I in my ignorance until very recently, believed that astrobiology started as a recognised science after the second world war possibly as late as the 1970’s.  This was because detailed knowledge of the structure of the universe and detailed knowledge of the beginnings of life on this planet both started at about that time.  In fact, Biology became a science in the late 1800’s mostly due to the work of Darwin and Wallace.  I failed to note that detailed knowledge of a subject is not needed to start thoughts of what might be, to help stimulate investigations as occurred with Biology.

In my work at Wells & Mendip Museum library, I was investigating the books written by Alfred Russel Wallace whose principal claim to fame is to be the partner of Charles Darwin in the discovery of Biological ‘Natural Selection’.  Much to my surprise, I found two books on Astronomy both on the subject of Astro-biology, and I also found that Wallace had a keen interest in astronomy throughout his life as well as being a biologist.  On further investigation, it appears that discussions on ‘Man’s place in the universe’ has been in progress by philosophers throughout the whole of the nineteenth century and indeed before. Wallace’s two books were entitled ‘Man’s place in the Universe’ printed by Cambridge University press in 1903, and ‘Is Mars habitable?’ printed by McMillan press London in1907.  At this age, neither book is still in copyright and so I can quote from them at will.

It appears that many 19th century philosophers considered both the purpose of the universe and the role of Man in it, as one of their key philosophical questions of the time.  During this period most philosophers took what they described as the ‘Pluralist view’, meaning that there were many intelligent civilisations on different planets.  Both these questions became widely public in 1859 on publication of books by Huxley and Whewell both leading philosophers of the time.  Wallace did not reply to these books at the time, as both he and Darwin were deeply involved in collecting the extra the supporting evidence they felt necessary for their own Theory.

However, in his 80’s when he was no longer fit for field work, he took to astronomy which was a subject he felt able to do from his armchair.  This was the first time an eminent Biologist had considered life on other planets.  Wallace was taping into the philosophical tradition of life on other worlds, while trying to give a scientific view to this question.

Wallace took the view that the human mind was special and was the only one of its kind in the Universe.  Darwin had taken the mainstream ‘pluralist’ view and wrote a book on ‘The Descent of Man’ to confirm his views and show what they meant to him.  Wallace’s book ‘a man’s place in the Universe’, started with five chapters on the most recent discoveries in astronomy to confirm his scientific credentials.  The theme of the book was Wallace’s amazement that ‘mild climates and generally uniform conditions had prevailed throughout all geological epochs; and on considering the delicate balance of conditions required to maintain such uniformity, he became convinced that the evidence was extremely strong against the probability of any other planet being inhabited’ (S728 1903b, v-vi).  Very interesting of itself but more so when you note that consistent climate is not an issue considered in the Drake equation.

One of Wallace’s main problems in writing his book was the lack of a scientific definition of life.  Philosophical definitions were of no use.  No other biologist (and only the philosopher Huxley) had tried to make the necessary definition.  Wallace needed this definition to determine the criteria for life to exist.  Wallace and Huxley’s definition of life was based on the existence of protoplasm which is found in in the majority of plant, animal and fungi cells. This only exists,

1. At temperatures between 32 – 104 degrees Fahrenheit;
2. At a minimum air pressure of between 20 – 25% of Earth’s;
3. In the presence of water and carbon dioxide.
   

In 1904 Wallace added an appendix to his book based on the theory of evolution.  Wallace argued that since humanity is the result of a very long chain of modifications in organic life which only occur under certain circumstances, then the chances of the same conditions and modifications occurring elsewhere in the universe were very small indeed.  Moreover, since no other animal on Earth, despite the great diversity of forms, approaches the intelligence or moral nature of humanity, these characters were unlikely to arise in any other form.

Based on what he knew in his day, (very different from what we think we know today,) Wallace had a go at estimating the chances of intelligent life arising on another planet.  The numbers he came up with are quite interesting.  ‘If the physical and cosmical improbabilities set out in the body of my book are somewhere about one million to one, then the evolutionary improbabilities cannot be less than perhaps100 million to one; the total chances of man or a being of equivalent intelligence arising on another planet are 100 million million to one. (S729 1904, Appendix, 334-5). The evolution of intelligence is one of the still unknown factors of the Drake equation, and perhaps there is no better person to estimate it than the person who helped create the modern view of evolution by natural selection. If the estimate of 100 million to one is anywhere near to correct then it is quite possible that we are the only intelligent life form in the milky way galaxy.  We must take great care of ourselves as a species!!

