Unusual Binary Neutron Stars With Gravity 300 Billion Times the Earth
An exotic pair of binary stars have proved that Albert Einstein’s theory of relativity is still right, even in the most extreme conditions tested yet. ”The unusual pair of stars is quite interesting in its own right but we’ve learned it is also a unique laboratory for testing the limits of one of our most fundamental physical theories, general relativity” says University of Toronto astronomy professor Marten van Kerkwijk, a member of the research team.
What makes the pair of stars exceptional are the unique characteristics of each and their close proximity to each other. One is a tiny but unusually heavyneutron star– one of the most massive confirmed to date. NamedPSRJ0348+0432, it is the remnant of a supernova explosion, and is twice as heavy as the Sun yet is only 20 kilometres across. The neutron star is a pulsar that gives off radio waves that can be picked up on Earth by radio telescopes.The gravity at its surface is more than 300 billion times stronger than that on Earth and at its centre every sugarcube-sized volume has more than one billion tonnes of matter squeezed into it, roughly the mass of every human past and present.
The massive star spins 25 times each second and is orbited by a rather lightweight dwarf star every two and a half hours, an unusually short period. Only slightly less exotic, the white dwarf is the glowing remains of a much lighter star that has lost its envelope and is slowly cooling. It can be observed in visible light, though only with large telescopes – it is about a million times too faint to be visible with the naked eye.
In the new work, led by Bonn PhD student John Antoniadis, very precise timing of the pulsar’s spin-modulated emission with radio telescopes was used to discover a tiny but significant change in the orbital period of the binary, of eight-millionths of a second per year. Given the masses of the pulsar and the white dwarf, inferred with the help of observations of the light emitted by the white dwarf – using techniques perfected by Antoniadis and van Kerkwijk – this turns out to match exactly what Einstein’s theory predicts.
Einstein’s general theory of relativityexplains gravity as a consequence of the curvature of spacetime created by the presence of mass and energy. As two stars orbit each other, gravitational waves are emitted – wrinkles moving out in spacetime. As a result, the binary slowly loses energy, the stars move closer, and the orbital period shortens.
The test posed by PSR J0348+0432 is particularly interesting because the massive star is a truly extreme object in terms of gravity, even compared to other pulsars that have been used to test general relativity. As a result, it causes exceptionally strong distortion of spacetime. In many alternatives to Einstein’s theory, this would cause the orbit to lose energy much faster than is observed.
“The observations disprove these alternatives,” says van Kerkwijk, “and thus give further confidence that Einstein’s theory is a good description of nature – even though we know it is not a complete one, given the unresolved inconsistencies with quantum mechanics.”
Astronomical Distances and MagnitudesMeasuring Astronomical distances
In the words of Douglas Adams, the author of The Hitch-Hiker’s Guide to the Galaxy:
Space is big. You just won’t believe how vastly, hugely, mind-bogglingly big it is. I mean, you may think it’s a long way down the road to the chemist’s, but that’s just peanuts to space.
The distances involved in the universe are so vast that metres or kilometers will just not suffice. We must introduce new length scales with which can span the heavens.
THE ASTRONOMICAL UNIT A.U.
One natural and practical unit we can devise is the distance from the Sun to the Earth. This is the A.U. or Astronomical Unit. 1 Astronomical Unit = 149 598 000 km
LIGHT YEAR
Moving to larger distances even the AU becomes unweildly and so the next suitable unit is the light-year. The light-year, as its name would suggest, is the distance travelled by light in one year. All electromagnetic waves travel at a speed of x 299,792,458 ms-1 in a vacuum and with an average year being 365.25 days, one light year is 299,792,458 x 108ms-1 x (365.25 x 24 x 60 x 60) s =
9.46073 x 1015 m. or 9.46073 x 1012 km.
1 lt-yr = 63 239.6717 AU
With our new measuring sticks to hand we can give a few examples of the scale of the universe.
The distance from the Earth to the nearest star (Alpha Centauri A or B) after our Sun is 4.3 ly.
