arXiv subjects

Nathan Smith

Publications and source records attributed to Nathan Smith.

At least 127 records · Page 7Linked to original sources

arXiv2022

The extreme scarcity of dust-enshrouded red supergiants: consequences for producing stripped stars via winds

Quiescent mass-loss during the red supergiant (RSG) phase has been shown to be far lower than prescriptions typically employed in single-star evolutionary models. Importantly, RSG winds are too weak to drive the production of Wolf-Rayets (WRs) and stripped-envelope supernovae (SE-SNe) at initial masses of roughly 20--40$M_{\odot}$. If single-stars are to make WRs and SE-SNe, this shifts the burden of mass-loss to rare dust-enshrouded RSGs (DE-RSGs), objects claimed to represent a short-lived high mass-loss phase. Here, we take a fresh look at the purported DE-RSGs. By modeling the mid-IR excesses of the full sample of RSGs in the LMC, we find that only one RSG has both a high mass-loss rate (\mdot $\ge$ 10$^{-4}$ $M_{\odot}$ yr$^{-1}$) and a high optical circumstellar dust extinction (7.92 mag). This one RSG is WOH G64, and it is the only one of the 14 originally proposed DE-RSGs that is actually dust enshrouded. The rest appear to be either normal RSGs without strong infrared-excess, or lower-mass asymptotic giant branch (AGB) stars. Only one additional object in the full catalog of RSGs (not previously identified as a DE-RSG) shows strong mid-IR excess. We conclude that if DE-RSGs do represent a pre-SN phase of enhanced \mdot\ in single-stars, it is extremely short-lived, only capable of removing $\leq$2\msun\ of material. This rules out the single-star post-RSG pathway for the production of WRs, LBVs, and SE-SN. Single-star models should not employ \mdot-prescriptions based on these extreme objects for any significant fraction of the RSG phase.

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arXiv2022

An Exceptional Dimming Event for a Massive, Cool Supergiant in M51

We present the discovery of an exceptional dimming event in a cool supergiant star in the Local Volume spiral M51. The star, dubbed M51-DS1, was found as part of a Hubble Space Telescope (HST) search for failed supernovae (SNe). The supergiant, which is plausibly associated with a very young ($\lesssim6$ Myr) stellar population, showed clear variability (amplitude $ΔF814W\approx0.7$ mag) in numerous HST images obtained between 1995 and 2016, before suddenly dimming by $>$2 mag in $F814W$ sometime between late 2017 and mid-2019. In follow-up data from 2021, the star rebrightened, ruling out a failed supernova. Prior to its near-disappearance, the star was luminous and red ($M_{F814W}\lesssim-7.6$ mag, $F606W-F814W=1.9$ - $2.2$ mag). Modeling of the pre-dimming spectral energy distribution of the star favors a highly reddened, very luminous ($\log[L/L_{\odot}] = 5.4$ - $5.7$) star with $T_{\mathrm{eff}}\approx3700$ - $4700$ K, indicative of a cool yellow or post-red supergiant (RSG) with an initial mass of $\approx26$ - $40$ $M_{\odot}$. However, the local interstellar extinction and circumstellar extinction are uncertain, and could be lower: the near-IR colors are consistent with an RSG, which would be cooler ($T_{\mathrm{eff}}\lesssim3700$ K) and slightly less luminous ($\log[L/L_{\odot}] = 5.2$ - $5.3$), giving an inferred initial mass of $\approx19$ - $22$ $M_{\odot}$. In either case, the dimming may be explained by a rare episode of enhanced mass loss that temporarily obscures the star, potentially a more extreme counterpart to the 2019 - 2020 "Great Dimming" of Betelgeuse. Given the emerging evidence that massive evolved stars commonly exhibit variability that can mimic a disappearing star, our work highlights a substantial challenge in identifying true failed SNe.

