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Imaging the Galaxy’s supermassive blackhole – part 1

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.

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.

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

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!

The February 2017 annular solar eclipse

Some of you may be aware that there is an annular eclipse of the Sun on Sunday 26 February, which is why I am posting this blog a few days before it. Annular eclipses occur when the Moon is a little too far away to block the Sun out entirely, so instead we see a ring of light around the Moon, as this picture below shows. This particular picture was taken during the May 20 2012 annular eclipse

An annular eclipse happens when the Moon is slightly too far away to block out the Sun entirely. This is a picture of the May 20 2012 annular eclipse.

The Moon’s elliptical orbit about the Earth

The diagram below shows an exaggerated cartoon of the Moon’s orbit about the Earth. The Moon’s orbit is an ellipse, it has an eccentricity of 0.0549 (a perfect circle has an eccentricity of 0). The average distance of the Moon from the Earth (actually, the distance between their centres) is 384,400 kilometres. The point at which it is furthest from the Earth is called the apogee, and is at a distance of 405,400 km. The point at which it is closest is called the perigee, and it is at a distance of 362,600 km.

The Moon orbits the Earth in an ellipse, not a circle. The furthest it is from the Earth in its orbit (the apogee) is at a distance of 405,400 km, the nearest (the perigee) is at a distance of 362,600 km.

The angular size of the Moon

It is pure coincidence that the Moon is the correct angular size to block out the Sun. The Moon is slightly oblate, but has a mean radius of 1,737 km. With its average distance of 384,400, this means that from the Earth’s surface (the Earth’s mean radius is 6,371 km) the Moon has an angular size on the sky of

$2 \times \tan^{-1} \left( \frac{ (1.737 \times 10^{6}) }{ (3.84 \times 10^{8} - 6.371 \times 10^{6}) } \right) = 2 \times \tan^{-1} (4.59975 \times 10^{-3} )$

$= 2 \times 0.2635 = \boxed{ 0.527 ^{\circ} \text{ or } 31.62 \text{ arc minutes} }$
So, just over half a degree on the sky. But, this of course will vary depending on its distance. When it is at apogee (furthest away), its angular size will be

$\boxed{ \text{ at apogee } 29.93 \text{ arc minutes } }$

and when it is at perigee (closest) it will be

$\boxed{ \text{ at perigee } 33.53 \text{ arc minutes } }$

The angular size of the Sun

The Sun has an equatorial radius of 695,700 km, and its average distance from us is 149.6 million km (the Astronomical Unit – AU). So, at this average distance the Sun has an angular size of

$2 \times \tan^{-1} \left( \frac{ (6.957 \times 10^{8}) }{ (1.496 \times 10^{11} - 6.371 \times 10^{6} ) } \right) = 2 \times 0.266 = \boxed {0.533^{\circ} }$

Converting this to arc minutes, we get that the angular size of the Sun at its average distance is

$\boxed{ 31.97 \text{ arc minutes} }$

Compare this to the angular size of the Moon at its average distance, which we found to be $31.62 \text{ arc minutes}$.

The angular size of the Sun varies much less than the variation in the angular size of the Moon, at aphelion (when we are furthest) from the Sun, we are at a distance of 152.1 million km, so this gives an angular size of

$\boxed{ \text{ at aphelion } 31.44 \text{ arc minutes } }$

and, at perielion, when the distance to the Sun is 147.095 million km, the angular size of the Sun is

$\boxed{ \text{ at perihelion } 32.52 \text{ arc minutes } }$

Annular Eclipses

So, from the calculations above one can see that, if the Moon is at or near perigee, its angular size of $33.53 \text{ arc minutes }$ is more than enough to block out the Sun. When the Moon is at its average distance, its angular size is $31.62 \text { arc minutes }$, which is enough to block out the Sun unless we are near perihelion. But, when the Moon is near apogee, its angular size drops to $29.93 \text{ arc minutes }$, and this is not enough to block out the Sun, even if we are at aphelion.

The Earth is currently at perihelion in early January (this year it was on January 4), so the Sun is slightly larger in the sky that it will be in August for the next solar eclipse. This, combined with the Moon being near its apogee, which occurred on February 18, (for a table of the dates of the Moon’s apogees and perigees in 2017 follow this link) means that the solar eclipse on Sunday February 26 is annular, and not total.

