How Do You Estimate the Mass Accretion Rate for a Quasar?

In summary, the typical quasar luminosity is about 1012 L and the mass accretion rate can be estimated using the formula L~de/dt~1/2 M c^2. The time it would take to build a mass of 108M is shorter compared to the age of the universe, supporting the idea that quasars are powered by accretion onto SMBH.
  • #1
leonne
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Homework Statement


A typical quasar luminosity is about 1012 L, where L = 3:83 1033 erg s1 is
the luminosity of the Sun. If the energy is released by mass falling into a SMBH,
estimate the mass accretion rate. (Convenient units are solar masses per year.)

B)If the mass accretion rate is roughly constant, how long would it take to build
a mass of 108M ? Is that long or short compared with the age of the Universe
(about 14 Gyr)? Comment on whether the idea that quasars are powered by
accretion onto SMBH makes sense or not.
2

Homework Equations


L~de/dt~1/2 M c^2

The Attempt at a Solution


Would this be the formula I use to solve it? Seems a little to easy lol were M is the accretion rate The original formula is Du~-(GM/2GM/c^2)m dt m is the accretion rate then after few steps they have the formula i listed on top So just solve for M?

for the second part thinking of using de~dk~ (GM/Rs) m dt thinking of taking the integral of both sides then just move T to the other side then plug in but seems like GM/rs would cancel out so not sure. Is this right or need to do something else?
 
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  • #2
For the last part, the age of universe is significantly longer than the time it would take to build the mass of 108M, so yes it makes sense.
 

FAQ: How Do You Estimate the Mass Accretion Rate for a Quasar?

1. What is "mass accretion rate"?

The mass accretion rate is a measure of the amount of matter that is added to an object, typically a star or black hole, per unit of time. It is an important factor in understanding the growth and evolution of these objects.

2. How is the mass accretion rate calculated?

The mass accretion rate is typically calculated by measuring the amount of material that is falling onto the object, such as gas or dust particles, and dividing it by the time it takes for the material to accrete onto the object.

3. What are some common units used to express mass accretion rate?

The most commonly used units to express mass accretion rate are solar masses per year (M☉/yr) for stars, and grams per second (g/s) for black holes. Other units, such as kilograms per second or Earth masses per year, may also be used depending on the context.

4. How does the mass accretion rate affect the object's properties?

The mass accretion rate has a significant impact on the object's properties, such as its luminosity and growth rate. A higher mass accretion rate typically leads to a brighter object and faster growth, while a lower rate may result in slower growth and a dimmer object.

5. What are some factors that can affect the mass accretion rate?

The mass accretion rate can be influenced by a variety of factors, including the object's gravitational pull, the density and temperature of the surrounding material, and the object's own rotation. Additionally, the presence of a companion object or other external forces can also affect the rate of accretion.

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