Our new facebook page has now over 100 ‘likes’ and followers. Thank you each for your support. It takes a time to produce our monthly articles and we appreciate the views and feedback we receive.
In local news, we are pleased to say we have republished our biography on the great French astronomer Francois Felix Tisserand, and this (ISBN 978-1-9999044-0-1) is now available in paperback form from our bookstore.
We have now had this printed (perfect binding) in a very convenient A5 sized and at just £6.99 we would recommend this as an ideal Christmas present / stocking filler, and easy read, for those interested in the history of our science and/or orbital dynamics.
Our blog this month looks at how bright the Sun is, and how we measure the ‘brightness’ of stars.
Nous remercions tous ceux qui ont aimé notre nouveau page facebook, nous l'apprécions beaucoup.
Nous sommes ravis d'annoncer que notre livre sur la vie de l'astronome François Félix Tisserand a été republié (ISBN 978-1-9999044-0-1). et est disponible en format de poche (A5) dans le magasin sur notre site. Il constituerait un bon petit cadeau de Noël pour ceux qui s'intéressent à l'histoire de l'astronomie. (prix £6.99).
Ce mois nous allons considérer la luminosité du Soleil, comment peut-on mesurer cette luminosité et la comparer avec celle d' autres étoiles?
Nous vous souhaitons une très bonne solstice d'hiver (16:28h on le 21 décembre) et un joyeux Noel.
Quelle est l'intensité lumineuse du Soleil?
Ce mois nous allons considérer la luminosité du Soleil et des étoiles
Il est évident que le Soleil est très lumineuse. Il ne faut JAMAIS observer le Soleil surtout pas avec un quelconque instrument d’optique, jumelles, lunette ou télescope. A l’oeil nu déjà, il provoque des brûlures de la rétine mais, avec un instrument, elles seraient très graves et irréversibles.
Le 'flux' ou combien d'énergie le Soleil émet est très constant (voir notre article sur l'irradiance solaire) Le soleil apparait plus lumineuse à midi qu'au coucher du Soleil parce qu'une partie de la luminosité est absorbé parl'atmosphere. Au coucher du Soleil la lumière du Soleil traverse plus de l'atmosphère qu'à midi.
How bright is the Sun?
One of the most obvious things about the Sun as far as we’re concerned is that it’s very bright. It hurts our eyes to look at and of course one should never look at the Sun, and especially not through binoculars or a normal telescope.
The flux – how much energy the Sun emits – is remarkably stable and varies only a very slightly. (Recall our blog post on the solar irradiance). We see the Sun brighter at say mid-day than at sunset as some of the brightness is absorbed by our atmosphere; at sunset the light from the Sun is passing through ‘more’ of our atmosphere (because it is lower in the sky) than during the time near noon.
The stars in the night sky are all at different levels of brightness and the term magnitude’is used to describe and measure how bright a star is. The apparent magnitude is how bright the star appears to us here on Earth.
The Greek mathematician and astronomer Hipparchus (circa 190BC to 120BC) made many astronomical discoveries (e.g. procession of the equinoxes; a method of determining solar eclipse; and advances in mathematics especially spherical trigonometry). Hipparchus also defined a ‘magnitude’ scale with which we can categorise the brightness of the stars. This system is still used as the basis of the scale we use today. Hipparchus classified the brightest 20 stars he could see from Greece (probably from the Island of Rhodes) as being of the first magnitude; the next set of not quite so bright stars as second magnitude; the next set, slightly dimmer again, as third magnitude; and so on until the sixth magnitude which were the stars that were only just visible to the naked eye.
The system was extended in 1856 by the English astronomer Norman Pogson (b.1829 d.1891) who recognised that Hipparchus’s 1st magnitude stars were about 100 times brighter than the 6th magnitude stars. He introduced a logarithmic scale by defining that a 1.0 difference in magnitude measured a 2.512 difference in brightness. This used the fact that the fifth root of 100 is 2.512, i.e. 1001/5= 2.512 (or conversely, 2.5125 = 100). His logarithmic based scale was immediately accepted.
