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109-427: As the closest Cepheid variable its distance is used as part of the cosmic distance ladder . The revised Hipparcos stellar parallax gives a distance to Polaris of about 433 light-years (133 parsecs ), while the successor mission Gaia gives a distance of about 448 light-years (137 parsecs ). Calculations by other methods vary widely. Although appearing to the naked eye as a single point of light, Polaris

218-451: A dimensionless quantity called z . If λ represents wavelength and f represents frequency (note, λf = c where c is the speed of light ), then z is defined by the equations: After z is measured, the distinction between redshift and blueshift is simply a matter of whether z is positive or negative. For example, Doppler effect blueshifts ( z < 0 ) are associated with objects approaching (moving closer to)

327-490: A ( t ) in the whole period from emission to absorption." If the universe were contracting instead of expanding, we would see distant galaxies blueshifted by an amount proportional to their distance instead of redshifted. In the theory of general relativity , there is time dilation within a gravitational well. This is known as the gravitational redshift or Einstein Shift . The theoretical derivation of this effect follows from

436-545: A Cepheid, partly because it is a member of a star cluster and the availability of precise parallaxes observed by the Hubble , Hipparcos , and Gaia space telescopes. The accuracy of parallax distance measurements to Cepheid variables and other bodies within 7,500 light-years is vastly improved by comparing images from Hubble taken six months apart, from opposite points in the Earth's orbit. (Between two such observations 2 AU apart,

545-441: A fact known as Hubble's law that implies the universe is expanding . All redshifts can be understood under the umbrella of frame transformation laws . Gravitational waves , which also travel at the speed of light , are subject to the same redshift phenomena. The value of a redshift is often denoted by the letter z , corresponding to the fractional change in wavelength (positive for redshifts, negative for blueshifts), and by

654-523: A lower frequency. A more complete treatment of the Doppler redshift requires considering relativistic effects associated with motion of sources close to the speed of light. A complete derivation of the effect can be found in the article on the relativistic Doppler effect . In brief, objects moving close to the speed of light will experience deviations from the above formula due to the time dilation of special relativity which can be corrected for by introducing

763-477: A parallax for Polaris, but a distance inferred from it is 136.6 ± 0.5  pc (445.5 ly) for Polaris B, somewhat further than most previous estimates and several times more accurate. This was further improved to 137.2 ± 0.3  pc (447.6 ly), upon publication of the Gaia Data Release 3 catalog on 13 June 2022 which superseded Gaia Data Release 2. Polaris is depicted in the flag and coat of arms of

872-403: A pardon by saying, "I am as constant as the northern star/Of whose true-fixed and resting quality/There is no fellow in the firmament./The skies are painted with unnumbered sparks,/They are all fire and every one doth shine,/But there's but one in all doth hold his place;/So in the world" (III, i, 65–71). Of course, Polaris will not "constantly" remain as the north star due to precession , but this

981-449: A qualitative characterization of a redshift. For example, if a Sun-like spectrum had a redshift of z = 1 , it would be brightest in the infrared (1000nm) rather than at the blue-green(500nm) color associated with the peak of its blackbody spectrum, and the light intensity will be reduced in the filter by a factor of four, (1 + z ) . Both the photon count rate and the photon energy are redshifted. (See K correction for more details on

1090-771: A remarkable change and is on record as saying that "if they are real, these changes are 100 times larger than [those] predicted by current theories of stellar evolution ". In 2024, researchers led by Nancy Evans at the Harvard & Smithsonian , have studied with more accuracy the Polaris' smaller companion orbit using the CHARA Array . During this observation campaign they have succeeded in shooting Polaris features on its surface; large bright places and dark ones have appeared in close-up images, changing over time. Further, Polaris diameter size has been re-measured to 46  R ☉ , using

1199-447: A shift in the frequency of electromagnetic radiation, including scattering and optical effects ; however, the resulting changes are distinguishable from (astronomical) redshift and are not generally referred to as such (see section on physical optics and radiative transfer ). The history of the subject began in the 19th century, with the development of classical wave mechanics and the exploration of phenomena which are associated with

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1308-428: A single emission or absorption line. By measuring the broadening and shifts of the 21-centimeter hydrogen line in different directions, astronomers have been able to measure the recessional velocities of interstellar gas , which in turn reveals the rotation curve of our Milky Way. Similar measurements have been performed on other galaxies, such as Andromeda . As a diagnostic tool, redshift measurements are one of

1417-521: A star at a distance of 7500 light-years = 2300 parsecs would appear to move an angle of / 2300 arc-seconds = 2 x 10 degrees, the resolution limit of the available telescopes.) The accepted explanation for the pulsation of Cepheids is called the Eddington valve, or " κ-mechanism ", where the Greek letter κ (kappa) is the usual symbol for the gas opacity. Helium is the gas thought to be most active in

1526-463: A strong direct relationship exists between a Cepheid variable's luminosity and its pulsation period . This characteristic of classical Cepheids was discovered in 1908 by Henrietta Swan Leavitt after studying thousands of variable stars in the Magellanic Clouds . The discovery establishes the true luminosity of a Cepheid by observing its pulsation period. This in turn gives the distance to