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arXiv2022

The Candidate Progenitor Companion Star of the Type Ib/c SN 2013ge

This Letter presents the detection of a source at the position of the Type Ib/c supernova (SN) 2013ge more than four years after the radioactive component is expected to have faded. This source could mark the first post-SN direct detection of a surviving companion to a stripped-envelope Type Ib/c explosion. We test this hypothesis and find the shape of the source's spectral energy distribution is most consistent with that of a B5 I supergiant. While binary models tend to predict OB-type stars for stripped-envelope companions, the location of the source on a color-magnitude diagram (CMD) places it redward of its more likely position on the main sequence (MS). The source may be temporarily out of thermal equilibrium, or a cool and inflated non-MS companion, which is similar to the suggested companion of Type Ib SN 2019yvr that was constrained from pre-SN imaging. We also consider other possible physical scenarios for the source, including a fading SN, circumstellar shock interaction, line of site coincidence, and an unresolved host star cluster, all of which will require future observations to more definitively rule out. Ultimately, the fraction of surviving companions ("binary fraction") will provide necessary constraints on binary evolution models and the underlying physics.

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arXiv2022

Infant-phase reddening by surface Fe-peak elements in a normal Type Ia Supernova

Type Ia Supernovae are thermonuclear explosions of white dwarf stars. They play a central role in the chemical evolution of the Universe and are an important measure of cosmological distances. However, outstanding questions remain about their origins. Despite extensive efforts to obtain natal information from their earliest signals, observations have thus far failed to identify how the majority of them explode. Here, we present infant-phase detections of SN 2018aoz from a brightness of -10.5 absolute AB magnitudes -- the lowest luminosity early Type Ia signals ever detected -- revealing a hitherto unseen plateau in the $B$-band that results in a rapid redward color evolution between 1.0 and 12.4 hours after the estimated epoch of first light. The missing $B$-band flux is best-explained by line-blanket absorption from Fe-peak elements in the outer 1% of the ejected mass. The observed $B-V$ color evolution of the SN also matches the prediction from an over-density of Fe-peak elements in the same outer 1% of the ejected mass, whereas bluer colors are expected from a purely monotonic distribution of Fe-peak elements. The presence of excess nucleosynthetic material in the extreme outer layers of the ejecta points to enhanced surface nuclear burning or extended sub-sonic mixing processes in some normal Type Ia Supernova explosions.

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arXiv2022

Optical Rebrightening of Extragalactic Transients from the Zwicky Transient Facility

Ongoing large-scale optical time-domain surveys, such as the Zwicky Transient Facility (ZTF), are producing alerts at unprecedented rates. Analysis of transient sources has so far followed two distinct paths: archival analysis of data on transient sources at a time when they are no longer observable and real-time analysis at the time when the sources are first detected. The latter is the realm of alert brokers such as the Arizona-NOIRLab Temporal Analysis and Response to Events System (ANTARES). In this paper, we synthesize the two analysis paths and present a first systematic study of archival alert-broker data, focusing on extragalactic transients with multipeaked light curves identified in the ANTARES archive of ZTF alerts. Our analysis yields a sample of 37 such sources, including core-collapse supernovae (with two analogs of iPTF14hls), thermonuclear supernovae interacting with their surrounding circumstellar medium, tidal disruption events, luminous blue variables, and as yet unclassified objects. A large fraction of the identified sources is currently active, warranting allocation of follow-up resources in the immediate future to further constrain their nature and the physical processes at work.

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arXiv2022

Massive stars dying alone: the remote environment of SN 2010jp and its associated late-time source

We present late-time images of the site of the peculiar jet-driven TypeIIn supernova SN2010jp, including HST images taken 2-5 yr post explosion and deep ground-based images over a similar time. These are used to characterise its unusually remote environment and to constrain the progenitor's initial mass and age. The position of SN2010jp is found to reside along a chain of diffuse starlight that is probably an outer spiral arm or tidal tail of the interacting galaxy pair NGC2207/IC2163. There is one bright HII region projected within 1 kpc, and there is faint extended Halpha emission immediately surrounding the continuum source at the position of SN2010jp, which has $M_{F555W} = -7.7 (\pm 0.2)$ mag. In principle, the lingering light could arise from late-time circumstellar material (CSM) interaction, an evolved supergiant, a host star cluster, or some combination of these. Steady flux over 3 yr and a lack of strong, spatially unresolved Halpha emission make ongoing CSM interaction unlikely. If an evolved supergiant dominates, its observed luminosity implies an initial mass of roughly 22 $M_{\odot}$ and an age older than roughly 8 Myr. If the source is a star cluster, then its colour and absolute magnitude imply an age of 8-13 Myr and a modest cluster initial mass of log($M/M_{\odot}$) = 3.6-3.8. Extended Halpha emission out to a radius of 30 pc reveals a faint evolved HII region, pointing to recent star formation with at least one late O-type star. Based on these various clues, we conclude that the progenitor of SN2010jp had a likely initial mass of 18-22 $M_{\odot}$.

