The color of a star is a combination of two phenomena. The first is the star’s temperature. This determines the wavelength (frequency) where the peak of its electromagnetic radiation will emerge in the spectrum. A cool object, like an iron rod heated to 3000 degrees, will emit most of its light at wavelengths near 9000 Angstroms ( the far-red part of the visible spectrum) in wavelength. A very hot object at a temperature of 30,000 degrees will emit its light near a wavelength of 900 Angstroms (the far-ultraviolet part of the visible spectrum). The amount of energy emitted at other wavelengths is precisely determined by the bodies temperature, and by Planck’s radiation law of ‘black bodies’. (Credit: Wikipedia)
It shows that as the temperature of the object increases, the peak shifts further to short wavelengths. But the phenomenon we call ‘color’ is another matter. Color does not exist as an objective property of nature.
Color is a perception we humans have because of the kinds of pigments used in our retinae. Our eyes do not sense light evenly across the visible spectrum but have a greater sensitivity for green light, and somewhat less so for red and blue light as the response spectrum below illustrates:
In effect, what you have to do is ‘multiply’ the spectrum of light you receive from a heated body, by the response of the eye to the various wavelengths of light in the spectrum. When this happens, a very unusual thing happens.
If I were to figure out how hot a star would have to be so that the peak of its emission was in the ‘green’ area near 4000 Angstroms, I would estimate that the temperature of the star would have to be about 10,000 degrees. There are many such stars in the sky. The two brightest of these ‘A-type’ stars are Vega in the constellation Lyra, and Sirius in Canes Major. But if you were to look at them in the sky, they would appear WHITE not green! Stars are ranked according to increasing temperature by the sequence of letters:
This is NOT the same sequence of colors you see in a rainbow (red, orange, yellow, green, blue, indigo, violet) because the distribution of energy in the light source is different, and in the case of the rainbow, optical refraction in a raindrop is added.
Another factor working against us is that we see stars in the sky using our black/white rods not our color-sensitive cones. This means that only the very brightest stars have much of a color, usually red, orange, yellow and blue. By chance there are no stars nearby that would have produced green colors had their spectral shapee been just right.
So, there are no genuinely green stars because stars with the expected temperature emit their light in a way that our eye combines into the perception of ‘whiteness’.
For more information on star colors, have a look at the article by Philip Steffey in the September, 1992 issue of Sky and Telescope (p. 266), which gives a thorough discussion of stellar colors and how we perceive them.
The minimum size for a star is believed to be near 0.04 times the mass of the Sun or about 80 times the mass of Jupiter. An object called a brown dwarf is really a large planet which was not massive enough for thermonuclear fusion to get ignited in the core. The difference between a brown dwarf and a planet is believed to be about 13 times the mass of Jupiter. The closest red dwarf is Proxima Centauri with a masss of about 130 times Jupiter. The closest brown dwarf to our sun as of 2014 is about 7.5 light years away and is called WISE J085510.83-071442.5, and is now the record-holder for the coldest brown dwarf, with a temperature between minus 54 and 9 degrees Fahrenheit (minus 48 to minus 13 degrees Celsius) and a mass of about 3-10 times Jupiter. The exciting thing about red dwarf stars is that they burn their nuclear fuel so slowly that they exist as stars for 10 times longer than our own sun!
The largest star is probably about 150-200 times the mass of the Sun. There are only a handful of these hyperstars in our own Milky Way which has over 200 billion stars in it. The Eta Carina nebula appears to have several dozen, mostly unstable stars with masses between 50 and 200 times the sun’s mass. These stars are so masssive that they run through their nuclear fuel in a few million years and explode as hypernovae, many times brighter than ordinary supernovae.
Although hyperstars are rare in a galaxy as large as the Milky Way, brown dwarfs and red dwarfs are not. In fact current searches for exoplanets favor the more numerous red and brown dwarf stars.
Black holes can have any mass from 0.00001 grams to 10 billion times the mass of the Sun…or more. The supermassive black holes are found in the cores of ‘active galaxies’ and quasars. Astronomers have never seen a black hole that is much smaller than the mass of our Sun yet, so we don’t know if they really exist.
There are several possibilities. If the collision speed is higher than a particular threshold speed, say about 300 miles per second, enough kinetic energy would be imparted to the two masses that the stellar material would dissipate into a vast expanding cloud of gas, never to reassemble itself into a new star.