1635-403: A twofold increase in the distance to M31, and the extragalactic distance scale. RR Lyrae stars, then known as Cluster Variables, were recognized fairly early as being a separate class of variable, due in part to their short periods. The mechanics of stellar pulsation as a heat-engine was proposed in 1917 by Arthur Stanley Eddington (who wrote at length on the dynamics of Cepheids), but it

1744-509: A wide scatter from the standard Hubble Law . The resulting situation can be illustrated by the Expanding Rubber Sheet Universe , a common cosmological analogy used to describe the expansion of the universe. If two objects are represented by ball bearings and spacetime by a stretching rubber sheet, the Doppler effect is caused by rolling the balls across the sheet to create peculiar motion. The cosmological redshift occurs when

1853-401: Is a constant, called the pulsation constant. Redshift In physics , a redshift is an increase in the wavelength , and corresponding decrease in the frequency and photon energy , of electromagnetic radiation (such as light ). The opposite change, a decrease in wavelength and increase in frequency and energy, is known as a blueshift , or negative redshift. The terms derive from

1962-544: Is a triple star system , composed of the primary, a yellow supergiant designated Polaris Aa, in orbit with a smaller companion, Polaris Ab; the pair is in a wider orbit with Polaris B. The outer pair AB were discovered in August 1779 by William Herschel , where the 'A' refers to what is now known to be the Aa/Ab pair. Polaris Aa is an evolved yellow supergiant of spectral type F7Ib with 5.4 solar masses ( M ☉ ). It

2071-491: Is changing rapidly due to the precession of Earth's axis , going from 2.5h in AD 2000 to 6h in AD 2100. Twice in each sidereal day Polaris's azimuth is true north; the rest of the time it is displaced eastward or westward, and the bearing must be corrected using tables or a rule of thumb . The best approximation is made using the leading edge of the " Big Dipper " asterism in the constellation Ursa Major. The leading edge (defined by

2180-443: Is commonly attributed to stretching of the wavelengths of photons propagating through the expanding space. This interpretation can be misleading, however; expanding space is only a choice of coordinates and thus cannot have physical consequences. The cosmological redshift is more naturally interpreted as a Doppler shift arising due to the recession of distant objects. The observational consequences of this effect can be derived using

2289-469: Is listed as one of the navigational stars . The modern name Polaris is shortened from Neo-Latin stella polaris " polar star ", coined in the Renaissance when the star had approached the celestial pole to within a few degrees. Gemma Frisius , writing in 1547, referred to it as stella illa quae polaris dicitur ("that star which is called 'polar'"), placing it 3° 8' from the celestial pole. In 2016,

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2398-439: Is not moving away from the observer. Even when the source is moving towards the observer, if there is a transverse component to the motion then there is some speed at which the dilation just cancels the expected blueshift and at higher speed the approaching source will be redshifted. In the earlier part of the twentieth century, Slipher, Wirtz and others made the first measurements of the redshifts and blueshifts of galaxies beyond

2507-601: Is not required. The effect is very small but measurable on Earth using the Mössbauer effect and was first observed in the Pound–Rebka experiment . However, it is significant near a black hole , and as an object approaches the event horizon the red shift becomes infinite. It is also the dominant cause of large angular-scale temperature fluctuations in the cosmic microwave background radiation (see Sachs–Wolfe effect ). The redshift observed in astronomy can be measured because

2616-403: Is now increasing again, a reversal not seen in any other Cepheid. The period, roughly 4 days, has also changed over time. It has steadily increased by around 4.5 seconds per year except for a hiatus in 1963–1965. This was originally thought to be due to secular redward (a long term change in redshift that causes light to stretch into longer wavelengths, causing it to appear red) evolution across

2725-583: Is one of the foremost problems in astronomy since the cosmological parameters of the Universe may be constrained by supplying a precise value of the Hubble constant. Uncertainties have diminished over the years, due in part to discoveries such as RS Puppis . Delta Cephei is also of particular importance as a calibrator of the Cepheid period-luminosity relation since its distance is among the most precisely established for

2834-493: Is only noticeable over centuries. In Inuit astronomy , Polaris is known as Nuutuittuq ( syllabics : ᓅᑐᐃᑦᑐᖅ ). In traditional Lakota star knowledge, Polaris is named "Wičháȟpi Owáŋžila". This translates to "The Star that Sits Still". This name comes from a Lakota story in which he married Tȟapȟúŋ Šá Wíŋ, "Red Cheeked Woman". However, she fell from the heavens, and in his grief Wičháȟpi Owáŋžila stared down from "waŋkátu" (the above land) forever. The Plains Cree call

2943-469: Is the closest Cepheid variable to Earth so its physical parameters are of critical importance to the whole astronomical distance scale . It is also the only one with a dynamically measured mass. The Hipparcos spacecraft used stellar parallax to take measurements from 1989 and 1993 with the accuracy of 0.97  milliarcseconds (970 microarcseconds), and it obtained accurate measurements for stellar distances up to 1,000 pc away. The Hipparcos data

