Abstract: The Sun being another star is common knowledge. However, as it happens with all things that are considered obvious, few can actually name exactly who and how the Sun was considered as just another star. It seems that besides evidence from stellar spectroscopy and the measurement of astronomical distances, philosophical principles also played a major role in the building of this knowledge. From the De l’infinito universon e mondi (On the Infinite Universe and Worlds) of Bruno in 1584 up to the Principia Philosophiae of Rene Descartes in 1644, people had started adhering to the idea of the Sun being nothing more than a common star. This idea – also enhanced by the ideas of Copernicus – was later on verified by spectral data and since the era of the Jesuit priest and astronomer Angelo Secchi it is considered an established fact nowadays. However the current huge gaps of our understanding on the nature of the universe call for being much more careful when calling any such knowledge a ‘fact’. More humility is highly advised, especially in a sector of knowledge where we have recently realized we can only account for only the ~5% of it. At the end, acknowledging our limitations is far more important than projecting our beliefs…

[Greek abstract can be found at the end of the article]

1. A question posed…

Once upon a time I had a discussion with friends on cosmology. There, among other things, the question of what are the stars came up. And it was very interesting for me to acknowledge that the answer to this seemingly simple question is not so simple after all…

So what are the stars?

How do we know our Sun is a star?

Who discovered that the stars are “Suns”?

To answer this we must first travel many centuries back and delve into philosophy and the history of science. There, we will find long forgotten assumptions that still dictate how we think about the cosmos.

At the end, you need not worry about the stars not being stars.

They could be, or they could be not – at the end it matters not.

What matters is the human tendency of clinging to dogmas for thousands of years without a single hint of remorse. And this is something we should certainly look into and fix if we are – ever – to unlock the mysteries of the cosmos around us…

2. Searching for an answer…

The first thing to do when you have a question is to search for an answer. But the answer to the question “How do we know the Sun is like the stars?” is not easy to find.

The questions seems to most people so obvious (and perhaps stupid) that they do not even care of explaining why we consider the Sun a star (or vice versa). When this is asked they most usually answer with a simple “Yes they are the same, end of story” attitude that leaves little room of questions, unless of course you want to be ridiculed online that you are unaware of basic astronomy that even kids in the kindergarden know.

Let us look together some of the answers found online for the matter…

2.1 Answers that are not clear answers…

Below I document what various resource in the Internet have to say on the nature of the Sun and the stars. They show clearly the main problem: When something is considered obvious, little effort is put into explaining it. And it is in these ‘obvious’ things that the problems usually arise…

Let us see some excerpts from these resources below…

Who determined that the sun was a star, like the stars in the nighttime sky? Answer: No single astronomer had this realization. Prominent thinkers considered the possibility since classical antiquity; they had creative rhetorical argument on their side, but no proof. By the late 19th century, we knew what stars were, and we knew the distances from the earth to a few stars and to the sun; with that data, astronomers determined that these bodies released energy in roughly comparable amounts. Then spectroscopic examination revealed that the chemical elements in the solar atmosphere were just like those found in common yellow-colored stars spread across the sky. (David H. DeVorkin, senior curator, National Air and Space Museum) [3]

In other words: That the Sun is a star and vice-versa we know because we… know.

Q: im having a hard time believing that the stars are really suns. So from a stars distance, does our sun look like a tiny little star? – Christine (age 16)
A: Yes. [4]

In other words: Don’t ask. The stars are suns. And it is a sin to question that.

Given that the only observational information we have on stars is the light we receive, you might think there isn’t much we can learn about them. But by comparing positions, brightness, and spectra over time, and comparing these with observations of our own star, the Sun, we can actually create accurate models that explain and predict stellar characteristics and behavior. [1]

In other words: We use the comparison between the Sun and the stars to draw conclusions. But what about the Sun being a star? Is that something we consider valid because of some specific reason? Again, this “knowledge” is implied but not specifically mentioned (let alone proved).

As astronomers gaze into the depths of space, they do so with unease: They don’t know precisely what the universe is made of. It’s not just the true nature of dark matter that eludes them; so does the essence of the stars that speckle the sky and populate the many galaxies throughout the cosmos. Surprisingly, no one knows the stars’ exact chemical composition: how many carbon, nitrogen and oxygen atoms they have relative to hydrogen, the most common element. These numbers are crucial, because they affect how stars live and die, what types of planets form and even how readily life might arise on other worlds. [5]

In other words: We do not know many things about stars or the universe. (keep that in the back of your head, we will use it again)

William Herschel was the first astronomer to attempt to determine the distribution of stars in the sky. During the 1780s, he established a series of gauges in 600 directions and counted the stars observed along each line of sight. From this he deduced that the number of stars steadily increased toward one side of the sky, in the direction of the Milky Way core. His son John Herschel repeated this study in the southern hemisphere and found a corresponding increase in the same direction.^[30] In addition to his other accomplishments, William Herschel is also noted for his discovery that some stars do not merely lie along the same line of sight, but are also physical companions that form binary star systems. [6]

In other words: Here is the first specific mention of something concrete. Someone did measure something regarding the stars and drew a specific conclusion. Of course the only thing he was based upon was what he saw: the light of the stars. (keep that also in mind)

The science of stellar spectroscopy was pioneered by Joseph von Fraunhofer and Angelo Secchi. By comparing the spectra of stars such as Sirius to the Sun, they found differences in the strength and number of their absorption lines—the dark lines in stellar spectra caused by the atmosphere’s absorption of specific frequencies. In 1865, Secchi began classifying stars into spectral types.^[31] However, the modern version of the stellar classification scheme was developed by Annie J. Cannon during the 1900s. [6]

In other words: Here we have another specific example of concrete science. We measure something and compare the data we have for the Sun and other stars (given that the other stars are suns of course). Spectroscopy is a big leap towards understanding the stars and their nature, since it can provide many data for the properties of these celestial objects. It is only a pitty that this is all we have, along with distance measurements. What else could we have anyway? We have never gone to the stars, we have only approached somehow our own star.