If the speed were very slow, the stars would merge into a new, more massive, star. The evolution of the new star would begin with a rejuvenated core of fresh fuel since the merging of the two stars would have mixed new hydrogen fuel into the core of the new star.
If the speed of the impact is moderate and off center, the stars will go into a very tight orbit around one another, perhaps even sharing a common gaseous envelope. Over time, the two separate cores would spiral into each other, and you would again be left with one new, massive star. Since the escape velocity of the Sun is about 1.3 million miles per hour, this is about equal to the threshold speed of the impact.
If a smaller star, like a white dwarf or neutron star, smashes into a bigger star, like a red giant, most of the giant’s outer envelope would be blown off as it absorbs the impact. The results get a little more violent when two smaller stars collide. Neutron stars are very small and dense. If a neutron star reaches a certain mass, it will implode and form a black hole. Therefore, if two neutron stars merge but their combined mass is more than the maximum mass a single neutron star can have, they implode into a black hole. If the circumstances are the same when two white dwarf stars collide, they will implode into a neutron star. Here is an artistic rendering of how messy a neutron star-neutron star collision would be. (Credit: ESA)
This artist’s impression shows two tiny but very dense neutron stars at the point at which they merge and explode as a kilonova. Such a very rare event is expected to produce both gravitational waves and a short gamma-ray burst, both of which were observed on 17 August 2017 by LIGO–Virgo and Fermi/INTEGRAL respectively. Subsequent detailed observations with many ESO telescopes confirmed that this object, seen in the galaxy NGC 4993 about 130 million light-years from the Earth, is indeed a kilonova. Such objects are the main source of very heavy chemical elements, such as gold and platinum, in the Universe.
A team of astronomers is making a bold prediction: In 2022, give or take a year, a pair of stars will merge and explode, becoming one of the brightest objects in the sky for a short period. It’s notoriously hard to predict when such stellar catastrophes will occur, but this binary pair is engaged in a well-documented dance of death that will inevitably come to a head in the next few years, they say. The researchers began studying the pair, known as KIC 9832227, in 2013 before they were certain whether it was actually a binary or a pulsating star. They found that the speed of the orbit was gradually getting faster and faster, implying the stars are getting closer together. The pair is so close, in fact, they share an atmosphere. KIC 9832227’s behavior reminded the researchers of another binary pair, V1309 Scorpii, which also had a merged atmosphere, was spinning up faster and faster, and exploded unexpectedly in 2008. Now, after 2 years of careful study to confirm the accelerating spin and eliminate alternative explanations, the team predicted in 2017 that the pair will explode as a “red nova”—an explosion caused by a binary merging—in about 5 years’ time.
Illustration of matter in an accretion disk falling into a black hole. (Credit: NASA’s Goddard Space Flight Center/Jeremy Schnittman). The actual image of the disk will be distorted due to the intense gravitational field and will probably look like the following image.
Outside the black hole, it depends on what form the matter takes. If it happens to be in the form of gas that has been orbiting the black hole in a so-called accretion disk, the matter gets heated to very high temperatures as the individual atoms collide with higher and higher speed producing friction and heat. The closer the gas is to the black hole and its Event Horizon, the more of the gravitational energy of the gas gets converted to kinetic energy and heat. Eventually the atoms collide so violently that they get stripped of their electrons and you then have a plasma. All along, the gas emits light at higher and higher energies, first as optical radiation, then ultraviolet, then X-rays and finally, just before it passes across the Event Horizon, gamma rays.
Here is what a model of such a disk looks like based on a typical calculation, in this case by physicist Kovak Zoltan (Phys Rev D84, 2011, pp 24018) for a 2 million solar mass black hole accreting mass at a rate of 2.5 solar masses every million years. Even around massive black holes, temperatures run very hot. The event horizon for this black hole is at a distance of 6 million kilometers. The first mark on the horizontal axis is ‘5’ meaning 5 times the horizon radius or a distance of 30 million km from the center of the black hole. This is about the distance from our sun to mercury!