3052-417: Is the first classical Cepheid to have a mass determined from its orbit. The two smaller companions are Polaris B, a 1.39  M ☉ F3 main-sequence star orbiting at a distance of 2,400  astronomical units (AU), and Polaris Ab (or P), a very close F6 main-sequence star with a mass of 1.26  M ☉ . Polaris B can be resolved with a modest telescope. William Herschel discovered

3161-417: Is the present-day Hubble constant , and z is the redshift. There are several websites for calculating various times and distances from redshift, as the precise calculations require numerical integrals for most values of the parameters. For cosmological redshifts of z < 0.01 additional Doppler redshifts and blueshifts due to the peculiar motions of the galaxies relative to one another cause

3270-425: Is used instead. Redshifts cannot be calculated by looking at unidentified features whose rest-frame frequency is unknown, or with a spectrum that is featureless or white noise (random fluctuations in a spectrum). Redshift (and blueshift) may be characterized by the relative difference between the observed and emitted wavelengths (or frequency) of an object. In astronomy, it is customary to refer to this change using

3379-476: Is variable and unpredictable. The erratic changes of temperature and the amplitude of temperature changes during each cycle, from less than 50  K to at least 170 K, may be related to the orbit with Polaris Ab. Research reported in Science suggests that Polaris is 2.5 times brighter today than when Ptolemy observed it, changing from third to second magnitude. Astronomer Edward Guinan considers this to be

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3488-424: The 91st century . The celestial pole was close to Thuban around 2750 BC, and during classical antiquity it was slightly closer to Kochab (β UMi) than to Polaris, although still about 10 ° from either star. It was about the same angular distance from β UMi as to α UMi by the end of late antiquity . The Greek navigator Pytheas in ca. 320 BC described the celestial pole as devoid of stars. However, as one of

3597-589: The Canadian Inuit territory of Nunavut , the flag of the U.S. states of Alaska and Minnesota , and the flag of the U.S. city of Duluth, Minnesota . Cepheid variable A Cepheid variable ( / ˈ s ɛ f i . ɪ d , ˈ s iː f i -/ ) is a type of variable star that pulsates radially , varying in both diameter and temperature. It changes in brightness, with a well-defined stable period and amplitude. Cepheids are important cosmic benchmarks for scaling galactic and extragalactic distances ;

3706-456: The Doppler effect . Consequently, this type of redshift is called the Doppler redshift . If the source moves away from the observer with velocity v , which is much less than the speed of light ( v ≪ c ), the redshift is given by where c is the speed of light . In the classical Doppler effect, the frequency of the source is not modified, but the recessional motion causes the illusion of

3815-503: The Doppler effect . The effect is named after the Austrian mathematician, Christian Doppler , who offered the first known physical explanation for the phenomenon in 1842. In 1845, the hypothesis was tested and confirmed for sound waves by the Dutch scientist Christophorus Buys Ballot . Doppler correctly predicted that the phenomenon would apply to all waves and, in particular, suggested that

3924-583: The Friedmann–Lemaître equations . They are now considered to be strong evidence for an expanding universe and the Big Bang theory. The spectrum of light that comes from a source (see idealized spectrum illustration top-right) can be measured. To determine the redshift, one searches for features in the spectrum such as absorption lines , emission lines , or other variations in light intensity. If found, these features can be compared with known features in

4033-636: The Gaia distance of 446 ± 1 light-years, and its mass was determined at 5.13  M ☉ . Because Polaris lies nearly in a direct line with the Earth's rotational axis "above" the North Pole —the north celestial pole—Polaris stands almost motionless in the sky, and all the stars of the northern sky appear to rotate around it. Therefore, it makes an excellent fixed point from which to draw measurements for celestial navigation and for astrometry . The elevation of

4142-559: The International Astronomical Union organized a Working Group on Star Names (WGSN) to catalog and standardize proper names for stars. The WGSN's first bulletin of July 2016 included a table of the first two batches of names approved by the WGSN; which included Polaris for the star α Ursae Minoris Aa. In antiquity, Polaris was not yet the closest naked-eye star to the celestial pole, and the entire constellation of Ursa Minor

4251-585: The Lorentz factor γ into the classical Doppler formula as follows (for motion solely in the line of sight): This phenomenon was first observed in a 1938 experiment performed by Herbert E. Ives and G.R. Stilwell, called the Ives–Stilwell experiment . Since the Lorentz factor is dependent only on the magnitude of the velocity, this causes the redshift associated with the relativistic correction to be independent of

4360-671: The Milky Way . They initially interpreted these redshifts and blueshifts as being due to random motions, but later Lemaître (1927) and Hubble (1929), using previous data, discovered a roughly linear correlation between the increasing redshifts of, and distances to, galaxies. Lemaître realized that these observations could be explained by a mechanism of producing redshifts seen in Friedmann's solutions to Einstein's equations of general relativity . The correlation between redshifts and distances arises in all expanding models. This cosmological redshift

4469-458: The Schwarzschild geometry : In terms of escape velocity : for v e ≪ c {\displaystyle v_{\text{e}}\ll c} If a source of the light is moving away from an observer, then redshift ( z > 0 ) occurs; if the source moves towards the observer, then blueshift ( z < 0 ) occurs. This is true for all electromagnetic waves and is explained by

