Misplaced Pages

#840159

128-898: The IceCube Neutrino Observatory (or simply IceCube ) is a neutrino observatory developed by the University of Wisconsin–Madison and constructed at the Amundsen–Scott South Pole Station in Antarctica . The project is a recognized CERN experiment (RE10). Its thousands of sensors are located under the Antarctic ice, distributed over a cubic kilometer . Similar to its predecessor, the Antarctic Muon And Neutrino Detector Array (AMANDA), IceCube consists of spherical optical sensors called Digital Optical Modules (DOMs), each with

256-416: A B x , a B y , a B z ) {\displaystyle \mathbf {a} _{B}=\left(a_{B_{x}},a_{B_{y}},a_{B_{z}}\right)} then the acceleration of point C relative to point B is the difference between their components: a C / B = a C − a B = (

384-460: A C x − a B x , a C y − a B y , a C z − a B z ) {\displaystyle \mathbf {a} _{C/B}=\mathbf {a} _{C}-\mathbf {a} _{B}=\left(a_{C_{x}}-a_{B_{x}},a_{C_{y}}-a_{B_{y}},a_{C_{z}}-a_{B_{z}}\right)} Alternatively, this same result could be obtained by computing

512-443: A | = | v ˙ | = d v d t . {\displaystyle |\mathbf {a} |=|{\dot {\mathbf {v} }}|={\frac {{\text{d}}v}{{\text{d}}t}}.} A relative position vector is a vector that defines the position of one point relative to another. It is the difference in position of the two points. The position of one point A relative to another point B

640-541: A τ ) d τ = r 0 + v 0 t + 1 2 a t 2 . {\displaystyle \mathbf {r} (t)=\mathbf {r} _{0}+\int _{0}^{t}\mathbf {v} (\tau )\,{\text{d}}\tau =\mathbf {r} _{0}+\int _{0}^{t}\left(\mathbf {v} _{0}+\mathbf {a} \tau \right){\text{d}}\tau =\mathbf {r} _{0}+\mathbf {v} _{0}t+{\tfrac {1}{2}}\mathbf {a} t^{2}.} Additional relations between displacement, velocity, acceleration, and time can be derived. Since

768-439: A x x ^ + a y y ^ + a z z ^ . {\displaystyle \mathbf {a} =\lim _{(\Delta t)^{2}\to 0}{\frac {\Delta \mathbf {r} }{(\Delta t)^{2}}}={\frac {{\text{d}}^{2}\mathbf {r} }{{\text{d}}t^{2}}}=a_{x}{\hat {\mathbf {x} }}+a_{y}{\hat {\mathbf {y} }}+a_{z}{\hat {\mathbf {z} }}.} Thus, acceleration

896-616: A y y ^ + a z z ^ . {\displaystyle \mathbf {a} =\lim _{\Delta t\to 0}{\frac {\Delta \mathbf {v} }{\Delta t}}={\frac {{\text{d}}\mathbf {v} }{{\text{d}}t}}=a_{x}{\hat {\mathbf {x} }}+a_{y}{\hat {\mathbf {y} }}+a_{z}{\hat {\mathbf {z} }}.} Alternatively, a = lim ( Δ t ) 2 → 0 Δ r ( Δ t ) 2 = d 2 r d t 2 =

1024-638: A ¯ x x ^ + a ¯ y y ^ + a ¯ z z ^ {\displaystyle \mathbf {\bar {a}} ={\frac {\Delta \mathbf {\bar {v}} }{\Delta t}}={\frac {\Delta {\bar {v}}_{x}}{\Delta t}}{\hat {\mathbf {x} }}+{\frac {\Delta {\bar {v}}_{y}}{\Delta t}}{\hat {\mathbf {y} }}+{\frac {\Delta {\bar {v}}_{z}}{\Delta t}}{\hat {\mathbf {z} }}={\bar {a}}_{x}{\hat {\mathbf {x} }}+{\bar {a}}_{y}{\hat {\mathbf {y} }}+{\bar {a}}_{z}{\hat {\mathbf {z} }}\,} where Δ v

1152-564: A + v ω ) θ ^ + a z z ^ . {\displaystyle \mathbf {a} _{P}={\frac {\text{d}}{{\text{d}}t}}\left(v{\hat {\mathbf {r} }}+v{\hat {\mathbf {\theta } }}+v_{z}{\hat {\mathbf {z} }}\right)=(a-v\theta ){\hat {\mathbf {r} }}+(a+v\omega ){\hat {\mathbf {\theta } }}+a_{z}{\hat {\mathbf {z} }}.} The term − v θ r ^ {\displaystyle -v\theta {\hat {\mathbf {r} }}} acts toward

1280-486: A t t = 1 2 a t 2 = a t 2 2 {\textstyle A={\frac {1}{2}}BH={\frac {1}{2}}att={\frac {1}{2}}at^{2}={\frac {at^{2}}{2}}} . Adding v 0 t {\displaystyle v_{0}t} and a t 2 2 {\textstyle {\frac {at^{2}}{2}}} results in the equation Δ r {\displaystyle \Delta r} results in

1408-505: A neutrino burst from supernova SN 1987A . Scientists detected 19 neutrinos from an explosion of a star inside the Large Magellanic Cloud – only 19 out of the octo-decillion (10 ) neutrinos emitted by the supernova. The Kamiokande detector was able to detect the burst of neutrinos associated with this supernova, and in 1988 it was used to directly confirm the production of solar neutrinos. The largest such detector

SECTION 10

#1732772078841

1536-406: A photomultiplier tube (PMT) and a single-board data acquisition computer which sends digital data to the counting house on the surface above the array. IceCube was completed on 18 December 2010. DOMs are deployed on strings of 60 modules each at depths between 1,450 and 2,450 meters into holes melted in the ice using a hot water drill. IceCube is designed to look for point sources of neutrinos in

1664-505: A "double bang" event, where a cascade is seen both at the tau creation and decay. This is only possible with very high energy taus. Hypothetically, to resolve a tau track, the tau would need to travel at least from one DOM to an adjacent DOM (17 m) before decaying. As the average lifetime of a tau is 2.9 × 10 s , a tau traveling at near the speed of light would require 20 TeV of energy for every meter traveled. Realistically, an experimenter would need more space than just one DOM to

1792-628: A convenient form. Recall that the trajectory of a particle P is defined by its coordinate vector r measured in a fixed reference frame F . As the particle moves, its coordinate vector r ( t ) traces its trajectory, which is a curve in space, given by: r ( t ) = x ( t ) x ^ + y ( t ) y ^ + z ( t ) z ^ , {\displaystyle \mathbf {r} (t)=x(t){\hat {\mathbf {x} }}+y(t){\hat {\mathbf {y} }}+z(t){\hat {\mathbf {z} }},} where x̂ , ŷ , and ẑ are

