Arcturus: Benchmark K Giant Star

• Arcturus is a benchmark K giant star with well-constrained parameters derived from spectrophotometry, interferometry, and spectroscopy.
• Interferometric and spectroscopic studies reveal its detailed photospheric, chromospheric, and wind structures, which are crucial for refining cool-star models.
• Its chemical abundances and dynamic measurements serve as a foundation for Galactic phase-space analyses and inspire applications across diverse research fields.

Arcturus, designated $\alpha$ Boo and cataloged as HD 124897, HIP 69673, and HR 5340, is a nearby K giant that occupies a central place in modern stellar astrophysics as a benchmark for cool-star atmospheres, interferometry, abundance analysis, and outer-atmosphere physics. In the cited literature it is treated primarily as a K1.5 III red giant with moderately subsolar metallicity and thick-disk kinematics, but the name also appears in derivative contexts, including the Arcturus stream in Galactic phase space, the ARCTURUS high-power laser system, and the cloud-native Global Accelerator framework “Arcturus” (Ramirez et al., 2011, Kushniruk et al., 2019, Grieser et al., 2018, Liu et al., 15 Jul 2025).

1. Stellar identity and benchmark status

Arcturus is repeatedly used as a reference red giant because its fundamental parameters are unusually well constrained for an evolved cool star. A self-consistent determination based on spectrophotometry, interferometry, parallax, and differential spectroscopy gives $T_{\mathrm{eff}} = 4286 \pm 30\ \mathrm{K}$, $\log g = 1.66 \pm 0.05$, $[\mathrm{Fe}/\mathrm{H}] = -0.52 \pm 0.04$, $M = 1.08 \pm 0.06\ M_\odot$, $R = 25.4 \pm 0.2\ R_\odot$, and $t = 7.1^{+1.5}_{-1.2}\ \mathrm{Gyr}$. The same study adopts a limb-darkened angular diameter $$\theta_{\mathrm{LD}} = 21.06 \pm 0.17\ \mathrm{mas}$$ and a parallax $\pi = 88.65 \pm 0.40\ \mathrm{mas}$, corresponding to $d \approx 11.29\ \mathrm{pc}$ (Ramirez et al., 2011).

Quantity	Representative value	Source
Spectral type	K1.5 III	(Ramirez et al., 2011)
$T_{\mathrm{eff}} = 4286 \pm 30\ \mathrm{K}$0	$T_{\mathrm{eff}} = 4286 \pm 30\ \mathrm{K}$1	(Ramirez et al., 2011)
$T_{\mathrm{eff}} = 4286 \pm 30\ \mathrm{K}$2	$T_{\mathrm{eff}} = 4286 \pm 30\ \mathrm{K}$3	(Ramirez et al., 2011)
$T_{\mathrm{eff}} = 4286 \pm 30\ \mathrm{K}$4	$T_{\mathrm{eff}} = 4286 \pm 30\ \mathrm{K}$5	(Ramirez et al., 2011)
Mass	$T_{\mathrm{eff}} = 4286 \pm 30\ \mathrm{K}$6	(Ramirez et al., 2011)
Radius	$T_{\mathrm{eff}} = 4286 \pm 30\ \mathrm{K}$7	(Ramirez et al., 2011)
Age	$T_{\mathrm{eff}} = 4286 \pm 30\ \mathrm{K}$8	(Ramirez et al., 2011)

The star’s benchmark status is not merely methodological. Its chemistry is described as typical of a local thick-disk star, consistent with its kinematics, and this has made it a cornerstone for differential abundance analyses of cool giants. Published analyses use closely similar atmospheric models, for example $T_{\mathrm{eff}} = 4286 \pm 30\ \mathrm{K}$9, $\log g = 1.66 \pm 0.05$0, $\log g = 1.66 \pm 0.05$1 in a vanadium study, or $\log g = 1.66 \pm 0.05$2, $\log g = 1.66 \pm 0.05$3, and $\log g = 1.66 \pm 0.05$4 in a combined NIR-optical “Arcturus Lab” analysis (Wood et al., 2017, Fanelli et al., 2020).

Interferometric work reinforces this benchmark role. In the $\log g = 1.66 \pm 0.05$5 continuum, a uniform-disk angular diameter of $\log g = 1.66 \pm 0.05$6 was measured, while a visible-light intensity-interferometry plus speckle analysis yielded $\log g = 1.66 \pm 0.05$7, explicitly consistent with earlier measurements (Ohnaka et al., 2018, Horch et al., 19 Jan 2026).