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4578-458: The Schwarzschild solution of the Einstein equations which yields the following formula for redshift associated with a photon traveling in the gravitational field of an uncharged , nonrotating , spherically symmetric mass: where This gravitational redshift result can be derived from the assumptions of special relativity and the equivalence principle ; the full theory of general relativity

4687-685: The T-rune is apparently associated with "a circumpolar constellation", or the planet Mars. In the Hindu Puranas , it became personified under the name Dhruva ("immovable, fixed"). In the later medieval period, it became associated with the Marian title of Stella Maris "Star of the Sea" (so in Bartholomaeus Anglicus , c. 1270s), due to an earlier transcription error. An older English name, attested since

4796-704: The brightness of astronomical objects through certain filters . When photometric data is all that is available (for example, the Hubble Deep Field and the Hubble Ultra Deep Field ), astronomers rely on a technique for measuring photometric redshifts . Due to the broad wavelength ranges in photometric filters and the necessary assumptions about the nature of the spectrum at the light-source, errors for these sorts of measurements can range up to δ z = 0.5 , and are much less reliable than spectroscopic determinations. However, photometry does at least allow

4905-451: The emission and absorption spectra for atoms are distinctive and well known, calibrated from spectroscopic experiments in laboratories on Earth. When the redshift of various absorption and emission lines from a single astronomical object is measured, z is found to be remarkably constant. Although distant objects may be slightly blurred and lines broadened, it is by no more than can be explained by thermal or mechanical motion of

5014-637: The "annual Doppler effect", the yearly change in the Doppler shift of stars located near the ecliptic, due to the orbital velocity of the Earth. In 1901, Aristarkh Belopolsky verified optical redshift in the laboratory using a system of rotating mirrors. Arthur Eddington used the term "red-shift" as early as 1923, although the word does not appear unhyphenated until about 1934, when Willem de Sitter used it. Beginning with observations in 1912, Vesto Slipher discovered that most spiral galaxies , then mostly thought to be spiral nebulae , had considerable redshifts. Slipher first reported on his measurement in

5123-563: The "circle described by the pole star about the pole". In Shakespeare's play Julius Caesar , written around 1599, Caesar describes himself as being "as constant as the northern star", though in Caesar's time there was no constant northern star. Despite its relative brightness, it is not, as is popularly believed, the brightest star in the sky. Polaris was referenced in Nathaniel Bowditch 's 1802 book, American Practical Navigator , where it

5232-473: The 14th century, is lodestar "guiding star", cognate with the Old Norse leiðarstjarna , Middle High German leitsterne . The ancient name of the constellation Ursa Minor, Cynosura (from the Greek κυνόσουρα "the dog's tail"), became associated with the pole star in particular by the early modern period. An explicit identification of Mary as stella maris with the polar star ( Stella Polaris ), as well as

5341-402: The Cepheid instability strip , but it may be due to interference between the primary and the first- overtone pulsation modes. Authors disagree on whether Polaris is a fundamental or first-overtone pulsator and on whether it is crossing the instability strip for the first time or not. The temperature of Polaris varies by only a small amount during its pulsations, but the amount of this variation

5450-452: The Doppler effect. The effect is sometimes called the "Doppler–Fizeau effect". In 1868, British astronomer William Huggins was the first to determine the velocity of a star moving away from the Earth by the method. In 1871, optical redshift was confirmed when the phenomenon was observed in Fraunhofer lines , using solar rotation, about 0.1 Å in the red. In 1887, Vogel and Scheiner discovered

5559-694: The Milky Way galaxy, such as the Sun's height above the galactic plane and the Galaxy's local spiral structure. A group of classical Cepheids with small amplitudes and sinusoidal light curves are often separated out as Small Amplitude Cepheids or s-Cepheids, many of them pulsating in the first overtone. Type II Cepheids (also termed Population II Cepheids) are population II variable stars which pulsate with periods typically between 1 and 50 days. Type II Cepheids are typically metal -poor, old (~10 Gyr), low mass objects (~half

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5668-458: The Polaris A system, with an eccentricity of 0.64. K. W. Kamper in 1996 produced refined elements with a period of 29.59 ± 0.02 years and an eccentricity of 0.608 ± 0.005 . In 2019, a study by R. I. Anderson gave a period of 29.32 ± 0.11 years with an eccentricity of 0.620 ± 0.008 . There were once thought to be two more widely separated components—Polaris C and Polaris D—but these have been shown not to be physically associated with

5777-433: The Polaris system. Polaris Aa, the supergiant primary component, is a low-amplitude Population I classical Cepheid variable , although it was once thought to be a type II Cepheid due to its high galactic latitude . Cepheids constitute an important standard candle for determining distance, so Polaris, as the closest such star, is heavily studied. The variability of Polaris had been suspected since 1852; this variation

5886-551: The Sun, and up to 100,000 times more luminous. These Cepheids are yellow bright giants and supergiants of spectral class F6 – K2 and their radii change by (~25% for the longer-period I Carinae ) millions of kilometers during a pulsation cycle. Classical Cepheids are used to determine distances to galaxies within the Local Group and beyond, and are a means by which the Hubble constant can be established. Classical Cepheids have also been used to clarify many characteristics of