1920-686: A detector does travel somewhat faster than the speed of light in the detector medium (although somewhat slower than the speed of light in vacuum ). The charged lepton generates a visible "optical shockwave" of Cherenkov radiation . This radiation is detected by the photomultiplier tubes and shows up as a characteristic ring-like pattern of activity in the array of photomultiplier tubes. As neutrinos can interact with atomic nuclei to produce charged leptons which emit Cherenkov radiation, this pattern can be used to infer direction, energy, and (sometimes) flavor information about incident neutrinos. Two water-filled detectors of this type ( Kamiokande and IMB ) recorded

2048-410: A long penetrating track and is easy to spot; The length of this muon track and its curvature in the magnetic field provide energy and charge ( μ versus μ ) information. An electron in the detector produces an electromagnetic shower, which can be distinguished from hadronic showers if the granularity of the active detector is small compared to the physical extent of

2176-540: A mechanism for a desired range of motion. In addition, kinematics applies algebraic geometry to the study of the mechanical advantage of a mechanical system or mechanism. The term kinematic is the English version of A.M. Ampère 's cinématique , which he constructed from the Greek κίνημα kinema ("movement, motion"), itself derived from κινεῖν kinein ("to move"). Kinematic and cinématique are related to

2304-954: A particle trajectory on a circular cylinder occurs when there is no movement along the z axis: r ( t ) = r r ^ + z z ^ , {\displaystyle \mathbf {r} (t)=r{\hat {\mathbf {r} }}+z{\hat {\mathbf {z} }},} where r and z 0 are constants. In this case, the velocity v P is given by: v P = d d t ( r r ^ + z z ^ ) = r ω θ ^ = v θ ^ , {\displaystyle \mathbf {v} _{P}={\frac {\text{d}}{{\text{d}}t}}\left(r{\hat {\mathbf {r} }}+z{\hat {\mathbf {z} }}\right)=r\omega {\hat {\mathbf {\theta } }}=v{\hat {\mathbf {\theta } }},} where ω {\displaystyle \omega }

2432-632: A particle's velocity is the time rate of change of its position. Furthermore, this velocity is tangent to the particle's trajectory at every position along its path. In a non-rotating frame of reference, the derivatives of the coordinate directions are not considered as their directions and magnitudes are constants. The speed of an object is the magnitude of its velocity. It is a scalar quantity: v = | v | = d s d t , {\displaystyle v=|\mathbf {v} |={\frac {{\text{d}}s}{{\text{d}}t}},} where s {\displaystyle s}

2560-435: A phenomenon called Cherenkov light . Cherenkov radiation is produced whenever charged particles such as electrons or muons are moving through a given detector medium somewhat faster than the speed of light in that medium . In a Cherenkov detector, a large volume of clear material such as water or ice is surrounded by light-sensitive photomultiplier tubes. A charged lepton produced with sufficient energy and moving through such

2688-819: A reference frame. The position vector of a particle is a vector drawn from the origin of the reference frame to the particle. It expresses both the distance of the point from the origin and its direction from the origin. In three dimensions, the position vector r {\displaystyle {\bf {r}}} can be expressed as r = ( x , y , z ) = x x ^ + y y ^ + z z ^ , {\displaystyle \mathbf {r} =(x,y,z)=x{\hat {\mathbf {x} }}+y{\hat {\mathbf {y} }}+z{\hat {\mathbf {z} }},} where x {\displaystyle x} , y {\displaystyle y} , and z {\displaystyle z} are

SECTION 20

#1732772078841

2816-450: A solution of cadmium chloride in water. Two scintillation detectors were placed next to the water targets. Antineutrinos with an energy above the threshold of 1.8 MeV caused charged current " Inverse beta decay " interactions with the protons in the water, producing positrons and neutrons. The resulting positrons annihilate with electrons, creating pairs of coincident photons with an energy of about 0.5 MeV each, which could be detected by

2944-501: A tank filled with a chlorine-containing fluid such as tetrachloroethylene . A neutrino occasionally converts a chlorine -37 atom into one of argon -37 via the charged current interaction. The threshold neutrino energy for this reaction is 0.814 MeV. The fluid is periodically purged with helium gas which would remove the argon. The helium is then cooled to separate out the argon, and the argon atoms are counted based on their electron capture radioactive decays. A chlorine detector in

3072-551: A time interval is defined as the ratio. a ¯ = Δ v ¯ Δ t = Δ v ¯ x Δ t x ^ + Δ v ¯ y Δ t y ^ + Δ v ¯ z Δ t z ^ =

3200-407: A very large active detector volume. Tracking calorimeters are only useful for high-energy ( GeV range) neutrinos. At these energies, neutral current interactions appear as a shower of hadronic debris and charged current interactions are identified by the presence of the charged lepton's track (possibly alongside some form of hadronic debris). A muon produced in a charged current interaction leaves

3328-543: Is a proposed extension that will allow detection of low energy neutrinos (GeV energy scale), with uses including determining the neutrino mass hierarchy, precision measurement of atmospheric neutrino oscillation (both tau neutrino appearance and muon neutrino disappearance), and searching for WIMP annihilation in the Sun. A vision has been presented for a larger observatory, IceCube-Gen2. Neutrinos are electrically neutral leptons , and only interact very rarely with matter through

3456-401: Is defined as the coordinate vector from the origin of a coordinate frame to the particle. For example, consider a tower 50 m south from your home, where the coordinate frame is centered at your home, such that east is in the direction of the x -axis and north is in the direction of the y -axis, then the coordinate vector to the base of the tower is r = (0 m, −50 m, 0 m). If

3584-451: Is sensitive mostly to high-energy neutrinos, in the range of 10 to about 10  eV . IceCube is more sensitive to muons than other charged leptons, because they are the most penetrating and thus have the longest tracks in the detector. Thus, of the neutrino flavors, IceCube is most sensitive to muon neutrinos . An electron resulting from an electron neutrino event typically scatters several times before losing enough energy to fall below

3712-608: Is sensitive to lower-energy neutrinos. A neutrino is able to react with an atom of gallium-71, converting it into an atom of the unstable isotope germanium-71. The germanium was then chemically extracted and concentrated. Neutrinos were thus detected by measuring the radioactive decay of germanium. This latter method is nicknamed the " Alsace-Lorraine " technique in a joke-reference to the Ga → Ge → Ga reaction sequence. The SAGE experiment in Russia used about 50 tons of gallium , and

3840-602: Is simply the difference between their positions which is the difference between the components of their position vectors. If point A has position components r A = ( x A , y A , z A ) {\displaystyle \mathbf {r} _{A}=\left(x_{A},y_{A},z_{A}\right)} and point B has position components r B = ( x B , y B , z B ) {\displaystyle \mathbf {r} _{B}=\left(x_{B},y_{B},z_{B}\right)} then

3968-882: Is simply the difference between their velocities v A / B = v A − v B {\displaystyle \mathbf {v} _{A/B}=\mathbf {v} _{A}-\mathbf {v} _{B}} which is the difference between the components of their velocities. If point A has velocity components v A = ( v A x , v A y , v A z ) {\displaystyle \mathbf {v} _{A}=\left(v_{A_{x}},v_{A_{y}},v_{A_{z}}\right)} and point B has velocity components v B = ( v B x , v B y , v B z ) {\displaystyle \mathbf {v} _{B}=\left(v_{B_{x}},v_{B_{y}},v_{B_{z}}\right)} then