Various Quora questions (Q) and answers (A) can also be found below:

Q: Are the stars we see in the sky actually Suns from other solar systems? – A: Yes – our Sun is just another “star” and those stars are really “suns”. Same exact thing. [7]

Q: Are the night sky stars all suns? A: Yes, almost all of what we see with our eyes in the night sky as ‘stars’, are actual stars (or suns, as it was stated in the question, presumably to avoid using the word ‘stars’ twice, with different meanings). [8]

In other words: Yes, the stars are like the sun. And it is obvious.

The Sun is the dominant object in the solar system by mass and total energy content. The irradiance of the Sun drives climate on the planets and is the primary source of energy for the biosphere of the earth. The Sun is a Rosetta Stone for the study of astrophysical processes at resolutions that cannot be easily attained for other stars. The results of these solar studies can be applied toward an understanding of other stars, including the properties of their atmospheres and interior structures. In the realm of physics the Sun plays a unique role. The element helium—the second most abundant element in the universe after hydrogen—was discovered in the solar spectrum. The Sun serves as among the test beds for Einstein’s theory of General Relativity. The nature of subatomic particles called neutrinos—the byproducts of nuclear reactions in the hot and dense core of the Sun and sun-like stars—was elucidated as a result of solar investigations. The Sun serves as a laboratory for the study of plasma physics, i.e., the study of the interactions between ionized gas and magnetic fields. [9]

In other words: The Sun is used as a reference to induce assumptions regarding the other stars. So the assumption that the Sun is like the other stars is even more important that we might have thought: The stars are used to draw conclusions for our Sun and the Sun is used to study better the other stars.

ELI5:How do we know that stars are suns? Answer 1: Through spectroscopy, we can determine the composition of stars through their emissions. The experiment you’re looking for is performing this spectroscopy on the sun, and on stars, and discovering that they have similar characteristics. Answer 2: I think to short answer is parallax and spectral analysis. Parallax is a small shift in relative position when the point of view changes. This can tell us the distance. Spectral analysis is a way of determining elemental make up because different sets of wavelengths of light are caused by different elements. [10]

In other words: Again the importance of spectroscopy is emphasized in determining the nature of the Sun and the stars. Indeed this is an excellent tool in analysing the temperature, the composition even the rotation of the celestial objects. Is it a perfect tool? Of course not. What tool is perfect? But it is a very scientific and credible tool in giving us insight in these fascinating objects that linger in the night sky…

So is this the answer we were looking for?

Is spectroscopy the answer to why we consider the Sun another star?

It seems so, yes.

Even though most resources do not mention it clearly, it is evident that similarities of the spectra of the Sun and the stars have made scientists figure out that they must be similar objects. However this answer should not satisfy the researcher here.

Is such a similarity enough?

Looking more into the subject we will discover that there are additional elements needed in order to accept that the sun and the stars are one and the same thing…

3. Regarding spectral analysis

A small parenthesis regarding the spectral analysis based on which we deduce the similarity between the Sun and the stars is needed here.

Electromagnetic radiation with the shortest wavelengths, no longer than 0.01 nanometer, is categorized as gamma rays. Electromagnetic radiation with wavelengths between 0.01 nanometer and 20 nanometers is referred to as X-rays. Radiation intermediate between X-rays and visible light is ultraviolet (meaning higher energy than violet). Electromagnetic radiation with wavelengths between roughly 400 and 700 nm is called visible light because these are the waves that human vision can perceive. Between visible light and radio waves are the wavelengths of infrared or heat radiation. After infrared comes the familiar microwave, used in short-wave communication and microwave ovens. All electromagnetic waves longer than microwaves are called radio waves, but this is so broad a category that we generally divide it into several subsections. [43]

Looking into the light coming to us from the sky, we can deduce many information. Essentially by using the emission or absorption spectra we can conclude things regarding the composition of the stars or the atmosphere of planets, their temperature, density, mass, radius, distance, luminosity, and relative motion [35] [40].

In 1860 Gustav Kirchhoff proposed the idea of a black body, a material that emits electromagnetic radiation at all wavelengths. In 1894 Wilhelm Wien derived an expression relating the temperature (T) of a black body to its peak emission wavelength (λ_max). [35]

This equation is called Wien’s Law. By measuring the peak wavelength of a star, the surface temperature can be determined. For example, if the peak wavelength of a star is 502 nm the corresponding temperature will be 5778 kelvins. [35] An object at a higher temperature emits more power at all wavelengths than does a cooler one. In a hot gas, for example, the atoms have more collisions and give off more energy. In the real world of stars, this means that hotter stars give off more energy at every wavelength than do cooler stars [43].

