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At least 1,063 records · Page 59

TU-AB-303-04: Characterizing CT-Derived Mass Change of Non-Tumor Pathology During Lung Radiotherapy

Purpose: Atelectasis and other commonly-observed non-tumor lung pathologies (NTPs) can change during thoracic radiotherapy altering normal anatomy and inducing large changes in tumor position. However, the characteristics of these changes are not well understood. This study investigates longitudinal NTP tissue mass change during radiotherapy. Methods: Delineation of corresponding atelectatic regions before and after re-aeration is challenging since it is difficult to detect atelectatic-region boundaries after re-aeration. Therefore, individual lobes were delineated and analyzed instead. A radiation oncologist contoured the tumor and individual lobes in the planning and mid-treatment CTs for 7 patients. Each lobe was eroded by 2–4 voxels, which was found to reduce effects of inadvertent chest wall in the lobe delineation but still preserve the mean density of the lobe. The mass of each lobe was calculated after removing the tumor region. The uninvolved lobes were used as controls. Results: Mean mass change for contralateral, ipsilateral without NTP, and NTP lobes were +2.1 (18.0) %, −9.4 (18.2) %, and −13.4 (40.1) %, respectively. For NTP lobes, the degree and direction of change depended on atelectasis resolution type (full or partial), with mean mass change for full resolution of −43.1 (16.2) % and +4.5 (40.1) % for partial. The standard deviation for NTP lobes is likely higher due to actual changes in mass as well as increased delineation variability in the presence of tumor and lung consolidation. Median mean density change was −46.4% for NTP lobes, showing significant difference from contralateral (p=8.2×10−{sup 4}) and NTP-free ipsilateral lobes (p=0.006). Conclusion: No noticeable mass change occurred for pathology-free lobes. As NTP fully resolved, mass of the lobe decreased. One possible explanation is that the release of retained fluid and infiltrate commonly associated with NTP accounts for the reduced mass. This work was supported by the National Cancer Institute of the National Institutes of Health under Award Number R01CA166119. The authors have no conflicts of interest.

60 APPLIED LIFE SCIENCES↗

Evolution of deep-bed filtration of engine exhaust particulates with trapped mass

Micro-scale filtration experiments were performed on cordierite filter samples using particulate matter (PM) generated by a spark-ignition direct-injection (SIDI) engine fueled with tier II EEE certification gasoline. Size-resolved mass and number concentrations were obtained from several engine operating conditions. The resultant mass-mobility relationships showed weak dependence on the operating condition. An integrated particle size distribution (IPSD) method was used estimate the PM mass concentration in the exhaust stream from the SIDI engine and a heavy duty diesel (HDD) engine. The average estimated mass concentration between all conditions was ~77****** % of the gravimetric measurements performed on Teflon filters. Despite the relatively low elemental carbon fraction (~0.4 to 0.7), the IPSD mass for stoichiometric SIDI exhaust was ~83±38 % of the gravimetric measurement. Identical cordierite filter samples with properties representative of diesel particulate filters were sequentially loaded with PM from the different SIDI engine operating conditions, in order of increasing PM mass concentration. Simultaneous particle size distribution measurements upstream and downstream of the filter sample were used to evaluate filter performance evolution and the instantaneous trapped mass within the filter for two different filter face velocities. The evolution of filtration performance for the different samples was sensitive only to trapped mass, despite using PM from a wide range of operating conditions. Higher filtration velocity resulted in a more rapid shift in the most penetrating particle size towards smaller mobility diameters.

33 ADVANCED PROPULSION SYSTEMS↗

A precise measurement of the top quark mass in dilepton final states using 9.7 fb$^{-1}$ of D{Ø} Run II data