IceCube Neutrino Observatory - Misplaced Pages Continue

4096-594: Is the angular velocity of the unit vector θ around the z axis of the cylinder. The acceleration a P of the particle P is now given by: a P = d ( v θ ^ ) d t = a θ ^ − v θ r ^ . {\displaystyle \mathbf {a} _{P}={\frac {{\text{d}}(v{\hat {\mathbf {\theta } }})}{{\text{d}}t}}=a{\hat {\mathbf {\theta } }}-v\theta {\hat {\mathbf {r} }}.} The components

4224-417: Is the arc-length measured along the trajectory of the particle. This arc-length must always increase as the particle moves. Hence, d s / d t {\displaystyle {\text{d}}s/{\text{d}}t} is non-negative, which implies that speed is also non-negative. The velocity vector can change in magnitude and in direction or both at once. Hence, the acceleration accounts for both

4352-411: Is the area under a velocity–time graph. We can take Δ r {\displaystyle \Delta r} by adding the top area and the bottom area. The bottom area is a rectangle, and the area of a rectangle is the A ⋅ B {\displaystyle A\cdot B} where A {\displaystyle A} is the width and B {\displaystyle B}

4480-441: Is the average velocity and Δ t is the time interval. The acceleration of the particle is the limit of the average acceleration as the time interval approaches zero, which is the time derivative, a = lim Δ t → 0 Δ v Δ t = d v d t = a x x ^ +

4608-948: Is the displacement vector during the time interval Δ t {\displaystyle \Delta t} . In the limit that the time interval Δ t {\displaystyle \Delta t} approaches zero, the average velocity approaches the instantaneous velocity, defined as the time derivative of the position vector, v = lim Δ t → 0 Δ r Δ t = d r d t = v x x ^ + v y y ^ + v z z ^ . {\displaystyle \mathbf {v} =\lim _{\Delta t\to 0}{\frac {\Delta \mathbf {r} }{\Delta t}}={\frac {{\text{d}}\mathbf {r} }{{\text{d}}t}}=v_{x}{\hat {\mathbf {x} }}+v_{y}{\hat {\mathbf {y} }}+v_{z}{\hat {\mathbf {z} }}.} Thus,

4736-406: Is the first derivative of the velocity vector and the second derivative of the position vector of that particle. In a non-rotating frame of reference, the derivatives of the coordinate directions are not considered as their directions and magnitudes are constants. The magnitude of the acceleration of an object is the magnitude | a | of its acceleration vector. It is a scalar quantity: |

4864-423: Is the height. In this case A = t {\displaystyle A=t} and B = v 0 {\displaystyle B=v_{0}} (the A {\displaystyle A} here is different from the acceleration a {\displaystyle a} ). This means that the bottom area is t v 0 {\displaystyle tv_{0}} . Now let's find

4992-451: Is the water-filled Super-Kamiokande . This detector uses 50,000 tons of pure water surrounded by 11,000 photomultiplier tubes buried 1 km underground. The Sudbury Neutrino Observatory (SNO) used 1,000 tonnes of ultrapure heavy water contained in a 12 metre-diameter vessel made of acrylic plastic surrounded by a cylinder of ultrapure ordinary water 22 metres in diameter and 34 metres high. In addition to

5120-441: Is to other neutrino experiments, such as Super-K (with inward-facing PMTs fixing the fiducial volume). IceCube is more sensitive to point sources in the northern hemisphere than in the southern hemisphere. It can observe astrophysical neutrino signals from any direction, but neutrinos coming from the direction of the southern hemisphere are swamped by the cosmic-ray muon background. Thus, early IceCube point source searches focus on

5248-412: Is used in astrophysics to describe the motion of celestial bodies and collections of such bodies. In mechanical engineering , robotics , and biomechanics , kinematics is used to describe the motion of systems composed of joined parts (multi-link systems) such as an engine , a robotic arm or the human skeleton . Geometric transformations, also called rigid transformations , are used to describe

IceCube Neutrino Observatory - Misplaced Pages Continue

5376-591: The Big Bang , and others are generated by nuclear reactions inside stars, planets, and by other interstellar processes. According to scientists' speculations, some may also originate from events in the universe such as "colliding black holes, gamma ray bursts from exploding stars, and/or violent events at the cores of distant galaxies". Despite how common they are, neutrinos are extremely difficult to detect, due to their low mass and lack of electric charge. Unlike other particles, neutrinos only interact via gravity and

5504-602: The Cartesian coordinates and x ^ {\displaystyle {\hat {\mathbf {x} }}} , y ^ {\displaystyle {\hat {\mathbf {y} }}} and z ^ {\displaystyle {\hat {\mathbf {z} }}} are the unit vectors along the x {\displaystyle x} , y {\displaystyle y} , and z {\displaystyle z} coordinate axes, respectively. The magnitude of

5632-465: The Cherenkov radiation emitted when an incoming neutrino creates an electron or muon in the water. The Sudbury Neutrino Observatory was similar, but used heavy water as the detecting medium. Other detectors have consisted of large volumes of chlorine or gallium which are periodically checked for excesses of argon or germanium , respectively, which are created by neutrinos interacting with

5760-570: The GALLEX / GNO experiments in Italy about 30 tons of gallium as reaction mass. The price of gallium is prohibitive, so this experiment is difficult to afford on large-scale. Larger experiments have therefore turned to a less costly reaction mass. Radiochemical detection methods are only useful for counting neutrinos; they provide almost no information on neutrino energy or direction of travel. "Ring-imaging" Cherenkov detectors take advantage of

5888-902: The Solar System and among those a pair of high energy neutrinos in the peta-electron volt range, making them the highest energy neutrinos discovered to date. The pair were nicknamed "Bert" and "Ernie" , after characters from the Sesame Street TV show. Later in 2013 the number of detection increased to 37 candidates including a new high energy neutrino at 2000-TeV given the name of " Big Bird ". IceCube measured 10–100 GeV atmospheric muon neutrino disappearance in 2014, using three years of data taken May 2011 to April 2014, including DeepCore, determining neutrino oscillation parameters ∆m 32 = 2.72 +0.19 −0.20 × 10 eV and sin(θ 23 ) = 0.53 +0.09 −0.12 (normal mass hierarchy), comparable to other results. The measurement

6016-480: The South Pole . The ice itself is the detector medium. The direction of incident neutrinos is determined by recording the arrival time of individual photons using a three-dimensional array of detector modules each containing one photomultiplier tube. This method allows detection of neutrinos above 50 GeV with a spatial resolution of approximately 2  degrees . AMANDA was used to generate neutrino maps of

6144-461: The blazar TXS 0506 +056 located 5.7 billion light-years away in the direction of the constellation Orion , the results had a statistical significance of 3-3.5 σ . This was the first time that a neutrino detector had been used to locate an object in space, and indicated that a source of cosmic rays had been identified. In 2020, evidence of the Glashow resonance at 2.3 σ (formation of

