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Local standard of rest
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 | This article may be too technical for most readers to understand. (July 2023) |
In astronomy, the local standard of rest (LSR) is a reference frame which follows the mean motion of material in the Milky Way in the neighborhood of the Sun (stars in radius 100 pc from the Sun),[1] on average sharing the same velocity around the Milky Way as the Sun.[2] The path of this material is not precisely circular.[3] The Sun follows the solar circle (eccentricity e < 0.1) at a speed of about 255 km/s in a clockwise direction when viewed from the galactic north pole at a radius of ≈ 8.34 kpc[4] about the center of the galaxy near Sgr A*, and has only a slight motion, towards the solar apex, relative to the LSR.[5][6]
LSR could be understood by analogy to a group of cars traveling at similar speed on a highway i.e. at LSR. If a faster car passes by or they pass a slower car then the faster and slower cars could be considered at not traveling at LSR. Typically a large variation of speed in astronomical bodies could be considered as indicator of their extraterrestrial nature. This analogy was used by theoretical physicist Avi Loeb in his 2021 book Extraterrestrial: The First Sign of Intelligent Life Beyond Earth.
The LSR velocity is anywhere from 202–241 km/s.[7] In 2014, very-long-baseline interferometry observations of maser emission in high-mass star-forming regions (HMSFR) placed tight constraints on combinations of kinematic parameters such as the circular orbit speed of the Sun (Θ0 + V☉ = 255.2 ± 5.1 km/s).[4] There is significant correlation between the circular motion of the solar circle, the solar peculiar motion, and the predicted counterrotation of star-forming regions.[8] Additionally, local estimates of the velocity of the LSR based on stars in the vicinity of the Sun[9] may potentially yield different results than global estimates derived from motions relative to the Galactic Center.[10]
See also
[edit]- Comoving coordinates for an example of another convenient astronomical reference frame.
References
[edit]- ^ Frank H Shu (1982). The Physical Universe. University Science Books. p. 261. ISBN 0-935702-05-9.
- ^ "LOCAL STANDARD OF REST definition and meaning". Collins English Dictionary. November 25, 2023. Retrieved November 25, 2023.
- ^ James Binney; Michael Merrifield (1998). Galactic Astronomy. Princeton University Press. p. 536. ISBN 0-691-02565-7.
- ^ a b Reid, M.; et al. (10 March 2014). "Trigonometric Parallaxes of High Mass Star Forming Regions: The Structure and Kinematics of the Milky Way". The Astrophysical Journal. 783 (2): 130 (14pp). arXiv:1401.5377. Bibcode:2014ApJ...783..130R. doi:10.1088/0004-637X/783/2/130. S2CID 119186799.
- ^ Mark Reid; et al. (2008). "Mapping the Milky Way and the Local Group". In F. Combes; Keiichi Wada (eds.). Mapping the Galaxy and Nearby Galaxies. Springer. pp. 19–20. ISBN 978-0-387-72767-7.
- ^ The Sun's peculiar motion relative to the LSR is 13.4 km/s. See, for example, Binney, J. & Merrifield, M. (6 September 1998). "§10.6". op. cit. Princeton University Press. ISBN 0-691-02565-7. or E.E. Mamajek (2008). "On the distance to the Ophiuchus star-forming region". Astron. Nachr. AN 329 (1): 12; §2.3. arXiv:0709.0505. Bibcode:2008AN....329...10M. doi:10.1002/asna.200710827. S2CID 14027548.
- ^ Steven R. Majewski1 (2008). "Precision Astrometry, Galactic Mergers, Halo Substructure and Local Dark Matter". Proceedings of IAU Symposium 248. 3: 450–457. arXiv:0801.4927. Bibcode:2008IAUS..248..450M. doi:10.1017/S1743921308019790. S2CID 18252986.
{{cite journal}}: CS1 maint: numeric names: authors list (link) - ^ Reid, M.; et al. (20 July 2009). "Trigonometric Parallaxes of High Mass Star Forming Regions. VI. Galactic Structure, Fundamental Parameters, and Noncircular Motions". The Astrophysical Journal. 700 (1): 137–148. arXiv:0902.3913. Bibcode:2009ApJ...700..137R. doi:10.1088/0004-637X/700/1/137. S2CID 11347166.
