In July’s WMA webinar, we looked at Hertzsprung-Russell diagrams. H-R diagrams are one of the most important tools available in stellar physics, since they indicate a great deal about the characteristic of stars. The H-R diagram below, known as a theoretical H-R diagram, is a scatter plot of stars photosphere temperature vs. luminosity.
Brian Davidson’s last couple of Blogs have mentioned the Summer Triangle asterism, consisting of Vega, Deneb, and Altair. Taking a sample of ‘nearby stars’ as shown below we have marked the Summer Triangle stars on the H-R diagram, showing how different these three stars are:
The spectral classes of the stars are indicated by the familiar ‘OBAFGKM’ legend. Before looking at the three stars, look at the track running from Alnitak at the top left to Proxima Centuri at the bottom right. This track is the Main Sequence, where in the stars interior hydrogen is converted into helium by nuclear fusion. Stars leave the main sequence once about 11% of the hydrogen-mass has fused to helium and the core of the star becomes unstable.
About 90% of stars are on the main sequence. It may not appear like this from the diagram, but that’s because of our sample, which is ‘nearby stars’.
Altair is a main sequence star, larger and hotter than the Sun. It will therefore have a shorter main sequence life than the Sun. Altair’s luminosity is 10.6 L⊙. Recall that luminosity is a measure of the power radiated by a star; the unit of luminosity is the Watt.
Vega has a photospheric temperature similar to that of Altair. But Vega’s hydrogen burning phase is now over. The star has entered the main sequence turnoff, on the way to becoming a red giant, before shedding its outer layers to form a planetary nebula. At that time, what will remain of Vega is a hot white dwarf star at the bottom left of the H-R diagram. This sequence of events will also be what happens to the Sun when main sequence turnoff occurs.
Deneb is a super-giant star. Although Deneb’s Photospheric temperature is comparable to both Vega and Altair, its luminosity is very much greater. Deneb has a luminosity of more than 104 L⊙, a mass of 19M⊙ and is destined to end its life in a Type II supernova event. This will leave a supernova remnant perhaps like the Crab Nebula, M1 and a neutron star which is way off scale at the bottom of the H-R diagram.
Open clusters and globular clusters
For this month’s Blog, we’ll consider a question asked at the July WMA webinar, “Can we make H-R diagrams of star clusters to help determine their characteristics?” The answer is yes.
Astronomers are familiar with both open clusters and globular clusters. Their main characteristics are shown in the table below.
How can we conclude that open clusters consist of young stars and globular clusters consist of old stars? The amount of hydrogen that a star has available for fusion is directly proportional to the star’s mass. In simple terms, the greater the mass of hydrogen packed in, the faster the reaction rate, and the higher the luminosity. The star’s luminosity determines how quickly the star will fuse the hydrogen into helium, and hence how long the star lives on the main sequence according to the relation:
Since from the mass-luminosity relation we know that:
The diagram below summarises how stars of different spectral classes leave the main sequence - the “main sequence turnoff” - as they evolve:
Plugging the numbers into the equations, this means that a star of 10M⊙ will have a lifetime of only about 13 million years.
Bear in mind that we know that about 80% of stars are red dwarfs, smaller than the Sun. A low mass star of about 0.6M⊙ has a life of ~34 billion years. That time is much greater than the age of the universe which means that no low mass star has yet completed its main sequence lifetime.
H-R diagram for open cluster M45
So, let’s plot an observational H-R diagram, (also known as a “colour-magnitude diagram”) for open cluster M45, known of course as the Pleiades:
The observational H-R diagram above is a plot of absolute magnitude (VMag) vs. colour index (BMag-VMag). The scale ranges are (x: colour index 0.2 à 1.45; y: absolute magnitude 8 à -2) .
We can see at the top left of the H-R diagram, only a few of the larger, more luminous (which of course implies more massive) stars in the Pleiades have begun their main sequence turnoff. These are the dots at the top left which are turning upward and to the right. The majority of the (less massive) stars in the plot remain very much on the main sequence. They are so young that hydrogen burning has a while to progress.
It is generally thought that open clusters disperse after a short time (in cosmological terms) before the stars in them have commenced main sequence turnoff. It is also thought that then Sun formed in an open cluster which subsequently dispersed and that this accounts for the fact that the Sun is isolated and not part of a multiple star system, although that is far less certain.
H-R diagram for globular cluster M14
Now, let’s look at the H-R diagram for globular cluster M14. This H-R diagram is markedly different to that of M45. The plot is a subset of the total data of over 1,000 stars and is plotted with the same scale ranges as the M45 plot.
In the M14 H-R diagram, just about no main sequence stars are evident. The reason is that most stars in M14 are very old, and have completed hydrogen burning and moved off the main sequence. Low mass stars are either ascending the red giant branch or have already become red giants. Like Altair, Vega, and the Sun, they will end their lives as white dwarfs. A few at the top right of the H-R diagram are supergiants and, like Deneb, will finish their lives in Type II supernova events.