Wallace’s book on ‘is Mars habitable?’ is a reply to Percival Lowell’s book ‘Mars and its Canals’.  Lowell has observations which he says proves that the canals are good evidence in proving habitation by intelligent beings of the red planet.  Wallace gives three separate facts in rebuttal:

1. The mean temperature on the surface of -35 F.
2. The very low atmospheric pressure on the planet surface.
3. The absence of water vapour and water on the surface.

Any one of the above would make the planet uninhabitable let alone to intelligent life.

Wallace in his first book sees an overall purpose to the Universe.
 
‘Lastly, I submit that the whole of the evidence that I have brought together in this book leads to the conclusion that our Earth is almost certainly the only inhabited planet in the solar system; further, there is no inconceivability, no improbability even-that in order to produce a world so precisely adapted in every detail for the orderly development of organic life, culminating in man, such a vast and complex universe as we know exists around us, may have been absolutely required.’(S728 1903b, 306)
 
Although most of us would disagree with Wallace’s conclusions today, I feel confident that this is a good scientific attempt at Astro biology as early as 1903, that is 60 to 70 years before I had thought this possible.  My view of Astrobiology is changed for ever.
 
Note:  The text in italics are direct quotes from for Wallace’s books.

Abstract
In this Blog, I examine the properties of four well known stars – the Sun, Betelgeuse, Sirius, and Canopus. Despite the distances to the last three stars, we do know quite a lot about them.  I examine how we can measure stellar characteristics, and equally important, what the uncertainties are in such measurement.  In historical context, I identify the key astronomers and physicists whose discoveries have led to our present-day understanding.

Introduction
We can't visit other stars to make measurements.  Any notion of inter-stellar travel is way beyond any technology that we possess today.  Even the closest star to us, Proxima Centauri is approximately 4.25 light-years (lyr) distant.  And yet we do know a lot about stars. In this Blog I will discuss some ways in which this has been achieved, and also see some of the limitations and uncertainties surrounding our observations and measurements.
The key discoveries underlying what we now know were made over a century ago.  Today, astronomers and physicists are still investigating ways to improve the accuracy and precision of measurement in these areas.
In this Blog, I describe two key stellar parameters that enable us to derive other stellar parameters.  These parameters are the luminosity of stars and the surface temperature of stars (known as the photospheric temperature).  I show how we can use these to calculate the size of a star and the radiation environment the stars produce.  Finally, I discuss how the radiation would affect any Earth-like lifeforms on exoplanets in orbit around the star.
From here on, we consider a small sample of four stars:

• The Sun
• Betelgeuse,  orionus, a red super-giant in Orion (apparent magnitude +0.50)
• Canopus,  carinae in the southern constellation of Carina and the second-brightest star in the sky (apparent magnitude −0.74).
• Sirius,  Canis Majoris in Canis Major, the brightest star in the sky (apparent magnitude -1.45)

Figure 1 shows a star map depicting the location of our four-star sample. This view is not fully visible from the  UK because Canopus is below the  hoirzon at our latitudes.  In the northern hemisphere, Canopus is visible as far north as Florida.

Spoiler alert: there are some equations in here (GCSE level), but don't worry we're just going to use them, not derive them from scratch.

Luminosity of stars
Let's ask "how bright is a star?" Scientifically, luminosity is a measure of the power of the radiation emitted by a star. The SI unit of luminosity is the Watt. The luminosity of the Sun is called one solar luminosity, quantitatively:

Luminosity of other stars is often expressed in units of solar luminosity as we shall see later.
We distinguish luminosity, which is independent of its distance from us, and the brightness we actually see which depends very much on how far away the star is because of Newton's inverse square law:

By measuring the brightness that we observe, we can work back from there to determine the star's intrinsic luminosity, so long as we know the distance. 
Figure 2 below shows the intrinsic luminosity of stars in our four-star sample:

But, how precise can we be? Let's take the case of the star Betelgeuse in Orion. The luminosity of Betelgeuse is stated as:

Perhaps this is a shorthand way of saying "we don't know the luminosity of Betelgeuse to high precision". The reason is that we don't know the distance to Betelgeuse to high precision.
We can see both Betelgeuse and Canopus are much more luminous than Sirius, so how can Sirius be the brightest star in the sky? The answer again is distance. Distances of our sample are shown in Figure 3 below:

We see from this plot that Betelgeuse is by far the most distant of our 4-star sample, while Sirius is the closest star to us, apart from the Sun of course. Sirius is only 8.6 lyr distant whereas Betelgeuse is 548 lyr distant. Sirius appears so bright to us because it is close to us.