6272-471: The cosmic microwave background , or gamma ray telescopes , which use particle terminology more like IceCube. Likewise, KM3NeT could complete the map for the southern hemisphere. IceCube scientists may have detected their first neutrinos on 29 January 2006. When protons collide with one another or with photons , the result is usually pions . Charged pions decay into muons and muon neutrinos whereas neutral pions decay into gamma rays . Potentially,

6400-473: The dot product , which is appropriate as the products are scalars rather than vectors. 2 ( r − r 0 ) ⋅ a = | v | 2 − | v 0 | 2 . {\displaystyle 2\left(\mathbf {r} -\mathbf {r} _{0}\right)\cdot \mathbf {a} =|\mathbf {v} |^{2}-|\mathbf {v} _{0}|^{2}.} The dot product can be replaced by

6528-442: The motion of points, bodies (objects), and systems of bodies (groups of objects) without considering the forces that cause them to move. Kinematics, as a field of study, is often referred to as the "geometry of motion" and is occasionally seen as a branch of both applied and pure mathematics since it can be studied without considering the mass of a body or the forces acting upon it. A kinematics problem begins by describing

SECTION 50

#1732772078841

6656-498: The teraelectronvolt (TeV) range to explore the highest-energy astrophysical processes. IceCube is part of a series of projects developed and supervised by the University of Wisconsin–Madison . Collaboration and funding are provided by numerous other universities and research institutions worldwide. Construction of IceCube was only possible during the Antarctic austral summer from November to February, when permanent sunlight allows for 24-hour drilling. Construction began in 2005, when

6784-842: The unit vectors along the x , y and z axes of the reference frame F , respectively. Consider a particle P that moves only on the surface of a circular cylinder r ( t ) = constant, it is possible to align the z axis of the fixed frame F with the axis of the cylinder. Then, the angle θ around this axis in the x – y plane can be used to define the trajectory as, r ( t ) = r cos ⁡ ( θ ( t ) ) x ^ + r sin ⁡ ( θ ( t ) ) y ^ + z ( t ) z ^ , {\displaystyle \mathbf {r} (t)=r\cos(\theta (t)){\hat {\mathbf {x} }}+r\sin(\theta (t)){\hat {\mathbf {y} }}+z(t){\hat {\mathbf {z} }},} where

6912-420: The weak interaction . The two types of weak interactions they (rarely) engage in are neutral current (which involves the exchange of a Z boson and only results in deflection) and charged current (which involves the exchange of a W boson and causes the neutrino to convert into a charged lepton : an electron , a muon , or a tauon , or one of their antiparticles, if an antineutrino). According to

7040-616: The 1/r distance dependence took over. IceCube is a member of the Supernova Early Warning System (SNEWS). A signature of sterile neutrinos would be a distortion of the energy spectrum of atmospheric neutrinos around 1 TeV, for which IceCube is uniquely positioned to search. This signature would arise from matter effects as atmospheric neutrinos interact with the matter of the Earth. The described detection strategy, along with its South Pole position, could allow

7168-567: The 22 string detector (about 1 ⁄ 4 of the full detector) than the AMANDA limits. IceCube can observe neutrino oscillations from atmospheric cosmic ray showers, over a baseline across the Earth. It is most sensitive at ~25 GeV, the energy range for which the DeepCore sub-array has been optimized. DeepCore consists of 6 strings deployed in the 2009–2010 austral summer with a closer horizontal and vertical spacing. In 2014, DeepCore data

7296-624: The Cherenkov threshold; this means that electron neutrino events cannot typically be used to point back to sources, but they are more likely to be fully contained in the detector, and thus they can be useful for energy studies. These events are more spherical, or "cascade"-like, than " track "-like; muon neutrino events are more track-like. Tau leptons can also create cascade events; but are short-lived and cannot travel very far before decaying, and are thus usually indistinguishable from electron cascades. A tau could be distinguished from an electron with

7424-480: The Earth with very little deflection, because neutrinos interact so rarely. IceCube could observe these neutrinos: its observable energy range is about 100 GeV to several PeV. The more energetic an event is, the larger volume IceCube may detect it in; in this sense, IceCube is more similar to Cherenkov telescopes like the Pierre Auger Observatory (an array of Cherenkov detecting tanks) than it

7552-504: The French word cinéma, but neither are directly derived from it. However, they do share a root word in common, as cinéma came from the shortened form of cinématographe, "motion picture projector and camera", once again from the Greek word for movement and from the Greek γρᾰ́φω grapho ("to write"). Particle kinematics is the study of the trajectory of particles. The position of a particle

7680-473: The Sun, with implications for WIMP–proton cross section . A shadowing effect from the Moon has been observed. Cosmic ray protons are blocked by the Moon, creating a deficit of cosmic ray shower muons in the direction of the Moon. A small (under 1%) but robust anisotropy has been observed in cosmic ray muons. In November 2013 it was announced that IceCube had detected 28 neutrinos that likely originated outside

7808-548: The W boson in antineutrino-electron collisions) was announced. In February 2021, the tidal disruption event (TDE) AT2019dsg was reported as candidate for a neutrino source and the TDE AT2019fdr as a second candidate in June 2022. In November 2022, IceCube announced strong evidence of a neutrino source emitted by the active galactic nucleus of Messier 77 . It is the second detection by IceCube after TXS 0506+056, and only

SECTION 60

#1732772078841

7936-424: The acceleration a P , which is the time derivative of the velocity v P , is given by: a P = d d t ( v r ^ + v θ ^ + v z z ^ ) = ( a − v θ ) r ^ + (

8064-729: The acceleration is constant, a = Δ v Δ t = v − v 0 t {\displaystyle \mathbf {a} ={\frac {\Delta \mathbf {v} }{\Delta t}}={\frac {\mathbf {v} -\mathbf {v} _{0}}{t}}} can be substituted into the above equation to give: r ( t ) = r 0 + ( v + v 0 2 ) t . {\displaystyle \mathbf {r} (t)=\mathbf {r} _{0}+\left({\frac {\mathbf {v} +\mathbf {v} _{0}}{2}}\right)t.} A relationship between velocity, position and acceleration without explicit time dependence can be had by solving

8192-472: The array are in the federal approval process. If approved, the detectors for IceCube2 will each be eight times the size of those currently emplaced. The observatory will be able to detect more sources of particles, and discern their properties more finely at both lower and higher energy levels. The IceCube Neutrino Observatory is composed of several sub-detectors which is also in addition to the main in-ice array. PINGU (Precision IceCube Next Generation Upgrade)

8320-436: The atmospheric muon incident flux is isotropic, a localised and anisotropic detection is discriminated in relation to the background betraying a cosmic event. For lower-energy experiments, the cosmic rays are not directly the problem. Instead, the spallation neutrons and radioisotopes produced by the cosmic rays may mimic the desired signals. For these experiments, the solution is to place the detector deep underground so that