2. Photosphere, interferometry, and temperature stratification

The photosphere of Arcturus has been constrained by complementary methods: spectral-energy-distribution fitting, Ca II H and K wing synthesis, and direct interferometry. In the SED approach, model fluxes were fitted from $\log g = 1.66 \pm 0.05$8 to $\log g = 1.66 \pm 0.05$9, with visible spectrophotometry, IRTF near-IR spectra, and ISO/SWS fluxes. This returned $[\mathrm{Fe}/\mathrm{H}] = -0.52 \pm 0.04$0, while direct integration of the surface flux gave $[\mathrm{Fe}/\mathrm{H}] = -0.52 \pm 0.04$1 (Ramirez et al., 2011).

A distinct semiempirical route uses the extended wings of Ca II H and K as a photospheric thermometer. Because these wings form over approximately $[\mathrm{Fe}/\mathrm{H}] = -0.52 \pm 0.04$2 to $[\mathrm{Fe}/\mathrm{H}] = -0.52 \pm 0.04$3 and are largely insensitive to NLTE effects and velocity broadening far from line center, they constrain the temperature gradient through most of the photosphere. This analysis found that the local continuum near Ca II H and K is underestimated by about $[\mathrm{Fe}/\mathrm{H}] = -0.52 \pm 0.04$4 in published atlases of Arcturus, and that the synthetic continuum exceeds the observed absolute flux by about $[\mathrm{Fe}/\mathrm{H}] = -0.52 \pm 0.04$5 over $[\mathrm{Fe}/\mathrm{H}] = -0.52 \pm 0.04$6–$[\mathrm{Fe}/\mathrm{H}] = -0.52 \pm 0.04$7. The recommended wavelength-dependent continuum-opacity correction is

$[\mathrm{Fe}/\mathrm{H}] = -0.52 \pm 0.04$8

with $[\mathrm{Fe}/\mathrm{H}] = -0.52 \pm 0.04$9 at $M = 1.08 \pm 0.06\ M_\odot$0, respectively. With this correction, the resulting stratification closely matches the theoretical model with $M = 1.08 \pm 0.06\ M_\odot$1, $M = 1.08 \pm 0.06\ M_\odot$2, and $M = 1.08 \pm 0.06\ M_\odot$3 (Sheminova, 2013).

Interferometry provides the direct geometric complement. For a uniform disk of diameter $M = 1.08 \pm 0.06\ M_\odot$4, the visibility is

$M = 1.08 \pm 0.06\ M_\odot$5

and this relation underlies both the VLTI/AMBER analysis and the later visible-light intensity interferometry. The Southern Connecticut Stellar Interferometer measured a squared visibility $M = 1.08 \pm 0.06\ M_\odot$6 at $M = 1.08 \pm 0.06\ M_\odot$7 and, combined with DSSI speckle data at $M = 1.08 \pm 0.06\ M_\odot$8 and $M = 1.08 \pm 0.06\ M_\odot$9, obtained $R = 25.4 \pm 0.2\ R_\odot$0 using a limb-darkened profile with $R = 25.4 \pm 0.2\ R_\odot$1 (Horch et al., 19 Jan 2026).

3. Outer atmosphere, chromosphere, wind, and X-rays

Arcturus is not a single-component giant atmosphere. Its outer layers are explicitly described as thermally inhomogeneous, containing both hot chromospheric plasma at approximately $R = 25.4 \pm 0.2\ R_\odot$2 and cool molecular gas. High-resolution VLTI/AMBER spectro-interferometry in the CO first-overtone lines at $R = 25.4 \pm 0.2\ R_\odot$3–$R = 25.4 \pm 0.2\ R_\odot$4 spatially resolved this multicomponent region and showed that Arcturus appears significantly larger in the individual CO lines than predicted by a hydrostatic MARCS photosphere (Ohnaka et al., 2018).