5995-771: The adiabatic radial pulsation period for a homogeneous sphere is related to its surface gravity and radius through the relation: T = k R g {\displaystyle T=k\,{\sqrt {\frac {R}{g}}}} where k is a proportionality constant. Now, since the surface gravity is related to the sphere mass and radius through the relation: g = k ′ M R 2 = k ′ R M R 3 = k ′ R ρ {\displaystyle g=k'{\frac {M}{R^{2}}}=k'{\frac {RM}{R^{3}}}=k'R\rho } one finally obtains: T ρ = Q {\displaystyle T{\sqrt {\rho }}=Q} where Q

6104-406: The ball bearings are stuck to the sheet and the sheet is stretched. The redshifts of galaxies include both a component related to recessional velocity from expansion of the universe, and a component related to peculiar motion (Doppler shift). The redshift due to expansion of the universe depends upon the recessional velocity in a fashion determined by the cosmological model chosen to describe

6213-523: The brighter stars close to the celestial pole, Polaris was used for navigation at least from late antiquity, and described as ἀεί φανής ( aei phanēs ) "always visible" by Stobaeus (5th century), also termed Λύχνος ( Lychnos ) akin to a burner or lamp and would reasonably be described as stella polaris from about the High Middle Ages and onwards, both in Greek and Latin. On his first trans-Atlantic voyage in 1492, Christopher Columbus had to correct for

6322-565: The changes in velocity along the line of sight were due to a combination of the four-day pulsation period combined with a much longer orbital period and a large eccentricity of around 0.6. Moore published preliminary orbital elements of the system in 1929, giving an orbital period of about 29.7 years with an eccentricity of 0.63. This period was confirmed by proper motion studies performed by B. P. Gerasimovič in 1939. As part of her doctoral thesis, in 1955 E. Roemer used radial velocity data to derive an orbital period of 30.46 y for

6431-490: The colours red and blue which form the extremes of the visible light spectrum . The main causes of electromagnetic redshift in astronomy and cosmology are the relative motions of radiation sources, which give rise to the relativistic Doppler effect , and gravitational potentials, which gravitationally redshift escaping radiation. All sufficiently distant light sources show cosmological redshift corresponding to recession speeds proportional to their distances from Earth,

6540-564: The distance. The next major step in high precision parallax measurements comes from Gaia , a space astrometry mission launched in 2013 and intended to measure stellar parallax to within 25 microarcseconds (μas). Although it was originally planned to limit Gaia's observations to stars fainter than magnitude 5.7, tests carried out during the commissioning phase indicated that Gaia could autonomously identify stars as bright as magnitude 3. When Gaia entered regular scientific operations in July 2014, it

6649-406: The entire Universe or was merely one of many galaxies in the Universe. In 1929, Hubble and Milton L. Humason formulated what is now known as Hubble's law by combining Cepheid distances to several galaxies with Vesto Slipher 's measurements of the speed at which those galaxies recede from us. They discovered that the Universe is expanding , confirming the theories of Georges Lemaître . In

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6758-407: The equations from general relativity that describe a homogeneous and isotropic universe . The cosmological redshift can thus be written as a function of a , the time-dependent cosmic scale factor : In an expanding universe such as the one we inhabit, the scale factor is monotonically increasing as time passes, thus, z is positive and distant galaxies appear redshifted. Using a model of

6867-435: The expansion of the universe, redshift can be related to the age of an observed object, the so-called cosmic time –redshift relation . Denote a density ratio as Ω 0 : with ρ crit the critical density demarcating a universe that eventually crunches from one that simply expands. This density is about three hydrogen atoms per cubic meter of space. At large redshifts, 1 + z > Ω 0 , one finds: where H 0

6976-403: The expansion of the universe, which is very different from how Doppler redshift depends upon local velocity. Describing the cosmological expansion origin of redshift, cosmologist Edward Robert Harrison said, "Light leaves a galaxy, which is stationary in its local region of space, and is eventually received by observers who are stationary in their own local region of space. Between the galaxy and

7085-458: The fact doubly ionized helium, the form adopted at high temperatures, is more opaque than singly ionized helium. As a result, the outer layer of the star cycles between being compressed, which heats the helium until it becomes doubly ionized and (due to opacity) absorbs enough heat to expand; and expanded, which cools the helium until it becomes singly ionized and (due to transparency) cools and collapses again. Cepheid variables become dimmest during

7194-403: The full form for the relativistic Doppler effect becomes: and for motion solely in the line of sight ( θ = 0° ), this equation reduces to: For the special case that the light is moving at right angle ( θ = 90° ) to the direction of relative motion in the observer's frame, the relativistic redshift is known as the transverse redshift , and a redshift: is measured, even though the object

7303-475: The inaugural volume of the Lowell Observatory Bulletin . Three years later, he wrote a review in the journal Popular Astronomy . In it he stated that "the early discovery that the great Andromeda spiral had the quite exceptional velocity of –300 km(/s) showed the means then available, capable of investigating not only the spectra of the spirals but their velocities as well." Slipher reported