If the matter is inside a star that has been gravitationally captured by the black hole, the orbit of the star may decrease due to the emission of gravitational radiation over the course of billions of years. Eventually, the star will pass so close to the black hole that its fate is decided by the mass of the black hole. If it is a stellar-mass black hole, the tidal gravitational forces of the black hole will deform the star from a spherical ball, into a football-shaped object, and then eventually the difference in the gravitational force between the side nearest the black hole, and the back side of the star, will be so large that the star can no longer hold itself together. It will be gravitationally shredded by the black hole, with the bulk of the star’s mass going into an accretion disk around the black hole. If the black hole has a mass of more than a billion times that of the sun, the tidal gravitational forces of the black hole are weak enough that the star may pass across the Event Horizon without being shredded. The star is, essentially, eaten whole and the matter in the star does not produce a dramatic increase in radiation before it enters the black hole. Here is an artist version of such a tidal encounter.
Once inside a black hole, beyond the Event Horizon, we can only speculate what the fate of captured matter is. General relativity tells us that there are two kinds of black holes; the kind that do not rotate, and the kind that do. Each of these kinds has a different anatomy inside the Event Horizon.For the non-rotating ‘Schwarzschild black hole’, there is no way for matter to avoid colliding with the Singularity. In terms of the time registered by a clock moving with this matter, it reaches the Singularity within a few micro seconds for a solar-massed black hole, and a few hours for a supermassive black hole. We can’t predict what happens at the Singularity because the theory says we reach a condition of infinite gravitational force.
For the rotating ‘ Kerr Black holes’, the internal structure is more complex, and for some ingoing trajectories for matter, you could in principle avoid colliding with the Singularity and possibly reemerge from the black hole somewhere else, or at some very different future time thousands or billions of years after you entered.
Some exotic theories say that you reemerge in another universe entirely, but physicists now don’t believe that interpretation is accurate. The problem is that for black holes created by real physical events, the interior of a black hole is awash with gravitational radiation which makes the geometry of space-time very unstable, preventing just these kinds of trips.
For the simplist non-rotating Schwarschild black holes, even they offer a mind-numbing prospect. The mathematics says that outside the event horizon, a particle will experience space and time normally. The particle (and you!) can travel freely in space along the R, radial coordinate, but have no control over your progression in time along the T coordinate. You can speed it up or slow it down a bit through the time dilation effect of high-sped travel, but you can not travel backwards in time. At the event horizon, something amazing happens. The mathematical variables we have been using for time and space, that is R and T, reverse their rolls in the equations that define the separation between points in spacetime. What this means is that the space coordinate, R, behaves like a time coordinate so that you have no freedom to maneuver and not be crushed at the Singularity at R=0. Meanwhile you have some freedom to move along the T coordinate as though it acted like the old familiar space coordinate out side the event horizon.
For Schwarschild black holes that form from supernovae, you have another problem. The event horizon in the mathematics only appears a LONG time after the implosion of matter. In fact it is what mathematicians call an asymptotic feature of the collapsing spacetime. What this means is that if you fell into the black hole long after the supernova created it, the collapse is still going on in the frame of someone far away with the surface of the star trying to pass inside the horizon, but this process has not yet completed. For you falling in, the bulk of the star is still outside the horizon and the black hole has not yet formed! The time dilation effect is so extreme at the horizon that the star literally freezes its motion from the standpoint of the distant observer and becomes a frozen-in-time, black star. As seen from the outside, it will take an eternity for you to actually reach the horizon, but from your frame of reference, it will only take an hour or less depending on where you start! Once you pass inside the horizon, the time to arriving at the singularity is approximately the gravitational free-fall time from the horizon distance. For a supermassive black hole this could take hours, but for a solar mass black hole this takes about 10 microseconds!
Yes and No. The faintest individual stars we can see with our naked eyes are brighter than an apparent magnitude of about +6.5. The bright star Betelgeuse in Orion is at a distance of 1500 light years and is 10,000 times as luminous as the Sun. To be outside our galaxy, the star has to be at least 3000 light years above the plane of the Milky Way in the so-called Halo region, which is still technically a part of our Milky Way, but at least not a part of the spiral disk. There are no supergiants like Betelgeuse in the halo of the Milky Way.
The most common stars are only a little more brighter than the Sun, which means they would be much fainter than the faintest star you could see with your eye. The famous Supernova of 1987 is, of course, the only recent exception. It was a single star located 160,000 light years outside the Milky Way which we could see easily with the naked eye. That’s what made it doubly spectacular.