The decisive result is a two-layer CO model above the photosphere. The inner layer lies at $R = 25.4 \pm 0.2\ R_\odot$5, is geometrically thin, and has $R = 25.4 \pm 0.2\ R_\odot$6 with $R = 25.4 \pm 0.2\ R_\odot$7. The outer layer extends to $R = 25.4 \pm 0.2\ R_\odot$8 with $R = 25.4 \pm 0.2\ R_\odot$9 and $t = 7.1^{+1.5}_{-1.2}\ \mathrm{Gyr}$0. A single layer cannot fit the wavelength-dependent visibilities on all baselines; the two-layer solution is required because the extended outer layer depresses the short-baseline visibility, while emission from the dense inner layer partly counteracts that effect at the longest baseline. The basic slab transfer used in the modeling is

$t = 7.1^{+1.5}_{-1.2}\ \mathrm{Gyr}$1

with $t = 7.1^{+1.5}_{-1.2}\ \mathrm{Gyr}$2 and approximate $t = 7.1^{+1.5}_{-1.2}\ \mathrm{Gyr}$3 (Ohnaka et al., 2018).

This resolved a longstanding ambiguity in favor of an extended cool molecular component. Earlier spatially unresolved analyses had already inferred cool $t = 7.1^{+1.5}_{-1.2}\ \mathrm{Gyr}$4–$t = 7.1^{+1.5}_{-1.2}\ \mathrm{Gyr}$5 gas coexisting with chromospheric material, and mid-IR H$t = 7.1^{+1.5}_{-1.2}\ \mathrm{Gyr}$6O lines had been modeled by lowering the upper-photospheric temperature, but the AMBER data directly resolved a quasi-static cool component extending to $t = 7.1^{+1.5}_{-1.2}\ \mathrm{Gyr}$7–$t = 7.1^{+1.5}_{-1.2}\ \mathrm{Gyr}$8. The observed non-zero closure phases and asymmetric differential phases show that the CO-forming layers are not point-symmetric. The “tilde-shaped” visibility asymmetries suggest localized upflows, downflows, or spots in the upper photosphere, while the very weak Mg I line at $t = 7.1^{+1.5}_{-1.2}\ \mathrm{Gyr}$9 shows analogous behavior (Ohnaka et al., 2018).

The outer atmosphere is also unusual at high energies. Chandra HRC-I pointings totaling about $$\theta_{\mathrm{LD}} = 21.06 \pm 0.17\ \mathrm{mas}$$0 confirmed a co-moving soft X-ray source at the stellar position, with an apparent $$\theta_{\mathrm{LD}} = 21.06 \pm 0.17\ \mathrm{mas}$$1–$$\theta_{\mathrm{LD}} = 21.06 \pm 0.17\ \mathrm{mas}$$2 flux of about $$\theta_{\mathrm{LD}} = 21.06 \pm 0.17\ \mathrm{mas}$$3 and an X-ray luminosity of about $$\theta_{\mathrm{LD}} = 21.06 \pm 0.17\ \mathrm{mas}$$4. The source followed the star’s large proper motion across a $$\theta_{\mathrm{LD}} = 21.06 \pm 0.17\ \mathrm{mas}$$5-year baseline, strongly disfavoring a background coincidence. The preferred interpretation is a very weak or strongly screened “buried corona,” consistent with the idea that a thick chromosphere and cool wind can absorb soft X-rays even if magnetic heating persists (Ayres, 2018).

Taken together, the interferometric and X-ray data point to a strongly structured outer atmosphere in which a quasi-static cool MOLsphere coexists with an accelerating hot wind. Chromospheric diagnostics imply electron temperatures rising to approximately $$\theta_{\mathrm{LD}} = 21.06 \pm 0.17\ \mathrm{mas}$$6 at approximately $$\theta_{\mathrm{LD}} = 21.06 \pm 0.17\ \mathrm{mas}$$7 and a wind reaching terminal speeds of $$\theta_{\mathrm{LD}} = 21.06 \pm 0.17\ \mathrm{mas}$$8–$$\theta_{\mathrm{LD}} = 21.06 \pm 0.17\ \mathrm{mas}$$9 within $\pi = 88.65 \pm 0.40\ \mathrm{mas}$0, whereas high-resolution CO spectra show no systematic outflow signature in the cool component down to approximately $\pi = 88.65 \pm 0.40\ \mathrm{mas}$1 (Ohnaka et al., 2018).