The Milky Way Galaxy is about 150,000 light-years across
The andromeda galaxy is 2.3 million light-years away.
The edge of the observable universe is 46.5 Giga light years away.
THE PARSEC
The other commonly used unit in astronomy and in Star Trek is called the Parsec (parallax of one arc second). The parsec is defined to be the distance at which a star would have a parallax angle p equal to one second of arc (1/3600 deg). The two dimensions that specify this triangle are the parallax angle (defined as 1 arcsecond) and the opposite side (defined as 1 Astronomical Unit (AU), the distance from the Earth to the Sun).
The parsec defined as the distance required to create a parallax angle of one second of arc.
Parallax is the apparent shift in the nearest stars due to the motion of the Earth around the Sun. The method of parallax gives rise to a natural distance unit that astronomers call the parsec (which we shall abbreviate as pc).
The parsec in trigonometric terms.
1 Parsec = 3.08568025 × 1016 m. also used are kpc =1000 pc and Mpc =1 million pc
1 Parsec = 3.26 lt yrs.
If the star is not further than 500 light-years, then the parallax shift of the star can be used to find the distance from the Earth.
Distance (in parsecs) = 1/parallex angle.
Magnitude of Stars
Apparent Magnitude
Early Greek astronomers used a scale of magnitude devised by Hipparchus around the 2nd century BC, which was based on how bright stars appeared with the naked eye. The Hipparchus scale went from magnitude 1, for the brightest stars, up to magnitude 6, for those stars which were barely visible.
Improvements in the light gathering power of telescopes made it possible to compare the intensities of the light from stars more accurately. In 1856, Norman Robert Pogson formalized the system by defining a typical first magnitude star as a star that is 100 times as bright as a typical sixth magnitude star. Thus, a first magnitude star is about 2.512 times as bright as a second magnitude star. The fifth root of 100 (since magnitude 6 stars must be 1: x5 is known as Pogson’s Ratio. In calculations, however, the factor 2.5 is often used.
To make things more confusing, the brightest stars in the sky exceed magnitude 1. These bright starts are accommodated by allowing negative magnitudes. The Sun has an apparent magnitude of -26.74, while Sirius has a magnitude of -1.46. At the other end of the scale, as the light gathering power of telescopes has increased, the magnitude scale has extended to encompass much fainter stars. The dimmest object currently observable with the largest telescopes have a magnitude of 30. As a useful reference point, the star, Vega is taken to be of 0 magnitude. More accurate measurements put its apparent magnitude at 0.03.
It is also important to note that the magnitude system is only meaningful when magnitudes are compared when measured through the same wavelength band.
Name Apparent Magnitude Distance from Earth
Sun -26.74 1 AU
Full Moon - 12 200,000 km
Venus -4.71 38 million km
Sirius -1.46 2.6pc
Vega 0.03 13pc
Canopus 0.7 96pc ±5pc
Faintest Stars 30 as seen with the European
Extremely Large Telescope (E-ELT) or Hubble Space
Telescope -
The apparent magnitude m is given by
m = - 2.5 log10(b) + C(1)
Where, b is the observed intensity or brightness of the star and C is a constant, depending on the band the object is observed in, i.e. ultra-violet U, blue, B or visible V.
If we measure the brightness of two different stars, using a detector in the same band, we can determine their difference in magnitude. The difference in their apparent magnitude is given by
m1 - m2 = - 2.5 log10(b1/b2)
where m1 and m2 two are apparent magnitudes of the two stars, and b1 and b2 are their respective brightness.
From the properties of logarithms, the ratio of the intensities / brightness of the two stars is.
m1 - m2 = - 2.5 [log10(b1) - log10(b2)]
m1 - m2 = - 2.5 log10(b1/b2)(3)
Absolute Magnitude
The apparent brightness of a star is how bright it seems when viewed from the Earth, but a large, bright star can appear dim if it is a long way from the Earth and a dim star can appear to be bright if it is close to the Earth. Therefore, the apparent magnitude has no bearing on the distance from the Earth.