Star field showing Vega (the bright star in the centre)
Notice also the different levels of brightness and colours of the stars.
(Image courtesy of Roberto Mura)
To define the scale, a specific calibration point was needed and the star Polaris (the North star, the brightest star in the constellation of Ursa Minor – the little bear) was originally chosen and ‘set’ at 2.00 as the calibration point from which all other stars were compared. However, it was found that Polaris is very slightly variable in brightness so the star Vega was used with calibration point of 0.00. Today, the flux (total energy received; often called the bolometric magnitude and which can be accurately measured) of a star is used to precisely define the scale and so the scale doesn’t depend on any object which could vary. (Vega now has an apparent magnitude of 0.03, Polaris is 1.98 but is variable by about 0.1 magnitude.)
Hence, the magnitude scale can take any real number, and importantly it can also take numbers less than 1, including negative values. So a 0.3 magnitude star is 2.512 times brighter than a 1.3 magnitude, a 2.6 magnitude star is 3.631 times less bright than a 1.2 magnitude star. The equation is:
ΔB = 2.512 ** Δm (where ** indicates to 'to the power of')
or Δm = 0.4Log(ΔB )
where ΔB is the difference in brightness and Δm is the difference in magnitude. The smaller the value the brighter is the object, and negative values can be used. A star of magnitude minus 1.46 (which is the apparent magnitude of Sirius, the brightest star in the night sky visible to unaided human eyes for us) is 5.65 times brighter that the star Betelgeuse (the bright red coloured star at the top left of the constellation of Orion), which has an apparent magnitude of 0.42. (We can work out this difference in brightness by putting as 1.88 (i.e. 0.42 - (-1.46)) into the equation above.)
The Sun’s apparent magnitude, because it is relatively close to us, compared to other stars, is a very high -26.72 (which is 12.7 x 10**9 times as bright as Sirius). The Earth’s moon also appears to us to be so much brighter than any night-time star; it has an apparent magnitude of -12.7 at full moon time. (Remember though that the moon generates no light of its own; we see it because it reflects sunlight.)
The Sun and Moon appear very bright to us because they are nearby. Many stars generate far greater emissions, and hence are very much brighter than the Sun so we need a way to have a standard comparison. The absolute magnitude of a star is the level of brightness that the star would appear were it to be at a standard distance away from us; and specifically, the absolute magnitude of a star is the apparent magnitude were that star to be precisely 10 parsecs away from us.
We will look at how distances are measured and what units we have to use when talking about the distances to the stars in a future blog article. For now, we will note that a ‘light-year’ is the distance covered by light (which ‘travels’ at almost 300,000 km / second) in the time of one Earth year. A parsec is equivalent to 3.26 light years.
The equation relating apparent and absolute magnitude is:
M = m + 5 - 5Log(d)
where is the absolute magnitude, m the apparent magnitude and is the distance in parsecs. This equation (which can be used to determine the distance D to a star if we can measure its apparent magnitude and can deduce its absolute magnitude) is also known as the distance modulus equation. A derivation of this formula is presented within item 2 in ‘further reading’
The absolute (visual wavelength) magnitude of the Sun is +4.83 and our Sun is nothing at all special amongst the stars. The white and blue coloured giant and supergiant stars are far brighter (up to about -11 absolute magnitude) and ‘Wolf-Rayet’ stars can be even brighter, up to around -12.5. Betelgeuse, the well-known star in Orion is over 600 light years from us and has absolute magnitude of about -6
So the Sun really isn’t very bright…(but still don’t look directly at it!)
(In ascending level of technical complexity)
Extreme Stars – At the edge of creation. James Kaler. 2010
The Sun – shining light on the Solar system. Neil Taylor. 2017
Next month we will take a one-month diversion from our topic on the physics of the Sun and to take a brief look at Astronomical distances. We will see why metres and kilometres are not used and what measurement units are used instead; how far away the planets, stars, and galaxies are; and how big we think the Universe is.