Figure: Radiation Laws Illustrated. This graph shows in arbitrary units how many photons are given off at each wavelength for objects at four different temperatures. The wavelengths corresponding to visible light are shown by the colored bands. Note that at hotter temperatures, more energy (in the form of photons) is emitted at all wavelengths. The higher the temperature, the shorter the wavelength at which the peak amount of energy is radiated (this is known as Wien’s law). [43]

Also the higher the temperature, the shorter the wavelength at which the maximum power is emitted [43] (see figure above).

So that could be a way to distinguish between planets and stars.

The study of many thousands of stellar spectra in the late Nineteenth Century led to the development of our modern classification system for stars [37].

However note that there are also hot planets at the size of Jupiter that have a temperature between an Earth-sized planet and a star. These planets reside in an intermediate section and called for corrections in the models used to analyze spectra [36].

Also note that there are other objects rthat are not exactly stars and which give out similar (but different) spectra, like the quasars or some types of exotic stars [37].

Credit: 2dF Quasar Survey Characteristic QSO spectrum showing distinct, strong, redshifted emission lines of a quasar. [37]

Credit: The Sloan Digital Sky Survey Exotic star spectra example [37]

These are examples that simply make the problem of accepting the similarity of the Sun with the other stars also more of a definition (and, thus, philosophical) one. What is the cut-off point beyond which we decide that a celestial object is ‘different’ than another?

It seems that searching into the philosophy behind modern cosmology we can find out more factors that weighted in the acceptance of the ‘stars-sun analogy’.

4. Assumptions in modern astronomy

Two basic assumptions of today’s cosmology are the homogeneity and isotropy [25] of the universe, something also known as the Cosmological Principle [24] [26] [27].

Also related to that principle is the Copernican principle, a principle on which many articles have been written in Harmonia Philosophica. You can see the “Earth at the center of the universe?” article for more on that.

Essentially the Copernican principle postulates that humans are not in any way in a priviledged position in the cosmos. As already said this is connected with the notion of isotropy in the cosmos (the Cosmological principle) in various ways: If we are in a non-priviledged position then we are not seeing anything ‘different’ in any direction and, vice-versa, if we do not look anything ‘different in any direction we are not in a priviledged position.

I will not argue here for or against these principles (you can read the above-mentioned article or the paper “Philosophical dogmatism inhibiting the anti-Copernican interpretation of the Michelson Morley experiment” if you want such an analysis). The main thing to remember is that they are… principles! In other words axioms accepted as true based on some evidence and… faith.

So to summarize…

• The universe is the same everywhere
• We are insignificant

Let us now start a journey in the history behind the acceptance of the Sun as being an ordinary star to see how philosophy had also a thing or two to say regarding what we believe about our star…

5. The role of philosophy in accepting that the Sun is a star

In everything, our philosophy plays a very important and crucial role in what we say, decide and believe. Astronomy and cosmology is not an exception.

The above-mentioned assumptions guided astronomers throughout the recent centuries in deriving conclusions for the stars, as much as observational data did.

To acknowledge this is important not only because it allows us a better understanding of the way science works, but also because it may help us avoid prejudiced thinking in the future.

5.1 A world of ‘worlds’: The philosophers speak of the Sun as a ‘star’

What is a world according to modern throught?

As a result of shifting views of the universe the very idea of “world” (in Latin, Mundi) was changing. In the Aristotelian cosmos, the world was effectively synonymous with the Earth. The sphere of the world and the terrestrial realm were one in the same [29].

In part, what we think to-day when we think of a ‘word’ is based on the ideas of the Dominican Friar Giordano Bruno (an Italian philosopher who lived from 1548 to 1600) who published De l’infinito universon e mondi (On the Infinite Universe and Worlds), in 1584. As part of a suite of mystical, magical and heretical ideas and in part, spurred on by Copernicus’s ideas, he suggested that Earth was one of many inhabited worlds in an infinite universe and that the stars were suns, which had their own worlds [29].

Giordano Bruno decided that if the Earth is a planet just like the others, then it does not make sense to divide the Universe into a sphere of fixed stars and a solar system. He said that the Sun is a star (i.e. not anything special), that the Universe is infinitely large, and that there are many worlds. He was condemned by both the Roman Catholic and Reformed Churches for this as well as other things and was burnt alive in Rome in 1600 for heresy [2]. As he wrote at the time: “The composition of our own star and world is the same as that of as many other stars and worlds as we can see” [13].

In other words, it seemed reasonable to him that the Sun was merely another star, and he subsequently made a distinction between “suns” which generate their own light and heat; and the “earths” and moons which revolve and are nourished and powered by them. One esteemed modern astrophysicist, Steven Soter, has even suggested that Bruno was the first person in history to truly grasp the concept that “stars are other suns with their own planets” [13].

