Frequency separation

Last updated

Frequency separation within astrophysics, is a term used in both Helioseismology and Asteroseismology. It refers to the spacing in frequency between adjacent modes of oscillation, having the same angular degree (l) but different radial order (n).

For a Sun-like star, the frequency can be further described using the 'large frequency spacing' between modes of different radial order (136 μHz in the Sun), and the 'small frequency spacing' between modes of even and odd angular degree within the same radial order (9.0 μHz in the Sun). The period corresponding to the large frequency spacing can be shown to be approximately the same as the time required for a sound wave to travel to the centre of the Sun and return, confirming the global nature of the oscillations seen. [1]

A further frequency separation, the rotational splitting can be seen in high-resolution solar data between modes of the same angular degree, but different azimuthal order (m). This gives information

StarLarge Frequency SeparationSmall Frequency Separation
The Sun 136 μHz9.0 μHz [1]
Arcturus 0.825 0.049 μHzNot Present [2]

Related Research Articles

<span class="mw-page-title-main">Oscillation</span> Repetitive variation of some measure about a central value

Oscillation is the repetitive or periodic variation, typically in time, of some measure about a central value or between two or more different states. Familiar examples of oscillation include a swinging pendulum and alternating current. Oscillations can be used in physics to approximate complex interactions, such as those between atoms.

<span class="mw-page-title-main">Polarization (waves)</span> Property of waves that can oscillate with more than one orientation

Polarization is a property of transverse waves which specifies the geometrical orientation of the oscillations. In a transverse wave, the direction of the oscillation is perpendicular to the direction of motion of the wave. One example of a polarized transverse wave is vibrations traveling along a taut string (see image), for example, in a musical instrument like a guitar string. Depending on how the string is plucked, the vibrations can be in a vertical direction, horizontal direction, or at any angle perpendicular to the string. In contrast, in longitudinal waves, such as sound waves in a liquid or gas, the displacement of the particles in the oscillation is always in the direction of propagation, so these waves do not exhibit polarization. Transverse waves that exhibit polarization include electromagnetic waves such as light and radio waves, gravitational waves, and transverse sound waves in solids.

<span class="mw-page-title-main">Resonance</span> Physical characteristic of oscillating systems

Resonance is a phenomenon that occurs when an object or system is subjected to an external force or vibration that matches its natural frequency. When this happens, the object or system absorbs energy from the external force and starts vibrating with a larger amplitude. Resonance can occur in various systems, such as mechanical, electrical, or acoustic systems, and it is often desirable in certain applications, such as musical instruments or radio receivers. However, resonance can also be detrimental, leading to excessive vibrations or even structural failure in some cases.

<span class="mw-page-title-main">Seismic wave</span> Seismic, volcanic, or explosive energy that travels through Earths layers

A seismic wave is a mechanical wave of acoustic energy that travels through the Earth or another planetary body. It can result from an earthquake, volcanic eruption, magma movement, a large landslide and a large man-made explosion that produces low-frequency acoustic energy. Seismic waves are studied by seismologists, who record the waves using seismometers, hydrophones, or accelerometers. Seismic waves are distinguished from seismic noise, which is persistent low-amplitude vibration arising from a variety of natural and anthropogenic sources.

Differential rotation is seen when different parts of a rotating object move with different angular velocities at different latitudes and/or depths of the body and/or in time. This indicates that the object is not rigid. In fluid objects, such as accretion disks, this leads to shearing. Galaxies and protostars usually show differential rotation; examples in the Solar System include the Sun, Jupiter and Saturn.

<span class="mw-page-title-main">CoRoT</span> European space telescope that operated between 2006 - 2014

CoRoT was a space telescope mission which operated from 2006 to 2013. The mission's two objectives were to search for extrasolar planets with short orbital periods, particularly those of large terrestrial size, and to perform asteroseismology by measuring solar-like oscillations in stars. The mission was led by the French Space Agency (CNES) in conjunction with the European Space Agency (ESA) and other international partners.

<span class="mw-page-title-main">Skin effect</span> Tendency of AC current flow in a conductors outer layer

In electromagnetism, skin effect is the tendency of an alternating electric current (AC) to become distributed within a conductor such that the current density is largest near the surface of the conductor and decreases exponentially with greater depths in the conductor. It is caused by opposing eddy currents induced by the changing magnetic field resulting from the alternating current. The electric current flows mainly at the skin of the conductor, between the outer surface and a level called the skin depth.