The fact that the majority of stars in this globular cluster are grouped at the red end of the colour index confirms the generally red appearance of the globular cluster.
Contreras Pena, C et al (2013). The globular cluster NGC6402 (M14). A new BV color-magnitude diagram. ApJ, September 2013. DOI: 0.1088/0004-6256/146/3/57 Accessed August 10th 2020
Australia Telescope National Facility
As promised Jupiter and Saturn are now in the late evening sky and they are on the diagram below but with Jupiter shining so brightly in the southern skies it doesn’t need a signpost. The highlight of last month was the appearance of the comet Neowise visible to the unaided eye in the northern sky and Josh Dury gives a description of where to look for it in his recent e-mail, ‘Identify the constellation, Ursa Major, and use the two stars marking the edge of the saucepan to draw a line at about a similar distance until you come across a faint, smudge patch in the sky. This is Comet Neowise’. It is not usually wise to predict when a comet will appear because over the years there have been many disappointments because of unfulfilled promises of a spectacular sight. One comet which did live up to and even exceed expectations was comet Hale-Bopp back in 1997 and I remember it well. I mention it because it was discovered by amateurs.
We talked about the Summer Triangle of Vega, Deneb and Altair last month so we will start from there. From Altair in the Summer Triangle, looking southerly, drop down the Milky Way close to the horizon and to the right is the constellation Sagittarius (the Archer) which lies on the ecliptic to the left of Scorpius. Yet again it is hard to distinguish the archer of mythology but what is easily recognisable is the asterism ‘the Teapot’. The planets Jupiter and Saturn are on the diagram and in fact Jupiter is by far the brightest object in that part of the sky and you cannot miss it. Sagittarius lies in the direction of the centre of our Milky Way. There are dense clouds of gas and dust along the plane of the Milky Way which obscure our view to the centre. See the recent picture of the Milky Way sent back by my granddaughter from New Zealand.
To the right of Sagittarius and also close to the horizon you will see the star Antares which we mentioned last month.
Now let us go to the other end of the Summer Triangle with Vega and Deneb and look at two circumpolar constellations. Face south and look up to find Polaris- the pole star. Obviously it is above your zenith so you need your deckchair again! If you look to the east you should recognise the ‘W’ shape of the constellation Cassiopeia which we found previously from the Plough via Polaris. So do the reverse trip from Navi through Polaris and you come to the Plough. You will see it is almost upside down now. Just as we have watched the Plough change its orientation so we can enjoy watching Cassiopeia continue on its anticlockwise journey around the pole star gradually taking on the proper ‘W’ shape we are accustomed to during the rest of the autumn as it heads south. Just east of Cassiopeia is a group of not very bright stars forming a shape roughly similar to the gable end of a house. This is the constellation Cepheus (King Cepheus of Ethiopia in ancient mythology and husband of Cassiopeia). Perhaps its claim to fame is that it contains the prototype of an important group of variable stars called ‘cepheid variables’ which have been fundamental in establishing a ‘standard candle’ for the measurement of intergalactic distances and the rate of expansion of the universe- a key area of research in cosmology at present. The prototype was delta Cep in the bottom left hand corner of the house shape.
I guarantee you will enjoy seeing Cassiopeia in the southern skies for the rest of the year.
Something to look out for
At the beginning of the month on Saturday 1st there is a close approach of a near full moon and Jupiter with Saturn just to the east. There is another close approach on Friday 28th August. We cannot all be together for the Perseid meteor shower as usual but if you want to see some shooting stars look out on the nights of 11th and 12th August and be prepared to stay up a little longer than usual to give yourself the best chance in spite of a Last Quarter Moon.
Precession is a phenomenon that occurs when massive bodies move, due to angular momentum being affected by other masses in space-time. In the words of John Archibald Wheeler, “mass tells space-time how to curve, space-time tells mass how to move”.
Precession of Earth’s rotational axis
The most familiar example is the precession of a gyroscope; its rotational axis appears to describe a circle under the influence of Earth’s gravity. Exactly the same applies to the rotational axis of the Earth under the influence of the Sun's (and to a lesser extent, the Moon's) gravity:
As most people are aware, Earth’s rotational axis is inclined ~23.5° to the plane of the ecliptic, which accounts for the seasons. Currently, the Earth’s rotational axis points almost exactly at Polaris, which is therefore called the ‘pole star’. However, the precession of Earth’s axis has a period of ~26,000 years, so that in around 13,000 years time, Earth’s axis will point at Vega, which will then be the ‘pole star’. Then, in about 26,000 years time, Polaris will again be the ‘pole star’. This is an example of rotational axis precession.
The precession of Earth’s rotational axis also accounts for the phenomenon of precession of the equinoxes. The First Point of Aries is one of the two points where the plane of the ecliptic intersects the celestial equator (Davidson, 2020). These are called vernal equinoxes. The first point of Aries was recognized in antiquity in the constellation Aries, but due to precession of Earth’s axial rotation is today located in the constellation of Pisces. Exactly 180° around the celestial equator is the first point of Libra, which today lies in the constellation Virgo.
