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The | The '''Navarro–Frenk–White profile''' or '''NFW profile''' is a spatial mass distribution of [[dark matter]] fitted to dark matter haloes identified in [[N-body]] simulations by [[Julio Navarro (astrophysicist)|Julio Navarro]], [[Carlos Frenk]] and [[Simon White]].<ref name="NAVARROETAL1996">{{cite journal|author=Navarro, Julio F.; Frenk, Carlos S.; White, Simon D. M.|title=The Structure of Cold Dark Matter Halos|journal=The Astrophysical Journal|volume=463|pages=563|date=May 10, 1996|bibcode=1996ApJ...462..563N|doi=10.1086/177173|arxiv=astro-ph/9508025}}</ref> The NFW profile is one of the most commonly used model profiles for dark matter halos.<ref name="BERTONE2005">{{Cite book|last=Bertone|first=Gianfranco|title=[[Particle Dark Matter|Particle Dark Matter: Observations, Models and Searches]]|publisher=Cambridge University Press|year=2010|pages=762|isbn=978-0-521-76368-4}}</ref> | ||
==Density distribution== | |||
<!-- Deleted image removed: [[File:rho nfw.svg|thumb|right|The NFW density profile on a log radius versus density plot.]] --> | |||
In the NFW profile, the density of dark matter as a function of radius is given by: | |||
<math> | |||
\rho (r)=\frac{\rho_0}{\frac{r}{R_s}\left(1~+~\frac{r}{R_s}\right)^2} | |||
</math> | |||
where ρ<sub>0</sub> and the "scale radius", ''R<sub>s</sub>'', are parameters which vary from halo to halo. | |||
The integrated mass inside of some radius ''R<sub>max</sub>'' is | |||
<math> | |||
M=\int_0^{R_{max}} 4\pi r^2 \rho (r) dr=4\pi \rho_0 R_s^3 \left[ | |||
\ln\left(\frac{R_s+R_{max}}{R_s}\right)-\frac{R_{max}}{R_s+R_{max}}\right] | |||
</math> | |||
The total mass is divergent, but it is often useful to take the edge of the halo to | |||
be the virial radius, ''R<sub>vir</sub> '', | |||
which is related to the "concentration parameter", ''c'', and scale radius via | |||
<math> | |||
R_{vir}=cR_s | |||
</math> | |||
The virial radius is often referred to as <math> R_{200} </math>, and is defined as the radius at which the average density within this radius is 200 times the critical density. In this case, the total mass in the halo is | |||
<math> | |||
M=\int_0^{R_{vir}} 4\pi r^2 \rho (r) dr=4\pi \rho_0 R_s^3 \left[\ln(1+c) - \frac{c}{1+c}\right] | |||
</math> | |||
The value of ''c'' is roughly 10 or 15 for the Milky Way, and may range from 4 to 40 | |||
for halos of various sizes. | |||
The integral of the ''squared density'' is | |||
<math> | |||
\int_0^{R_{max}} 4\pi r^2 \rho (r)^2 dr=\frac{4\pi}{3} R_s^3 \rho_0^2 | |||
\left[1-\frac{R_s^3}{(R_s+R_{max})^3}\right] | |||
</math> | |||
so that the mean squared density inside of ''R<sub>max</sub>'' is | |||
<math> | |||
\langle \rho^2 \rangle_{R_{max}}=\frac{R_s^3\rho_0^2}{R_{max}^3} | |||
\left[1-\frac{R_s^3}{(R_s+R_{max})^3}\right] | |||
</math> | |||
which for the virial radius simplifies to | |||
<math> | |||
\langle \rho^2 \rangle_{R_{vir}}=\frac{\rho_0^2}{c^3} | |||
\left[1-\frac{1}{(1+c)^3}\right] | |||
\approx \frac{\rho_0^2}{c^3} | |||
</math> | |||
and the mean squared density inside the scale radius is simply | |||
<math> | |||
\langle \rho^2 \rangle_{R_s}=\frac{7}{8}\rho_0^2 | |||
</math> | |||
==Dark matter simulations== | |||
The NFW profile is an approximation to the [[Thermodynamic equilibrium|equilibrium]] configuration of dark matter produced in simulations of [[collision]]less dark matter particles by numerous groups of scientists.<ref>{{cite journal|author=Y. P. Jing|title=The Density Profile of Equilibrium and Nonequilibrium Dark Matter Halos|journal=The Astrophysical Journal|date=20 May 2000|volume=535|issue=1|pages=30–36|bibcode=2000ApJ...535...30J|doi=10.1086/308809|arxiv=astro-ph/9901340}}</ref> Before the dark matter [[virial theorem|virializes]], the distribution of dark matter deviates from an NFW profile, and significant substructure is observed in simulations both during and after the collapse of the halos. | |||