<span class="mw-page-title-main">Ring laser gyroscope</span> Instrument to measure angular velocity

A ring laser gyroscope (RLG) consists of a ring laser having two independent counter-propagating resonant modes over the same path; the difference in phase is used to detect rotation. It operates on the principle of the Sagnac effect which shifts the nulls of the internal standing wave pattern in response to angular rotation. Interference between the counter-propagating beams, observed externally, results in motion of the standing wave pattern, and thus indicates rotation.

<span class="mw-page-title-main">Asteroseismology</span> Study of oscillations in stars

Asteroseismology is the study of oscillations in stars. Stars have many resonant modes and frequencies, and the path of sound waves passing through a star depends on the local speed of sound, which in turn depends on local temperature and chemical composition. Because the resulting oscillation modes are sensitive to different parts of the star, they inform astronomers about the internal structure of the star, which is otherwise not directly possible from overall properties like brightness and surface temperature.

Helioseismology is the study of the structure and dynamics of the Sun through its oscillations. These are principally caused by sound waves that are continuously driven and damped by convection near the Sun's surface. It is similar to geoseismology, or asteroseismology, which are respectively the studies of the Earth or stars through their oscillations. While the Sun's oscillations were first detected in the early 1960s, it was only in the mid-1970s that it was realized that the oscillations propagated throughout the Sun and could allow scientists to study the Sun's deep interior. The term was coined by Douglas Gough in the 90s. The modern field is separated into global helioseismology, which studies the Sun's resonant modes directly, and local helioseismology, which studies the propagation of the component waves near the Sun's surface.

<span class="mw-page-title-main">Normal mode</span> Pattern of oscillating motion in a system

A normal mode of a dynamical system is a pattern of motion in which all parts of the system move sinusoidally with the same frequency and with a fixed phase relation. The free motion described by the normal modes takes place at fixed frequencies. These fixed frequencies of the normal modes of a system are known as its natural frequencies or resonant frequencies. A physical object, such as a building, bridge, or molecule, has a set of normal modes and their natural frequencies that depend on its structure, materials and boundary conditions.

<span class="mw-page-title-main">Pulse-Doppler radar</span> Type of radar system

A pulse-Doppler radar is a radar system that determines the range to a target using pulse-timing techniques, and uses the Doppler effect of the returned signal to determine the target object's velocity. It combines the features of pulse radars and continuous-wave radars, which were formerly separate due to the complexity of the electronics.

The Womersley number is a dimensionless number in biofluid mechanics and biofluid dynamics. It is a dimensionless expression of the pulsatile flow frequency in relation to viscous effects. It is named after John R. Womersley (1907–1958) for his work with blood flow in arteries. The Womersley number is important in keeping dynamic similarity when scaling an experiment. An example of this is scaling up the vascular system for experimental study. The Womersley number is also important in determining the thickness of the boundary layer to see if entrance effects can be ignored.

A bias tee is a three-port network used for setting the DC bias point of some electronic components without disturbing other components. The bias tee is a diplexer. The low-frequency port is used to set the bias; the high-frequency port passes the radio-frequency signals but blocks the biasing levels; the combined port connects to the device, which sees both the bias and RF. It is called a tee because the 3 ports are often arranged in the shape of a T.

Atmospheric tides are global-scale periodic oscillations of the atmosphere. In many ways they are analogous to ocean tides. They can be excited by:

Solar-like oscillations are oscillations in stars that are excited in the same way as those in the Sun, namely by turbulent convection in its outer layers. Stars that show solar-like oscillations are called solar-like oscillators. The oscillations are standing pressure and mixed pressure-gravity modes that are excited over a range in frequency, with the amplitudes roughly following a bell-shaped distribution. Unlike opacity-driven oscillators, all the modes in the frequency range are excited, making the oscillations relatively easy to identify. The surface convection also damps the modes, and each is well-approximated in frequency space by a Lorentzian curve, the width of which corresponds to the lifetime of the mode: the faster it decays, the broader is the Lorentzian. All stars with surface convection zones are expected to show solar-like oscillations, including cool main-sequence stars, subgiants and red giants. Because of the small amplitudes of the oscillations, their study has advanced tremendously thanks to space-based missions.