The most distant, individual star known was discovered by astronomer Bruce Margon while searching for the optical candidate for an X-ray source. He found a very red, carbon star about 400,000 light years from the Milky Way. With a velocity of 40 kilometers per second, at its distance it is only weakly bound to the Milky Way. It lies not far from the orbital track of the Magellanic Clouds and may be an escaped star from one of them. It is an 18th magnitude star, even though it is nearly 1000 times more luminous than the Sun. See Sky and Telescope magazine, April 1984, p. 316 for more details.
Astronomers such as Saul Perlmutter have also seen supernova in galaxies that are billions of light years distant, so these are the truly most distant individual stars we know about at least at the time that they detonated! The above figure is a supernova seen by Perlmutter’s Supernova Cosmology Project team. In their caption they note:The third image shows the same supernova as observed with the Hubble Space Telescope. This much sharper picture allows a much better measurement of the apparent brightness and hence the distance of this supernova. Because their intrinsic brightness is predictable, such supernovae help to determine the deceleration, and so the eventual fate, of the universe.
This detailed image from the Hubble Space Telescope shows a section of the Andromeda Galaxy, Messier 31 located 2.5 million light years from the Milky Way. Several object types are labelled, including dust lanes, stellar clusters, Milky Way stars, and star-forming regions. (Credit: NASA/ESA Hubble)
Lets take a walk through the universe to see what individual stars look like in various Hubble Space Telescope and ground-based telescope images!
At a distance of 56 million light years you can still resolve some of the brightest stars in the barred spiral NGC 1365 shown above.
NGC 1309 is located 130 million light years from the sun and as this Hubble Heritage image shows, you can see individual bright stars in its spiral arms at this distance. These stars are thousands of times brighter than our own sun and are giant or supergiant stars.
Based on tons of scientific data and decades of research, here is an artist’s impression of the Milky Way Galaxy, as seen from above the galactic “North pole”. (Credit: NASA. JPL-Caltech/R. Hurt (SSC/Ca)
All of the basic elements have been established including its spiral arm pattern and the shape of its central bulge of stars. To directly answer this question, however, is a difficult, if not impossible, task. The problem is that we cannot directly see every star in the Milky Way because most are located behind interstellar clouds from our vantage point in the Milky Way. The best we can do is to figure out the total mass of the Milky Way, subtract the portion that is contributed by interstellar gas and dust clouds ( about 1 – 5 percent or so), and then divide the remaining mass by the average mass of a single star.
From a number of studies, the mass of the Milky Way inside the orbit of our sun can be estimated to an accuracy of perhaps 20 percent as 140 billion times the mass of the Sun, if you use the Sun’s speed around the core of the galaxy. Radio astronomers have detected much more material outside the orbit of the Sun, so the above number is probably an underestimate by a factor of 2 to 5 times in mass alone.
Now, to find out how many stars this represents, you have to divide by the average mass of a star. If you like the sun, then use ‘one solar mass’ and you then get about 140 billion sun-like stars for what’s inside the sun’s orbit. But astronomers have known for a long time that stars like the sun in mass are not that common. Far more plentiful are stars with half the mass of the sun, and even one tenth the mass of the sun. The problem is that we don’t know exactly how much of the Milky Way is in the form of these low-mass stars. In text books, you will therefore get answers that range anywhere between a few hundred billion and as high as a trillion stars depending on what the author used as a typical mass for the most abundant type of star. This is a pretty embarrasing uncertainty, but then again, why would you need to know this number exactly?
The best estimates come from looking at the motions of nearby galaxies such as a recent study by G. R. Bell (Harvey Mudd/USNO Flagstaff), S. E. Levine (USNO Flagstaff):
Using radial velocities and the recently determined proper motions for the Magellanic Clouds and the dwarf spheroidal galaxies in Sculptor and Ursa Minor, we have modeled the satellite galaxies’ orbits around the Milky Way. Assuming the orbits of the dwarf spheroidals are bound, have apogalacticon less than 300 kpc, and are of low eccentricity, then the minimum mass of our galaxy contained within a radius of 100 kpc is 590 billion solar masses, and the most likely mass is 700 billion. These mass estimates and the orbit models were used to place limits on the possible maximum tangential velocities and proper motions of the other known dwarf spheroidal galaxies and to assess the likelihood of membership of the dwarf galaxies in various streams.