Once Earth became one planet among many orbiting the sun, those planets became Earth like worlds. This new understanding of worlds is reflected in the title of The Discovery of a World in the Moon from the 1630’s [29]. But as it took a long time for the Copernican model of the cosmos to win out over competing models, it took a considerable bit of time for ideas similar to Bruno’s to come to fruition. [29]

The overlapping circles in Tycho Brahe’s geocentric model of the cosmos created a significant problem for the Aristotelian notions of the heavenly spheres. If Brahe was right and the orbits of the planets crossed each other each other then they couldn’t be a set of solid. Rene Descartes offered a solution to this problem in his 1644 Principia Philosophiae. In Descartes system, like Aristotle’s, the universe was full of matter, there was no such thing as empty space. To explain motion Descartes introduced the concept of vortices. The system consisted of different kinds of mater or elements rubbing up against each other. His model included three different kinds of elements: luminous, transparent, and opaque. Luminous was the smallest and was what the stars were made of. Earth and the planets were made up of the denser opaque. The space between the planets and the stars was made up of transparent He stated that Lumnious would settle at the center of these vortices and the transparent and opaque elements would keep shifting around each other. This shifting created the movement of objects in the heavens. [30]

The increasing acceptance of Descartes theory of vortices in the later half of the 17th century brought with it the idea that the stars were like our sun and had their own planets orbiting around them. Bernard le Bovier de Fontenelle’s popular 1686 book Entretriens sur la pluralite des mondes (Conversations on the plurality of worlds) broadly disseminated this notion, in a range of editions and translations. (You can read a full-digitized copy External of an 1803 English translation of Conversations on the Plurality of Worlds online from the Library of Congress collections) [29].

The book Conversations on the Plurality of Worlds presents fictional discussions between a philosopher and his hostess, a marquise. As the two characters walk the grounds of her garden at night they discuss the stars above them. Their conversations touch on the features of the Copernican system, potential encounters with extraterrestrial life and the idea of the universe as a boundless expanse. As the book was translated into a variety of languages and republished in new editions for hundreds of years, it presented both this cosmology and the idea of life on other worlds to a range of audiences [29].

Changing ideas about the structure of the universe are also well illustrated in diagrams from William Derham’s 1715 book Astro-Theology. Derham, an English natural philosopher, astronomer and clergymen wrote a series of works exploring connections between natural history and theology. From his perspective, the shift to thinking about the plurality of worlds was significant enough that it should be set alongside the Copernican Revolution as one of the three major shifts in thinking about the nature of the universe [29].

The above history provides a good description on how philosophy and most importantly our idea of us being insignificant (part of a larger universe where everything is the same everywhere – a.k.a. Cosmological principle) like postulated by the Copernical principle dictated our journey towards understanding the cosmos.

The next steps came from ‘science’, in the modern sense of the word…

5.2 The advent of spectroscopy: The scientists speak of the Sun as a ‘star’

In 1666, Isaac Newton showed that a prism separated white light into a spectrum of its constituent parts, rather than creating the rainbow colors that are seen. In 1802, William Wollaston then constructed a spectrometer which showed the Sun’s spectrum on a screen, but noted that there were dark bands of missing colors [13].

In 1814, Joseph von Fraunhofer invented the spectroscope and mapped 574 of these lines, after which a number of scientists helped advance the study of spectroscopy, including Gustav Kirchhoff and Robert Bunsen who in 1857 were able to establish a connection between chemical elements and their own individual spectral patterns. [13]

Further study revealed that each element absorbs light of a particular color, thus leaving a specific “signature” line. And after spectroscopes were coupled to telescopes, scientist were able to identify additional chemical elements, and work our the chemical composition of the stars, as well as distinguish between nebulae and galaxies in the night sky. [13]

During this period, an Italian Jesuit priest and astronomer, Angelo Secchi (1818-1878), became a pioneer in the study of stellar spectroscopy, and through analysis of some 4,000 stellar spectrograms discovered that the stars came in a limited variety of types distinguishable by their unique spectral patterns. He subsequently devised the first stellar classification system, and is recognized as being one of the first scientists to definitively state that the Sun is a star [13].

So there you go.

What philosophers postulated centuries ago, was now verified by scientists. Strange how we always verify things we already know, is it not?

But again, could we even know what we do not?

Note: Search Harmonia Philosophica for more on the limits of knowledge, the limits of science and the limits of sensing the cosmos.

Instead of Conclusion: Things we do not know…

But what do we know exactly?

In astronomy the things we do not know are much more than the things we do. Cosmology is full of mysteries that are bravely admitted by astronomers are big gaps in our understanding of the cosmos.

Examples of things that we do not know include:

• How does universe’s inflation work [32].
• How singularities form and what they actually are [32].
• How galaxies or stars formed [32].
• Ultra-energetic cosmic rays [33].
• Dark matter/ Dark energy [33] [34].
• The Pioneer anomaly [33].
• The Wow signal [33].
• Details about massive stars: How far away they are, how they form, what is their maximum mass etc. [31]
• Missing baryons [34].
• How do stars explode [34].
• Why is the sun’s corona so hot? [34]

All in all, even the example of dark matter and dark energy that account for more than ~95% of the cosmos [45] is enough for someone to understand that our knowledge is too much limited for us to draw safe conclusions about the cosmos around us.

So what is the Sun?

What are the stars?

Sure, stellar spectroscopy gives us many indications of the answer. But this is the only thing it provides: indications. We cannot know know unless we see. There are many other objects in the sky with similar yet different spectra, like quasars for example.

What is more one of the basic elements used for the classification and study of stars – distance – is measured by methods that have limitations (look at the Appendix I – Stellar parallax for more on that).