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arXiv2021

Ionized carbon around IRC +10216

Asymptotic giant branch (AGB)stars create a rich inventory of molecules in their envelopes as they lose mass during later stages of their evolution. These molecules cannot survive the conditions in interstellar space, where they are exposed to ultraviolet photons of the interstellar radiation field. As a result, daughter molecules are the ones injected into space, and a halo of those molecules is predicted to exist around cool evolved stars. The most abundant molecule in the envelopes other than H2 is CO, which dissociates into C that is rapidly ionized in a halo around the star that is optically thin to the interstellar radiation field. We develop the specific predictions of the ionized carbon halo size and column density for the well-studied, nearby star IRC +10216. We compare those models to observations of the [C II] 157.7 micron far-infrared fine-structure line using SOFIA and Herschel. The combination of bright emission toward the star and upper limits to extended [C II] is inconsistent with any standard model. The presence of [C II] toward the star requires some dissociation and ionization in the inner part of the outflow, possibly due to a hot companion star. The lack of extended [C II] emission requires that daughter products from CO photodissociation in the outer envelope remain cold. The [C II] profile toward the star is asymmetric, with the blue-shifted absorption due to the cold outer envelope.

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arXiv2021

A High-Velocity Scatterer Revealed in the Thinning Ejecta of a Type II Supernova

We present deep, nebular-phase spectropolarimetry of the Type II-P/L SN 2013ej, obtained 167 days after explosion with the European Southern Observatory's Very Large Telescope. The polarized flux spectrum appears as a nearly perfect (92% correlation), redshifted (by ~4,000 km/sec) replica of the total flux spectrum. Such a striking correspondence has never been observed before in nebular-phase supernova spectropolarimetry, although data capable of revealing it have heretofore been only rarely obtained. Through comparison with 2D polarized radiative transfer simulations of stellar explosions, we demonstrate that localized ionization produced by the decay of a high-velocity, spatially confined clump of radioactive 56-Ni -- synthesized by and launched as part of the explosion with final radial velocity exceeding 4,500 km/sec -- can reproduce the observations through enhanced electron scattering. Additional data taken earlier in the nebular phase (day 134) yield a similarly strong correlation (84%) and redshift, whereas photospheric-phase epochs that sample days 8 through 97, do not. This suggests that the primary polarization signatures of the high-velocity scattering source only come to dominate once the thick, initially opaque hydrogen envelope has turned sufficiently transparent. This detection in an otherwise fairly typical core-collapse supernova adds to the growing body of evidence supporting strong asymmetries across Nature's most common types of stellar explosions, and establishes the power of polarized flux -- and the specific information encoded by it in line photons at nebular epochs -- as a vital tool in such investigations going forward.

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arXiv2021

The impact of realistic red supergiant mass-loss on stellar evolution

Accurate mass-loss rates are essential for meaningful stellar evolutionary models. For massive single stars with initial masses between 8 - 30\msun the implementation of cool supergiant mass loss in stellar models strongly affects the resulting evolution, and the most commonly used prescription for these cool-star phases is that of de Jager. Recently, we published a new \mdot\ prescription calibrated to RSGs with initial masses between 10 - 25\msun, which unlike previous prescriptions does not over estimate \mdot\ for the most massive stars. Here, we carry out a comparative study to the MESA-MIST models, in which we test the effect of altering mass-loss by recomputing the evolution of stars with masses 12-27\msun\ with the new \mdot-prescription implemented. We show that while the evolutionary tracks in the HR diagram of the stars do not change appreciably, the mass of the H-rich envelope at core-collapse is drastically increased compared to models using the de Jager prescription. This increased envelope mass would have a strong impact on the Type II-P SN lightcurve, and would not allow stars under 30\msun\ to evolve back to the blue and explode as H-poor SN. We also predict that the amount of H-envelope around single stars at explosion should be correlated with initial mass, and we discuss the prospects of using this as a method of determining progenitor masses from supernova light curves.