8448-739: The average acceleration for time and substituting and simplifying t = v − v 0 a {\displaystyle t={\frac {\mathbf {v} -\mathbf {v} _{0}}{\mathbf {a} }}} ( r − r 0 ) ⋅ a = ( v − v 0 ) ⋅ v + v 0 2   , {\displaystyle \left(\mathbf {r} -\mathbf {r} _{0}\right)\cdot \mathbf {a} =\left(\mathbf {v} -\mathbf {v} _{0}\right)\cdot {\frac {\mathbf {v} +\mathbf {v} _{0}}{2}}\ ,} where ⋅ {\displaystyle \cdot } denotes

8576-421: The balance of the data which is sent north once a year via ship. Once the data reaches experimenters, they can reconstruct kinematical parameters of the incoming neutrino. High-energy neutrinos may cause a large signal in the detector, pointing back to their origin. Clusters of such neutrino directions indicate point sources of neutrinos. Each of the above steps requires a certain minimum energy, and thus IceCube

8704-635: The case of acceleration always in the direction of the motion and the direction of motion should be in positive or negative, the angle between the vectors ( α ) is 0, so cos ⁡ 0 = 1 {\displaystyle \cos 0=1} , and | v | 2 = | v 0 | 2 + 2 | a | | r − r 0 | . {\displaystyle |\mathbf {v} |^{2}=|\mathbf {v} _{0}|^{2}+2\left|\mathbf {a} \right|\left|\mathbf {r} -\mathbf {r} _{0}\right|.} This can be simplified using

8832-460: The center of curvature of the path at that point on the path, is commonly called the centripetal acceleration . The term v ω θ ^ {\displaystyle v\omega {\hat {\mathbf {\theta } }}} is called the Coriolis acceleration . If the trajectory of the particle is constrained to lie on a cylinder, then the radius r is constant and

8960-412: The components of their accelerations. If point C has acceleration components a C = ( a C x , a C y , a C z ) {\displaystyle \mathbf {a} _{C}=\left(a_{C_{x}},a_{C_{y}},a_{C_{z}}\right)} and point B has acceleration components a B = (

9088-2770: The constant distance from the center is denoted as r , and θ ( t ) is a function of time. The cylindrical coordinates for r ( t ) can be simplified by introducing the radial and tangential unit vectors, r ^ = cos ⁡ ( θ ( t ) ) x ^ + sin ⁡ ( θ ( t ) ) y ^ , θ ^ = − sin ⁡ ( θ ( t ) ) x ^ + cos ⁡ ( θ ( t ) ) y ^ . {\displaystyle {\hat {\mathbf {r} }}=\cos(\theta (t)){\hat {\mathbf {x} }}+\sin(\theta (t)){\hat {\mathbf {y} }},\quad {\hat {\mathbf {\theta } }}=-\sin(\theta (t)){\hat {\mathbf {x} }}+\cos(\theta (t)){\hat {\mathbf {y} }}.} and their time derivatives from elementary calculus: d r ^ d t = ω θ ^ . {\displaystyle {\frac {{\text{d}}{\hat {\mathbf {r} }}}{{\text{d}}t}}=\omega {\hat {\mathbf {\theta } }}.} d 2 r ^ d t 2 = d ( ω θ ^ ) d t = α θ ^ − ω r ^ . {\displaystyle {\frac {{\text{d}}^{2}{\hat {\mathbf {r} }}}{{\text{d}}t^{2}}}={\frac {{\text{d}}(\omega {\hat {\mathbf {\theta } }})}{{\text{d}}t}}=\alpha {\hat {\mathbf {\theta } }}-\omega {\hat {\mathbf {r} }}.} d θ ^ d t = − θ r ^ . {\displaystyle {\frac {{\text{d}}{\hat {\mathbf {\theta } }}}{{\text{d}}t}}=-\theta {\hat {\mathbf {r} }}.} d 2 θ ^ d t 2 = d ( − θ r ^ ) d t = − α r ^ − ω 2 θ ^ . {\displaystyle {\frac {{\text{d}}^{2}{\hat {\mathbf {\theta } }}}{{\text{d}}t^{2}}}={\frac {{\text{d}}(-\theta {\hat {\mathbf {r} }})}{{\text{d}}t}}=-\alpha {\hat {\mathbf {r} }}-\omega ^{2}{\hat {\mathbf {\theta } }}.} Using this notation, r ( t ) takes

9216-590: The constant tangential acceleration is applied along that path , so v 2 = v 0 2 + 2 a Δ r . {\displaystyle v^{2}=v_{0}^{2}+2a\Delta r.} This reduces the parametric equations of motion of the particle to a Cartesian relationship of speed versus position. This relation is useful when time is unknown. We also know that Δ r = ∫ v d t {\textstyle \Delta r=\int v\,{\text{d}}t} or Δ r {\displaystyle \Delta r}

9344-574: The cosine of the angle α between the vectors (see Geometric interpretation of the dot product for more details) and the vectors by their magnitudes, in which case: 2 | r − r 0 | | a | cos ⁡ α = | v | 2 − | v 0 | 2 . {\displaystyle 2\left|\mathbf {r} -\mathbf {r} _{0}\right|\left|\mathbf {a} \right|\cos \alpha =|\mathbf {v} |^{2}-|\mathbf {v} _{0}|^{2}.} In

9472-481: The current models. Weakly interacting massive particle (WIMP) dark matter could be gravitationally captured by massive objects like the Sun and accumulate in the core of the Sun . With a high enough density of these particles, they would annihilate with each other at a significant rate. The decay products of this annihilation could decay into neutrinos, which could be observed by IceCube as an excess of neutrinos from

9600-803: The detector from atmospheric muons. Secondly, these environments are transparent and dark, vital criteria in order to detect the faint Cherenkov light . In practice, because of Potassium 40 decay, even the abyss is not completely dark, so this decay must be used as a baseline. Located at a depth of about 2.5 km in the Mediterranean Sea , the ANTARES telescope (Astronomy with a Neutrino Telescope and Abyss environmental Research) has been fully operational since 30 May 2008. Consisting of an array of twelve separate 350  meter -long vertical detector strings 70 meters apart, each with 75  photomultiplier optical modules, this detector uses

9728-427: The detector planes provide the tracking information. Steel is a popular absorber choice, being relatively dense and inexpensive and having the advantage that it can be magnetised. The active detector is often liquid or plastic scintillator, read out with photomultiplier tubes, although various kinds of ionisation chambers have also been used. The NOνA proposal suggests eliminating the absorber planes in favor of using

9856-510: The detector to provide the first robust experimental evidence of extra dimensions predicted in string theory . Many extensions of the Standard Model of particle physics, including string theory, propose a sterile neutrino; in string theory this is made from a closed string . These could leak into extra dimensions before returning, making them appear to travel faster than the speed of light. An experiment to test this may be possible in

9984-462: The direction of the Sun. This technique of looking for the decay products of WIMP annihilation is called indirect, as opposed to direct searches which look for dark matter interacting within a contained, instrumented volume. Solar WIMP searches are more sensitive to spin -dependent WIMP models than many direct searches, because the Sun is made of lighter elements than direct search detectors (e.g. xenon or germanium ). IceCube has set better limits with