To give an acurate measurement of the brightness of a star we need to make an absolute magnitude scale. The absolute magnitude is how bright a star is when viewed from a set distance. Stars being rather large objects, a distance of 10 parsecs was chosen.
The absolute magnitude is the brightness of a star at a distance of 10 parsecs.
Absolute Magnitude and Inverse Square Law of Intensity
In order to find the absolute magnitude, we need to know the distance of the star from the Sun. How do we do this? The intensity or brightness of light decreases with distance from the star. The rate at which it decreases is inversely proportional to the square of the distance. Thus, if we have a star of luminosity L and we move a distance d the same quantity of light has to cover a larger spherical area. Therefore, the brightness or intensity is given by
b = L/(4πd2) (4)
Or in more simple terms, the apparent brightness of the star is proportional to the 1/distance2
To calculate the absolute magnitude we are essentially using the relative magnitude formula and the inverse square law to allow us to substitute distance for brightness. Now we can compare its magnitude with a star at set distance of 10pc.
M- m = -2.5 log10(d2) - (-2.5 log10102)
Using the rules of logarithms to make some simplifications.
M = m -2.5 log10(d2/102)
M = m - 5 log(d/10)(5)
M = m - 5 [log(d) - 1]
M = m - 5 log(d) + 5(6)
Distance Modulus
Starting from equation (6) we can calculate the distance d from the Earth if we know the absolute magnitude. In practice we don’t know the absolute magnitude because we cannot travel 10 parsecs from the star in question. We can use several indirect methods to determine its absolute magnitude. If the star is on the main sequence of stars then we can determine the brightness from its parallax.
If we know the apparent magnitude m and the absolute magnitude then we can find the distance in parsecs to the star.
m - M = 5 log10(d) + 5
Rearranging for d
d = 10((m-M)+5)/5
Puzzle of Spiral Galaxies Solved —“Self-perpetuating, Persistent, and Surprisingly Long Lived”
Some 15 percent of all galaxies in the visible Universe are spirals. The great fog-like clouds of stars, the oldest and largest galaxies in the Universe are ellipticals. Becasue ellipticals also include many of the smallest galaxies, they are the most numerous. Our own Milky Way, astronomers believe, is a spiral. Our solar system and Earth reside somewhere near one of its filamentous, swept-back arms. And nearly 70 percent of the galaxies closest to the Milky Way are spirals, suggesting they have taken the most ordinary of galactic forms in a universe with somewhere between 100 billion and 200 billion galaxies.
But a long-standing question has been: how do galaxies like the Milky Way get and maintain their characteristic arms has proved to be an enduring puzzle in astrophysics. How do the arms ofspiral galaxies arise? Do they change or come and go over time?*The answers to these and other questions are now coming into focus as researchers capitalize on powerful new computer simulations to follow the motions of as many as 100 million “stellar particles” as gravity and other astrophysical forces sculpt them into familiar galactic shapes.Writing April 1 in The Astrophysical Journal, a team of researchers from the University of Wisconsin-Madison and Harvard-Smithsonian Center for Astrophysics report simulations that seem to resolve longstanding questions about the origin and life history of spiral arms in disk galaxies.
“We show for the first time that stellar spiral arms are not transient features, as claimed for several decades,” says UW-Madison astrophysicist Elena D’Onghia, who led the new research along with Harvard-Smithsonian Center for Astrophysics colleagues Mark Vogelsberger and Lars Hernquist. “They are self-perpetuating, persistent and surprisingly long lived.”
The origin and fate of the emblematic spiral arms in disk galaxies have been debated by astrophysicists for decades, with two theories predominating: One holds that the arms come and go over time. A second and widely held theory is that the material that makes up the arms – stars, gas and dust – is affected by differences in gravity and jams up, like cars at rush hour, sustaining the arms for long periods.