The February 26 2017 Annular Eclipse

Here is a map of the path of the eclipse, it is taken from the wonderful NASA Eclipse website. If you follow this link, you can find interactive maps of all the eclipses from -1999 BC to 3000 AD! If you have about 6 years to waste, this is an ideal place to do it!

The February 26 2017 annular eclipse will start in the southern Pacific ocean, sweep across Chile and Argentina, then across the Atlantic Ocean, before reaching Angola, Zambia and the Democratic Republic of Congo (Congo-Kinshasa)

The eclipse finishes in Africa and, as luck would have it, I am going to be in Namibia on the day of the eclipse. In fact, if you are reading this anytime in the week before the eclipse, I am already there. I am in Namibia for a week as part of Cardiff University’s Phoenix Project, and I will be giving a public lecture at the University of Namibia about the eclipse on Wednesday 22 February. I also hope to give a public lecture to the Namibian Scientific Society on the Friday, and on the Sunday I will be helping University of Namibia astronomers with a public observing session in Windhoek.

The February 20 2017 annular eclipse will finish in Africa, passing through Angola, Zambia and the Democratic Republic of Congo (Congo Kinshasa)

The interactive map to this eclipse, which you can find by following this link, allows you to click on any place and find out the eclipse details for that location. So, for Windhoek, the eclipse begins at 15:09 UT (which will be 17:09 local time), with the maximum of the partial eclipse being at 16:16 UT (18:16 local time), and the eclipse ending at 17:16 UT (19:16 local time). Because Windhoek is to the south of the path which will experience an annular eclipse, it will be a partial eclipse, with a coverage of 69%.

As seen from Windhoek, where I will be for the annular eclipse, the obscuration will be 69%.

So, if you are anywhere Chile, Argentina, in western South Africa, in Namibia, in Angola, or the western parts of Congo-Kinshasa and Congo-Brazzaville, look out for this wonderful astronomical event this coming Sunday. And, remember to follow the safety advise when viewing an eclipse; never look directly at the Sun and only look through a viewing device that has correct filtration. Failure to follow these precautions can result in permanently damaging your eyesight.

Evidence for the Galaxy’s supermassive black hole

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.

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.

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.

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.

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.

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.

The Galaxy’s supermassive black hole

There is now overwhelming evidence that our Galaxy harbours a supermassive black hole at its centre. Not only that, but the Hubble Space Telescope has discovered that all spiral galaxies harbour supermassive black holes at their centres, and the mass of that black hole is directly proportional to the mass of the galaxy in which it resides. The reasons for this are still unclear.

The idea of supermassive black holes driving the prodigious energy output at the centre of some galaxies was first proposed by Edwin Salpeter in a 1964 paper. Salpeter is probably better known for his work on the initial mass function of star formation, but in this paper (follow this link to read it), Salpeter proposed that supermassive black holes may be the energy source behind the then newly discovered quasars.

In a 1964 paper, Edwin Salpeter (possibly more famous for his work on the initial mass function of star-formation) was the first to propose supermassive black holes as the energy source of the newly-discovered quasars (or QSOs).

In 1971, Donald Lynden-Bell and Martin Rees wrote an important paper entitled “On quasars, dust and the galactic centre”, (follow this link to the paper). It was the first paper to suggest that our own Galaxy, the Milky Way, may harbour a supermassive black hole at its centre.

The possibility that our Milky Way harboured a supermassive blackhole at its centre was first proposed by Donald Lynden-Bell and Martin Rees in 1971.

Another important paper entitled “Accretion onto Massive Black Holes” was written in 1973 by Pringle, Rees and Pacholczyk (follow this link), who considered the observable effects that matter accreting onto a (super)massive black hole would have.

In a 1973 paper, Pringle, Rees and Packolczyk considered the observable effects of the accretion of matter onto a supermassive black hole.

Pringle etal. draw two main conclusions, the second of which is possibly the more important; that material falling onto a (super)massive black hole will emit a huge amount of radiation.

The two main conclusions of the Pringle etal. (1973) paper.

In a 1974 review article in The Observatory entitled “Black Holes”, Martin Rees further stated the arguments for supermassive black holes at the centres of galaxies.

In a 1974 review article in The Observatory, Martin Rees wrote that “a black hole might lurk in the centres of most galaxies.”. 35-40 years later, he was shown to be correct.