4. Chemical composition and abundance diagnostics

Arcturus functions as a laboratory for abundance methodology because its spectrum is rich, high-quality, and repeatedly observed from the near-UV to the mid-IR. The standard abundance notation used in several studies is

$\pi = 88.65 \pm 0.40\ \mathrm{mas}$2

with differential metallicities defined by

$\pi = 88.65 \pm 0.40\ \mathrm{mas}$3

Within this framework, a weak-line MARCS analysis of Fe I and Fe II profiles gave $\pi = 88.65 \pm 0.40\ \mathrm{mas}$4 and $\pi = 88.65 \pm 0.40\ \mathrm{mas}$5 relative to a similarly analyzed Sun, while a broader self-consistent atmospheric study adopted $\pi = 88.65 \pm 0.40\ \mathrm{mas}$6 from Fe I lines (Sheminova, 2015, Ramirez et al., 2011).

The iron-peak inventory is correspondingly detailed. A vanadium study based on $\pi = 88.65 \pm 0.40\ \mathrm{mas}$7 V I lines between $\pi = 88.65 \pm 0.40\ \mathrm{mas}$8 and $\pi = 88.65 \pm 0.40\ \mathrm{mas}$9 derived $d \approx 11.29\ \mathrm{pc}$0, implying $d \approx 11.29\ \mathrm{pc}$1 and $d \approx 11.29\ \mathrm{pc}$2, with no significant trends with wavelength, line strength, or lower excitation energy. That same work also resolved a discrepancy in near-IR $d \approx 11.29\ \mathrm{pc}$3 values around $d \approx 11.29\ \mathrm{pc}$4 by showing that the Lawler et al. calibration, not the Holmes et al. alternative, is internally consistent in Arcturus (Wood et al., 2017).

CNO abundances and isotopic diagnostics are especially rich because Arcturus exhibits the characteristic mixed-giant pattern. Using new CN line lists, one study found $d \approx 11.29\ \mathrm{pc}$5, $d \approx 11.29\ \mathrm{pc}$6, $d \approx 11.29\ \mathrm{pc}$7, and $d \approx 11.29\ \mathrm{pc}$8. A later combined GIANO-B plus UVES analysis obtained a very similar pattern, with $d \approx 11.29\ \mathrm{pc}$9, $T_{\mathrm{eff}} = 4286 \pm 30\ \mathrm{K}$00, $T_{\mathrm{eff}} = 4286 \pm 30\ \mathrm{K}$01, $T_{\mathrm{eff}} = 4286 \pm 30\ \mathrm{K}$02, $T_{\mathrm{eff}} = 4286 \pm 30\ \mathrm{K}$03, $T_{\mathrm{eff}} = 4286 \pm 30\ \mathrm{K}$04, and again $T_{\mathrm{eff}} = 4286 \pm 30\ \mathrm{K}$05 (Sneden et al., 2014, Fanelli et al., 2020).

The GIANO-B study is methodologically notable for introducing two diagnostics specialized for oxygen-rich giants. The “carbon thermometer” requires consistency between atomic and molecular carbon,

$T_{\mathrm{eff}} = 4286 \pm 30\ \mathrm{K}$06

and sets $T_{\mathrm{eff}} = 4286 \pm 30\ \mathrm{K}$07 by $T_{\mathrm{eff}} = 4286 \pm 30\ \mathrm{K}$08. The “oxygen gravitometer” requires consistency between [O I] and OH,

$T_{\mathrm{eff}} = 4286 \pm 30\ \mathrm{K}$09

and sets $T_{\mathrm{eff}} = 4286 \pm 30\ \mathrm{K}$10 by $T_{\mathrm{eff}} = 4286 \pm 30\ \mathrm{K}$11. Applied to Arcturus, these gave $T_{\mathrm{eff}} = 4286 \pm 30\ \mathrm{K}$12 and $T_{\mathrm{eff}} = 4286 \pm 30\ \mathrm{K}$13 (Fanelli et al., 2020).

The benchmark status extends beyond Fe and CNO. A WINERED analysis of Fe I lines in the $T_{\mathrm{eff}} = 4286 \pm 30\ \mathrm{K}$14–$T_{\mathrm{eff}} = 4286 \pm 30\ \mathrm{K}$15 region found that MB99 oscillator strengths give $T_{\mathrm{eff}} = 4286 \pm 30\ \mathrm{K}$16 and $T_{\mathrm{eff}} = 4286 \pm 30\ \mathrm{K}$17 for Arcturus, while an NLTE study of strontium reduced the Sr I/Sr II ionization discrepancy from about $T_{\mathrm{eff}} = 4286 \pm 30\ \mathrm{K}$18 in LTE to about $T_{\mathrm{eff}} = 4286 \pm 30\ \mathrm{K}$19 in NLTE, yielding approximately $T_{\mathrm{eff}} = 4286 \pm 30\ \mathrm{K}$20 (Kondo et al., 2019, Bergemann et al., 2012).