Let’s put that precession cycle into context. The period of precession of Earth’s rotational axis is:
Human civilisations are known to have started ~6,000 years ago. The number of precession cycles during that time is not yet one quarter:
Modern Homo sapiens are believed to have emerged ~200,000 years ago. The number of precession cycles during that time is almost eight:
Earth formed ~4.5 Bn years ago. The number of precession cycles during that time is more than 170,000:
Precession of planetary orbits
As was discovered by Kepler, a planet follows an elliptical path as it orbits the Sun. The point at which the planet makes its closest approach is known as periastron. For many years, it could not be explained by Newtonian theory that the periastron of Mercury does not always occur at the same place in the Mercury’s orbit. This is because the orbit itself is subject to precession, so that over a period of time periastron occurs at a point further around the orbit. This was established by careful observation in the nineteenth century.
Since Mercury is the planet orbiting closest to the Sun, the precession of Mercury’s orbit is higher than any of the other planets.
How orbital precession works is illustrated in the diagram below.
PLEASE NOTE that a) this diagram is looking at the solar system from ABOVE; b) the diagram is emphatically NOT TO SCALE ; c) also, the orbital eccentricities are GREATLY exaggerated; and d) the angular precession angle is GREATLY exaggerated.
Newtonian gravitational theory predicts that the magnitude of the orbital precession of Mercury should be slightly more than half what is actually observed. Although many explanations were produced to account for the observations, none were considered conclusive. Einstein’s General relativity (GR), published in 1917, predicted the rate of orbital precession to be 43 arc-seconds per century. This matched the observations exactly.
In turn, let’s put that into context. How long does it take Mercury’s orbit to precess a full 360 degrees? Based on angular measure (Helps, 2020), the answer is approximately 3 million years:
Or, looked at another way: Mercury is estimated to have formed 4.5Bn years ago. That would imply that Mercury’s orbit has completed
precessions since Mercury’s formation.
This accurate prediction of 43 arc-seconds per century was the first major observational proof that General Relativity is a valid theory. Note that we say a “valid” theory rather than a “true” theory. A scientific theory cannot be proved to be true; it can be showed to accurately account for observations. A scientific theory can only ever be “proved” to be untrue. Later, GR was also able to exactly predict the much smaller orbital precession of Venus (8.6 arc-seconds per century).
The second observational evidence pointing to the validity of GR was that gravity of a large mass would “bend” light rays passing close by it - recall John Archibald Wheeler’s ‘mass tells space-time how to curve’ above. This was verified by an expedition lead by Sir Arthur Eddington to observe a total solar eclipse in 1921. But that’s another story.
John Archibald Wheeler: https://phy.princeton.edu/department/history/faculty-history/john-wheeler
Mathematics of precession: https://en.wikipedia.org/wiki/Precession
Angular size: Helps, L; WMA Blog, May 2020
Celestial equator and plane of the ecliptic: Davidson, B; WMA Blog, May 2020
The summer solstice has passed now so we will gradually get improved lighting conditions for observing. The notes here apply at 11.00pm BST at the end of the first week of the month and at 10.00pm BST at the beginning of the last week in the month. However I find that at present the sky doesn’t really get dark until after midnight and this month you will need a clear view to the southern horizon with no obstructions and free from local light pollution. I did have a look out on the morning of June 19th to see the close approach of Venus and the Moon but I’m afraid the cloudy skies were against me.
Back at the beginning of April if you looked directly above you while facing south, the Plough was directly overhead (at your zenith) and looked like a plough. Now you will notice that it has moved anti-clockwise about the North Pole and is now upright on its handle. Keep checking the orientation of the Plough as the year progresses.
So while facing south, look directly above you and just before your zenith you will see a very bright star. Perhaps this is the time to get your deckchair out and lie flat on your back! This star is easily recognisable due to its brilliance and a grouping of four stars to its bottom left hand side. These stars make up the compact constellation Lyra (the Lyre or Harp) and the bright star is Vega, alpha Lyr, the 3rd brightest star visible from the northern hemisphere. The lighter region of the diagram to the left of Vega represents the Milky Way, the star filled disc of our galaxy, and there you find a giant cross in the sky and this is the constellation Cygnus (the Swan) with the bright star Deneb, alpha Cyg, representing the tail of the swan which is flying down the Milky Way. Deneb is the 14th brightest star visible from the northern hemisphere. At the head of the long neck is the star Alberio, beta Cyg, about which I have heard our chairman, Hugh, wax lyrical on more than one occasion so do look at it through a telescope if you get the chance.
Now face Vega and Deneb and drop down about halfway to the horizon till you find the star Altair in the constellation Aquila (the Eagle). Altair, alpha Aql, is identified by two fainter stars either side of it and together they point to Vega.
I hope you have been keeping count of these bright stars because Altair is the 8th brightest star visible from the northern hemisphere and you have now become acquainted with eight of the eighteen brightest stars. These three stars Vega, Deneb and Altair form what is called the Summer Triangle depicted in yellow in the diagram. The Summer Triangle is something you will be able to enjoy looking at for the rest of the summer into autumn. Like the Plough it is a big help in finding your bearings.