7412-475: The instability strip have periods of less than 2 days, similar to RR Lyrae variables but with higher luminosities. Anomalous Cepheid variables have masses higher than type II Cepheids, RR Lyrae variables, and the Sun. It is unclear whether they are young stars on a "turned-back" horizontal branch, blue stragglers formed through mass transfer in binary systems, or a mix of both. A small proportion of Cepheid variables have been observed to pulsate in two modes at

7521-519: The instability strip where it crosses the horizontal branch . Delta Scuti variables and RR Lyrae variables are not generally treated with Cepheid variables although their pulsations originate with the same helium ionisation kappa mechanism . Classical Cepheids (also known as Population I Cepheids, type I Cepheids, or Delta Cepheid variables) undergo pulsations with very regular periods on the order of days to months. Classical Cepheids are Population I variable stars which are 4–20 times more massive than

7630-640: The mass of the Sun). Type II Cepheids are divided into several subgroups by period. Stars with periods between 1 and 4 days are of the BL Her subclass , 10–20 days belong to the W Virginis subclass , and stars with periods greater than 20 days belong to the RV Tauri subclass . Type II Cepheids are used to establish the distance to the Galactic Center , globular clusters , and galaxies . A group of pulsating stars on

7739-731: The mid 20th century, significant problems with the astronomical distance scale were resolved by dividing the Cepheids into different classes with very different properties. In the 1940s, Walter Baade recognized two separate populations of Cepheids (classical and type II). Classical Cepheids are younger and more massive population I stars, whereas type II Cepheids are older, fainter Population II stars. Classical Cepheids and type II Cepheids follow different period-luminosity relationships. The luminosity of type II Cepheids is, on average, less than classical Cepheids by about 1.5 magnitudes (but still brighter than RR Lyrae stars). Baade's seminal discovery led to

7848-439: The most important spectroscopic measurements made in astronomy. The most distant objects exhibit larger redshifts corresponding to the Hubble flow of the universe . The largest-observed redshift, corresponding to the greatest distance and furthest back in time, is that of the cosmic microwave background radiation; the numerical value of its redshift is about z = 1089 ( z = 0 corresponds to present time), and it shows

7957-449: The observer with the light shifting to greater energies . Conversely, Doppler effect redshifts ( z > 0 ) are associated with objects receding (moving away) from the observer with the light shifting to lower energies. Likewise, gravitational blueshifts are associated with light emitted from a source residing within a weaker gravitational field as observed from within a stronger gravitational field, while gravitational redshifting implies

8066-410: The observer, light travels through vast regions of expanding space. As a result, all wavelengths of the light are stretched by the expansion of space. It is as simple as that..." Steven Weinberg clarified, "The increase of wavelength from emission to absorption of light does not depend on the rate of change of a ( t ) [the scale factor ] at the times of emission or absorption, but on the increase of

8175-439: The opposite conditions. In general relativity one can derive several important special-case formulae for redshift in certain special spacetime geometries, as summarized in the following table. In all cases the magnitude of the shift (the value of z ) is independent of the wavelength. For motion completely in the radial or line-of-sight direction: For motion completely in the transverse direction: Hubble's law : For

8284-400: The orientation of the source movement. In contrast, the classical part of the formula is dependent on the projection of the movement of the source into the line-of-sight which yields different results for different orientations. If θ is the angle between the direction of relative motion and the direction of emission in the observer's frame (zero angle is directly away from the observer),

8393-409: The part of the cycle when the helium is doubly ionized. The term Cepheid originates from the star Delta Cephei in the constellation Cepheus , which was one of the early discoveries. On September 10, 1784, Edward Pigott detected the variability of Eta Aquilae , the first known representative of the class of classical Cepheid variables. The eponymous star for classical Cepheids, Delta Cephei ,

8502-525: The photometric consequences of redshift.) In nearby objects (within our Milky Way galaxy) observed redshifts are almost always related to the line-of-sight velocities associated with the objects being observed. Observations of such redshifts and blueshifts have enabled astronomers to measure velocities and parametrize the masses of the orbiting stars in spectroscopic binaries , a method first employed in 1868 by British astronomer William Huggins . Similarly, small redshifts and blueshifts detected in

8611-552: The precise movements of the photosphere of the Sun . Redshifts have also been used to make the first measurements of the rotation rates of planets , velocities of interstellar clouds , the rotation of galaxies , and the dynamics of accretion onto neutron stars and black holes which exhibit both Doppler and gravitational redshifts. The temperatures of various emitting and absorbing objects can be obtained by measuring Doppler broadening —effectively redshifts and blueshifts over

8720-416: The process. Doubly ionized helium (helium whose atoms are missing both electrons) is more opaque than singly ionized helium. As helium is heated, its temperature rises until it reaches the point at which double ionisation spontaneously occurs and is sustained throughout the layer in much the same way a fluorescent tube 'strikes'. At the dimmest part of a Cepheid's cycle, this ionized gas in the outer layers of

8829-417: The prototype ζ Geminorum . A relationship between the period and luminosity for classical Cepheids was discovered in 1908 by Henrietta Swan Leavitt in an investigation of thousands of variable stars in the Magellanic Clouds . She published it in 1912 with further evidence. Cepheid variables were found to show radial velocity variation with the same period as the luminosity variation, and initially this