The new results fall somewhere in between the two theories and suggest that the arms arise in the first place as a result of the influence of giant molecular clouds, star forming regions or nurseries common in galaxies. Introduced into the simulation, the clouds, says D’Onghia, a UW-Madison professor of astronomy, act as “perturbers” and are enough to not only initiate the formation of spiral arms but to sustain them indefinitely.
“We find they are forming spiral arms,” explains D’Onghia. “Past theory held the arms would go away with the perturbations removed, but we see that (once formed) the arms self-perpetuate, even when the perturbations are removed. It proves that once the arms are generated through these clouds, they can exist on their own through (the influence of) gravity, even in the extreme when the perturbations are no longer there.”
The Giant Magellan Telescope - GMT
WIth the James Webb telescope launch set for 2015, the GMT, and a lot more telescopes being built, the questions of our universe almost seem to be closer and closer waiting to be solved. I wrote about the GMT almost a year ago and it quickly became one of my favorite telescopes. It will be operational in 10 years the engineers say. I don’t know if that’s too short or too long. Either way let me tell you a little about this amazing telescope.
The Namesake - Magellan
Ferdinand Magellan, everybody knows the famous explorer, he led an expedition in 1522 which was the first to circumnavigate the earth, an ambitious feat for exploration. Astronomy was the primary tool of navigation of that time and Magellan was a certainly a student of astronomy. The expedition saw in the southern hemisphere obscure clouds in the night sky, later named the Magellanic Clouds. These clouds turned out to be island universes, filled with millions of stars orbiting another island universe, our Milky Way.
The Giant Magellan Telescope will continue the tradition of exploration that was set forth 500 years ago. The telescope is also peering into the unknown, maybe finding new questions to our Universe and searching for new worlds.
The Telescope - A Giant
The GMT will utilize a new and unique design. There will be seven 27ft segmented mirrors surrounding a central segment forming a single optical surface. This precision will give the telescope a resolving power 10x that of the Hubble Telescope. The light will be concentrated into CCD (Charge Coupled Device) image cameras which will measure the distance of objects and what their composition is.
This is Where is Gets More Interesting
The telescopes segmented mirrors are flexible. Under each mirror there are hundreds of ‘actuators’ that constantly adjust the mirrors to counteract atmospheric turbulence. These actuators will turn flickering stars into sharp points of light.
High and Dry
A huge advantage is the location of the GMT. Located in Chile in the Atacama Desert at an altitude of approximately 8,500 ft it is the highest and driest location on Earth.
How Do Aurorae (Northern and Southern Lights) Occur?
As solar particles from an incoming Coronal Mass Ejection (or CME) move into Earth’s magnetosphere they travel around to its back side — or night side, since it is on the opposite side from the Sun — along the magnetic field lines.
When these magnetic field lines reconnect in an area known as the magnetotail, energy is released and it sends the particles down onto Earth’s poles, and sometimes even lower latitudes. As the particles bombard oxygen and nitrogen in the upper atmosphere, the atoms release a photon of light that we see as the beautiful colors of the aurora.
(via: NASA Solar Dynamics Observatory)
Discovery: Kepler-37b, a planet only slightly larger than the Moon | NASA
Is Kepler-37b truly a planet or is it a dwarf planet? The 26th General Assembly of the International Astronomical Union (IAU) defined a planet as “a celestial body that (a) is in orbit around the Sun, (b) has sufficient mass for its self-gravity to overcome rigid body forces so that it assumes a hydrostatic equilibrium (nearly round) shape, and (c) has cleared the neighborhood around its orbit.” For exoplanets, part (a) becomes “is in orbit around a star.” So far so good. For the second criterion (b), the Kepler team estimates the mass of Kepler-37b to be greater than 0.01 Earth mass, which is ample mass to insure the body is nearly round. This mass is also sufficient to satisfy the 3rd criterion (c) that the planet clear out lesser bodies in the neighborhood of its orbit. The team therefore confidently concludes that Kepler-37b is truly a planet.