But there are uncertainties in distance measurement. Being further distant makes the distance measurement less precise. We can see in the chart above that the error bars on Sirius' distance are very small. The error bars on Canopus' distance are wider. The error bars on Betelgeuse's distance are much wider – which means our distance measurement is far less precise (Joyce et al, 2020). In fact, Betelgeuse is just about as far distant as we can measure using the parallax method.

How large are stars?
The Stefan–Boltzmann Law is named for Slovene physicist Josef Stephan (1835–1893) and Austrian physicist, Ludwig Boltsmann (1844-1906) – see Figure 4.

The Stefan–Boltzmann Law describes the power radiated by a body that absorbs all radiation that falls on its surface in terms of its temperature. This type of object is called a black body. Any object at a stable temperature above the absolute zero is a black body.
We assume that stars are examples of a black body, and that they are spheres; as a first approximation these assumptions are true. With those assumptions, we may use Stefan–Boltzmann law, in the form of the equation:

where the Stephan-Bolzmann constant, σ = 5.67 *10-8J s-1m-2K-4,   is the stellar radius, which is the size of the star that we want to determine; and T is the temperature of the star’s surface.   
Because the Sun is so close, we can measure its luminosity directly. We can also measure its surface temperature.  Re-arranging the Stephan-Bolzmann equation, we get:

Which enables us to derive the Solar radius. Note also that this measure of Solar radius can be verified by other techniques.  The solar parameters we need are:

Remember we said that parameters of distant stars are often expressed in terms of Solar units.  Why would we want to do this?  Suppose that we have determined luminosity of a distant star, L*, and we have measured the star’s photospheric temperature, T*. using spectroscopy.
Now, using the Stephan-Bolzmann equation for the Sun and for the remote star respectively, and dividing one by the other, we see all the constants cancel out:

We now re-arrange this equation to give us an equation for the remote star’s radius:

This equation is in terms of things we can measure.  At first glance, it may look a bit ugly, but it’s easily solvable with a scientific calculator (or Excel, our whatever your preference may be), and gives us the data shown in Figure 5 for our four-star sample:

But what about the precision of our measurements?  Returning to the case of Betelgeuse, which was the first star ever to be observed as a disk (as opposed to just a point of light). Here we come to some further uncertainties.  Looking at the Figure 6 below, we can see that Betelgeuse is not a black body – if it was, it would appear with uniform brightness over its entire surface.  Also, Betelgeuse is variable in brightness over quite short periods.   Figure 6 shows the recent and unusual dimming of Betelgeuse over a period of ~ 1 year

However, like many red supergiants, Betelgeuse has more than one periodicity of variability (Joyce et al, 2020).  This variability over a period of approximately 14 years is shown by the observed light curve in Figure 7 below:

We can see two things in Figure 7.  First there is a long-term pulsation in brightness with a period of approximately 420 days, indicating Betelgeuse is in an unstable state.  Second, superimposed on the long-term cycle, there was an unusual dip in brightness in 2019 (see Figure 6).
Thirdly, it's very difficult to measure the radius of Betelgeuse by astrometry because what we see is a fuzzy view of the star's atmosphere. There is no sharp looking outer limit such as we see at the top of the atmospheres of gas giant planets in the Solar system. We must accept that we don't know the stellar parameters of Betelgeuse with high precision.
Allowing for these uncertainties, we can say that Betelgeuse is approximately 3 orders of magnitude larger than the Sun - in this case, orders of magnitude being in the mathematical sense rather than astronomical magnitudes. Canopus is ≈2 orders of magnitude larger than the Sun. Sirius is of similar size to the Sun (1.71R⊙).