- ^ Dehnen, W.; Binney, J.J. (October 1998). "Local stellar kinematics from HIPPARCOS data". Monthly Notices of the Royal Astronomical Society. 298 (2): 387–394. arXiv:astro-ph/9710077. Bibcode:1998MNRAS.298..387D. doi:10.1046/j.1365-8711.1998.01600.x. S2CID 15936627.
- ^ Bovy, J.; et al. (10 November 2012). "The Milky Way's Circular-velocity Curve between 4 and 14 kpc from APOGEE data". The Astrophysical Journal. 759 (2): 131 (20pp). arXiv:1209.0759. Bibcode:2012ApJ...759..131B. doi:10.1088/0004-637X/759/2/131. S2CID 119279938.
Local standard of rest
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Definition and Concept
Core Definition
The Local Standard of Rest (LSR) is a reference frame in astronomy defined such that the mean velocity of stars in the solar neighborhood—typically the volume of space within approximately 100 parsecs of the Sun—is zero.[2][5][8] This frame serves as the hypothetical "rest" condition for the average motion of material in this local region, providing a baseline for measuring deviations in stellar and interstellar kinematics.[9] It effectively represents the rest frame of the local interstellar medium by averaging out the collective orbital motion around the Galactic center.[6] The LSR conceptualizes the average star population in the solar neighborhood as following a circular orbit at the Sun's galactocentric distance, thereby isolating the peculiar velocities of individual stars relative to this mean galactic rotation.[10][11] This assumption allows astronomers to distinguish random motions from the systematic rotation of the Milky Way's disk in the vicinity of the Sun.[12] The solar neighborhood is particularly suited for this definition due to its relatively uniform stellar density and dynamics, where the LSR is most applicable. Averaging for the LSR is generally based on samples of main-sequence stars in this region, which provide a representative cross-section of the local population for determining the zero-velocity frame.[13] The terminology "Local Standard of Rest" derives from its focus on the Sun's immediate vicinity ("local"), a conventional mean motion ("standard"), and the resulting null net velocity ("rest") for the averaged stars.[14]Velocity Assumptions
The velocity components defining the Local Standard of Rest (LSR) are expressed in a right-handed Cartesian system aligned with cylindrical Galactic coordinates at the Sun's position, where the radial component is positive towards the Galactic anti-center, the tangential component is positive in the direction of Galactic rotation, and the vertical component is positive towards the north Galactic pole. In this frame, the LSR is characterized by the assumption that the mean velocities of a representative population of local thin-disk stars vanish: , , and .[15] This implies that the average motion of nearby stars is purely circular and confined to the Galactic plane, with any deviations representing peculiar motions. The Sun exhibits a peculiar velocity relative to the LSR of km/s (as of Gaia DR3 in 2022), directed towards the solar apex at Galactic coordinates .[16] These zero-mean assumptions for the LSR are empirically derived from statistical analyses of stellar proper motions and radial velocities in large catalogs. The Gaia mission's Data Release 3 (DR3), with precise astrometry for billions of stars, enables fitting of the local velocity field by selecting kinematically unbiased samples of main-sequence disk stars and extrapolating mean velocities to zero internal dispersion using the asymmetric drift relation.[17] Such analyses yield solar peculiar motion components with typical uncertainties better than 0.5 km/s, confirming the LSR as the frame where stellar velocity distributions are centered at zero. The Oort constants and , which parameterize the systematic velocity gradients in the local disk, relate to these assumptions by quantifying deviations from uniform circular motion while preserving the zero-mean peculiar velocities in the LSR. Specifically, measures the local shear (difference between rotation speed and its radial gradient), and measures the vorticity (angular momentum gradient); typical values as of 2019 are km s kpc and km s kpc, derived from Gaia and other data.[16]Historical Context
Origins in Early Astronomy
The early conceptual foundations of the Local Standard of Rest (LSR) emerged from 18th- and 19th-century observations of stellar proper motions, which suggested that stars exhibit systematic drifts relative to the Sun. In 1783, William Herschel published a pioneering analysis of proper motions for several bright stars, including Sirius, Procyon, and Arcturus, concluding that the solar system moves through space at approximately 5 arcseconds per year toward a point in the constellation Hercules, which he termed the solar apex. This direction, near the star Lambda Herculis, implied that nearby stars appear to converge toward this apex and diverge from an opposite point, hinting at differential motions within the local stellar population. However, Herschel's work treated the stellar system as largely at rest, lacking a formalized frame to standardize these relative velocities.