Again, you have to divide this by the average mass of a star…say 0.3 solar masses, to get an estimate for the number of stars which is well into the trillions!
Another factor that confuses the problem is that our Milky Way contains a lot of dark matter that also produces its own gravity and upsets the estimates for actual stellar masses. Our galaxy is embedded in a roughly spherical cloud of dark matter. Various theoretical calculations show that these should be very common among galaxies. Here is an example of such a model in which the luminous galaxy is embedded in a massive DM halo. (Credit:Wikipedia-Dark Matter Halo N-body simulation)
By using the motions of distant galaxies astronomers have ‘weighed’ the entire Milky Way and deduce that the dark matter halo is likely to include around 3 trillion solar masses of dark matter.
The locations of stars in the sky are given by their Equatorial coordinates, which are stated as Right Ascension and Declination and given as a pair of numbers (RA, DEC). RA is given in hours, minutes and secionds while Declination is given in degrees.
For math calculations, we want to work in degrees so we convert RA into degrees by multiplying RA x 360/24.0.
Let RA1 and DEC1 be the right ascension and declinations of Star 1 in degrees.
Let RA2 and DEC2 be the right ascension and declination of Star 2 in degrees,
The angular separation A, in degrees, between them is:
Let’s do an example.
Sirius is at RA1=6h 41m and DEC1=-16d 35′ so RA1 = 6.68h x 360/24 = 100.2 degrees and DEC1 = -16.58 degrees.
Betelgeuse is at RA2=5h 50m and DEC2=+7d 23′ so RA2 = 87.5degrees and DEC2 = 7.38 degrees. Then
To get distances, we use a variety of techniques. The most basic one is geometric parallax. By photographing the same star 6 months apart from points 1 and 2 in earth’s orbit, the shift of the star relative to more distant background stars when R = 1 Astronomical Unit amounts to 1 second of arc at 1 parsec ( 3.26 light years), 1/2 arcsecond at 2 parsecs, 1/10 arcsecond at 10 parsecs etc. By the way, at 1 parsec, an arcsecond also subtends 206265 astronomical units.
The Hipparcos astrometric satellite has determined the distance to over 100 thousand stars in this way. Read an ESA Press Release about the mission accomplishments. For example, the distances to the Nearest 10 stars can be found in their Table of 150 closest stars which I reprint below:
Name Parallax Alpha Centauri C 772.33 Alpha2 Centauri C 742.12 Alpha1 Centauri C 742.12 Barnard's Star 549.01 Alpha Canis Majoris (Sirius) 379.12 Epsilon Eridani 310.75 61 Cygni A 287.13 Alpha Canis Minoris 285.93 61 Cygni B 285.42 Epsilon Indi 275.76 Tau Ceti 274.17
Note: the Parallax is measured in 1/arcseconds. To calculate the distance in parsecs you have to take 1000.0 and divide it by the parallax number in the last column above. For example, Alpha Centauri C (Proxima) is at a distance of 1000.0/772.33 = 1.295 parsecs which equals 1.295 x 3.26 = 4.22 light years. Alpha Centauri is at 1000/742 = 1.34 parsecs or 4.39 light years. I leave it as a simple calculator exercise for you to convert the parallaxes above into light years!
Stellar diameters can be measured for some nearby giant and supergiant stars by using a technique called stellar interferometry. The Navy Prototype Optical Interferometer has been operating for over a decade at Mount Wilson Observatory, and routinely measures the angular diameters of bright stars to fractions of a milli arcsecond (0.001 arcseconds) accuracy. The table below shows only a few stars that have had their diameters measured. Once their distances are accurately known…from the Hipparcos Survey…their linear diameters in millions of kilometers can easily be found.
The table below shows the sizes in multiples of the solar diameter for some typical stars that have measured angular diameters in column 5 given in arcseconds. The highest resolution of the Hubble Space Telescope is about 0.046 arcseconds. So it is just able to see Betelgeuse as a resolved ‘disk’
The size in kilometers = 3 x 10^13 (d /3.26) (D/3600)/57.3 or 44.6 million x d x D where d = the distance in light years and D is the angular diameter in arcseconds. In terms of solar diameters (1,390,000 km) you get Size = 32 d x D solar diameters. The later formula gives you the above entries in the last column. The super giant star Betelgeuse is 734.4 times the diameter of the Sun.