8938-411: The redshift, one has to know the wavelength of the emitted light in the rest frame of the source: in other words, the wavelength that would be measured by an observer located adjacent to and comoving with the source. Since in astronomical applications this measurement cannot be done directly, because that would require traveling to the distant star of interest, the method using spectral lines described here

9047-419: The same pattern of intervals is seen in an observed spectrum from a distant source but occurring at shifted wavelengths, it can be identified as hydrogen too. If the same spectral line is identified in both spectra—but at different wavelengths—then the redshift can be calculated using the table below. Determining the redshift of an object in this way requires a frequency or wavelength range. In order to calculate

9156-400: The same time, usually the fundamental and first overtone, occasionally the second overtone. A very small number pulsate in three modes, or an unusual combination of modes including higher overtones. Chief among the uncertainties tied to the classical and type II Cepheid distance scale are: the nature of the period-luminosity relation in various passbands , the impact of metallicity on both

9265-464: The size and shape of the Milky Way and of the placement of the Sun within it. In 1924, Edwin Hubble established the distance to classical Cepheid variables in the Andromeda Galaxy , until then known as the "Andromeda Nebula " and showed that those variables were not members of the Milky Way. Hubble's finding settled the question raised in the " Great Debate " of whether the Milky Way represented

9374-416: The source. For these reasons and others, the consensus among astronomers is that the redshifts they observe are due to some combination of the three established forms of Doppler-like redshifts. Alternative hypotheses and explanations for redshift such as tired light are not generally considered plausible. Spectroscopy, as a measurement, is considerably more difficult than simple photometry , which measures

9483-422: The spectroscopic measurements of individual stars are one way astronomers have been able to diagnose and measure the presence and characteristics of planetary systems around other stars and have even made very detailed differential measurements of redshifts during planetary transits to determine precise orbital parameters. Finely detailed measurements of redshifts are used in helioseismology to determine

9592-416: The spectrum of various chemical compounds found in experiments where that compound is located on Earth. A very common atomic element in space is hydrogen . The spectrum of originally featureless light shone through hydrogen will show a signature spectrum specific to hydrogen that has features at regular intervals. If restricted to absorption lines it would look similar to the illustration (top right). If

9701-463: The star above the horizon gives the approximate latitude of the observer. In 2018 Polaris was 0.66° (39.6 arcminutes) away from the pole of rotation (1.4 times the Moon disc) and so revolves around the pole in a small circle 1.3° in diameter. It will be closest to the pole (about 0.45 degree, or 27 arcminutes) soon after the year 2100. Because it is so close to the celestial north pole, its right ascension

9810-401: The star by comparing its known luminosity to its observed brightness, calibrated by directly observing the parallax distance to the closest Cepheids such as RS Puppis and Polaris . Cepheids change brightness due to the κ–mechanism , which occurs when opacity in a star increases with temperature rather than decreasing. The main gas involved is thought to be helium . The cycle is driven by

9919-514: The star in Nehiyawewin : acâhkos êkâ kâ-âhcît "the star that does not move" ( syllabics : ᐊᒑᐦᑯᐢ ᐁᑳ ᑳ ᐋᐦᒌᐟ ). In Mi'kmawi'simk the star is named Tatapn . In the ancient Finnish worldview, the North Star has also been called taivaannapa and naulatähti ("the nailstar") because it seems to be attached to the firmament or even to act as a fastener for the sky when other stars orbit it. Since

10028-456: The star in August 1779 using a reflecting telescope of his own, one of the best telescopes of the time. In January 2006, NASA released images, from the Hubble telescope , that showed the three members of the Polaris ternary system. The variable radial velocity of Polaris A was reported by W. W. Campbell in 1899, which suggested this star is a binary system. Since Polaris A is a known cepheid variable, J. H. Moore in 1927 demonstrated that

10137-403: The star is relatively opaque, and so is heated by the star's radiation, and due to the increasing temperature, begins to expand. As it expands, it cools, but remains ionised until another threshold is reached at which point double ionization cannot be sustained and the layer becomes singly ionized hence more transparent, which allows radiation to escape. The expansion then stops, and reverses due to

10246-418: The star's gravitational attraction. The star's states are held to be either expanding or contracting by the hysterisis generated by the doubly ionized helium and indefinitely flip-flops between the two states reversing every time the upper or lower threshold is crossed. This process is rather analogous to the relaxation oscillator found in electronics. In 1879, August Ritter (1826–1908) demonstrated that

10355-581: The starry sky seemed to rotate around it, the firmament is thought of as a wheel, with the star as the pivot on its axis. The names derived from it were sky pin and world pin . Many recent papers calculate the distance to Polaris at about 433 light-years (133 parsecs), based on parallax measurements from the Hipparcos astrometry satellite. Older distance estimates were often slightly less, and research based on high resolution spectral analysis suggests it may be up to 110 light years closer (323 ly/99 pc). Polaris

10464-427: The stars Dubhe and Merak ) is referenced to a clock face, and the true azimuth of Polaris worked out for different latitudes. The apparent motion of Polaris towards and, in the future, away from the celestial pole, is due to the precession of the equinoxes . The celestial pole will move away from α UMi after the 21st century, passing close by Gamma Cephei by about the 41st century , moving towards Deneb by about