Now let us be a little more subtle because biggest and brightest isn’t always the best. Last month we found Arcturus by following round the arc of the handle of the Plough. Between Vega and Arcturus you find the constellations Hercules (the strong man from Greek mythology) and Corona Borealis (the Northern Crown). Hercules is a fairly faint constellation and looks more like flailing windmill blades than a strong man but the most distinctive feature is the four central stars in the shape of a quadrilateral forming an asterism known as the Keystone. Corona Borealis is small but distinctive, consisting of seven faint stars in a horseshoe shape if you cannot envisage a crown.
We are quite unashamedly going back to bright star ‘bagging’. We are doing this because the object in question is best observed in summertime. Imagine a line from Vega to Arcturus and from its midpoint follow a line to the horizon between Hercules and Corona Borealis until you see a reddish star. Remember you will need a good unobstructed view to your southern horizon. This star is Antares, the brightest star in the constellation Scorpius (the scorpion) and is the sole attraction because most of Scorpius and specifically its fish-hook shaped tail is not visible from our latitude. Antares is the 10th brightest star visible from the northern hemisphere and that is because it is a red supergiant and if it were to replace our sun, its surface would lie between the orbits of Mars and Jupiter. That is big! It is said to represent the heart of the scorpion.
Something to look out for
The major planets, Jupiter and Saturn, return to the late evening sky this month quite close together and visible all night. On July 14th Jupiter will be at opposition, on the opposite side of the Earth from the Sun, so will be at its closest and brightest. A week later on the 20th July, Saturn reaches opposition but unfortunately both planets will be quite low in the southern sky and although bright are not ideally located for good viewing.
This year, we celebrate 30 years of the history of the Hubble Space Telescope Here’s the HST itself, and one of its most famous images, taken in 1995.
The extent of the universe
The HST is named after the American astronomer, Edwin P Hubble, whose observations in the early 20th Century, lead to two, profound discoveries. Looking into these we will also meet several other important characters.
Hubble was physically large and imposing. he was a US Army boxing champion, serving at the closing stages of WW1, although his unit did not go into combat. He affected an English accent despite being very much an American.
For the first twenty or so years of the twentieth Century, there was great scientific debate about the extent of the universe. Many scientists believed at the time that the whole of the universe consisted of our Milky Way galaxy, and that what were then called “spiral nebulae” were some kind of structure within the Milky Way. Following painstaking observations at the 100 inch Hooker telescope at the Mount Wilson Observatory in California, Hubble and his assistant Humasson established in 1924 that spiral nebulae are in fact remote galaxies in their own right; they are now called spiral galaxies.
Hubble’s discovery was made possible by way of an earlier crucial discovery made by Henrietta Swan Leavitt, who worked at the Harvard College Observatory. Leavitt had the task of examining photographic plates to measure and catalog the brightness of stars.
This work led Leavitt to discover the so-called 'period-luminosity relationship' of Cepheid variable stars. Probably the best known Cepheid variable star is Polaris, the current pole star. Leavitt’s discovery was that the rate at which these stars appeared to vary in brightness was directly related to their intrinsic luminosity. This meant that measuring the period of change provided astronomers with the first "standard candle" with which to measure the distance to remote astronomical objects. Hubble used this technique to show that Cepheids in the Andromeda galaxy, M31, was too far distant to be part of the Milky Way Galaxy. It was later discovered that there different types of Cepheid variables, and this meant that M31 is actually twice as far distant as Hubble first calculated.
The expansion of the universe
Hubble’s second observational discovery was to prove equally profound. It was in fact preceded by a theoretical discovery by Georges Lemaître, a Belgian Catholic priest and professor of physics at the Catholic University of Louvain. Lemaître applied Einstein’s general relativity (GR) to cosmology deriving solutions to Einsteins field equations, giving results that implied an expanding universe.
Extrapolating back in time, Lemaître postulated an origin of the universe in what he called a 'primeval atom' – in effect, the “big bang”. This was in 1927, two years before Hubble's publication of his observational findings of expansion of the universe.
An advanced mathematician, Lemaître could hold his corner in intellectual argument with Einstein (no less!). The two met on several occasions, including at the Solvay Conference in 1931.
Albert Einstein of course needs no introduction. Einstein published his theory of General Relativity in 1917. Developed from his theory of Special Relativity (published in 1905), GR included an explanation of the phenomenon of gravity. Among other things, GR successfully accounted for variations in the precession of the orbit of Mercury which Newtonian gravitational theory was unable to explain. Einstein had believed that the universe was static, although others (including Alexander Friedman and Georges Lemaître) provided solutions to his equations that indicated that the universe must be either expanding or contracting.
In January 1931, Einstein visited Hubble at the Mount Wilson Observatory where the 100 inch Hooker telescope is located.