The top quark is a very special fundamental particle in the Standard Model (SM) mainly due to its heavy mass. The top quark has extremely short lifetime and decays before hadronization. This reduces the complexity for the measurement of its mass. The top quark couples very strongly to the Higgs boson since the fermion-Higgs Yukawa coupling linearly depends on the fermion’s mass. Therefore, the top quark is also heavily involved in Higgs production and related study. A precise measurement of the top quark mass is very important, as it allows for self-consistency check of the SM, and also gives a insight about the stability of our universe in the SM context. This dissertation presents my work on the measurement of the top quark mass in dilepton final states of t$\bar{t}$ events in p$\bar{p}$ collisions at √s = 1.96 TeV, using the full DØ Run II data corresponding to an integrated luminosity of 9.7 fb -1 at the Fermilab Tevatron. I extracted the top quark mass by reconstructing event kinematics, and integrating over expected neutrino rapidity distributions to obtain solutions over a scanned range of top quark mass hypotheses. The analysis features a comprehensive optimization that I made to minimize the expected statistical uncertainty. I also improve the calibration of jets in dilepton events by using the calibration determined in t$\bar{t}$ → lepton+jets events, which reduces the otherwise limiting systematic uncertainty from the jet energy scale. The measured mass is 173.11 ± 1.34(stat) +0.83 -0.72 (sys) GeV .

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

The role of supernova convection for the lower mass gap and the isolated binary formation of gravitational wave sources

Understanding astrophysical phenomena involving compact objects requires an insight about the engine behind core-collapse supernovae (SNe) and the fate of the stellar collapse of massive stars. In particular, this insight is crucial in developing an understanding of the origin and formation channels of the growing populations of detected black hole-black hole, black holeneutron star and neutron star-neutron star mergers. The timescale of convection growth may have a large effect on the strength of SN explosion and therefore also on the mass distribution of stellar remnants. We adopt new formulas for the relation between the pre-SN star properties and their remnants (Fryer et al. 2022) and check how they impact population of double compact object (DCO) mergers formed via isolated binary evolution. The new formulas give one ability to test wide spectrum of assumptions on the convection growth time. In particular, different variants allow for a smooth transition between having a deep mass gap and a remnant mass distribution filled by massive neutron stars and low mass black holes. We present distribution of masses, mass ratios and the local merger rate densities of DCO for different variants of new formulas and test them together with different approaches to other highly uncertain processes. We find that mass distribution of DCO mergers is sensitive to adopted assumption on SN convection growth timescale up to $m_1$ + $m_2$ ≲ 35$M_⊙$. Between two extreme tested variants the probability of compact object formation within the mass gap may differ up to ~ 2 orders of magnitude.

79 ASTRONOMY AND ASTROPHYSICS↗

Does the intermediate-mass black hole in LEDA 87300 (RGG 118) follow the near-quadratic M{sub bh}–M{sub spheroid} relation?

The mass scaling relation between supermassive black holes and their host spheroids has previously been described by a quadratic or steeper relation at low masses (10{sup 5} < M{sub bh}/M{sub ⊙} ≲ 10{sup 7}). How this extends into the realm of intermediate-mass black holes (10{sup 2} < M{sub bh}/M{sub ⊙} < 10{sup 5}) is not yet clear, although for the barred Sm galaxy LEDA 87300, Baldassare et al. recently reported a nominal virial mass of M{sub bh} = 5 × 10{sup 4} M{sub ⊙} residing in a “spheroid” of stellar mass equal to 6.3 × 10{sup 8} M{sub ⊙}. We point out, for the first time, that LEDA 87300 therefore appears to reside on the near-quadratic M{sub bh}–M{sub sph,*} relation. However, Baldassare et al. modeled the bulge and bar as the single spheroidal component of this galaxy. Here we perform a 3-component bulge+bar+disk decomposition and find a bulge luminosity which is 7.7 times fainter than the published “bulge” luminosity. After correcting for dust, we find that M{sub bulge} = 0.9 × 10{sup 8} M{sub ⊙} and M{sub bulge}/M{sub disk} = 0.04—which is now in accord with ratios typically found in Scd–Sm galaxies. We go on to discuss slight revisions to the stellar velocity dispersion (40 ± 11 km s{sup −1}) and black hole mass (M{sub bh}=2.9{sub −2.3}{sup +6.7}×10{sup 4} f{sub 2.3} M{sub ⊙}) and show that LEDA 87300 remains consistent with the M{sub bh}–σ relation, and also the near-quadratic M{sub bh}–M{sub sph,*} relation when using the reduced bulge mass. LEDA 87300 therefore offers the first support for the rapid but regulated (near-quadratic) growth of black holes, relative to their host bulge/spheroid, extending into the domain of intermediate-mass black holes.