Put these notes together along with our knowledge gaps mentioned above, and you will see that our understanding of the Sun as a star (or the stars as Suns) is so safe as the understanding of a Neanderthal gazing the Sun millions of years ago.

Surely the stars may be sun and they most probably are. But our current knowledge of that is based as much in philosophy as it is based on scientific evidence from spectroscopy.

It is important to not only understand but also acknowledge that. Because through that acknowledgement we will understand not the stars but our own self here on Earth better.

At the end it is not about what is or what is not.

It is not about the Sun is a star or not.

All that matters is that we can think in the dark.

Without anything. Within everything.

Admiring the cosmos without need to categorize.

Because, as Shestov once said, when we try to categorize and understand things we just break them down into pieces that fit into the little boxes we have in our mind. (Shestov also wrote many interesting notes regarding astronomy and astrology, search Harmonia Philosophica for them)

Petty human.

Do you think you understand the stars?

Look again.

There is nothing new to see.

(Are you afraid?)

Except what you already have…

References

[1] How we Know what we know about Stars?, web lecture by Dr. Christe Ann McMenomy

[2] Who discovered that the Sun was a star?, Stanford Solar Center

[3] Who Determined That the Sun Was a Star, Smisthonian Magazine

[4] Q & A: What Are Stars?, University of Illinois, Department of Physics

[5] Astronomers still don’t know exactly what the sun is made of, PBS News

[6] Star, Wikipedia article

[7] Are the stars we see in the sky actually Suns from other solar systems?, Quora question

[8] Are the night sky stars all suns?, Quora question

[9] Sun as a star, Dr. Mark Giampapa, National Solar Observatory

[10] ELI5:How do we know that stars are suns?, reddit

[11] Parallax and Distance measurement, Las Cumbres Observatory

[12] Parallax and distance measurement limitations, NRAO

[13] Who Discovered the Sun is a Star?, Astronomy Trek

[14] Estimating distances from parallaxes, Coryn A.L. Bailer-Jones, Max Planck Institute for Astronomy, Heidelberg

[15] The problem with stellar distances, Astronomy Trek

[16] Negative parallax, Physics Stack Exchange

[17] What is the proper interpretation of a negative parallax, Astronomy stack exchange

[18] Gaia Data Release 2: Using Gaia parallaxes, Luri et al, 2018, Astronomy & Astrophysics manuscript no. 32964_Arxiv

[19] What’s with negative parallaxes?, Anthony G.A. Brown

[20] About negative parallax, Celestia forums

[21] On a reason for the appearance of negative parallaxes in the determination of the distances of stars, Lee, O. J., Annals of the Dearborn Observatory, vol. 4, pp.1-4

[22] Stellar parallax, Wikipedia article

[23] What is parallax? Space.com article

[24] Astronomy without a telescope – Assumptions, Universe today

[25] K. Migkas, G. Schellenberger, T. H. Reiprich, F. Pacaud, M. E. Ramos-Ceja, L. Lovisari. Probing cosmic isotropy with a new X-ray galaxy cluster sample through the LX–T scaling relation. Astronomy & Astrophysics, 2020; 636: A15 DOI: 10.1051/0004-6361/201936602

[26] Doubts about basic assumption for the universe, ScienceDaily

[27] Cosmological assumptions

[28] Negative parallax, article

[29] Stars as Suns & The Plurality of Worlds, Library of Congress

[30] Physical Astronomy for the Mechanistic Universe, Library of Congress

[31] 10 things we don’t know about massive stars, Astronomy.com

[32] What astronomers don’t know, IRC article

[33] 13 things that do not make sense, New Scientist article

[34] 8 Modern Astronomy Mysteries Scientists Still Can’t Explain, Space.com article

[35] Astronomical spectroscopy, Wikipedia article

[36] Modelling the spectra of planets, brown dwarfs and stars using VSTAR, Jeremy Bailey, Lucyna Kedziora-Chudczer, Monthly Notices of the Royal Astronomical Society, Volume 419, Issue 3, January 2012, Pages 1913–1929, https://doi.org/10.1111/j.1365-2966.2011.19845.x

[37] Types of Astronomical Spectra, Australia Telescope National Facility

[38] Using Light to Study Planets, JPL, NASA

[39] Spectroscopy of planetary atmospheres in our Galaxy, Tinetti, G., Encrenaz, T. & Coustenis, A., Astron Astrophys Rev 21, 63 (2013). https://doi.org/10.1007/s00159-013-0063-6

[40] Using Spectra to Measure Stellar Radius, Composition, and Motion, lumen astronomy article

[41] Spectroscopy of exoplanets, Michael Richmond

[42] Solar system analogs for extrasolar planet observations, Washington university