Einstein, perhaps rather reluctantly, conceded that the expansion predicted by general relativity must be real, added a term called the 'cosmological constant' to his field equations. In later life, he said that this was "his biggest blunder", although today the cosmological constant is now thought by many cosmologists to account for the role of dark energy.
Confirming Hubble’s discovery using modern data
Hubble's observations, published in 1929, established that the spectra of majority of galaxies exhibit a redshift, showing they are moving away from us, and that the further away they are, the faster they appear to be receding. This became what is now called Hubble's Law and is a cornerstone of modern cosmology.
The data plot below shows the plot published in Hubble's 1929 paper.
The slope of the trendline indicates the value of what is called the Hubble parameter, H₀, a measure of the velocity of recession of galaxies vs. distance. Hubble's early estimate was that H₀ ~500 km s¯¹ Mpc¯¹ . This was quickly realized to be much too high, as it implied an age of the universe of less than 2 million years, whereas it was known that Earth was much older than this.
The plot below has been constructed from modern data in the NASA Extragalactic Database (NED).
As in Hubble’s work, the plot shows recessional velocities against distances. The red trendline represents H₀. Observations since Hubble's time have refined and reduced the value of H₀ and today the value is thought to be in the range 60-90 km s¯¹ Mpc¯¹ - the exact value is still highly debated in the community. The slope indicates on this plot for this sample of 44 galaxies, H₀ ~64 km s¯¹ Mpc¯¹ .
For Hubble’s confirmation of the extent of the universe and for Hubble’s Law, the Hubble Space Telescope, which has made so many discoveries of its own in its 30 year operation, is named in his honour.
Well I’m pleased to say that the planets Mercury and Venus didn’t disappoint during the month of May. They were within one degree of each other on Friday 22nd although Mercury is challenging to spot unless you are located in a good site and your eyesight is quite sharp. They repeated with a more separated appearance on Sunday 24th but with the addition of a beautiful crescent Moon nearby. My eyesight isn’t what it used to be but I still managed to see Mercury naked eye. Seeing all three together was something special. This is a difficult time of year for astronomers as there is so little light free time and any local light pollution makes the matter worse.
We’ll start where we left off last month when we used the Plough to locate Polaris (the Pole star). You will notice that the Plough is not directly overhead anymore because Ursa Major is a circumpolar constellation and as it rotates about the Pole star, the Plough moves so that its pointer stars Merak and Dubhe keep pointing towards the Pole star and it changes its orientation in the sky so that looking north at present it appears to be standing on end. This is something to keep an eye on throughout the year until it returns to its original orientation in the sky.
Courtesy In-the-sky.org edited by B Davidson
So facing north, use the pointers, Merak and Dubhe, to find the Pole star and then from the third star in from the end of the Plough handle, Alioth, make a line through the Pole star and continue about the same distance beyond until you see a bright star. It will be the central star of a W formation, an asterism in the constellation Cassiopeia. Most people see the W shape and call it Cassiopeia. The bright star was never given a name in Western or Middle Eastern culture so is referred to as gamma (g) Cas. The convention is to name stars using the letters of the Greek alphabet and an abbreviated form of the constellation. Generally this is done in the order of brightness of the star but it is not a hard and fast rule.
However this star has been given the name Navi, allegedly by the American astronaut Virgil (Gus) Ivan Grissom as an anagram of his middle name because it was used for navigation in the early space missions. A fitting tribute to someone who made the ultimate sacrifice for space exploration. The constellation Cassiopeia is circumpolar and because it is directly opposite the Plough across the North Celestial Pole the two will have exchanged positions in six months so we will see Cassiopeia much better in November. As we will the other circumpolar constellation shown on the diagram, Cepheus, which is rather indistinct at present suffering from being too close to the horizon, the lack of proper darkness and the Bristol glow when looking north.
Now let’s go in the opposite direction. Follow the arc of the handle of the Plough round to the star, Arcturus which has the distinction of being the second brightest star visible in the northern hemisphere. Also known as alpha(a) Boo.
Courtesy In-the-sky.org edited by B Davidson
It is the brightest star in the constellation Bootes (The Herdsman) and again it is difficult to distinguish such a figure whereas the Kite asterism is easier to see. Carry on following the curve of the arc for about the same distance until you see a bright star on the Ecliptic. This is Spica the brightest star in the constellation Virgo (The Maiden). It may be easier to memorise this procedure using the expression "Arc on to Arcturus and Speed on to Spica". Now that you are on the ecliptic you can follow it round to the west (the same path followed by the Sun earlier in the day) and from last month you should recognise Regulus in the constellation Leo. So face west to Regulus then look up and you are back at the Plough.
Something to look out for
It is a challenging time for observing the skies when there is so little darkness but it is the summer solstice on June 20th so things will start to improve from then onwards. What about some daytime observation. Our favourite planet at present, Venus, is approaching inferior conjunction, the point in its orbit when it lies between the Earth and the Sun so we cannot see it during the first half of June but it soon makes an appearance in the morning sky and on June 19th it will be close to the waning crescent Moon at dawn. That would mean an early rise! It will be occulted by the crescent Moon (ie the Moon will pass between us and Venus) from 8.35am (BST) onwards but unfortunately it will not be visible to the naked eye. Perhaps some of our imaging friends will try to capture the event but great care needs to be taken as the Sun is up and in the same direction. It is a C shaped waning crescent so Venus will disappear behind the crescent then reappear about an hour later.
