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Growth rate of MWBH due to photon flux in W or fluence in W/m^2 at
Hello,
I find a lot of papers dealing with black hole growth rate due to accretion. But haven't been able to find anything on growth due to photon consumption. A paper 2013 by Victor Debattista, of the University of Central Lancashire in England estimated the growth rate for MW BH at 1 M_sun / 3000 years. This works out to a consumption of E_dot = 1.89E36 W average. but this is total "accretion" rate which includes matter, gas, stars, objects.... mass energy plus photon energy. I didn't see explicit mention of photon mass gain. I'm trying to determine the growth of the MW BH due solely to photon consumption. Alternately, knowing radius and area, I could compute the value if I knew the fluence near the core of the MW, "What is the fluence of photon energy near the center of the MW, in Watts per square meter?" Any assistance / direction appreciated, rt [[Mod. note -- I educated-guess that the photon flux will be many orders of magnitude less than the E=mc^2 equivalent of the infalling matter flux. But specific numbers would be welcome. -- jt]] |
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Growth rate of MWBH due to photon flux in W or fluence in W/m^2 at
Erm, photons are massless.
[[Mod. note -- I htink the question was asking about mass-energy, and photons can certainly carry that. -- jt]] |
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Growth rate of MWBH due to photon flux in W or fluence in W/m^2 at
In article ,
wrote: Alternately, knowing radius and area, I could compute the value if I knew the fluence near the core of the MW, "What is the fluence of photon energy near the center of the MW, in Watts per square meter?" [[Mod. note -- I educated-guess that the photon flux will be many orders of magnitude less than the E=mc^2 equivalent of the infalling matter flux. But specific numbers would be welcome. -- jt]] OK, back of the envelope: the energy density in starlight in the MW is ~ 10^-13 J/m^3: this is the dominant photon field (the CMB is about half this). So the fluence is Uc/4 ~ 10^-5 W/m^2. For a 4 x 10^6 solar mass black hole, R_S = 10^10 m, so the energy being added is ~ 1 x 10^16 W, or the equivalent of the accretion of 0.1 kg/s, or, in SMBH terms, peanuts. All numbers to order of magnitude only. Assuming I've not screwed up somewhere, the main error in this calculation is taking a typical starlight energy density in the MW to represent the energy density in the Galactic centre, but that won't get this number more than ~ 1 order of magnitude higher. Martin -- Martin Hardcastle School of Physics, Astronomy and Mathematics, University of Hertfordshire, UK Please replace the xxx.xxx.xxx in the header with herts.ac.uk to mail me |
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Growth rate of MWBH due to photon flux in W or fluence in W/m^2 at
In article 20161004070749.GA495@sirius,
Martin Hardcastle writes: OK, back of the envelope: the energy density in starlight in the MW is ~ 10^-13 J/m^3: this is the dominant photon field (the CMB is about half this). You could do a better job by looking up the stellar density near the Galactic center and assuming a mass-to-light ratio. M/L will be somewhere near 1 in solar units, but the stellar density is much higher (maybe a couple or three orders of magnitude, but I'm just guessing) than near the Sun's location in the disk. So the fluence is Uc/4 ~ 10^-5 W/m^2. That quantity is a "flux," which is in fact what you want. "Fluence" is flux integrated over time, so its units would be J/m^2. That would give the energy absorbed by the black hole over time rather than the current accretion rate. -- Help keep our newsgroup healthy; please don't feed the trolls. Steve Willner Phone 617-495-7123 Cambridge, MA 02138 USA |
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Growth rate of MWBH due to photon flux in W or fluence in W/m^2 at
On Tuesday, October 11, 2016 at 12:39:59 PM UTC-7, Steve Willner wrote:
In article 20161004070749.GA495@sirius, Martin Hardcastle m.j.hardcastle writes: OK, back of the envelope: the energy density in starlight in the MW is ~ 10^-13 J/m^3: this is the dominant photon field (the CMB is about half this). You could do a better job by looking up the stellar density near the Galactic center and assuming a mass-to-light ratio. M/L will be somewhere near 1 in solar units, Thanks.... Best I found for stellar density is "several" hundred thousand stars per cubic pc "very near" the center (so far anyway). http://abyss.uoregon.edu/~js/ast122/lectures/lec26.html using 0.1 pc for "very near" and 300,000 stars per pc^3 for "several hundred thousand" as guesses, I get Energy Density = 1.22E-11 J/m^3 This is energy from stars L within sphere 0.1pc radius being emitted outward (and in all directions) per second, divided by A at 0.1pc radius This is about 100x Martin's previous envelope estimate, so pretty close, and increases energy flow into MWBH to about 10kg/s equivalent mass flow rate. This is also 1.22E-11 Pa, which is close to values estimated for cosmological dark energy. Wiki gives two values, which when converted to energy yield 6E-10 and 9E-11, J/m^3 = Pa so the value I get (1.22E-11Pa) is about in between. Sound about right? Thanks for the help. Ross |
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