[43] The Electromagnetic Spectrum, lumen astronomy article

[44] Spectra of Stars, Sloan Digital Sky Survey

[45] Dark matter, CERN

Ελληνική Σύνοψις (Greek abstract): Το ότι ο Ήλιος είναι ένα απλό αστέρι είναι κοινή γνώση. Ωστόσο, όπως συμβαίνει με όλα τα πράγματα που θεωρούνται προφανή, λίγοι μπορούν στην πραγματικότητα να ονομάσουν ακριβώς ποιος το διατύπωσε πρώτος και πως και γιατί ο Ήλιος θεωρήθηκε αστέρι. Φαίνεται ότι εκτός από στοιχεία από την αστρική φασματοσκοπία και τη μέτρηση αστρονομικών αποστάσεων, ορισμένες φιλοσοφικές αρχές έπαιξαν επίσης σημαντικό ρόλο στην οικοδόμηση αυτής της γνώσης. Από το De l’infinito universon e mondi (On the Infinite Universe and Worlds) του Μπρούνο το 1584 έως το Principia Philosophiae of Rene Descartes το 1644, οι άνθρωποι είχαν αρχίσει να συνηθίζουν στην ιδέα ότι ο Ήλιος δεν είναι τίποτα περισσότερο από ένα κοινό αστέρι. Αυτή η ιδέα – ενισχυμένη και από τις ιδέες του Κοπέρνικου – επαληθεύτηκε αργότερα με τα φασματικά δεδομένα και από την εποχή του Ιησουίτη ιερέα και αστρονόμου Angelo Secchi θεωρείται ως καθιερωμένο γεγονός στις μέρες μας. Ωστόσο, τα σημερινά τεράστια κενά στην κατανόησή μας σχετικά με τη φύση του σύμπαντος απαιτούν να είμαστε πολύ πιο προσεκτικοί όταν αποκαλούμε τέτοια γνώση ως «γεγονός». Συνιστάται περισσότερη ταπεινοφροσύνη, ειδικά σε έναν τομέα της γνώσης όπου έχουμε πρόσφατα συνειδητοποιήσει ότι μπορούμε να μιλήσουμε μόνο το ~ 5% αυτής. Εν τέλει, το να αναγνωρίζουμε τα όρια μας είναι πολύ σημαντικότερο από το να προβάλλουμε τα πιστεύω μας…

APPENDIX I – Stellar parallax

Stellar parallax is the apparent shift of position of any nearby star (or other object) against the background of distant objects. Created by the different orbital positions of Earth, the extremely small observed shift is largest at time intervals of about six months, when Earth arrives at opposite sides of the Sun in its orbit, giving a baseline distance of about two astronomical units between observations. The parallax itself is considered to be half of this maximum, about equivalent to the observational shift that would occur due to the different positions of Earth and the Sun, a baseline of one astronomical unit (AU) [22].

The first known astronomical measurement using parallax is thought to have occurred in 189 B.C., when a Greek astronomer, Hipparchus, used observations of a solar eclipse from two different locations to measure the distance to the moon [23].

Limitations of Distance Measurement Using Stellar Parallax

Parallax angles of less than 0.01 arcsec are very difficult to measure from Earth because of the effects of the Earth’s atmosphere. This limits Earth based telescopes to measuring the distances to stars about 1/0.01 or 100 parsecs away. Space based telescopes can get accuracy to 0.001, which has increased the number of stars whose distance could be measured with this method. However, most stars even in our own galaxy are much further away than 1000 parsecs, since the Milky Way is about 30,000 parsecs across. The next section describes how astronomers measure distances to more distant objects. [11]

Although it is correct to take account of the relative motion of the solar system and the star being measured, in fact the trigonometric parallax method is limited to measurements of relatively nearby stars, so this relative motion is rather small. [12]

Astrometric surveys such as Gaia and LSST will measure parallaxes for hundreds of millions of stars. Yet they will not measure a single distance. Rather, a distance must be estimated from a parallax. In this didactic article, I show that doing this is not trivial once the fractional parallax error is larger than about 20%, which will be the case for about 80% of stars in the Gaia catalogue. Estimating distances is an inference problem in which the use of prior assumptions is unavoidable. I investigate the properties and
performance of various priors and examine their implications. A supposed uninformative uniform prior in distance is shown to give very poor distance estimates (large bias and variance). Any prior with a sharp cut-off at some distance has similar problems. The choice of prior depends on the information one has available – and is willing to use – concerning, for example, the survey and the Galaxy. I demonstrate that a simple prior which decreases asymptotically to zero at infinite distance has good performance, accommodates non-positive parallaxes, and does not require a bias correction. [14]

Calculating the distance to the object is easy since the parallax calculations are based on simple trigonometry, although the triangles found in parallax measurements have no relation to those found in “normal” trigonometry. In the picture at the top of the page, the distance that the star appears to have moved when viewed from different perspectives represents its distance. However, even at a relatively close distance, such as that of Proxima Centauri, which is only 4.2 light years away, this angle is extremely small. In fact, Proxima Centauri has a parallax angle of only 0.7687 ± 0.0003 seconds of arc, which roughly equates to an angle that subtends an object 2 cm across, but seen from a distance of 5.3 km away. As distances to objects increase, parallax angles get progressively smaller, until they become so small that they are impossible to measure, even with the most sophisticated equipment available today, and it is at this point that discrepancies in the distance/luminosity stats for objects arise.

The problem of negative parallax

The parallaxes of distant stars should be zero (or at least indistinguishable from zero). If the parallaxes have an uncertainty (which they do), then half of the parallaxes of distant stars will be negative. I think this is all that you are finding in the case of absolute Hipparcos parallaxes. The quote you give from the 1943 paper is talking about relative parallaxes. When you determine relative parallax you find the apparent movement in the sky with respect to a bunch of comparision stars in the same region. You make the assumption that most of these stars are very far away and have zero parallax. If a large fraction of the stars in fact have a positive and large parallax (because you are looking towards a nearby cluster), then the relative parallaxes of the genuinely distant stars in the cluster can end up negative on average. [16]

How should we handle negative parallax?