So what is Dark Matter?
Presumably there must be some kind of exotic particles that constitute Dark Matter (DM). The ‘Standard Model’ of particle physics looks like this:
It turns out there are candidates for DM in this model. ‘Neutrinos (the ‘e’, ‘μ’ and ‘τ’ in the leptons group) are DM candidates. Millions of neutrinos pass through the Earth and through our bodies every second, only very rarely interacting with matter. However, neutrinos have an extremely small mass and there are not nearly enough of them to account for the amount of DM required. One group of researchers postulates ‘sterile neutrinos’ which supposedly only interact with other neutrinos, arising when an ordinary neutrino morphs into a sterile neutrino. These results are highly contentious in the community, so neutrinos may only offer a partial explanation.
Another theoretical possibility is called a ‘Massive Compact Halo Objects’ (MACHO), a body composed of normal matter whilst emitting little or no radiation. Possible MACHOs include black holes, neutron stars, red dwarf stars and brown dwarf stars, or even planets not associated with any stars. These would be very faint and emit mainly at infra-red wavelengths rather than optical. Some, not completely conclusive observational evidence for MACHOs has been obtained via gravitational micro-lensing observations. Future observations by the upcoming James Webb Space Telescope, which will observe in the infra-red, may detect MACHOs, but there is still a problem. Theoretical studies indicate MACHOs cannot comprise more that 20% of the required dark matter. Add to that the 3% of normal matter we can see, and we still have the question “where is the other 77%?”
Another DM candidate is a theoretical, non-baryonic particle named ‘Weakly Interacting Massive particle (WIMP). The characteristics of a WIMP are framed such that if they exist it would answer the question as to what DM is. The theory is that WIMPs ought to interact very weakly with baryonic matter. The inferred distribution of dark matter in our galaxy (i.e. the DM halo) shows a considerable contribution in our location, so as we move through space, we ought to pass through much DM. If DM is made of WIMPs, then we could directly detect the rare interactions between WIMPs and ordinary matter. The existence of WIMPs is allowed under an extension of the standard model of elementary particles called supersymmetry. The first problem with WIMPs is that supersymmetry theory has no observational basis. And the second snag; nobody has detected a WIMP.
The last current theory for DM postulates particles named Axions. As with WIMPs, the properties of Axions are framed such that they would account for DM. Because of these properties, axions would interact only minimally with ordinary matter. Axions are predicted to be electrically neutral, have very small mass and very low interaction cross-sections for the strong and weak nuclear forces. This would require modifications to Maxwell’s Equations. Axions would also change to and from photons in magnetic fields. Quite a wish list!
Current physics assumes gravity has always acted as it does now; acts the same everywhere; and under all conditions. Suppose that isn’t the case? The leading –though by no means widely accepted - alternative theory to DM is Modified Newtonian Dynamics (MOND) which postulates that under conditions of low acceleration, gravity behaves differently. It also asserts that the inverse square law, while being true over comparatively small ranges such as the solar system, is not applicable over galactic scales. While MOND appears to account for the motions of galaxies without the need for DM, it does not account well for the observed motions within galaxy clusters – reminding us of Fritz Zwicky’s 1933 DM conclusions.
MOND also flies right in the face of Einsteins General Relativity, which has passed every experimental test that has been thrown at it since 1917.
Most physicists believe DM exists. We do know what DM does. We have little idea about what DM is. Current explanations involve serious modifications of the Standard Model of particle physics, or serious modifications to General Relativity, maybe even both. It’s uncomfortable to think that we don’t know what most of the matter in the universe is. It’s an interesting time to be involved in astrophysics.
The author wishes to acknowledge the assistance of Bob Merritt in the preparation of this article.
In these days of electronic gadgets, multiple apps and go-to telescopes it is easy to forget that the best observational devices we have are our eyes. They have a large field of view, can change direction almost instantaneously but can focus in on detail as well. They don’t involve additional cost, need little preparation and no tidying away after you have finished your observations! But do treat them well. Give yourself fifteen minutes to get accustomed to the dark and avoid the use of bright white lights outside. Red LED lights are readily available if you need them to avoid obstacles or read documents and this will enable you to maintain your night vision. Having said that many people find a pair of binoculars very useful for picking out fainter stars when light conditions aren’t optimum.
The objective of this series of articles is to help people find their way around the night sky using only their eyes so there will not be lots of detail on individual stars or planets as that can be found elsewhere. If a star has a number after it that tells its rank in the order of brightness of stars in the northern hemisphere. The idea is that constellations and asterisms (star patterns) are like addresses and signposts for where you want to go. There are 88 constellations in all so only the main ones which are easily recognised will be looked at. As well as this it is hoped that it will be possible to highlight any unusual phenomena which may occur as the year progresses such as planets in good observational positions, planetary conjunctions, special Moon effects, meteor showers or comets.