10112-444: The earth above can reduce the cosmic ray rate to acceptable levels. Neutrino detectors can be aimed at astrophysics observations, since many astrophysical events are believed to emit neutrinos. Underwater neutrino telescopes: Under-ice neutrino telescopes: Underground neutrino observatories: Others: Kinematical Kinematics is a subfield of physics and mathematics , developed in classical mechanics , that describes

10240-449: The equation Δ r = v 0 t + a t 2 2 {\textstyle \Delta r=v_{0}t+{\frac {at^{2}}{2}}} . This equation is applicable when the final velocity v is unknown. It is often convenient to formulate the trajectory of a particle r ( t ) = ( x ( t ), y ( t ), z ( t )) using polar coordinates in the X – Y plane. In this case, its velocity and acceleration take

10368-472: The exceedingly rare occasions when a neutrino does interact with an atom of ice or water. The Radio Ice Cherenkov Experiment uses antennas to detect Cherenkov radiation from high-energy neutrinos in Antarctica. The Antarctic Impulse Transient Antenna (ANITA) is a balloon-borne device flying over Antarctica and detecting Askaryan radiation , produced as cosmic ultra-high-energy neutrinos travel through

10496-484: The fact that they are traveling downwards. Most of the remaining (up-going) events are from neutrinos, but most of these neutrinos are from cosmic rays hitting the far side of the Earth; some unknown fraction may come from astronomical sources, and these neutrinos are the key to IceCube point source searches. Estimates predict the detection of about 75 upgoing neutrinos per day in the fully constructed IceCube detector. The arrival directions of these astrophysical neutrinos are

10624-400: The first IceCube string was deployed and sufficient data was collected to verify that the optical sensors functioned correctly. In the 2005–2006 season, an additional eight strings were deployed, making IceCube the largest neutrino telescope in the world. Construction was completed on 17 December 2010. The total cost of the project was $ 279 million. As of 2024, plans for further upgrades to

10752-414: The flavor of the neutrino. Most neutrino experiments must address the flux of cosmic rays that bombard the Earth's surface. The higher-energy (>50 MeV or so) neutrino experiments often cover or surround the primary detector with a "veto" detector which reveals when a cosmic ray passes into the primary detector, allowing the corresponding activity in the primary detector to be ignored ("vetoed"). Since

10880-780: The form, r ( t ) = r r ^ + z ( t ) z ^ . {\displaystyle \mathbf {r} (t)=r{\hat {\mathbf {r} }}+z(t){\hat {\mathbf {z} }}.} In general, the trajectory r ( t ) is not constrained to lie on a circular cylinder, so the radius R varies with time and the trajectory of the particle in cylindrical-polar coordinates becomes: r ( t ) = r ( t ) r ^ + z ( t ) z ^ . {\displaystyle \mathbf {r} (t)=r(t){\hat {\mathbf {r} }}+z(t){\hat {\mathbf {z} }}.} Where r , θ , and z might be continuously differentiable functions of time and

11008-430: The former Homestake Mine near Lead, South Dakota , containing 520  short tons (470  metric tons ) of fluid, was the first to detect the solar neutrinos, and made the first measurement of the deficit of electron neutrinos from the sun (see Solar neutrino problem ). A similar detector design, with a much lower detection threshold of 0.233 MeV, uses a gallium (Ga) → germanium (Ge) transformation which

11136-479: The fourth known source including SN1987A and solar neutrinos . OKS 1424+240 and GB9 are other possible candidates. In June 2023 IceCube identified as a galactic map the neutrino diffuse emission from the Galactic plane at the 4.5σ level of significance. Neutrino observatory Various detection methods have been used. Super Kamiokande is a large volume of water surrounded by phototubes that watch for

11264-972: The function notation is dropped for simplicity. The velocity vector v P is the time derivative of the trajectory r ( t ), which yields: v P = d d t ( r r ^ + z z ^ ) = v r ^ + r ω θ ^ + v z z ^ = v ( r ^ + θ ^ ) + v z z ^ . {\displaystyle \mathbf {v} _{P}={\frac {\text{d}}{{\text{d}}t}}\left(r{\hat {\mathbf {r} }}+z{\hat {\mathbf {z} }}\right)=v{\hat {\mathbf {r} }}+r\mathbf {\omega } {\hat {\mathbf {\theta } }}+v_{z}{\hat {\mathbf {z} }}=v({\hat {\mathbf {r} }}+{\hat {\mathbf {\theta } }})+v_{z}{\hat {\mathbf {z} }}.} Similarly,

11392-427: The geometry of the system and declaring the initial conditions of any known values of position, velocity and/or acceleration of points within the system. Then, using arguments from geometry, the position, velocity and acceleration of any unknown parts of the system can be determined. The study of how forces act on bodies falls within kinetics , not kinematics. For further details, see analytical dynamics . Kinematics

11520-414: The highest energy cosmic rays. These cosmic rays have energies high enough that they cannot be contained by galactic magnetic fields (their gyroradii are larger than the radius of the galaxy), so they are believed to come from extra-galactic sources. Astrophysical events which are cataclysmic enough to create such high energy particles would probably also create high energy neutrinos, which could travel to

11648-693: The ice below and produce a shower of secondary charged particles, which emits a cone of coherent radiation in the radio or microwave part of the electromagnetic spectrum. Currently the Radio Neutrino Observatory Greenland is being built, exploiting the Askaryan effect in ice to detect neutrinos with energies >10 PeV. Tracking calorimeters such as the MINOS detectors use alternating planes of absorber material and detector material. The absorber planes provide detector mass while

11776-463: The ice via the neutral current instead, the final state contains no information of the neutrino flavor since no charged lepton was created. The signals from the PMTs are digitized and then sent to the surface of the glacier on a cable. These signals are collected in a surface counting house, and some of them are sent north via satellite for further analysis. Since 2014, hard drives rather than tape store

11904-408: The ice, similar to the bow shock of a boat traveling faster than the waves it crosses. This light can then be detected by photomultiplier tubes within the digital optical modules making up IceCube. The detector signatures of the three charged leptons are distinct, and as such it's possible to determine the neutrino flavor of charged current events. On the other hand if the neutrino scattered off

12032-605: The laws of physics neutrinos must have mass, but only a "smidgen of rest mass" – perhaps less than a "millionth as much as an electron" – so the gravitational force caused by neutrinos has so far proved too weak to detect, leaving the weak interaction as the main method of detection: Antineutrinos were first detected near the Savannah River nuclear reactor by the Cowan–Reines neutrino experiment in 1956. Frederick Reines and Clyde Cowan used two targets containing

12160-464: The mass hierarchy only works as the mixing angle θ 13 is large. Despite the fact that individual neutrinos expected from supernovae have energies well below the IceCube energy cutoff, IceCube could detect a local supernova. It would appear as a detector-wide, brief, correlated rise in noise rates. The supernova would have to be relatively close (within our galaxy) to get enough neutrinos before

