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Posts Tagged ‘Event Horizon’

Last week, I blogged about the theoretical arguments for the Galaxy harbouring a supermassive black hole at its centre, and here I blogged about the observational evidence. The work done by the UCLA and MPE teams, discussed here, has led to a determination that the central black hole has a mass of between 4.4 and 4.5 million solar  masses. I am going to take the upper end  of this range, just for convenience.

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An artist’s impression of Sgr A*, showing the central supermassive black hole and the accretion disk which surrounds it.

The size of the event horizon

In this blog here I showed that the radius of a blackhole’s event horizon can be calculated by using the equation for the escape velocity v_{esc} when that velocity is equal to the speed of light c. That is

v_{esc} = c = \sqrt{ \frac{2GM }{ R } }

where M is the mass of the blackhole, G is the universal gravitational constant, and R is the size of the object, which in this case is the radius of the event horizon (also known as the Swarzchild radius R_{s}). So, we can write

R_{s} = \frac{ 2GM }{ c^{2} }

Putting in a mass of 4.5 million solar masses, we find

R_{s} = 1.33 \times 10^{10} \text{ metres}

Converting this to AUs, we find the radius of the event horizon is 0.09 AUs, much smaller than the radius of Mercury’s orbit, which is about 0.3 AUs.

At the distance of the Galactic centre, 8 kpc, this would subtend an angle of
\theta = 6.17 \times 10^{-9} \text{ degrees} (remember to double R_{s} to get the diameter of the event horizon). This is the same as

\boxed{ \theta = 22.22 \text{ micro arc seconds} }

Converting this to radians, we get

\theta ( \text{in radians}) = 1.08 \times 10^{-10}

In fact, we do not need to resolve the event horizon itself, but rather the “shadow” of the event horizon, which is about four times the size, so we need to resolve an angle of

\theta ( \text{in radians}) \approx 4 \times 10^{-10}

The resolution of a telescope

There is a very simple formula for the resolving power of a telescope, it is given by

\theta( \text{in radians}) = \frac{ 1.22 \lambda }{ D }

where D is the diameter of the telescope and \lambda is the wavelength of the observation. Let us work out the diameter of a telescope necessary to resolve an object with an angular size of 50 \times 10^{-4} \text{ radians } at various wavelengths.

For visible light, assuming \lambda = 550 \text{ nanometres}

D = \frac{ 1.22 \times 550 \times 10^{-9} }{ 4 \times 10^{-10 } }, \boxed{ D = 1.68 \text { km} }

There is no visible light telescope this large, nor will there ever be. At the moment, visible-light interferometry is still not technically feasible over this kind of a baseline, so imaging the event horizon of the Galaxy’s supermassive blackhole is not currently possible at visible wavelengths.

For 21cm radio radiation (the neutral hydrogen line)

D = \frac{ 1.22 \times 21 \times 10^{-2} }{ 4 \times 10^{-10 } }, \boxed{ D = 640,000 \text { km} }

This is more than the distance to the Moon (which is about 400,000 km away). So, until we have a radio dish in space, we cannot resolve the supermassive blackhole at 21cm either.

For millimetre waves, we have

D = \frac{ 1.22 \times 1 \times 10^{-3} }{ 4 \times 10^{-10 } }, \boxed{ D = 3,100 \text { km} }

which is feasible with very long baseline interferometry (VLBI). So, with current technology, imaging the event horizon of the Milky Way’s supermassive blackhole is only feasible at millimetre wavelengths. Millimetre waves lie in a niche between visible light and radio waves. They are long enough that we can do VLBI, but they are short enough that the baseline to image the supermassive black hole’s event horizon is small enough to be possible with telescope on the Earth.

Next week I will talk about a project to do just that!

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On Tuesday, I blogged about the theoretical work done in the early 1970s by Martin Rees, and others, which proposed that there may be a supermassive black hole at the centre of our Galaxy and most spiral galaxies.

What about the observational evidence?

In the early 1980s two teams set about observing the orbits of stars near Sgr A*. The two teams, working separately, were at UCLA and The Max Planck Institute For Extra-terrestrial Physics (MPE). The team at UCLA is known as the UCLA Galactic Center Group, the team at the MPE doesn’t have a snazzy name, but their website can be found here. Gradually, over many years, each of the two teams has determined the orbits of several dozens of stars, and hence have been able to use the laws of gravity to determine the mass of the enclosed mass which the stars are orbiting.

Below is an image of Sgr A* taken by the MPE team using the NACO near-infrared camera on the VLT with adaptive optics. The entire image is only 30 arc seconds across.

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A combined H, K and L-band near infrared image of the Galactic Centre obtained by the NACO camera on the VLT using adaptive optics. This image is from the MPE website.

Here is a paper, published in 2009, entitled “Monitoring Stellar Orbits Around the Massive Black Hole in the Galactic Center”, published by the MPE group in The Astrophysical Journal. Here is a link to the paper.

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This paper, published in The Astrophysical Journal in 2009, is one of several showing overwhelming evidence for a supermassive blackhole at the centre of the Milky Way galaxy.

In this paper, entitled “The Galactic Center massive black hole and nuclear star cluster”, Reinhard Genzel (the director of the MPE) and colleagues summarise the evidence from their studies of their being a supermassive blackhole at the centre of the Milky Way, with a calculated mass of about 4.4 million solar masses. Here is a link to the paper.

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In a paper entitled “The Galactic Center massive black hole and nuclear star cluster”, Genzel etal. summarise their finding that the Galaxy harbours a massive black hole with a mass of about 4.4 million solar masses.

The UCLA group published this paper “Measuring Distance and Properties of the Milky Way’s Central Supermassive Black Hole With Stellar Orbits”, in 2008 in The Astrophysical Journal (here is a link to the paper). In it,they calculate the mass of the supermassive black hole to be 4.5 million solar masses, with an error of plus or minus 0.4 million solar masses.

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Ghez etal. (2008) find the  mass of the supermassive black hole to be 4.5 million solar masses, slightly higher than the MPE group, but well within the errors of the two groups’ measurements.

The mass of this black hole is about 4.45 million times the mass of the Sun (the two groups calculate different masses, with the UCLA group calculating about 4.5 million solar masses, the MPE group about 4.4 million solar masses). Let us assume it is 4.5 million solar masses, just to round up to the nearest half a million solar masses.

As some of you may know, blackholes are observable in certain ways. They clearly affect the orbit of nearby objects (this is how the UCLA and MPE teams have garnered the evidence for the supermassive blackhole), but also the accretion disk which usually surrounds a blackhole has very hot gas spiralling into the blackhole. This very hot gas emits radiation as a blackbody, so most of it comes out in the X-ray part of the spectrum due to the very high temperature of several millions of Kelvin.

But, a blackbody will also radiate at other wavelengths (see my blog here to remind yourself of the shape of a blackbody curve), so such accretion disks will also radiate visible light, infrared light, and even radio emission. The question then arises, is it possible to observe the accretion disk way in towards the event horizon of the Galaxy’s supermassive blackhole?

I will answer that question next week.

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