The Celestial Sphere
Before we venture outside let us recall some helpful facts. It is useful to think of the sky as a hollow sphere which has the Earth at its centre and to which all the heavenly objects are attached. This sphere is known as the celestial sphere. Just like when you visit a planetarium. Far away objects such as stars and galaxies are in more or less ‘fixed positions’ on the celestial sphere whereas the Sun, Moon and planets continually shift their positions but stay close to a circular path on the sphere’s surface called the ‘ecliptic’ which is tilted to the celestial equator because the Earth’s axis is tilted by 23.5 degrees to the plane of its orbit. In reality of course the Earth revolves round the Sun and the ecliptic is where the plane of the Earth’s orbit cuts the celestial sphere. This makes sense because when we observe the Sun we are looking along the radius of the Earth’s orbit and hence in the plane of its orbit. The celestial sphere also has north and south poles directly above the corresponding poles on Earth and a celestial equator directly above the Earth’s equator.
For us in the northern hemisphere we see the stars rotate about the north celestial pole. Don’t worry about some of the additional information on the diagram. The yellow line is the ecliptic and it shows the signs of the zodiac (representing the constellations) and how the Sun appears to pass in front of them as the Earth revolves around the Sun. Remember we are using a model for what we see and this is governed by the movement of the Earth. The Earth spins about its axis from West to East once a day (ie 360 degrees in 24 hours or 15 degrees per hour) and that is why we see the Sun move across the sky daily from East to West. It may not be so obvious that the stars are doing the same thing at night and they move across the sky from East to West at 15 degrees per hour as well. Of course, they also do it during the day, but we cannot see them for the glare of the Sun.
The Earth also revolves about the Sun once a year (ie 360 degrees in 365 days or about 1 degree per day or 15 degrees in 15 days) which is why the sky at 10.00pm one day will look like the sky at 9.00pm 15 days later. If you wait till 10.00pm again the celestial sphere has moved on by 15 degrees or 1 hour and all the stars have moved that amount further west.
Okay, it is time to look at the stars. We have to start with the planet Venus because it has given a brilliant display over the past two months and continues to do so. Venus is breaking records at present because it reached its brightest on the 28th April and is nearest to the highest altitude in the sky at sunset that it can be. It is well worth observing in twilight when there is nothing else in the sky. Just go outside and look westwards and provided the sky is clear I defy anyone not to see it! After a cup of coffee you can go back out when the sky has darkened. Those of you with telescopes may want to observe Venus as a crescent before it enters inferior conjunction (passes directly between the Earth and the Sun). Make the most of it because by the end of May it will have ceased to be an evening star as it passes between the Earth and the Sun but it won’t be gone for long, reappearing as a morning star by mid-June.
While facing Venus turn southwards and trace a path back along the ecliptic, the path that the Sun took earlier in the evening, until you see two bright stars. You will have to go about 35 degrees ( see Lilli’s article on measuring Angular Size). These two stars are Castor (17) and Pollux (12) the dominant stars in the constellation Gemini- the Twins. The other stars are much fainter and may not be visible if lighting conditions are poor.
Now continue backwards along the ecliptic about another 35 degrees and you will find another bright star, Regulus (15), the brightest star in the constellation Leo- the Lion, which unlike many constellations does look like what it represents, a crouching lion. Above Regulus and representing the lion’s mane is theasterism known as the Sickle, looking like a backwords question-mark with Regulus the dot at the bottom.
For the final star hop all you have to do is raise your head till it is looking upwards at the zenith, the point on the celestial sphere directly above your head. You will immediately recognise the Plough, not a constellation this time but probably the best known asterism. ‘Pan’ would be a better name in modern times and in the USA it is known as the Big Dipper.
The Plough is part of the constellation Ursa Major- the Great Bear. But like many constellations it takes a lot of imagination to see a bear. In the diagram there are two stars named on the Plough, Merak and Dubhe, and these are called the pointers. A line from Merak to Dubhe continued onwards leads to Polaris- the Pole Star. The distance is about x5 the distance between Merak and Dubhe. Polaris is very close to the celestial north pole and easily found because although not very bright it is the only star visible in that area.
Now let us retrace our steps. Follow a line from Dubhe through Merak downwards and you come back to Leo. Now go westwards along the ecliptic and you come to Gemini again. Then how could anyone resist taking another look at Venus! Hopefully this hopping about the sky from one known star group to another will give you confidence to continue on the journey to other constellations in the weeks ahead. The next article will be on the website ready for the beginning of June and we’ll be starting from the Plough so you will know where you are. The same pattern will be adopted for the following months.