5. Velocity fields, rotation, and non-convective mixing

The photospheric velocity field of Arcturus has been measured from line profiles and interpreted in the context of giant-star convection. Fourier analysis of three strong Fe I lines at $T_{\mathrm{eff}} = 4286 \pm 30\ \mathrm{K}$21 favored an isotropic Gaussian microturbulence of $T_{\mathrm{eff}} = 4286 \pm 30\ \mathrm{K}$22 and an anisotropic radial-tangential macroturbulence of $T_{\mathrm{eff}} = 4286 \pm 30\ \mathrm{K}$23, with rotation fixed at $T_{\mathrm{eff}} = 4286 \pm 30\ \mathrm{K}$24. A separate weak-line fitting study found $T_{\mathrm{eff}} = 4286 \pm 30\ \mathrm{K}$25. The difference reflects methodology, line selection, and the partition between rotational and macroturbulent broadening, not a contradiction in the existence of large-scale convective motions (Sheminova et al., 2010, Sheminova, 2015).

On longer dynamical scales, a mean-field model motivated by the star’s spectroscopic variability and Ca II H+K modulation predicts solar-type surface differential rotation, but with only about one-tenth of the solar absolute shear. For a rotation period of about two years, the model gives $T_{\mathrm{eff}} = 4286 \pm 30\ \mathrm{K}$26, surface meridional flow with maximum speed of $T_{\mathrm{eff}} = 4286 \pm 30\ \mathrm{K}$27, and turbulent magnetic diffusivity of order $T_{\mathrm{eff}} = 4286 \pm 30\ \mathrm{K}$28–$T_{\mathrm{eff}} = 4286 \pm 30\ \mathrm{K}$29. The rotation rate increases monotonically with depth at all latitudes, the horizontal shear vanishes in the lower convection zone, and the authors conclude that the conditions are not favorable for a circulation-dominated dynamo (Küker et al., 2010).

Surface composition independently implies transport beneath the convective envelope. High-resolution $T_{\mathrm{eff}} = 4286 \pm 30\ \mathrm{K}$30 CO spectroscopy yielded $T_{\mathrm{eff}} = 4286 \pm 30\ \mathrm{K}$31, $T_{\mathrm{eff}} = 4286 \pm 30\ \mathrm{K}$32, $T_{\mathrm{eff}} = 4286 \pm 30\ \mathrm{K}$33, and $T_{\mathrm{eff}} = 4286 \pm 30\ \mathrm{K}$34. The carbon ratio is far below pure first-dredge-up expectations, and parametric transport models require non-convective mixing that reaches layers just below the H-burning shell with preferred parameters $T_{\mathrm{eff}} = 4286 \pm 30\ \mathrm{K}$35 and $T_{\mathrm{eff}} = 4286 \pm 30\ \mathrm{K}$36, corresponding to $T_{\mathrm{eff}} = 4286 \pm 30\ \mathrm{K}$37–$T_{\mathrm{eff}} = 4286 \pm 30\ \mathrm{K}$38. The circulation–diffusion correspondence used is

$T_{\mathrm{eff}} = 4286 \pm 30\ \mathrm{K}$39

Very slow diffusion is explicitly found to be inadequate (Abia et al., 2012).

These constraints converge on a consistent dynamical picture. Arcturus is a low-gravity giant with vigorous but extended convective flows, photospheric macroturbulence at a few $T_{\mathrm{eff}} = 4286 \pm 30\ \mathrm{K}$40, large-scale differential rotation that is weak in absolute terms, and envelope abundances that require transport faster than standard thermohaline diffusion alone (Sheminova et al., 2010, Küker et al., 2010, Abia et al., 2012).