For closely aligned sources (separated by 0.2–0.3 arcsec), which are only occasionally resolved in the Gaia observations, confusion in the observation-to-source matching can lead to spurious parallax values which are either very large or have a negative value very far away from zero in terms of the formal parallax uncertainty quoted in the catalogue. These sources tend to be faint and located in crowded regions and are also associated with unreliable (large) proper motions (Gaia Collaboration et al. 2018b). Guidance on how to clean samples from spurious parallax values is provided in Lindegren et al. (2018). [17]

The systematic errors in the parallaxes are estimated to be below the 0.1 mas level (Lindegren et al. 2018) but the following systematics remain. There is an overall parallax zeropoint which, from an examination of QSO parallaxes, is estimated to be around −0.03 mas (in the sense of the Gaia DR2 parallaxes being too small). The estimated parallax zeropoint depends on the sample of sources examined (Arenou et al. 2018) and the value above should not be used to ’correct’ the catalogue parallax values. [17]

It depends how negative the parallax is and what your “prior” knowledge is of the distance to the star is. As another answer suggests, there are some spurious large negative (and positive) parallaxes for faint, crowded sources. If possible, these should be removed. If this is not the case, and the parallax is negative, but close to zero within its uncertainty, then it is telling you that you have a lower limit to the distance of the object (i.e. measurement uncertainties have led to a small negative parallax). Crudely speaking, you could add a couple of error bars to the parallax and treat that as a 95% upper limit (remember the 0.1 mas possible systematic error too). Under no circumstances should you “use them as is”, since there is no physical basis for a negative parallax or negative distance. [17]

Although should not use the negative parallaxes, you should not ignore them either. If you are looking at populations of objects, removing those with negative parallaxes will lead to significant bias in your results, as Luri et al. 2018 [18] has shown. [17]

Negative parallaxes can be interpreted as the observer (in this case Gaia satellite) going the “wrong way around the sun” as mentioned in this Jupyter Notebook by Anthony Brown. [17]

Any astrometric catalogue that lists parallaxes will contain negative parallaxes, which at first sight appear physically implausible, yet they are an entirely valid measurement of the true positive parallax in the presence of (large) noise. This notebook discusses how negative parallaxes may arise even for “perfect” measurements (suffering only from random Gaussian noise, without any systematic errors). [19]

The reason a parallax can turn up negative is simple. Errors can cause a star position to off by any direction. During the six months we measure the parallax, we expect the star’s position to shift from A to B. In this case, the true parallax was about the same size as a typical error, but the first error pushed the position reading to roughly where B is, and the second error pushed the star to roughly where A is. So the star appears to move from B to A instead of A to B: the parallax is the wrong way round. We can’t know what the error was, so we can’t subtract those. [20]

Other papers also emphasize that negative parallaxes are simply errors [21].

At the end, everything could be just a problem with the assumptions on which stars are “background stars”: Stellar parallax is the apparent motion of stars relative to other stars, which also have parallaxes. We do not know beforehand which stars are closer than the others, and these have to be inferred using statistical analysis from the entire data. The parallaxes of distant stars should be practically zero. And because they have a statistical uncertainty, then half of these near-zero parallaxes will be negative. [28]

Of course again this places the negative parallax in the category of an ‘error’, thus dismissing it altogether. It is like saying ‘If you have a negative parallax, then your measurement is wrong’.

All in all, the phenomenon deserves more attention and perhaps the advances in astronomy will soon provide a more definite answer on the problem of astronomical distance measurements.

APPENDIX II – Astronomical spectroscopy

Astronomical spectroscopy is the study of astronomy using the techniques of spectroscopy to measure the spectrum of electromagnetic radiation, including visible light and radio, which radiates from stars and other celestial objects. A stellar spectrum can reveal many properties of stars, such as their chemical composition, temperature, density, mass, distance, luminosity, radius and relative motion using Doppler shift measurements. Spectroscopy is also used to study the physical properties of many other types of celestial objects such as planets, nebulae, galaxies, and active galactic nuclei. [35] [40]

Electromagnetic radiation with the shortest wavelengths, no longer than 0.01 nanometer, is categorized as gamma rays. Electromagnetic radiation with wavelengths between 0.01 nanometer and 20 nanometers is referred to as X-rays. Radiation intermediate between X-rays and visible light is ultraviolet (meaning higher energy than violet). Electromagnetic radiation with wavelengths between roughly 400 and 700 nm is called visible light because these are the waves that human vision can perceive. Between visible light and radio waves are the wavelengths of infrared or heat radiation. After infrared comes the familiar microwave, used in short-wave communication and microwave ovens. All electromagnetic waves longer than microwaves are called radio waves, but this is so broad a category that we generally divide it into several subsections. [43]

Different celestial objects produce different types of spectra. The spectrum of an object is one means of identifying what type of object it is. How different spectra arise is shown in the schematic diagram below. [37]

Credit: Adapted from a diagram by James B. Kaler, in “Stars and their Spectra,” Cambridge University Press, 1989.: How continuous, emission and absorption spectra can be produced from same source. [37]