79 ASTRONOMY AND ASTROPHYSICS↗

MOA-2009-BLG-319Lb: A Sub-Saturn Planet inside the Predicted Mass Desert

We present an adaptive optics (AO) analysis of images from the Keck II telescope NIRC2 instrument of the planetary microlensing event MOA-2009-BLG-319. The ∼10 yr baseline between the event and the Keck observations allows the planetary host star to be detected at a separation of 66.5 ± 1.7 mas from the source star, consistent with the light-curve model prediction. The combination of the host star brightness and light-curve parameters yields host star and planet masses of M {sub host} = 0.524 ± 0.048M {sub ⊙} and m {sub p} = 67.3 ± 6.2M {sub ⊕} at a distance of D {sub L} = 7.1 ± 0.7 kpc. The star−planet projected separation is 2.03 ± 0.21 au. The planet-to-star mass ratio of this system, q = (3.857 ± 0.029) × 10{sup −4}, places it in the predicted “planet desert” at 10{sup −4} < q < 4 × 10{sup −4} according to the runaway gas accretion scenario of the core accretion theory. Seven of the 30 planets in the Suzuki et al. sample fall in this mass ratio range, and this is the third with a measured host mass. All three of these host stars have masses of 0.5 ≤ M {sub host}/M {sub ⊙} ≤ 0.7, which implies that this predicted mass ratio gap is filled with planets that have host stars within a factor of two of 1M {sub ⊙}. This suggests that runaway gas accretion does not play a major role in determining giant planet masses for stars somewhat less massive than the Sun. Our analysis has been accomplished with a modified DAOPHOT code that has been designed to measure the brightness and positions of closely blended stars. This will aid in the development of the primary method that the Nancy Grace Roman Space Telescope mission will use to determine the masses of microlens planets and their hosts.

47 OTHER INSTRUMENTATION↗

True Masses of the Long-period Companions to HD 92987 and HD 221420 from Hipparcos–Gaia Astrometry

The extensive time span of modern radial velocity surveys has made the discovery of long-period substellar companions more common in recent years; however, measuring the true masses of these objects remains challenging. Astrometry from the Gaia mission is expected to provide mass measurements for many of these long-period companions, but these data are not yet available. However, combining proper-motion data from Gaia DR2 and the earlier Hipparcos mission makes it possible to measure true masses of substellar companions in favorable cases. In this work, we combine radial velocities with Hipparcos–Gaia astrometry to measure the true masses of two recently discovered long-period substellar companion candidates, HD 92987 B and HD 221420 b. In both cases, we find that the true masses are significantly higher than implied by radial velocities alone. A 2087 ± 19 m s{sup −1} astrometric signal reveals that HD 92987 B is not close to its 17 M {sub J} minimum mass but is instead a 0.2562 ± 0.0045 M {sub ⊙} star viewed at a near-polar orbital inclination, whereas the 22.9 ± 2.2 M {sub J} HD 221420 b can be plausibly interpreted as a high-mass “superplanet” or a low-mass brown dwarf. With semimajor axes of ∼10 au, both companions are interesting targets for direct imaging, and HD 221420 b in particular would be a benchmark metal-rich substellar object if it proves possible to directly detect. Our results demonstrate the power of Hipparcos–Gaia astrometry for studying long-period planet and brown dwarf candidates discovered from radial velocity surveys.