6. Historical record, pedagogical use, and derivative nomenclature

Arcturus also appears outside stellar-atmosphere work in historical, didactical, and nominal contexts. In Safaitic inscriptions from the Al-Hara Zone, the star is identified as “Alsamak” and functions as a seasonal marker rather than primarily as a navigation star. The cited inscriptions place it as the star that ends the heat season, qayz, and as the “last star” of the summer, saief. The key textual example is CIS216, read in the paper as “w n z r s m k m hr n,” glossed as “aintazar samak min huran.” The authors treat “Alsamak” as Arcturus and explicitly connect it to a pre-Islamic Arabian seasonal framework (Talafha et al., 2019).

A modern pedagogical use appears in an “occultation” exercise in Vatican City. There, the rim of the dome of Saint Peter’s Basilica plays the role of the Moon and Arcturus serves as the target star. The setup uses the daily sidereal drift of approximately $T_{\mathrm{eff}} = 4286 \pm 30\ \mathrm{K}$41 against a nearby fixed obstruction. With a camera objective of diameter $T_{\mathrm{eff}} = 4286 \pm 30\ \mathrm{K}$42 at a distance $T_{\mathrm{eff}} = 4286 \pm 30\ \mathrm{K}$43 from the dome, the small-angle estimate

$T_{\mathrm{eff}} = 4286 \pm 30\ \mathrm{K}$44

gives about $T_{\mathrm{eff}} = 4286 \pm 30\ \mathrm{K}$45, implying a predicted disappearance time of about $T_{\mathrm{eff}} = 4286 \pm 30\ \mathrm{K}$46. The paper quotes an angular diameter of Arcturus of about $T_{\mathrm{eff}} = 4286 \pm 30\ \mathrm{K}$47 and notes that a true lunar occultation is impossible because Arcturus is “not in the Zodiacal Catalogue” (Sigismondi, 2013).

The name also designates a Galactic kinematic structure. The Arcturus stream is an overdensity in velocity space, not a coeval stellar population born with the star Arcturus. In Gaia DR2-based action-space analyses it appears as a low-velocity, low-angular-momentum structure with thick-disk-like chemistry, median $T_{\mathrm{eff}} = 4286 \pm 30\ \mathrm{K}$48, and a wide abundance spread incompatible with a dissolved open cluster. Its properties, together with those of AF06 and KFR08, are interpreted as more consistent with a phase-space wave caused by an ancient merger event than with a bar-originated resonance (Kushniruk et al., 2019).

Finally, “Arcturus” has been adopted as a technical system name in other branches of research. In laser-plasma physics, ARCTURUS is a $T_{\mathrm{eff}} = 4286 \pm 30\ \mathrm{K}$49 Ti:Sapphire laser system used with a cryogenic hydrogen cluster-jet target; the reported configuration used $T_{\mathrm{eff}} = 4286 \pm 30\ \mathrm{K}$50, $T_{\mathrm{eff}} = 4286 \pm 30\ \mathrm{K}$51 pulses focused to $T_{\mathrm{eff}} = 4286 \pm 30\ \mathrm{K}$52, operated at $T_{\mathrm{eff}} = 4286 \pm 30\ \mathrm{K}$53, and produced proton energies of roughly $T_{\mathrm{eff}} = 4286 \pm 30\ \mathrm{K}$54 (Grieser et al., 2018). In cloud systems research, “Arcturus” denotes a cloud-native multi-cloud Global Accelerator overlay with a two-plane design; the reported evaluation states up to $T_{\mathrm{eff}} = 4286 \pm 30\ \mathrm{K}$55 acceleration performance, a $T_{\mathrm{eff}} = 4286 \pm 30\ \mathrm{K}$56 cost reduction relative to AWS GA for million-RPS acceleration, and sustained resource utilization over $T_{\mathrm{eff}} = 4286 \pm 30\ \mathrm{K}$57 (Liu et al., 15 Jul 2025).

Arcturus therefore combines an unusually rich set of meanings. As $T_{\mathrm{eff}} = 4286 \pm 30\ \mathrm{K}$58 Boo it is a benchmark red giant whose photosphere, extended atmosphere, chemical inventory, and dynamical transport have been resolved in exceptional detail. As a name, it has also propagated into epigraphy, pedagogy, Galactic dynamics, laser-plasma experimentation, and distributed systems research, each usage preserving the distinctiveness of a canonical stellar reference point (Ramirez et al., 2011, Ohnaka et al., 2018, Fanelli et al., 2020).