Sun’s Next-Door Twin: Cool Layer in the Atmosphere of Alpha Centauri A
(Image Credit: ESA)
“The European Space Agency’s Herschel space observatory has detected a cool layer in the atmosphere of Alpha Centauri A, the first time this has been seen in a star beyond our own Sun. The finding is not only important for understanding the Sun’s activity, but could also help in the quest to discover proto-planetary systems around other stars.
The Sun’s nearest neighbours are the three stars of the Alpha Centauri system. The faint red dwarf, Proxima Centauri, is nearest at just 4.24 light-years, with the tight double star, Alpha Centauri AB, slightly further away at 4.37 light-years.
Alpha Centauri B has recently been in the news after the discovery of an Earth-mass planet in orbit around it. But Alpha Centauri A is also very important to astronomers: almost a twin to the Sun in mass, temperature, chemical composition and age, it provides an ideal natural laboratory to compare other characteristics of the two stars.
One of the great curiosities in solar science is that the Sun’s wispy outer atmosphere — the corona — is heated to millions of degrees while the visible surface of the Sun is ‘only’ about 6000ºC. Even stranger, there is a temperature minimum of about 4000ºC between the two layers, just a few hundred kilometres above the visible surface in the part of Sun’s atmosphere called the chromosphere.
Both layers can be seen during a total solar eclipse, when the Moon briefly blocks the bright face of the Sun: the chromosphere is a pink-red ring around the Sun, while the ghostly white plasma streamers of the corona extend out millions of kilometres.”
Dark Matter Could Play a Role in Creating Life in The Universe
First Image : A Hubble Space Telescope image of Dark Matter mapped in a 3d representation.
Second Image: Abel 1689 galaxy cluster.
Dark matter makes up the majority of mass in our universe. However, we cannot directly measure the stuff as it doesn’t interact with electromagnetic radiation (i.e. it doesn’t emit or reflect any light), but we can indirectly observe its presence. In the Hubble Space Telescope image above, the distribution of mostly dark matter has been calculated and mapped. Basically, the location and density of anything with mass has been plotted in a 3D representation of the cosmos.
A 2011 study suggests that mysterious, invisible dark matter could warm millions of starless planets in regions such as Abell 1689 (image below) and make them habitable.
Scientists think the invisible, as-yet-unidentified dark matter which we know exists because of the gravitational effects it has on galaxies, makes up about 85 percent of all matter in the universe. Current prime candidates for what dark matter might be are massive particles that only rarely interact with normal matter.These particles could be their own antiparticles, meaning they annihilate each other when they meet, releasing energy. These invisible particles could get captured by a planet’s gravity and unleash energy that could warm that world, according to physicist Dan Hooper and astrophysicist Jason Steffen at the Fermi National Accelerator Laboratory.Hooper and Steffen’s propose that rocky “super-Earths” in regions with high densities of slow-moving dark matter could be warmed enough to keep liquid water on their surfaces, even in the absence of additional energy from starlight or other sources.The density of dark matter is expected to be hundreds to thousands of times greater in the innermost regions of the Milky Way and in the cores of dwarf spheroidal galaxies than it is in our solar system.
The scientists concluded that on planets in dense “dark-matter” regions, it may be dark matter rather than light that creates the basic elements you need for organic life without a star”
While the expression ‘it’s Ancient Greek to me’ is used to mean something incomprehensible, the truth is that Ancient Greek is both accessible and still very much alive in Modern English. Today’s word, star, is a great example. If you were to get in a time machine and travel back to to Ancient Greece you would be able to share many words that are virtually unchanged. You could point to the night sky and say ‘a star’ which is so close to the Ancient Greek aster (αστερ) they would understand it immediately. You could perform this time travel trick over a huge exspanse of land and time with similar results: the Old English steorra, from Proto-Germanic *sterron, *sternon (and for other Proto-Germanic derivatives see also Old Saxon sterro, Old Norse stjarna, Old Frisian stera, Dutch ster, Old High German sterro, German Stern, Gothic stairno), the Proto Indo-European *ster- (see also Sanskrit tar-, Hittite shittar, Latin stella, Breton sterenn, Welsh seren). Some words play such a powerful role on the imagination and and culture that they pass down from generation to generation like valuable treasure. Today star has dozens of metaphorical and poetic uses, from Shakespeare’s star-crossed lovers to soccer stars and five star restaurants. We wish upon stars, celebrities are known as stars, and we still treat the word with the highest metaphorical value: a star is distant, beautiful and inspiring.