12288-433: The movement of components in a mechanical system , simplifying the derivation of the equations of motion. They are also central to dynamic analysis . Kinematic analysis is the process of measuring the kinematic quantities used to describe motion. In engineering, for instance, kinematic analysis may be used to find the range of movement for a given mechanism and, working in reverse, using kinematic synthesis to design

12416-490: The near future. Furthermore, if high energy neutrinos create microscopic black holes (as predicted by some aspects of string theory) it would create a shower of particles, resulting in an increase of "down" neutrinos while reducing "up" neutrinos. In 2016, scientists at the IceCube detector did not find any evidence for the sterile neutrino. The IceCube collaboration has published flux limits for neutrinos from point sources, gamma-ray bursts , and neutralino annihilation in

12544-460: The neutrino flux and the gamma ray flux may coincide in certain sources such as gamma-ray bursts and supernova remnants , indicating the elusive nature of their origin. Data from IceCube is being used in conjunction with gamma-ray satellites like Swift or Fermi for this goal. IceCube has not observed any neutrinos in coincidence with gamma ray bursts, but is able to use this search to constrain neutrino flux to values less than those predicted by

12672-602: The neutrino interactions visible in a regular water detector, a neutrino can break up the deuterium in heavy water. The resulting free neutron is subsequently captured, releasing a burst of gamma rays that can be detected. All three neutrino flavors participate equally in this dissociation reaction. The MiniBooNE detector employs pure mineral oil as its detection medium. Mineral oil is a natural scintillator , so charged particles without sufficient energy to produce Cherenkov light still produce scintillation light. Low-energy muons and protons, invisible in water, can be detected. Thus

12800-519: The next to distinguish two cascades, so double bang searches are centered at PeV scale energies. Such searches are underway but have not so far isolated a double bang event from background events. Another way to detect lower energy tau neutrinos is through the "double pulse" signature, where a single DOM detect two distinct light arrival times corresponding to the neutrino interaction and tau decay vertices. One can also use machine learning (ML) techniques, such as Convolutional Neural Networks, to distinguish

12928-429: The northern hemisphere, and the extension to southern hemisphere point sources takes extra work. Although IceCube is expected to detect very few neutrinos (relative to the number of photons detected by more traditional telescopes), it should have very high resolution with the ones that it does find. Over several years of operation, it could produce a flux map of the northern hemisphere similar to existing maps like that of

13056-524: The northern sky to search for extraterrestrial neutrino sources and to search for dark matter . AMANDA has been upgraded to the IceCube observatory, eventually increasing the volume of the detector array to one cubic kilometer. Ice Cube sits deep underneath the South Pole in a cubic kilometre of perfectly clear, bubble-free ancient ice. Like AMANDA it relies on detecting the flickers of light emitted on

13184-438: The notation for the magnitudes of the vectors | a | = a , | v | = v , | r − r 0 | = Δ r {\displaystyle |\mathbf {a} |=a,|\mathbf {v} |=v,|\mathbf {r} -\mathbf {r} _{0}|=\Delta r} where Δ r {\displaystyle \Delta r} can be any curvaceous path taken as

13312-666: The original substance. MINOS used a solid plastic scintillator watched by phototubes; Borexino uses a liquid pseudocumene scintillator also watched by phototubes; and the NOνA detector uses a liquid scintillator watched by avalanche photodiodes . The proposed acoustic detection of neutrinos via the thermoacoustic effect is the subject of dedicated studies done by the ANTARES , IceCube , and KM3NeT collaborations. Neutrinos are omnipresent in nature: every second, tens of billions of them "pass through every square centimetre of our bodies without us ever noticing." Many were created during

13440-410: The particle's position as a function of time. The velocity of a particle is a vector quantity that describes the direction as well as the magnitude of motion of the particle. More mathematically, the rate of change of the position vector of a point with respect to time is the velocity of the point. Consider the ratio formed by dividing the difference of two positions of a particle ( displacement ) by

13568-399: The points with which the IceCube telescope maps the sky. To distinguish these two types of neutrinos statistically, the direction and energy of the incoming neutrino is estimated from its collision by-products. Unexpected excesses in energy or excesses from a given spatial direction indicate an extraterrestrial source. A point source of neutrinos could help explain the mystery of the origin of

13696-558: The position of point A relative to point B is the difference between their components: r A / B = r A − r B = ( x A − x B , y A − y B , z A − z B ) {\displaystyle \mathbf {r} _{A/B}=\mathbf {r} _{A}-\mathbf {r} _{B}=\left(x_{A}-x_{B},y_{A}-y_{B},z_{A}-z_{B}\right)} The velocity of one point relative to another

13824-439: The position vector | r | {\displaystyle \left|\mathbf {r} \right|} gives the distance between the point r {\displaystyle \mathbf {r} } and the origin. | r | = x 2 + y 2 + z 2 . {\displaystyle |\mathbf {r} |={\sqrt {x^{2}+y^{2}+z^{2}}}.} The direction cosines of

13952-993: The position vector provide a quantitative measure of direction. In general, an object's position vector will depend on the frame of reference; different frames will lead to different values for the position vector. The trajectory of a particle is a vector function of time, r ( t ) {\displaystyle \mathbf {r} (t)} , which defines the curve traced by the moving particle, given by r ( t ) = x ( t ) x ^ + y ( t ) y ^ + z ( t ) z ^ , {\displaystyle \mathbf {r} (t)=x(t){\hat {\mathbf {x} }}+y(t){\hat {\mathbf {y} }}+z(t){\hat {\mathbf {z} }},} where x ( t ) {\displaystyle x(t)} , y ( t ) {\displaystyle y(t)} , and z ( t ) {\displaystyle z(t)} describe each coordinate of

14080-399: The rate of change of the magnitude of the velocity vector and the rate of change of direction of that vector. The same reasoning used with respect to the position of a particle to define velocity, can be applied to the velocity to define acceleration. The acceleration of a particle is the vector defined by the rate of change of the velocity vector. The average acceleration of a particle over

14208-403: The second time derivative of the relative position vector r B/A . Assuming that the initial conditions of the position, r 0 {\displaystyle \mathbf {r} _{0}} , and velocity v 0 {\displaystyle \mathbf {v} _{0}} at time t = 0 {\displaystyle t=0} are known, the first integration yields

14336-641: The shower. Tau leptons decay essentially immediately to either another charged lepton or pions , and cannot be observed directly in this kind of detector. (To directly observe taus, one typically looks for a kink in tracks in photographic emulsion.) At low energies, a neutrino can scatter from the entire nucleus of an atom, rather than the individual nucleons, in a process known as coherent neutral current neutrino-nucleus elastic scattering or coherent neutrino scattering . This effect has been used to make an extremely small neutrino detector. Unlike most other detection methods, coherent scattering does not depend on