Alternative models, in particular the [[Einasto profile]], have been shown to represent the dark matter profiles of simulated halos as well as or better than the NFW profile.<ref>{{cite journal|author=[[David Merritt|Merritt, David]]; Graham, Alister; Moore, Benjamin; Diemand, Jurg; Terzić, Balsa|title=Empirical Models for Dark Matter Halos|journal=The Astronomical Journal|date=20 December 2006|volume=132|issue=6|pages=2685–2700|bibcode=2006AJ....132.2685M|doi=10.1086/508988|arxiv=astro-ph/0509417|url=http://adsabs.harvard.edu/abs/2006AJ....132.2685M}}</ref><ref>{{cite journal|last1=Merritt|first1=David|authorlink1=David Merritt|last2=et al.|title=A Universal Density Profile for Dark and Luminous Matter?|journal=The Astrophysical Journal|date=May 2005|volume=624|issue=2|pages=L85–L88|bibcode=2005ApJ...624L..85M|doi=10.1086/430636|arxiv=astro-ph/0502515|url=http://adsabs.harvard.edu/abs/2005ApJ...624L..85M}}</ref> The Einasto profile has a finite (zero) central slope, unlike the NFW profile which has a divergent (infinite) central density. Because of the limited resolution of N-body simulations, it is not yet known which model provides the best description of the central densities of simulated dark-matter halos. | |||
==Observations of halos== | |||
The observations of both the [[Milky Way]] and [[Andromeda Galaxy|M31]] may be compatible with the NFW profile for the dark matter halo.<ref name="KLYPIN2002">{{cite journal|author=Klypin, Anatoly; Zhao, HongSheng; Somerville, Rachel S.|title=ΛCDM-based Models for the Milky Way and M31. I. Dynamical Models|date=10 July 2002|journal=The Astrophysical Journal|volume=573|issue=2|pages=597–613|bibcode=2002ApJ...573..597K|doi=10.1086/340656|arxiv=astro-ph/0110390}}</ref> The dark matter profile of smaller galaxies tend to have flatter distributions of dark matter in the central region, known as the [[Cuspy halo problem]]. | |||
==References== | |||
{{reflist}} | |||
{{Dark matter}} | |||
{{DEFAULTSORT:Navarro-Frenk-White profile}} | |||
[[Category:Dark matter]] |
Revision as of 17:00, 15 October 2013
The Navarro–Frenk–White profile or NFW profile is a spatial mass distribution of dark matter fitted to dark matter haloes identified in N-body simulations by Julio Navarro, Carlos Frenk and Simon White.[1] The NFW profile is one of the most commonly used model profiles for dark matter halos.[2]
Density distribution
In the NFW profile, the density of dark matter as a function of radius is given by:
where ρ0 and the "scale radius", Rs, are parameters which vary from halo to halo.
The integrated mass inside of some radius Rmax is
The total mass is divergent, but it is often useful to take the edge of the halo to be the virial radius, Rvir , which is related to the "concentration parameter", c, and scale radius via
The virial radius is often referred to as , and is defined as the radius at which the average density within this radius is 200 times the critical density. In this case, the total mass in the halo is
The value of c is roughly 10 or 15 for the Milky Way, and may range from 4 to 40 for halos of various sizes.
The integral of the squared density is
so that the mean squared density inside of Rmax is
which for the virial radius simplifies to
and the mean squared density inside the scale radius is simply
Dark matter simulations
The NFW profile is an approximation to the equilibrium configuration of dark matter produced in simulations of collisionless dark matter particles by numerous groups of scientists.[3] Before the dark matter virializes, the distribution of dark matter deviates from an NFW profile, and significant substructure is observed in simulations both during and after the collapse of the halos.
Alternative models, in particular the Einasto profile, have been shown to represent the dark matter profiles of simulated halos as well as or better than the NFW profile.[4][5] The Einasto profile has a finite (zero) central slope, unlike the NFW profile which has a divergent (infinite) central density. Because of the limited resolution of N-body simulations, it is not yet known which model provides the best description of the central densities of simulated dark-matter halos.
Observations of halos
The observations of both the Milky Way and M31 may be compatible with the NFW profile for the dark matter halo.[6] The dark matter profile of smaller galaxies tend to have flatter distributions of dark matter in the central region, known as the Cuspy halo problem.
References
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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 - ↑ 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