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arXiv2021

AT 2019qyl in NGC 300: Internal Collisions in the Early Outflow from a Very Fast Nova in a Symbiotic Binary

Nova eruptions, thermonuclear explosions on the surfaces of white dwarfs (WDs), are now recognized to be among the most common shock-powered astrophysical transients. We present the early discovery and rapid ultraviolet (UV), optical, and infrared (IR) temporal development of AT 2019qyl, a recent nova in the nearby Sculptor Group galaxy NGC 300. The light curve shows a rapid rise lasting $\lesssim 1$ day, reaching a peak absolute magnitude of $M_V = -9.2$ mag, and a very fast decline, fading by 2 mag over 3.5 days. A steep dropoff in the light curves after 71 days and the rapid decline timescale suggest a low-mass ejection from a massive WD with $M_{\rm WD} \gtrsim 1.2~M_{\odot}$. We present an unprecedented view of the early spectroscopic evolution of such an event. Three spectra prior to the peak reveal a complex, multicomponent outflow giving rise to internal collisions and shocks in the ejecta of an He/N-class nova. We identify a coincident IR-variable counterpart in the extensive preeruption coverage of the transient location and infer the presence of a symbiotic progenitor system with an O-rich asymptotic-giant-branch donor star, as well as evidence for an earlier UV-bright outburst in 2014. We suggest that AT 2019qyl is analogous to the subset of Galactic recurrent novae with red-giant companions such as RS Oph and other embedded nova systems like V407 Cyg. Our observations provide new evidence that internal shocks between multiple, distinct outflow components likely contribute to the generation of the shock-powered emission from such systems.

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arXiv2021

Discovery of a 310-day Period from the Enshrouded Massive System NaSt1 (WR 122)

We present optical and infrared (IR) light curves of NaSt1, also known as Wolf-Rayet (WR) 122, with observations from Palomar Gattini-IR (PGIR), the Zwicky Transient Facility (ZTF), the Katzman Automatic Imaging Telescope (KAIT), the Asteroid Terrestrial-impact Last Alert System (ATLAS), and the All-Sky Automated Survey for Supernovae (ASAS-SN). We identify a $P=309.7\pm0.7$ d photometric period from the optical and IR light curves that reveal periodic, sinusoidal variability between 2014 July and 2021 July. We also present historical IR light curves taken between 1983 July and 1989 May, which show variability consistent with the period of the present-day light curves. In the past, NaSt1 was brighter in the $J$ band with larger variability amplitudes than the present-day PGIR values, suggesting that NaSt1 exhibits variability on longer ($\gtrsim$ decade) timescales. Sinusoidal fits to the recent optical and IR light curves show that the amplitude of NaSt1's variability differs at various wavelengths and also reveal significant phase offsets of $17.0\pm2.5$ d between the ZTF $r$ and PGIR $J$ light curves. We interpret the $310$ d photometric period from NaSt1 as the orbital period of an enshrouded massive binary. We suggest that the photometric variability of NaSt1 may arise from variations in the line-of-sight optical depth toward circumstellar optical/IR emitting regions throughout its orbit due to colliding-wind dust formation. We speculate that past mass transfer in NaSt1 may have been triggered by Roche-lobe overflow (RLOF) during an eruptive phase of an Ofpe/WN9 star. Lastly, we argue that NaSt1 is no longer undergoing RLOF mass transfer.

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arXiv2021

The Blue Supergiant Progenitor of the Supernova Imposter AT~2019krl

Extensive archival \textit{Hubble Space Telescope}, \textit{Spitzer Space Telescope}, and Large Binocular Telescope imaging of the recent intermediate-luminosity transient, AT~2019krl in M74, reveal a bright optical and mid-infrared progenitor star. While the optical peak of the event was missed, a peak was detected in the infrared with an absolute magnitude of $M_{4.5\,μ{\rm m}} = -18.4$ mag, leading us to infer a visual-wavelength peak absolute magnitude of $-$13.5 to $-$14.5. The pre-discovery light curve indicated no outbursts over the previous 16\,yr. The colors, magnitudes, and inferred temperatures of the progenitor best match a 13--14 M$_{\sun}$ yellow or blue supergiant (BSG), if only foreground extinction is taken into account, or a hotter and more massive star, if any additional local extinction is included. A pre-eruption spectrum of the star reveals strong H$α$ and [N~{\sc ii}] emission with wings extending to $\pm 2000$\,km\,s$^{-1}$. The post-eruption spectrum is fairly flat and featureless with only H$α$, \ion{Na}{1}~D, [\ion{Ca}{2}], and the \ion{Ca}{2} triplet in emission. As in many previous intermediate-luminosity transients, AT~2019krl shows remarkable observational similarities to luminous blue variable (LBV) giant eruptions, SN~2008S-like events, and massive-star mergers. However, the information about the pre-eruption star favors either a relatively unobscured BSG or a more extinguished LBV with $M > 20$\,M$_{\sun}$ likely viewed pole-on.

