses were in error.[5]
Present constraints
As of 2008, the best constraints for the supermassive black hole mass per cubic megaparsec in the local universe derived from the Sołtan argument is between 2 - 5 x 105 solar masses. This value is consistent with observations of the mass of local supermassive black holes.[6]
See also
References
43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.
- ↑ One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting
In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang
Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules
Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.
A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running
The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more
There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang - ↑ One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting
In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang
Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules
Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.
A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running
The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more
There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang - ↑ 3.0 3.1 One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting
In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang
Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules
Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.
A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running
The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more
There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang - ↑ Magorrian, J. et al. (1998), The Demography of Massive Dark Objects in Galaxy Centers, The Astronomical Journal, 115, 2285-2305
- ↑ 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534 - ↑ Merritt, D. and Ferrarese, L. (January 2001). "Black Hole Demographics from the M-sigma Relation". Monthly Notices of the Royal Astronomical Society 320: L30-L34