10573-550: The use of Cynosura as a name of the star, is evident in the title Cynosura seu Mariana Stella Polaris (i.e. "Cynosure, or the Marian Polar Star"), a collection of Marian poetry published by Nicolaus Lucensis (Niccolo Barsotti de Lucca) in 1655. Its name in traditional pre-Islamic Arab astronomy was al-Judayy الجدي ("the kid", in the sense of a juvenile goat ["le Chevreau"] in Description des Etoiles fixes), and that name

10682-443: The varying colors of stars could be attributed to their motion with respect to the Earth. Before this was verified, it was found that stellar colors were primarily due to a star's temperature , not motion. Only later was Doppler vindicated by verified redshift observations. The Doppler redshift was first described by French physicist Hippolyte Fizeau in 1848, who noted the shift in spectral lines seen in stars as being due to

10791-498: The velocities for 15 spiral nebulae spread across the entire celestial sphere , all but three having observable "positive" (that is recessional) velocities. Subsequently, Edwin Hubble discovered an approximate relationship between the redshifts of such "nebulae", and the distances to them, with the formulation of his eponymous Hubble's law . Milton Humason worked on those observations with Hubble. These observations corroborated Alexander Friedmann 's 1922 work, in which he derived

10900-456: The wavelength ratio 1 + z (which is greater than 1 for redshifts and less than 1 for blueshifts). Examples of strong redshifting are a gamma ray perceived as an X-ray , or initially visible light perceived as radio waves . Subtler redshifts are seen in the spectroscopic observations of astronomical objects, and are used in terrestrial technologies such as Doppler radar and radar guns . Other physical processes exist that can lead to

11009-468: The zero-point and slope of those relations, and the effects of photometric contamination (blending with other stars) and a changing (typically unknown) extinction law on Cepheid distances. All these topics are actively debated in the literature. These unresolved matters have resulted in cited values for the Hubble constant (established from Classical Cepheids) ranging between 60 km/s/Mpc and 80 km/s/Mpc. Resolving this discrepancy

11118-428: Was configured to routinely process stars in the magnitude range 3 – 20. Beyond that limit, special procedures are used to download raw scanning data for the remaining 230 stars brighter than magnitude 3; methods to reduce and analyse these data are being developed; and it is expected that there will be "complete sky coverage at the bright end" with standard errors of "a few dozen μas". Gaia Data Release 2 does not include

11227-411: Was confirmed by Ejnar Hertzsprung in 1911. The range of brightness of Polaris is given as 1.86–2.13, but the amplitude has changed since discovery. Prior to 1963, the amplitude was over 0.1 magnitude and was very gradually decreasing. After 1966, it very rapidly decreased until it was less than 0.05 magnitude; since then, it has erratically varied near that range. It has been reported that the amplitude

11336-402: Was discovered to be variable by John Goodricke a few months later. The number of similar variables grew to several dozen by the end of the 19th century, and they were referred to as a class as Cepheids. Most of the Cepheids were known from the distinctive light curve shapes with the rapid increase in brightness and a hump, but some with more symmetrical light curves were known as Geminids after

11445-432: Was examined again with more advanced error correction and statistical techniques. Despite the advantages of Hipparcos astrometry , the uncertainty in its Polaris data has been pointed out and some researchers have questioned the accuracy of Hipparcos when measuring binary Cepheids like Polaris. The Hipparcos reduction specifically for Polaris has been re-examined and reaffirmed but there is still not widespread agreement about

11554-520: Was interpreted as evidence that these stars were part of a binary system . However, in 1914, Harlow Shapley demonstrated that this idea should be abandoned. Two years later, Shapley and others had discovered that Cepheid variables changed their spectral types over the course of a cycle. In 1913, Ejnar Hertzsprung attempted to find distances to 13 Cepheids using their motion through the sky. (His results would later require revision.) In 1918, Harlow Shapley used Cepheids to place initial constraints on

11663-491: Was not until 1953 that S. A. Zhevakin identified ionized helium as a likely valve for the engine. Cepheid variables are divided into two subclasses which exhibit markedly different masses, ages, and evolutionary histories: classical Cepheids and type II Cepheids . Delta Scuti variables are A-type stars on or near the main sequence at the lower end of the instability strip and were originally referred to as dwarf Cepheids. RR Lyrae variables have short periods and lie on

11772-468: Was used for navigation rather than any single star. Polaris moved close enough to the pole to be the closest naked-eye star, even though still at a distance of several degrees, in the early medieval period, and numerous names referring to this characteristic as polar star have been in use since the medieval period. In Old English, it was known as scip-steorra ("ship-star") . In the Old English rune poem ,

11881-527: Was used in medieval Islamic astronomy as well. In those times, it was not yet as close to the north celestial pole as it is now, and used to rotate around the pole. It was invoked as a symbol of steadfastness in poetry, as "steadfast star" by Spenser . Shakespeare 's sonnet 116 is an example of the symbolism of the north star as a guiding principle: "[Love] is the star to every wandering bark / Whose worth's unknown, although his height be taken." In Julius Caesar , he has Caesar explain his refusal to grant

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