14464-594: The surrounding sea water as the detector medium. The next generation deep sea neutrino telescope KM3NeT will have a total instrumented volume of about 5 km . The detector will be distributed over three installation sites in the Mediterranean. Implementation of the first phase of the telescope was started in 2013. The Antarctic Muon And Neutrino Detector Array (AMANDA) operated from 1996–2004. This detector used photomultiplier tubes mounted in strings buried deep (1.5–2 km) inside Antarctic glacial ice near

14592-445: The tau neutrino signal. In 2024 the IceCube collaboration published its findings of seven astrophysical tau neutrino candidates using such a technique. There is a large background of muons created not by neutrinos from astrophysical sources but by cosmic rays impacting the atmosphere above the detector. There are about 10 times more cosmic ray muons than neutrino-induced muons observed in IceCube. Most of these can be rejected using

14720-404: The time derivative of the relative position vector r B/A . The acceleration of one point C relative to another point B is simply the difference between their accelerations. a C / B = a C − a B {\displaystyle \mathbf {a} _{C/B}=\mathbf {a} _{C}-\mathbf {a} _{B}} which is the difference between

14848-1152: The time interval. This ratio is called the average velocity over that time interval and is defined as v ¯ = Δ r Δ t = Δ x Δ t x ^ + Δ y Δ t y ^ + Δ z Δ t z ^ = v ¯ x x ^ + v ¯ y y ^ + v ¯ z z ^ {\displaystyle \mathbf {\bar {v}} ={\frac {\Delta \mathbf {r} }{\Delta t}}={\frac {\Delta x}{\Delta t}}{\hat {\mathbf {x} }}+{\frac {\Delta y}{\Delta t}}{\hat {\mathbf {y} }}+{\frac {\Delta z}{\Delta t}}{\hat {\mathbf {z} }}={\bar {v}}_{x}{\hat {\mathbf {x} }}+{\bar {v}}_{y}{\hat {\mathbf {y} }}+{\bar {v}}_{z}{\hat {\mathbf {z} }}\,} where Δ r {\displaystyle \Delta \mathbf {r} }

14976-471: The top area (a triangle). The area of a triangle is 1 2 B H {\textstyle {\frac {1}{2}}BH} where B {\displaystyle B} is the base and H {\displaystyle H} is the height. In this case, B = t {\displaystyle B=t} and H = a t {\displaystyle H=at} or A = 1 2 B H = 1 2

15104-558: The total antineutrino flux . The detected antineutrinos thus all carried an energy greater than 1.8 MeV, which is the threshold for the reaction channel used (1.8 MeV is the energy needed to create a positron and a neutron from a proton). Only about 3% of the antineutrinos from a nuclear reactor carry enough energy for the reaction to occur. A more recently built and much larger KamLAND detector used similar techniques to study oscillations of antineutrinos from 53 Japanese nuclear power plants. A smaller, but more radiopure Borexino detector

15232-481: The tower is 50 m high, and this height is measured along the z -axis, then the coordinate vector to the top of the tower is r = (0 m, −50 m, 50 m). In the most general case, a three-dimensional coordinate system is used to define the position of a particle. However, if the particle is constrained to move within a plane, a two-dimensional coordinate system is sufficient. All observations in physics are incomplete without being described with respect to

15360-428: The two scintillation detectors above and below the target. The neutrons were captured by cadmium nuclei, resulting in delayed gamma rays of about 8 MeV that were detected a few microseconds after the photons from a positron annihilation event. This experiment was designed by Cowan and Reines to give a unique signature for antineutrinos, to prove the existence of these particles. It was not the experimental goal to measure

15488-572: The use of natural environment as a measurement medium emerged. Since the neutrino flux incoming to earth decreases with increasing energy, the size of neutrino detectors must increase too. Though building a kilometer-sized cube detector underground covered by thousands of photomultiplier would be prohibitively expensive, detection volumes of this magnitude can be achieved by installing Cherenkov detector arrays deep inside already existing natural water or ice formations, with several other advantages. Firstly, hundreds of meters of water or ice partly protect

15616-803: The velocity and acceleration vectors simplify. The velocity of v P is the time derivative of the trajectory r ( t ), v P = d d t ( r r ^ + z z ^ ) = r ω θ ^ + v z z ^ = v θ ^ + v z z ^ . {\displaystyle \mathbf {v} _{P}={\frac {\text{d}}{{\text{d}}t}}\left(r{\hat {\mathbf {r} }}+z{\hat {\mathbf {z} }}\right)=r\omega {\hat {\mathbf {\theta } }}+v_{z}{\hat {\mathbf {z} }}=v{\hat {\mathbf {\theta } }}+v_{z}{\hat {\mathbf {z} }}.} A special case of

15744-676: The velocity of point A relative to point B is the difference between their components: v A / B = v A − v B = ( v A x − v B x , v A y − v B y , v A z − v B z ) {\displaystyle \mathbf {v} _{A/B}=\mathbf {v} _{A}-\mathbf {v} _{B}=\left(v_{A_{x}}-v_{B_{x}},v_{A_{y}}-v_{B_{y}},v_{A_{z}}-v_{B_{z}}\right)} Alternatively, this same result could be obtained by computing

15872-683: The velocity of the particle as a function of time. v ( t ) = v 0 + ∫ 0 t a d τ = v 0 + a t . {\displaystyle \mathbf {v} (t)=\mathbf {v} _{0}+\int _{0}^{t}\mathbf {a} \,{\text{d}}\tau =\mathbf {v} _{0}+\mathbf {a} t.} A second integration yields its path (trajectory), r ( t ) = r 0 + ∫ 0 t v ( τ ) d τ = r 0 + ∫ 0 t ( v 0 +

16000-403: The weak force. When they do react with the molecules of water in the ice via the charged current interaction, they create charged leptons ( electrons , muons , or taus ) corresponding to the flavor of the neutrino. These charged leptons can, if they are energetic enough, emit Cherenkov radiation . This happens when the charged particle travels through the ice faster than the speed of light in

16128-437: Was able to measure the most important components of the neutrino spectrum from the Sun, as well as antineutrinos from Earth and nuclear reactors. The SNO+ experiment uses linear alkylbenzene as a liquid scintillator, in contrast to its predecessor Sudbury Neutrino Observatory which used heavy water and detected Cherenkov light (see below). Chlorine detectors, based on the method suggested by Bruno Pontecorvo , consist of

16256-699: Was improved using more data in 2017, and in 2019 atmospheric tau neutrino appearance was measured. The latest measurement with improved detector calibration and data processing from 2023 has resulted in more precise values of the oscillation parameters, determining ∆m 32 = (2.41 ± 0.07) × 10 eV and sin(θ 23 ) = 0.51 ± 0.05 (normal mass hierarchy). In July 2018, the IceCube Neutrino Observatory announced that they had traced an extremely-high-energy neutrino that hit their detector in September ;2017 back to its point of origin in

16384-449: Was used to determine the mixing angle θ 23 and mass splitting Δm 23 . This measurement has since been improved with more data and improved detector calibration and data processing. As more data is collected and IceCube measurements are refined further, it may be possible to observe the characteristic modification of the oscillation pattern at ~15 GeV that determines the neutrino mass hierarchy . This mechanism for determining

#840159