Continuum spectrum: In this diagram, a dense hot object such as the core of a star acts like a black body radiator. If we were able to view the light from this source directly without any intervening matter then the resultant spectrum would appear to be a continuum as shown bottom left in the figure above. [37] [38]

Absorption spectrum: Most stars are surrounded by outer layers of gas that are less dense than the core. The photons emitted from the core cover all frequencies (and energies). Photons of specific frequency can be absorbed by electrons in the diffuse outer layer of gas, causing the electron to change energy levels. Eventually the electron will de-excite and jump down to a lower energy level, emitting a new photon of specific frequency. The direction of this re-emission however is random so the chances of it travelling in the same path as the original incident photon is very small. The net effect of this is that the intensity of light at the wavelength of that photon will be less in the direction of an observer. This means that the resultant spectrum will show dark absorption lines or a decrease in intensity as shown in the dips in the absorption spectrum top right in the diagram above. Stellar spectra typically look like this. [37]

Emission spectrum: A third possibility occurs if an observer is not looking directly at a hot black body source but instead at a diffuse cloud of gas that is not a black body. If this cloud can be excited by a nearby source of energy such as hot, young stars or an active galactic nucleus then the electrons in atoms of the gas cloud can get excited. When they de-excite they emit photons of specific frequency and wavelength. As these photons can re emitted in any direction an external observer will detect light at these wavelengths. The spectrum formed is an emission or bright line spectrum, as shown by the middle spectrum in the figure above. [37]

Newton used a prism to split white light into a spectrum of color, and Fraunhofer’s high-quality prisms allowed scientists to see dark lines of an unknown origin. In the 1850s, Gustav Kirchhoff and Robert Bunsen described the phenomena behind these dark lines. Hot solid objects produce light with a continuous spectrum, hot gases emit light at specific wavelengths, and hot solid objects surrounded by cooler gases show a near-continuous spectrum with dark lines corresponding to the emission lines of the gases. By comparing the absorption lines of the Sun with emission spectra of known gases, the chemical composition of stars can be determined. [35]

An ideal thermal spectrum is shown on the left below. A spectrum of an actual star is shown on the right.

In addition to the continuous spectrum, a star’s spectrum includes a number of dark lines (absorption lines). Absorption lines are produced by atoms whose electrons absorb light at a specific wavelength, causing the electrons to move from a lower energy level to a higher one. This process removes some of the continuum being produced by the star and results in dark features in the spectrum [44].

In 1860 Gustav Kirchhoff proposed the idea of a black body, a material that emits electromagnetic radiation at all wavelengths. In 1894 Wilhelm Wien derived an expression relating the temperature (T) of a black body to its peak emission wavelength (λ_max). [35]

This equation is called Wien’s Law. By measuring the peak wavelength of a star, the surface temperature can be determined. For example, if the peak wavelength of a star is 502 nm the corresponding temperature will be 5778 kelvins. [35] An object at a higher temperature emits more power at all wavelengths than does a cooler one. In a hot gas, for example, the atoms have more collisions and give off more energy. In the real world of stars, this means that hotter stars give off more energy at every wavelength than do cooler stars [43].

Figure: Radiation Laws Illustrated. This graph shows in arbitrary units how many photons are given off at each wavelength for objects at four different temperatures. The wavelengths corresponding to visible light are shown by the colored bands. Note that at hotter temperatures, more energy (in the form of photons) is emitted at all wavelengths. The higher the temperature, the shorter the wavelength at which the peak amount of energy is radiated (this is known as Wien’s law). [43]

By measuring the peak wavelength of a star, the surface temperature can be determined. For example, if the peak wavelength of a star is 502 nm the corresponding temperature will be 5778 kelvins. [35]

The spectra of galaxies look similar to stellar spectra, as they consist of the combined light of billions of stars. [35]

The reflected light of a planet contains absorption bands due to minerals in the rocks present for rocky bodies, or due to the elements and molecules present in the atmosphere. To date over 3,500 exoplanets have been discovered. These include so-called Hot Jupiters, as well as Earth-like planets. Using spectroscopy, compounds such as alkali metals, water vapor, carbon monoxide, carbon dioxide, and methane have all been discovered. [35]

Until recently, the modelling of the atmospheres of stars (e.g. Gray 2005) and that of the atmospheres of the Earth and other Solar system planets (e.g. Liou 2002) have developed largely independently. Models of stars applied to high-temperature objects with effective temperatures T_eff > 3000K, with opacity dominated by the line and continuum absorption of atoms and atomic ions, whereas planetary atmosphere models applied to cool objects T_eff∼ 100–300K, where the important processes were molecular absorption and scattering from molecules and cloud particles. [36]

This situation changed with the discovery in the mid-1990s of the first unambiguous brown dwarf, Gl 229B. (Nakajima et al. 1995; Oppenheimer et al. 1995) and the first hot Jupiter planets beginning with 51 Peg b (Mayor & Queloz 1995; Marcy et al. 1997). Many more such objects have now been discovered and reveal that planets and brown dwarfs populate an intermediate range of temperatures not explored previously. This has led to the requirement to develop new methods to model these atmospheres that cover the effective temperature range from below 1000K to more than 2000K. [36]

Spectroscopy is also used nowadays to detect exoplanets around distant stars [41] [42]. For example Transit spectroscopy is the ideal technique to probe temperate planets around M-dwarfs [38].

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