Image courtesy NASA, in the public domain.
A Dying Star in a Different Light
This image composite shows two views of a puffy, dying star, or planetary nebula, known as NGC 1514. The view on the left is from a ground-based, visible-light telescope; the view on the right shows the object in infrared light, as seen by NASA’s Wide-field Infrared Survey Explorer, or WISE.
The object is actually a pair of stars — one star is a dying giant somewhat heavier and hotter than our sun, and the other was an even larger star that has now contracted into a dense body called a white dwarf. As the giant star ages, it sheds some its outer layers of material to form a large bubble around the two stars. Jets of material from the white dwarf are thought to have smashed into this bubble wall. The areas where the jets hit the cavity walls appear as orange rings in the WISE image. This is because dust in the rings is being heated and glows with infrared light that WISE detects.
The green cloud seen in the WISE view is an inner shell of previously shed material. In the visible image, this shell is seen in bright, light blues. An outer shell can also be seen in the visible image in more translucent shades of blue. This outer shell is too faint to be seen by WISE.
NGC 1514 is located 800 light-years away, in the constellation Taurus.
In the WISE image, infrared light with a wavelength of 3.4 microns is blue; 4.6-micron light is cyan; 12-micron light is green; and 22-micron light is red.
The visible-light image is from the Digitized Sky Survey, based at the Space Telescope Science Institute in Baltimore, Md.
JPL manages the Wide-field Infrared Survey Explorer for NASA’s Science Mission Directorate, Washington. The principal investigator, Edward Wright, is at UCLA. The mission was competitively selected under NASA’s Explorers Program managed by the Goddard Space Flight Center, Greenbelt, Md. The science instrument was built by the Space Dynamics Laboratory, Logan, Utah, and the spacecraft was built by Ball Aerospace & Technologies Corp., Boulder, Colo. Science operations and data processing take place at the Infrared Processing and Analysis Center at the California Institute of Technology in Pasadena. Caltech manages JPL for NASA.
Credit: NASA/JPL-Caltech/UCLA/DSS
NGC 6357’s Cathedral to Massive Stars
Image Credit: NASA, ESA and Jesús Maíz Apellániz (IAA, Spain)
“How massive can a normal star be? Estimates made from distance, brightness and standard solar models had given one star in the open cluster Pismis 24 over 200 times the mass of our Sun, nearly making it the record holder. This star is the brightest object located just above the gas front in the above image. Close inspection of images taken with the Hubble Space Telescope, however, have shown that Pismis 24-1 derives its brilliant luminosity not from a single star but from three at least. Component stars would still remain near 100 solar masses, making them among the more massive stars currently on record. Toward the bottom of the image, stars are still forming in the associated emission nebula NGC 6357. Appearing perhaps like a Gothic cathedral, energetic stars near the center appear to be breaking out and illuminating a spectacular cocoon.”
This gorgeous shot of the complexity that is the STAR detector at Brookhaven comes from amateur photographer Enrique Diaz, who won our recent photography competition.
Two months ago, Brookhaven National Lab invited 50 amateur and professional photographers to a three-hour, behind-the-scenes tour of the laboratory. Our cutting-edge experiments explore the fringes of fundamental science and represent singular achievements in design and engineering and these photographers lent their considerable talent to capturing these marvels and showing off the beauty of science.
We received more than 100 stunning submissions that revealed our facilities through fresh eyes, and we’ll be featuring a few of Top 10 here throughout the next week.