<span class="mw-page-title-main">Wilberforce pendulum</span> Coupled mechanical oscillator

A Wilberforce pendulum, invented by British physicist Lionel Robert Wilberforce around 1896, consists of a mass suspended by a long helical spring and free to turn on its vertical axis, twisting the spring. It is an example of a coupled mechanical oscillator, often used as a demonstration in physics education. The mass can both bob up and down on the spring, and rotate back and forth about its vertical axis with torsional vibrations. When correctly adjusted and set in motion, it exhibits a curious motion in which periods of purely rotational oscillation gradually alternate with periods of purely up and down oscillation. The energy stored in the device shifts slowly back and forth between the translational 'up and down' oscillation mode and the torsional 'clockwise and counterclockwise' oscillation mode, until the motion eventually dies away.

<span class="mw-page-title-main">Neutron-star oscillation</span> Extreme movement of neutron stars

Asteroseismology studies the internal structure of the Sun and other stars using oscillations. These can be studied by interpreting the temporal frequency spectrum acquired through observations. In the same way, the more extreme neutron stars might be studied and hopefully give us a better understanding of neutron-star interiors, and help in determining the equation of state for matter at nuclear densities. Scientists also hope to prove, or discard, the existence of so-called quark stars, or strange stars, through these studies. Fundamental information can be obtained of the General Relativity Theory by observing the gravitational radiation from oscillating neutron stars.

Coronal seismology is a technique of studying the plasma of the Sun's corona with the use of magnetohydrodynamic (MHD) waves and oscillations. Magnetohydrodynamics studies the dynamics of electrically conducting fluids - in this case the fluid is the coronal plasma. Observed properties of the waves (e.g. period, wavelength, amplitude, temporal and spatial signatures, characteristic scenarios of the wave evolution, combined with a theoretical modelling of the wave phenomena, may reflect physical parameters of the corona which are not accessible in situ, such as the coronal magnetic field strength and Alfvén velocity and coronal dissipative coefficients. Originally, the method of MHD coronal seismology was suggested by Y. Uchida in 1970 for propagating waves, and B. Roberts et al. in 1984 for standing waves, but was not practically applied until the late 90s due to a lack of necessary observational resolution. Philosophically, coronal seismology is similar to the Earth's seismology, helioseismology, and MHD spectroscopy of laboratory plasma devices. In all these approaches, waves of various kind are used to probe a medium.

<span class="mw-page-title-main">Nuclear magnetic resonance</span> Spectroscopic technique based on change of nuclear spin state

Nuclear magnetic resonance (NMR) is a physical phenomenon in which nuclei in a strong constant magnetic field are disturbed by a weak oscillating magnetic field and respond by producing an electromagnetic signal with a frequency characteristic of the magnetic field at the nucleus. This process occurs near resonance, when the oscillation frequency matches the intrinsic frequency of the nuclei, which depends on the strength of the static magnetic field, the chemical environment, and the magnetic properties of the isotope involved; in practical applications with static magnetic fields up to ca. 20 tesla, the frequency is similar to VHF and UHF television broadcasts (60–1000 MHz). NMR results from specific magnetic properties of certain atomic nuclei. High-resolution nuclear magnetic resonance spectroscopy is widely used to determine the structure of organic molecules in solution and study molecular physics and crystals as well as non-crystalline materials. NMR is also routinely used in advanced medical imaging techniques, such as in magnetic resonance imaging (MRI). The original application of NMR to condensed matter physics is nowadays mostly devoted to strongly correlated electron systems. It reveals large many-body couplings by fast broadband detection and should not be confused with solid state NMR, which aims at removing the effect of the same couplings by Magic Angle Spinning techniques.

References

  1. 1 2 Chaplin, William J. (2006). Music of the Sun: The story of Helioseismology. Oneworld. ISBN   1-85168-451-4.
  2. Retter, A; Bedding, T; Buzasi, D; Kjeldsen, H; Kiss L (July 2003). "Oscillations in Arcturus from WIRE Photometry". Astrophysical Journal Letters. 591 (2): L151–L154. arXiv: astro-ph/0306056 . Bibcode:2003ApJ...591L.151R. doi:10.1086/377211. S2CID   119083930.