Something to look out for
There is a chance to see Mercury just after sunset at the end of May. Its orbit lies between the Earth’s orbit and the Sun and it will be at half phase (dichotomy) on the 29th May, so shining brightly. However it will be tricky to see as it is close to the horizon with an altitude of 16 degrees at sunset. Sunset is at 9-09 pm BST and Mercury sets at 11-17 pm BST but it is losing altitude all the time after sunset. Mercury will be located in the west to the bottom right hand side of Gemini. There is a chance to identify it more easily between the 22nd and the 24th of the month when it will be close to Venus but not so bright and both near the horizon.
How big objects look in the night sky is often described by their angular size. But what exactly does this mean and how is it measured?
The angular size of an object tells us how big something looks in the night sky. If you have two objects which are identical but at different distances away from you, the one which is furthest away will have a smaller angular size. Bigger objects will have a larger angular size than smaller objects at the same distance away.
Luckily most celestial objects are roughly spherical so they look like a circle in the night sky. This means 1 angular size is enough to describe the size of the object. Otherwise we would need one for the object’s width and one for its height!
You are probably familiar with angle being measured in degrees, with 360 degrees to make a full a circle. In astronomy they work in the same way, with the night sky being 180 degrees - that’s with completely clear horizons.
If we divide each degree up into 60 equal slices, each slice represents an angle that is 1 arcminute across. If we then divide an arcminute up into 60 yet smaller evenly spaced slices, those slices each represent an angle that is 1 arcsecond across.
We can measure angles by specifying the number of degrees, arcminutes, and arcseconds that they span. An arcsecond is an extremely tiny angle, it’s 1/3,600th of a degree!
Here is a handy trick that you can use to estimate the angular size of something. All you need to know is that if you hold your hand at arm's length, the distance across the end of your pinky finger spans an angle of about 1 degree.
Have a go by looking at the moon. You should gets an angular size of about 30 arc minutes.
A question often asked is “what is dark matter?” The answer touches all our understanding of physics - from the very large, at the scale of galaxy clusters; down to the very small, at the level of fundamental particles. Our best answer: we do not know. We know something of what dark matter does. But we don’t know what dark matter is.
To be concise, I’ll call dark matter ‘DM’ from now on. “Normal matter” interacts with gravity, and particularly with electromagnetic radiation. In everyday terms, if we heat up normal matter, it will emit electromagnetic radiation. If it shines in the visible region, we can see it with our own eyes. This is exactly what we see when looking at the night sky. In complete contrast, DM does not appear to interact with electromagnetic radiation at all. We see only its gravitational effects. So, what kind of evidence do we have pointing to the existence of DM?
Let’s look at just three of the many pieces of evidence for the existence of DM.
Clue 1: Motion of galaxies in galaxy clusters
The first person to postulate the existence of DM was Swiss astrophysicist Fritz Zwicky, in 1933. Zwicky spent most of his life at Princeton and his observations showed that the gravitational attraction between all the visible matter in the Coma galaxy cluster could not account for the observed velocities of the individual galaxies.
The galaxies are moving so fast that they would exceed the escape velocity of the system (as shown in the inset equation) and would therefore fly apart. The cluster of galaxies would not exist, whereas we can see it plainly using telescopes. Zwicky concluded that there must be much more mass than could be seen visually.
Since this missing mass is invisible, Zwicky called it “dunkle materie”- DM. And it was not just a little missing mass – it was a massive amount, many times the mass of the visible matter. At the time, many scientists were openly sceptical of this idea.
Clue 2: Rotation Curves of spiral galaxies
In the solar system with its eight planets orbiting the Sun, the innermost planet Mercury orbits faster than the second planet, Venus. In turn, Earth orbits slower, Mars slower still and so on. This is called Kepler’s second law, or Keplerian motion, after Johannes Kepler, and it was confirmed later by Sir Isaac Newton. Theory indicates that any system where the majority of the mass is at the centre – as with the solar system – will have a rotation curve like this:
In 1975, Vera Rubin, an astronomer at the Carnegie Institution of Washington and her colleague Kent Ford announced the surprise discovery that most stars in spiral galaxies orbit at roughly the same speed, rather than showing Keplerian motion - these galaxies showed a so-called flat rotation curve. The implication of this is that galaxy mass is distributed approximately linearly with radius well beyond the location of most of the stars. The results suggest that at least 50% or more of the galaxies mass is contained in a DM halo around the galaxy extending to a radius of 100kpc or more. The diagram below shows the rotation curve of our own Galaxy, the Milky Way:
From this data, at least out to 8.5kpc, where our Sun lies, the rotation curve is flat, rather than Keplerian; evidence for DM.
Clue 3: Gravitational lensing
Gravitational lensing – the bending of space time due to large masses, which causes light rays to appear to bend was predicted by Einstein’s General Relativity in 1917.
The blue arcs in Figure 4 show the gravitationally lensed image of a galaxy 10 billion light-years away as it appears through the gravitational lens around the galaxy cluster RCS2 032727-132623 about 5 billion light-years away. However, the amount of lensing is too strong to be accounted for by the mass of normal matter in the foreground galaxy. The mass required is much larger: further evidence for DM.
So what is DM? Come back in a couple of weeks for a possible answer......