SN 2006X, before and after the Type Ia Supernova explosion (artist’s impression)
Left : artist’s impression of the favoured configuration for the progenitor system of SN2006X before the explosion. The White Dwarf (on the right) accretes material from the Red Giant star, which is losing gas in the form of stellar wind (the diffuse material surrounding the giant). Only part of the gas is accreted by the White Dwarf, through a so-called accretion disk which surrounds the compact star. The remaining gas escapes the system and eventually dissipates into the interstellar medium. The Red Giant star has a radius about 100 times larger than our Sun, while the White Dwarf is about 100 times smaller than the Sun.
Credit: ESO


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Astronomical Distances and Magnitudes
Measuring Astronomical distancesIn the words of Douglas Adams, the author of The Hitch-Hiker’s Guide to the Galaxy: Space is big. You just won’t believe how vastly, hugely, mind-bogglingly big it is. I mean, you may think it’s a long way down the road to the chemist’s, but that’s just peanuts to space. The distances involved in the universe are so vast that metres or kilometers will just not suffice. We must introduce new length scales with which can span the heavens.THE ASTRONOMICAL UNIT A.U. One natural and practical unit we can devise is the distance from the Sun to the Earth. This is the A.U. or Astronomical Unit. 1 Astronomical Unit = 149 598 000 kmLIGHT YEAR Moving to larger distances even the AU becomes unweildly and so the next suitable unit is the light-year. The light-year, as its name would suggest, is the distance travelled by light in one year. All electromagnetic waves travel at a speed of x 299,792,458 ms-1 in a vacuum and with an average year being 365.25 days, one light year is 299,792,458 x 108ms-1 x (365.25 x 24 x 60 x 60) s = 9.46073 x 1015 m. or 9.46073 x 1012 km. 1 lt-yr = 63 239.6717 AU With our new measuring sticks to hand we can give a few examples of the scale of the universe. The distance from the Earth to the nearest star (Alpha Centauri A or B) after our Sun is 4.3 ly. The Milky Way Galaxy is about 150,000 light-years across The andromeda galaxy is 2.3 million light-years away. The edge of the observable universe is 46.5 Giga light years away.THE PARSEC The other commonly used unit in astronomy and in Star Trek is called the Parsec (parallax of one arc second). The parsec is defined to be the distance at which a star would have a parallax angle p equal to one second of arc (1/3600 deg). The two dimensions that specify this triangle are the parallax angle (defined as 1 arcsecond) and the opposite side (defined as 1 Astronomical Unit (AU), the distance from the Earth to the Sun). The parsec defined as the distance required to create a parallax angle of one second of arc. Parallax is the apparent shift in the nearest stars due to the motion of the Earth around the Sun. The method of parallax gives rise to a natural distance unit that astronomers call the parsec (which we shall abbreviate as pc). The parsec in trigonometric terms. 1 Parsec = 3.08568025 × 1016 m. also used are kpc =1000 pc and Mpc =1 million pc 1 Parsec = 3.26 lt yrs. If the star is not further than 500 light-years, then the parallax shift of the star can be used to find the distance from the Earth. Distance (in parsecs) = 1/parallex angle.Magnitude of StarsApparent Magnitude Early Greek astronomers used a scale of magnitude devised by Hipparchus around the 2nd century BC, which was based on how bright stars appeared with the naked eye. The Hipparchus scale went from magnitude 1, for the brightest stars, up to magnitude 6, for those stars which were barely visible. Improvements in the light gathering power of telescopes made it possible to compare the intensities of the light from stars more accurately. In 1856, Norman Robert Pogson formalized the system by defining a typical first magnitude star as a star that is 100 times as bright as a typical sixth magnitude star. Thus, a first magnitude star is about 2.512 times as bright as a second magnitude star. The fifth root of 100 (since magnitude 6 stars must be 1: x5 is known as Pogson’s Ratio. In calculations, however, the