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arXiv2021

The electron-capture origin of supernova 2018zd

In the transitional mass range ($\sim$ 8-10 solar masses) between white dwarf formation and iron core-collapse supernovae, stars are expected to produce an electron-capture supernova. Theoretically, these progenitors are thought to be super-asymptotic giant branch stars with a degenerate O+Ne+Mg core, and electron capture onto Ne and Mg nuclei should initiate core collapse. However, no supernovae have unequivocally been identified from an electron-capture origin, partly because of uncertainty in theoretical predictions. Here we present six indicators of electron-capture supernovae and show that supernova 2018zd is the only known supernova having strong evidence for or consistent with all six: progenitor identification, circumstellar material, chemical composition, explosion energy, light curve, and nucleosynthesis. For supernova 2018zd, we infer a super-asymptotic giant branch progenitor based on the faint candidate in the pre-explosion images and the chemically-enriched circumstellar material revealed by the early ultraviolet colours and flash spectroscopy. The light-curve morphology and nebular emission lines can be explained with the low explosion energy and neutron-rich nucleosynthesis produced in an electron-capture supernova. This identification provides insights into the complex stellar evolution, supernova physics, cosmic nucleosynthesis, and remnant populations in the transitional mass range.

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arXiv2021

GRB 180418A: A possibly-short GRB with a wide-angle outflow in a faint host galaxy

We present X-ray and multi-band optical observations of the afterglow and host galaxy of GRB 180418A, discovered by ${\it Swift}$/BAT and ${\it Fermi}$/GBM. We present a reanalysis of the GBM and BAT data deriving durations of the prompt emission of $T_{90}\approx$2.56s and $\approx$1.90s, respectively. Modeling the ${\it Fermi}$/GBM catalog of 1405 bursts (2008-2014) in the Hardness-$T_{90}$ plane, we obtain a probability of $\approx$60% that GRB 180418A is a short-hard burst. From a combination of ${\it Swift}$/XRT and ${\it Chandra}$ observations, the X-ray afterglow is detected to $\approx$38.5 days after the burst, and exhibits a single power-law decline with $F_{\rm X} \propto t^{-0.98}$. Late-time Gemini observations reveal a faint r$\approx$25.69 mag host galaxy at an angular offset of $\approx$0.16''. At the likely redshift range of z$\approx$1-2.25, we find that the X-ray afterglow luminosity of GRB 180418A is intermediate between short and long GRBs at all epochs during which there is contemporaneous data, and that GRB 180418A lies closer to the $E_{γ,{\rm peak}}-E_{γ,{\rm iso}}$ correlation for short GRBs. Modeling the multi-wavelength afterglow with the standard synchrotron model, we derive the burst explosion properties and find a jet opening angle of $θ_{\rm j} \gtrsim 9-14^{\circ}$. If GRB 180418A is a short GRB that originated from a neutron star merger, it has one of the brightest and longest-lived afterglows along with an extremely faint host galaxy. If instead the event is a long GRB that originated from a massive star collapse, it has among the lowest luminosity afterglows, and lies in a peculiar space in terms of the Hardness-$T_{90}$ and $E_{γ,{\rm peak}}-E_{γ,{\rm iso}}$ planes.