Absolute Zero is an ‘asympotic’ state which you can only get close to but never reach. In fact there are quantum mechanical phenomena that intervene that probably prevent you from actually reaching it because the physical vacuum itself even at ‘Absolute Zero’ contains energy that interferes with any physical system in space. Einstein-Bose Condensates are a good example of what happens when you try to cool a small collection of atoms to very cold temperatures. Their wave functions spread out and you end up with an indivisible ‘super particle’ rather than a collection of even more frigid discrete particles.
Among the coldest naturally-occurring things in nature is the cosmic fireball radiation which fills all space in the universe and has a temperature of 2.7 degrees above absolute zero. Above you see in the image of this radiation across the sky, created by NASA’s COBE spacecraft, how this very cold light still has faint irregularities in it from the vast collections of matter that it has passed through to get to us.
We define time in terms of clocks which are collections of matter that change their states. At Absolute Zero, there would be no thermal energy to keep such collections moving, but that doesn’t mean that very large collections of matter would not move. Temperature is only defined for collections of ‘small’ things such as atoms…or quanta of energy like photons. Planets would still orbit stars and spin on their axis so a physical clock would still exist, and therefore we would still have ‘time’.
In the mid-1970’s physicists were excited with the recent success of Steven Weinberg, Abdus Salam and Sheldon Glashow in creating a unification theory for the electromagnetic and weak forces. By applying what is called ‘group theory’ , physicists such as Glashow, Georgi and others proposed that you could use the symmetries of ‘SU(5)’ to unite the weak and electromagnetic forces with the strong nuclear force which is mediated by gluons. This became known as ‘Grand Unification Theory’ or ‘GUT’, and quickly evolved into many variants including ‘super-symmetric GUTs (SUSY- GUTs)’, ‘super gravity theory’ and ‘dimensionally-extended SUSY GUTs’, before being replaced by string theory in the early 1980’s.
It produced a lot of excitement in the late-70s and early-80’s because it seemed as though it could provide an explanation for the strong, weak and electromagnetic forces, and do so in a common mathematical language. It’s major prediction was that at the enormous energy of 1000 billion billion volts (10^15 GeV) the strong nuclear force would become similar (or unified) with the electromagnetic and weak forces. Applying these ideas to cosmology also led to the creation of Inflationary Cosmology.
Today, the so-called Standard Model of nuclear physics unifies physics (except for gravity) and uses some of the basic ideas of GUT to do so. Physicists worked very hard to confirm several basic ideas in GUT theory such as ‘spontaneous symmetry breaking’ by looking for the Higgs Boson. In 2012 this elusive particle was discovered at the Large Hadron Collider some 50 years after it was predicted. This wass a revolutionary discovery because it demonstrated that the entire concept of spontaneous symmetry breaking seemed to be valid. It was the keystone idea in the unification of the electromagnetic and weak forces for which Abdus Salam, Steven Weinberg and George Glashow received the Nobel Prize in the mid-1970s. SSB was also the workhorse concept behind much of the mathematical work into GUTs.
GUT research in the booming 1970s also uncovered a new ‘Supersymmetry’ in nature, which continues to be searched for. The unpleasant thing about the current Standard Model is that it has several dozen adjustable constants that have to be experimentally fine-tuned to reproduce our physical world including such numbers as the constant of gravity, speed of light, fine structure constant, and the constants that determine how strongly the leptons and quarks interact. Physicists think that this is way too much, and so the search is on for a better theory that has far fewer ad hoc constants. There is also the problem that the Standard Model doesn’t include gravity.
The hope that gravity could some how be incorporated into GUTs pursued in the 1970s was ultimately never realized because of the advent of String Theory which provided a newer way to look at gravity as a ‘quantum field’. Yet most popular versions of string theory include supersymmetry, hense they are called superstring theories.
Supersymmetry has grown to become a lynchpin concept behind many ideas for unifying all of the four foruces including gravity, however after five years of searching for signs of it at the CERN Large Hadron Collider, not so much as a trace of it has been detected. It seems as though the Standard Model is all there is, but in which the strong force and the ‘electroweak’ forces may possibly not be unified further.
An astronomer's point-of-view on matters of space, space travel, general science and consciousness