factor 2.5 is often used. To make things more confusing, the brightest stars in the sky exceed magnitude 1. These bright starts are accommodated by allowing negative magnitudes. The Sun has an apparent magnitude of -26.74, while Sirius has a magnitude of -1.46. At the other end of the scale, as the light gathering power of telescopes has increased, the magnitude scale has extended to encompass much fainter stars. The dimmest object currently observable with the largest telescopes have a magnitude of 30. As a useful reference point, the star, Vega is taken to be of 0 magnitude. More accurate measurements put its apparent magnitude at 0.03. It is also important to note that the magnitude system is only meaningful when magnitudes are compared when measured through the same wavelength band.Name Apparent Magnitude Distance from Earth Sun -26.74 1 AU Full Moon - 12 200,000 km Venus -4.71 38 million km Sirius -1.46 2.6pc Vega 0.03 13pc Canopus 0.7 96pc ±5pc Faintest Stars 30 as seen with the European Extremely Large Telescope (E-ELT) or Hubble Space Telescope - The apparent magnitude m is given by m = - 2.5 log10(b) + C(1) Where, b is the observed intensity or brightness of the star and C is a constant, depending on the band the object is observed in, i.e. ultra-violet U, blue, B or visible V. If we measure the brightness of two different stars, using a detector in the same band, we can determine their difference in magnitude. The difference in their apparent magnitude is given by m1 - m2 = - 2.5 log10(b1/b2) where m1 and m2 two are apparent magnitudes of the two stars, and b1 and b2 are their respective brightness. From the properties of logarithms, the ratio of the intensities / brightness of the two stars is. m1 - m2 = - 2.5 [log10(b1) - log10(b2)] m1 - m2 = - 2.5 log10(b1/b2)(3)Absolute Magnitude The apparent brightness of a star is how bright it seems when viewed from the Earth, but a large, bright star can appear dim if it is a long way from the Earth and a dim star can appear to be bright if it is close to the Earth. Therefore, the apparent magnitude has no bearing on the distance from the Earth. To give an acurate measurement of the brightness of a star we need to make an absolute magnitude scale. The absolute magnitude is how bright a star is when viewed from a set distance. Stars being rather large objects, a distance of 10 parsecs was chosen. The absolute magnitude is the brightness of a star at a distance of 10 parsecs. Absolute Magnitude and Inverse Square Law of Intensity In order to find the absolute magnitude, we need to know the distance of the star from the Sun. How do we do this? The intensity or brightness of light decreases with distance from the star. The rate at which it decreases is inversely proportional to the square of the distance. Thus, if we have a star of luminosity L and we move a distance d the same quantity of light has to cover a larger spherical area. Therefore, the brightness or intensity is given by b = L/(4πd2) (4) Or in more simple terms, the apparent brightness of the star is proportional to the 1/distance2 To calculate the absolute magnitude we are essentially using the relative magnitude formula and the inverse square law to allow us to substitute distance for brightness. Now we can compare its magnitude with a star at set distance of 10pc. M- m = -2.5 log10(d2) - (-2.5 log10102) Using the rules of logarithms to make some simplifications. M = m -2.5 log10(d2/102) M = m - 5 log(d/10)(5) M = m - 5 [log(d) - 1] M = m - 5 log(d) + 5(6)Distance Modulus Starting from equation (6) we can calculate the distance d from the Earth if we know the absolute magnitude. In practice we don’t know the absolute magnitude because we cannot travel 10 parsecs from the star in question. We can use several indirect methods to determine its absolute magnitude. If the star is on the main sequence of stars then we can determine the brightness from its parallax. If we know the apparent magnitude m and the absolute magnitude then we can find the distance in parsecs to the star. m - M = 5 log10(d) + 5 Rearranging for d d = 10((m-M)+5)/5](http://25.media.tumblr.com/8f8a86f05a9ed1631fc78b4ad91c79cd/tumblr_mhotgs1ujj1qdvdz5o1_500.jpg)