[18][19] By the early 20th century, Jacobus Kapteyn refined these observations using larger datasets of proper motions from catalogs like those compiled by Boss and Gill. In 1904, Kapteyn announced the discovery of two distinct "star streams" based on statistical analysis of over 800 stars, revealing that their motions were not random but clustered around two opposing vertices in the sky, separated by about 180 degrees. One stream converged toward a point in Sagittarius, the other in the opposite direction, with velocities differing by roughly 40 km/s. Kapteyn interpreted this as evidence of systematic local motion, possibly due to the Sun's passage through a structured stellar system, though he initially favored a non-rotational explanation like tidal influences. This finding challenged Herschel's simpler model and spurred investigations into organized stellar kinematics, providing a precursor to distinguishing local systematic drifts from individual peculiar velocities.[20] In the 1920s, Bertil Lindblad built on Kapteyn's star streams by proposing a dynamical model of differential galactic rotation. Through theoretical analysis published in 1926, Lindblad demonstrated that the observed streaming could result from the Milky Way's overall rotation, with stars at different distances from the galactic center exhibiting varying orbital speeds due to a non-constant gravitational potential. He divided the stellar system into rotating subsystems, where local motions relative to the mean rotation represent deviations from circular orbits. This framework established the need to separate local peculiar velocities—random deviations from the average—from the global rotational flow, setting the stage for a standardized local reference. Lindblad's ideas were observationally supported by radial velocity data, emphasizing epicyclic approximations for stellar paths around the galactic center.[21] The LSR concept, representing the hypothetical circular motion of stars at the Sun's position in the galaxy, gained adoption in the 1930s amid ongoing debates over galactic rotation curves and the interpretation of high-velocity stars. Astronomers like Jan Oort integrated Lindblad's theory with new spectroscopic data, using the LSR to quantify the Sun's peculiar motion relative to this average local frame, typically around 20 km/s toward the solar apex near the constellation Hercules. This adoption resolved inconsistencies in earlier models by providing a consistent basis for analyzing rotation amid varying estimates of galactic parameters, such as the distance to the center (around 8-10 kpc) and rotation speed (220-260 km/s).Development in the 20th Century
In the 1920s and 1930s, Dutch astronomer Jan Oort played a pivotal role in formalizing the concept of local velocity fields within the Milky Way, laying the groundwork for the local standard of rest (LSR). Building on Bertil Lindblad's hypothesis of galactic rotation, Oort analyzed the proper motions and radial velocities of nearby stars to derive empirical evidence for differential rotation near the Sun.[22] In his seminal 1927 paper, he introduced the Oort constants—A and B—which quantify the shearing and vorticity of the local velocity field, respectively, and directly relate stellar motions to the circular velocity of the LSR at the solar position. These constants, derived from observations of high-velocity stars, provided a framework for distinguishing peculiar motions from the systematic rotation assumed for the LSR, enabling the first quantitative estimates of the Sun's velocity relative to this reference frame. Oort's work shifted the understanding of local kinematics from qualitative descriptions to a mathematically rigorous model, influencing subsequent refinements of the LSR throughout the century.[23] Following World War II, advancements in radio astronomy significantly refined LSR parameters through observations of the 21 cm neutral hydrogen (HI) line. The line's discovery in 1951 by Hendrik Ewen and Edward Purcell enabled mapping of interstellar gas kinematics, with early Dutch observations by Christiaan Muller and Jan Oort confirming galactic rotation via Doppler shifts in HI emission. In the 1950s, extensive surveys using telescopes like the Dwingeloo radiotelescope measured HI radial velocities across the galactic plane, revealing deviations from circular motion and allowing precise calibration of the LSR's circular velocity near the Sun, estimated at around 220 km/s. These data-driven refinements reduced uncertainties in local velocity fields by incorporating gas dynamics, which traced the average motion of stars and gas more reliably than optical star counts alone, and highlighted asymmetries in the rotation curve that informed LSR definitions.[24] The International Astronomical Union (IAU) formalized key LSR parameters in 1985 during its General Assembly, adopting a galactic rotation speed of 220 km/s at 8.5 kpc from the center based on synthesized optical and early radio data. This consensus provided a uniform reference for kinematic studies, minimizing discrepancies in velocity corrections across astronomical catalogs and establishing the LSR as a practical tool for analyzing stellar and gaseous motions in the solar neighborhood.[11]Mathematical Framework
Formal Definition
