Estimating the Size of Sgr A*'s Emitting Region

[albega]

Homework Statement

Sgr A* is the radio source at the centre of the galaxy. When it flares at X-ray wavelengths the flux increases by x 40 in 40 minutes. Estimate the size of the emitting region.

The Attempt at a Solution

The solution is to consider the distance traveled by the light in 40 minutes, which gives 40*60*3x10^8m or around 5AU.

However I really don't understand how that is relevant in terms of finding the size of the emitting region. Any hints? Thanks.

 

[Bandersnatch]

Imagine the region being a cloud of emitters of some radial extent. If all of the emitters begin flashing at the same instant, which ones will you notice first, and when will you finally see all of them?

 

[albega]

Imagine the region being a cloud of emitters of some radial extent. If all of the emitters begin flashing at the same instant, which ones will you notice first, and when will you finally see all of them?

Ahhhhh thanks :)

Also, does the above calculation then give the diameter of the region?

 

[Bandersnatch]

Also, does the above calculation then give the diameter of the region?

It only gives you an upper bound on the radial extent. You can't really extract the tangential dimensions just from the time it takes to reach maximum flux.
You can, though, assume shperical symmetry of the region, and use the radial extent as the diametre.
Neither of the assumptions(shperical symmetry and instantenous flashing of the whole region) is likely to be correct(the second one's physically impossible), but they do give you a ballpark result that later can be narrowed down by future observations.

 

[HalfLostAndSearching]

I would approach this problem by first considering the nature of the flare. X-ray flares are typically produced by high-energy particles being accelerated in a compact region, such as a black hole or neutron star. In the case of Sgr A*, it is believed that the flare is caused by material being accreted onto a supermassive black hole.

To estimate the size of the emitting region, we can use the concept of the light travel time. This is the time it takes for light to travel a certain distance. In this case, we know that the flux increases by a factor of 40 in 40 minutes. This means that the emitting region must be no larger than the distance light can travel in 40 minutes, which is approximately 5 AU (astronomical units).

Now, we can use this information to estimate the size of the emitting region. Since the emitting region is likely to be very compact, we can assume that it is roughly spherical in shape. Therefore, the radius of the emitting region would be approximately 5 AU/2 = 2.5 AU.

However, it's important to note that this is just an estimate and the actual size of the emitting region may be smaller or larger depending on various factors, such as the strength of the magnetic field and the properties of the material being accreted onto the black hole. Further observations and analysis would be needed to accurately determine the size of the emitting region of Sgr A*.