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arXiv2021

The Age of Westerlund 1 Revisited

The cluster Westerlund~1 (Wd1) is host to a large variety of post main-sequence (MS) massive stars. The simultaneous presence of these stars can only be explained by stellar models if the cluster has a finely-tuned age of 4-5Myr, with several published studies independently claiming ages within this range. At this age, stellar models predict that the cool supergiants (CSGs) should have luminosities of $\log(L/L_\odot) \approx 5.5$, close to the empirical luminosity limit. Here, we test that prediction using archival data and new photometry from SOFIA to estimate bolometric luminosities for the CSGs. We find that these stars are on average 0.4dex too faint to be 5Myr old, regardless of which stellar evolution model is used, and instead are indicative of a much older age of $10.4^{+1.3}_{-1.2}$Myr. We argue that neither systematic uncertainties in the extinction law nor stellar variability can explain this discrepancy. In reviewing various independent age estimates of Wd1 in the literature, we firstly show that those based on stellar diversity are unreliable. Secondly, we re-analyse Wd1's pre-MS stars employing the Damineli extinction law, finding an age of $7.2^{+1.1}_{-2.3}$Myr; older than that of previous studies, but which is vulnerable to systematic errors that could push the age close to 10Myr. However, there remains significant tension between the CSG age and that inferred from the eclipsing binary W13. We conclude that stellar evolution models cannot explain Wd1 under the single age paradigm. Instead, we propose that the stars in the Wd1 region formed over a period of several Myr.

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arXiv2021

Simulating the formation of $η$ Carinae's surrounding nebula through unstable triple evolution and stellar merger-induced eruption

$η$ Carinae is an extraordinary massive star famous for its 19th century Great Eruption and the surrounding Homunculus nebula ejected in that event. The cause of this eruption has been the centre of a long-standing mystery. Recent observations, including light-echo spectra of the eruption, suggest that it most likely resulted from a stellar merger in an unstable triple system. Here we present a detailed set of theoretical calculations for this scenario; from the dynamics of unstable triple systems and the mass ejection from close binary encounters, to the mass outflow from the eruption caused by the stellar merger and the post-merger wind phase. In our model the bipolar post-merger wind is the primary agent for creating the Homunculus, as it sweeps up external eruption ejecta into a thin shell. Our simulations reproduce many of the key aspects of the shape and kinematics of both the Homunculus nebula and its complex surrounding structure, providing strong support for the merger-in-a-triple scenario.

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arXiv2021

A Bright Ultraviolet Excess in the Transitional 02es-like Type Ia Supernova 2019yvq

We present photometric and spectroscopic observations of the nearby Type Ia SN 2019yvq, from its discovery $\sim$1 day after explosion to $\sim$100 days after its peak brightness. This SN exhibits several unusual features, most notably an extremely bright UV excess seen within $\sim$5 days of its explosion. As seen in Swift UV data, this early excess outshines its "peak" brightness, making this object more extreme than other SNe with early UV/blue excesses (e.g. iPTF14atg and SN 2017cbv). In addition, it was underluminous ($M_B=-18.4$), relatively quickly declining ($Δm_{15}(B)=1.35$), and shows red colors past its early blue bump. Unusual (although not unprecedented) spectral features include extremely broad-lined and high-velocity Si absorption. Despite obvious differences in peak spectra, we classify SN 2019yvq as a transitional member of the 02es-like subclass due to its similarities in several respects (e.g. color, peak luminosity, peak Ti, nebular [Ca II]). We model this dataset with a variety of published models, including SN ejecta - companion shock interaction and sub-Chandrasekhar mass WD double detonation models. Radio constraints from the VLA place an upper limit of $(4.5 - 20) \times 10^{-8}$ M$_{\odot}$/yr on the mass-loss rate from a symbiotic progenitor, which does not exclude a red giant or main sequence companion. Ultimately we find that no one model can accurately replicate all aspects of the dataset, and further we find that the ubiquity of early excesses in 02es-like SNe Ia requires a progenitor system that is capable of producing isotropic UV flux, ruling out some models for this class of objects.

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arXiv2021

Gaia EDR3 confirms that Westerlund 1 is closer and older than previously thought

Using {\it Gaia} Early Data Release 3 (EDR3) parallaxes and Bayesian inference, we infer a parallax of the Westerlund 1 (Wd1) cluster. We find a parallax of $0.34\pm{0.05}$ mas corresponding to a distance of $2.8^{+0.7}_{-0.6}$ kpc. The new {\it Gaia} EDR3 distance is consistent with our previous result using {\it Gaia} DR2 parallaxes. This confirms that Wd1 is less massive and older than previously assumed. Compared to DR2, the EDR3 individual parallax uncertainties for each star decreased by 30\%. However, the aggregate parallax uncertainty for the cluster remained the same. This suggests that the uncertainty is dominated by systematics, which is possibly due to crowding, motions within the cluster, or motions due to binary orbits.

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