He stated (my highlight)

If we regard quasars as hyperactive galactic nuclei, then a black hole might lurk in the centres of most normal galaxies.

How prescient were these words!

Later in the same year, radio astronomers Bruce Balick and Robert Brown discovered a compact radio source in the constellation Sagittarius. They announced their result in a paper entitled “Intense Sub-Arcsecond Structure in the Galactic Center” (here is a link to the paper).

In 1974, Bruce Balick and Robert Brown used the Very Large Array of radio telescopes in New Mexico to discover a compact radio source at the centre of the Milky Way. We now call this source Sagittarius A*

Using the Very Large Array of radio telescopes in New Mexico, Balick and Brown found a sub-arcsecond radio source at both 2695 MHz (11cm) and 8085 MHz (3.7cm). We now call this source Sagittarius A*, and it is believed to be where the Galaxy’s supermassive black hole resides. Here is their image obtained at 2695 MHz (at right, the image at left is the base-line coverage in the u-v plane, the interferometry plane of the array).

Bruce Balick and Robert Brown discovered a sub-arcsecond radio source in the constellation Sagittarius. We now call this source Sagittarius A*. Their discovery was made at 2695 MHz (which corresponds to a wavelength of 11 centimetres)

Since these discovery observations, Sagittarius A* (or Sgr A* as it is often known) has been observed at many other wavelengths (but not in visible light, the dust extinction is too great). For example, here is a combined infrared and X-ray image.

A composite infrared and X-ray image of Sagittarius A*

And, here are some images taken by the SPIRE camera on the Herschel Space Observatory at 250, 350 and 500 microns.

Images of Sagittarius A* taken by the SPIRE camera on the Herschel Space Telescope. The observations are at (from left to right) 250, 350 and 500 microns.

Later this week I will blog about the observational evidence for this compact object being a supermassive black hole.

What is that bright object in the evening sky?

A number of people have been asking me over the last two or three weeks what the (very) bright object is in the evening sky. It is Venus, the brightest of all the planets. If you look towards the west (the same part of the sky as where the Sun has set) on any clear(ish) evening over the next two months, within a few hours of sunset, you should easily be able to see Venus.

Here is a diagram showing the evening sky for this evening (12 January 2017) as seen from Cardiff, and I have set it up to show the sky at 6pm. In Cardiff today the Sun sets at 16:29. Venus will not set until 20:51, nearly 3.5 hours after the Sun has set. This is why it is visible for such a long time after sunset.

The western sky at 6pm as seen from Cardiff. Today the Sun will set in Cardiff at 4:29pm, with Venus not setting until 8:51pm. This is nearly 3.5 hours after sunset, and today is the day of maximum eastern elongation.

In fact, today (12 January) is the day when the time between the Sun setting and the time at which Venus sets is at its greatest. That is why I chose today to blog about Venus. This is called maximum eastern elongation, and it is shown in the diagram below.

When the angle between a line from Earth to Venus and Venus to the Sun is a right angle, we have maximum elongation. As Venus is currently to the East of the Sun (rising after and setting after the Sun), it is today at maximum eastern elongation.

Venus will dominate the evening sky for another 6 weeks or so, although it will start setting closer and closer to the time of sunset now that we have passed maximum eastern elongation. It will swing in front of the Sun (something called inferior conjunction) on 25 March, so will be lost in the glow of the Sun for a few weeks before that. A few weeks after inferior conjunction, it will reappear as a morning object, becoming increasingly visible before sunrise as opposed to after sunset.

So, enjoy the wonderful sight of Venus in the evening sky over the next 6 weeks or so. And, if you can get hold of a pair of binoculars or a small telescope, you will see that Venus exhibits phases. Currently it is a quarter phase (half of it is illuminated), but as it approaches inferior conjunction it will become more and more crescent, but also appear to get larger in your viewing device (this cannot be seen with the naked eye). It was observations like these which enabled Galileo to show in 1610/1611 that Venus could not be orbiting the Earth, but that both Earth and Venus must be orbiting the Sun.

Is there life on Mars? (part 1)

As those of you following my blog will know, I am currently on a cruise around New Zealand, giving astronomy talks. One of my six talks is about our current understanding of whether there is (or was) life on Mars. I try to only talk about objects which are visible during the cruise, and Mars is currently visible in the evening sky, albeit a lot fainter than it was in May when it was at opposition.