What part of the spectrum do stars radiate at?
If you've read this far,  you'll appreciate that nowhere have we yet mentioned wavelengths of the radiation. The wavelengths at which a star radiates is a key parameter in determining whether any of its planets might harbour life. For example, if an exoplanet is bombarded with ultra-violet radiation, it certainly won't harbour life anything like human beings.
Wien’s Law is named after the German Physicist Wilhelm Wien (1864–1928), who published his Law in 1893 and won the Nobel Prize for Physics in 1911.

Wien’s Law shows that objects of different temperatures emit radiation that peaks at different wavelengths. The peak wavelength is given by the empirical equation:

Once again assuming the stars in our 4-star sample to be black bodies, the radiation curve at various temperatures has a form shown in Figure 9 below:

Examining the green curve, which shows the peak wavelength of the Sun, we see that it peaks in the visible light spectrum. The Sun does also radiate in the near ultra-violet but, fortunately for us, Earth's atmosphere blocks most ultra-violet radiation.
In contrast, examining the black curve, we see that the peak wavelength of Sirius is in the ultra-violet (UV). Sirius is a binary system (Bond et al 2017).  Sirius A is a spectral class A star, and its companion Sirius B is a white dwarf. No planetary system has been found orbiting around either or both stars. If there are any planets in the Sirius system, the UV radiation from Sirius A would mean that any lifeforms on those planets would of necessity have evolved differently to life on Earth

Energy radiated by stars
We can get a good idea of how damaging the UV radiation from Sirius A is. If we look at the black (Sirius) curve, and compare it to the green (Sun) curve, we can see straight away that the area under the Sirius curve is dramatically larger than that under the Sun curve.  Also, there is a lot more area under the Sirius curve in UV wavebands than in the case of the Sun. Simply put, there is not only a lot more energy being radiated by Sirius, but also a greater proportion of Sirius’ energy is radiated as UV.
Starting from Wein’s Law, the peak emitted wavelength of Sirius A is:

We quantify the radiation by starting from the Planck-Einstein equation, which gives us the energy per photon:

Where  is Planck's constant,  is the speed of light in vacuum,  is the frequency of the radiation, and  is the corresponding wavelength of the radiation.
Hence, the photon energy of Sirius A at the peak wavelength is:

If we do the same calculation for the Sun, the peak photon energy

In other words, every photon radiated from Sirius A at its peak wavelength carries almost twice the energy of a photon radiated by the Sun at its peak wavelength, as we see in the Figure 10 below:

How dangerous to Earthly lifeforms would this be? UV radiation is divided into three wave-bands:

Sirius-A's radiation is mainly in the UV-B waveband, and an appreciable amount is in the UV-C waveband.  Any advanced Earth-like lifeforms would be at high risk of skin cancer – unless those lifeforms had evolved differently (for example so that UV was actually required for their life), or their planet's atmosphere blocked the UV-B out, as does Earth's atmosphere.

Conclusion
Figure 11 shows a summary of the characteristics of our four-star sample.  This indicates:

Betelgeuse is both by far the most luminous star in the sample, and also by far the largest star.  Even the next largest star in the sample, Canopus, is much smaller than Betelgeuse.
The Sun is comparable in size to Sirius, but has a much lower photospheric temperature.  The Sun does radiate UV, but not nearly to the extent as Sirius does.  No planets have been discovered in the Sirius system but if planets did exist, the UV radiation created by Sirius if potentially harmful to Earth-like lifeforms.
Due to its size and its high photospheric temperature, Canopus has a much higher luminosity than either the Sun or Sirius.

The most well-known and important diagram in astronomy is the Hertzsprung-Russel diagram, which helps us study stellar evolution, whereas the diagrams in Figure 11 show stellar parameters of out four-star sample as they appear today. I won't go into H-R diagrams here as I've already exceeded my word count - maybe in a future Blog.
Thanks for your interest.

Acknowledgement
The author gratefully acknowledges Dr. Ovidiu Borchin and Mr. Bob Merritt for reviewing this paper.  Their suggestions have resulted in significant improvements to this work.