The Local Standard of Rest (LSR) is formally defined as the reference frame in galactic dynamics that corresponds to the velocity of a hypothetical star at the Sun's galactocentric position moving in a perfectly circular orbit around the Galactic center, providing a local benchmark for peculiar motions of nearby stars.[25][3][26] In the standard local galactic Cartesian coordinate system centered on the Sun—with the U component positive toward the Galactic center, V positive in the direction of Galactic rotation, and W positive toward the north Galactic pole—the velocity vector of the LSR is given by , where is the circular speed at the Sun's position.[27] For nearby stars, their velocities relative to the LSR are expressed as , where represents the peculiar velocity components with respect to the LSR, and the peculiar motions have zero mean over the local stellar population.[27][28] The velocity dispersion of stars in the LSR frame, which quantifies the spread of peculiar motions, is characterized by the velocity ellipsoid rather than being isotropic, with principal axes aligned approximately with the U, V, and W directions and typical dispersions satisfying (e.g., around 35–40 km/s, 20–25 km/s, and 18–20 km/s for young disk stars, respectively).[3][29] This ellipsoid arises from the underlying dynamics of the Galactic potential and can exhibit a slight tilt relative to the Galactic plane, as observed in distributions projected onto planes involving galactic longitude and latitude.[29] Within the epicycle approximation, which linearizes stellar orbits in the nearly axisymmetric Galactic potential near the Sun, the LSR serves as the guiding center velocity for local stars, around which individual stars execute small radial and vertical oscillations; the epicycle frequency and vertical frequency govern these motions, with the guiding center angular speed matching the local circular rotation.[30] As of analyses incorporating Gaia DR3 data (released in 2022 and refined through 2025), the accepted value for the circular speed is km/s, derived from kinematic modeling of old stars tracing the rotation curve.[31][32]Coordinate Transformations
To transform observed stellar velocities from the heliocentric frame to the Local Standard of Rest (LSR), a series of coordinate rotations and vector corrections are applied to account for the Sun's peculiar motion relative to the local galactic frame. The core transformation involves converting the heliocentric velocity vector (typically derived from radial velocity and proper motions in equatorial coordinates) to the galactic frame and then adding the Sun's velocity with respect to the LSR. This is expressed as , where is the rotation matrix that aligns equatorial Cartesian coordinates with the galactic system, defined by the position of the north galactic pole (at RA , Dec in B1950 equinox, or RA , Dec in J2000 equinox) and the longitude of the ascending node (). The explicit elements of follow the standard formulation for right-handed galactic coordinates, with positive toward the galactic center, in the direction of galactic rotation, and toward the north galactic pole. The step-by-step process begins with converting the star's position from equatorial coordinates (right ascension and declination ) to galactic coordinates (longitude and latitude ) using the rotation matrix , which projects the unit vector in the direction of the star onto the galactic plane. Next, the heliocentric velocity components are computed: the radial component is directly the observed line-of-sight velocity, while the tangential components are derived from proper motions (in RA direction, corrected for ) and (in Dec direction), scaled by the distance (from parallax) and the conversion factor . These yield the equatorial Cartesian velocity vector . The vector is then rotated to galactic Cartesian coordinates via , after which the solar peculiar motion is added component-wise; standard values are , , . This yields the star's peculiar velocity relative to the LSR. Common implementations of these transformations are available in astronomical software libraries, facilitating automated computation. In Python's Astropy package, the LSR frame is defined as an affine transformation of the ICRS (International Celestial Reference System), with velocity offsets applied via theSkyCoord class and its transform_to method; for instance, a coordinate object with attached differential velocities can be directly transformed to the LSR frame, incorporating the default solar motion from Schönrich et al. (2010). Similar routines exist in other tools, such as the gal_uvw function in the PyAstronomy library, which computes using the Johnson & Soderblom (1987) matrices.[33]
Error propagation in these transformations arises primarily from uncertainties in input measurements and the solar motion parameters. Proper motion errors from Gaia data releases, typically 0.02–0.1 mas yr for magnitudes , propagate to tangential velocity uncertainties of km s (with in kpc and in mas yr), while radial velocity errors (e.g., 0.1–1 km s from spectroscopy) and parallax uncertainties (affecting distance) contribute additively; the covariance matrix for is derived via Jacobian propagation of the rotation and addition steps, often resulting in correlated errors of 1–5 km s at 1 kpc distances.[34] Uncertainties in itself, at the 0.5 km s level, further amplify these by up to 10% in the final LSR velocities.