One of the talks I am giving on this cruise is our current understanding of whether there is (or was) life on Mars.

The question of whether there is life on Mars, or whether there ever has been in its history, is a fascinating one. I thought I would do a series of blogs to explore the question. But, I have to begin by saying that ANY search for life beyond Earth is predicated by our understanding of life on Earth. The only thing, it would seem, required by all forms of life which we have found on earth is water. Extremophiles show that life can exist without oxygen, without light, at high pressure, in radioactive environments; in fact in all sorts of environments which humans would find impossible. But, none of the life so far found on Earth can exist without water.

As a consequence, all searches for life in our Solar System tend to begin with the search for water. Now, it may be that life beyond Earth could have evolved to exist without the need for water. I am no chemist, but I don’t think there is anything particularly unique about water in its chemistry which makes it impossible for living cells to use some other substance. Water is the only substance on Earth which can exist in all three forms naturally (solid, liquid and gas), so it does occupy an unique place in the environment found on Earth. But, on Titan for example, methane seems to exist in all three forms. Maybe life has evolved on Titan to metabolise using methane in the same way that life on Earth has evolved to metabolise using water. We don’t know.

So, I thought I would start this series of blogs with the big news in the 1890s, that Martians had built canals on the red planet!

Schiaparelli and Martian ‘canali’

The Schiaparelli space probe which ESA sadly failed to land on Mars recently was named after Italian astronomer Giovanni Schiaparelli. In the late 1880s he reported seeing ‘canali’ on the surface of Mars. Although this means ‘channels’, it got mis-translated to ‘canals’, and led to a flurry of excitement that this was evidence of an intelligent civilisation on Mars.

The idea grew that Martians had built canals to transport water from the “wet” regions near the poles to the arid equatorial regions. The ice caps of Mars are easily visible through a small telescope, so astronomers had known for decades that Mars had ice caps which they assumed were similar to the ice caps on Earth.

Giovanni Schiaparelli’s map of ‘canali’ on Mars, from 1888.

One person who became particularly taken with this idea of canals on Mars was American Percival Lowell. Lowell came from a rich Bostonian family, and had enough personal wealth to build an observatory in Flagstaff, Arizona. He set about proving the existence of life on Mars, writing several books on the subject. He published Mars (1895), Mars and Its Canals (1906), and Mars As the Abode of Life (1908). But, by 1909 the 60-inch telescope at Mount Wilson Observatory had shown that the ‘canali’ were natural features, and Lowell was forced to abandon his ideas that intelligent life existed on Mars.

However, his Flagstaff Observatory was to go on and make important contributions to astronomy. In the 1910s Vesto Slipher was the first person to show that nearly all spiral nebulae (spiral galaxies as we now call them) showed a redshift, the first bit of observational evidence that the Universe is expanding. And, in 1930 Clyde Tombaugh discovered Pluto at Flagstaff Observatory.

In part 2 of this blog, next week, I will talk about the first space probes sent to Mars, and the first images taken of Mars by a space probe which successfully orbited the planet, Mariner 4.

Off to New Zealand

Tomorrow (Friday 25 November) I am boarding a plane which will eventually get me to Brisbane (Australia), via Seoul. Yes, I’m aware that Brisbane is not New Zealand, but in Brisbane I am joining a cruise which is going around New Zealand. The cruise will last for 14 nights, and I will give about 6 talks during the two weeks.

The Princess Cruise leaves Brisbane on 27 November and returns on 11 December. I will be giving astronomy talks on the 14-night cruise.

This will be the 5th cruise which I’ve done with Princess, and the 6th in total. The last time I did a cruise in the southern hemisphere was in February, when I cruised from Buenos Aires to Santiago around Cape Horn. Unfortunately, during that 14-night cruise, we had only one clear night! I am hoping for better weather this time, as in addition to my talks I run star parties to show the guests what is visible in the night-time sky.

Many of the guests will probably be from Europe or the United States, and so will be very keen to see the Southern Cross. I will also show them the Magellanic Clouds if weather permits. The New Moon is on the 29 November, so the first week of the cruise will be ideal to see the Magellanic Clouds if the skies are clear. After that, the brightening moon will render them all by invisible. So, fingers crossed we get some clear skies during the first week!