References
Bond, H et al (2017). The Sirius System and Its Astrophysical Puzzles: Hubble Space Telescope and Ground-based Astrometry.  ApJ, , 840:70 (17pp), 2017 May 10.  https://iopscience.iop.org/article/10.3847/1538-4357/aa6af8/pdf   Accessed July 11, 2022
Joyce, M et al (2020). Standing on the Shoulders of Giants: New Mass and Distance Estimates for Betelgeuse through Combined Evolutionary, Asteroseismic, and Hydrodynamic Simulations with MESA. ApJ, 902:63 (25pp), 2020 October 10.
https://iopscience.iop.org/article/10.3847/1538-4357/abb8db/pdf .   Accessed July 11, 2022

The July evening sky didn’t disappoint with lots of comments about the full Moon and the nice clear skies. The striking images released from the James Webb Space Telescope were an added bonus.
 
Observing
The following chart represent the night sky at 11.00pm BST on the 8th of August and at 10.00pm BST on the 23rd August. To use the chart, face your northern horizon (we normally face south) at the appropriate time and you will see the stars in the chart.

Our focus this month is a few of the circumpolar constellations. These are the ones which rotate anti-clockwise about the north pole star (Polaris) and never drop below the horizon and are visible all year round during the hours of darkness. So facing north you will immediately see towards your lefthand side, The Plough, the well known asterism in the constellation Ursa Major- The Great Bear. It is one of the larger constellations but it is difficult to make out the shape of a bear whereas The Plough, outlined in red on the chart, is instantly recognisable. Names are shown for three of its stars and we shall use these to navigate our way around the sky. First extend the line from Merak to Dubhe (known as the pointers) about x5 the distance between the two stars (shown by a yellow line in the chart) and you arrive at Polaris- The North Pole star. It is a yellow supergiant, not particularly bright at magnitude 2 but easy to locate as it is on its own. It lies about half a degree from the north celestial pole and has been used by mariners for centuries to find their way about the oceans particularly in the days of sailing ships. It is the brightest star in the constellation Ursa Minor- The Little Bear. This small constellation mimics the shape of The Plough and so Polaris sits at the end of its handle.
            Now take a line from Alioth in The Plough and extend it through Polaris about the same distance again (shown by the second yellow line in the chart) and you see a bright star, the central one of a ‘W’ formation. This ‘W’ shape is an asterism in the constellation Cassiopeia- Queen Cassiopeia in Greek mythology and wife of King Cepheus. Most people see the ‘W’ shape and call it Cassiopeia. The bright star was never given a name but it was apparently used for navigation in early space missions and has been given the name Navi, an anagram of the middle name of Virgil (Gus) Ivan Grissom who lost his life in the pursuit of space exploration. This is probably the best time of year to see The Plough and Cassiopeia because neither one is close to the horizon. These two always keep their same shape but change their orientation as they rotate about Polaris throughout the year. Maybe it’s just me but I find it a great pleasure to watch them as they change positions in the sky. It is also a great help to have two such easily recognisable star formations to find your way about the sky. For the next few months Cassiopeia will rise higher in the sky and you will be able to enjoy it at its best while the plough sinks closer to the horizon.
            Still facing north you will see to the west of Cassiopeia and towards your zenith a group of not very bright stars forming a shape similar to the gable end of a house. This is the constellation Cepheus- King Cepheus in Greek mythology and husband of Queen Cassiopeia and father of Princess Andromeda. 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.
            Another large constellation, Draco- The Dragon, has no stars brighter than magnitude 2 but its tail is to be found wrapping itself around Ursa Minor. It has one star of particular significance, Thuban, due to the fact that 5,000 years ago it used to be the north pole star but due to the precession of the earth’s axis (like the wobble of a spinning top) the celestial pole traces out a circle over a period of about 26,000 years and over the last 5,000 years it has moved from Thuban to Polaris.
            Finally, and just for completeness, above Cassiopeia lies the small and obscure constellation, Lacerta- The Lizard. Even its brightest star is just brighter than magnitude 4 so unaided observation becomes a challenge.
 
Something to look out for
            There will be a close approach of the Saturn and the Moon on Friday 11th August, being visible as they rise about 10.00pm BST above your south-eastern horizon and reaching their highest point about 1.30am above your southern horizon. Saturn will be at opposition on Sunday 14th August so we will soon be able to enjoy it in the evening sky for some time. (Sorry for my mistake last month, I inadvertently put in the date for 2021.) We can also look forward to Jupiter being at opposition on the 26th September.
 
Clear skies.