36 MATERIALS SCIENCE↗

Wide Dust Gaps in Protoplanetary Disks Induced by Eccentric Planets: A Mass-eccentricity Degeneracy

The tidal perturbation of embedded protoplanets on their natal disks has been widely attributed to be the cause of gap-ring structures in submillimeter images of protoplanetary disks around T Tauri stars. Numerical simulations of this process have been used to propose scaling of characteristic dust-gap width/gap-ring distance with respect to planet mass. Applying such scaling to analyze observed gap samples yields a continuous mass distribution for a rich population of hypothetical planets in the range of several Earth to Jupiter masses. In contrast, the conventional core-accretion scenario of planet formation predicts a bimodal mass function due to (1) the onset of runaway gas accretion above ~20 Earth masses and (2) suppression of accretion induced by gap opening. Here, we examine the dust disk response to the tidal perturbation of eccentric planets as a possible resolution of this paradox. Based on simulated gas and dust distributions, we show the gap-ring separation of Neptune-mass planets with small eccentricities might become comparable to that induced by Saturn-mass planets on circular orbits. Furthermore, this degeneracy may obliterate the discrepancy between the theoretical bimodal mass distribution and the observed continuous gap width distribution. Despite damping due to planet–disk interaction, modest eccentricity may be sustained either in the outer regions of relatively thick disks or through resonant excitation among multiple super Earths. Moreover, the ring-like dust distribution induced by planets with small eccentricities is axisymmetric even in low viscosity environments, consistent with the paucity of vortices in Atacama Large Millimeter/submillimeter Array images.

79 ASTRONOMY AND ASTROPHYSICS↗

An Isolated Stellar-mass Black Hole Detected through Astrometric Microlensing

We report the first unambiguous detection and mass measurement of an isolated stellar-mass black hole (BH). We used the Hubble Space Telescope (HST) to carry out precise astrometry of the source star of the long-duration (t E ≃ 270 days), high-magnification microlensing event MOA-2011-BLG-191/OGLE-2011-BLG-0462 (hereafter designated as MOA-11-191/OGLE-11-462), in the direction of the Galactic bulge. HST imaging, conducted at eight epochs over an interval of 6 yr, reveals a clear relativistic astrometric deflection of the background star's apparent position. Ground-based photometry of MOA-11-191/OGLE-11-462 shows a parallactic signature of the effect of Earth's motion on the microlensing light curve. Combining the HST astrometry with the ground-based light curve and the derived parallax, we obtain a lens mass of 7.1 ± 1.3 M ⊙ and a distance of 1.58 ± 0.18 kpc. We show that the lens emits no detectable light, which, along with having a mass higher than is possible for a white dwarf or neutron star, confirms its BH nature. Our analysis also provides an absolute proper motion for the BH. The proper motion is offset from the mean motion of Galactic disk stars at similar distances by an amount corresponding to a transverse space velocity of ~45 km s -1 , suggesting that the BH received a "natal kick" from its supernova explosion. Previous mass determinations for stellar-mass BHs have come from radial velocity measurements of Galactic X-ray binaries and from gravitational radiation emitted by merging BHs in binary systems in external galaxies. Our mass measurement is the first for an isolated stellar-mass BH using any technique.

79 ASTRONOMY AND ASTROPHYSICS↗

Photometric Objects Around Cosmic Webs (PAC) Delineated in a Spectroscopic Survey. IV. High-precision Constraints on the Evolution of the Stellar–Halo Mass Relation at Redshift z < 0.7

Taking advantage of the Photometric objects Around Cosmic webs method developed in Paper I, we measure the excess surface density $\overline{n}$ 2 w p of the photometric objects around spectroscopic objects down to stellar masses 10 8.0 M ⊙ , 10 9.2 M ⊙ , and 10 9.8 M ⊙ in the redshift ranges of z s < 0.2, 0.2 < z s < 0.4, and 0.5 < z s < 0.7, respectively, using data from the DESI Legacy Imaging Surveys and spectroscopic samples from the Sloan Digital Sky Survey (i.e., the Main, LOWZ, and CMASS samples). We model the measured in an N-body simulation, using the abundance matching method, and we constrain the stellar–halo mass relations (SHMRs) in the three redshift ranges to percent levels. With the accurate modeling, we demonstrate that the stellar mass scatter for a given halo mass is nearly a constant, and that the empirical form of Behroozi et al. describes the SHMR better than the double-power-law form at low mass. Our SHMR accurately captures the downsizing of massive galaxies from z s = 0.7, while it also indicates that small galaxies are still growing faster than their host halos. The galaxy stellar mass functions (GSMFs) from our modeling are in perfect agreement with the model-independent measurements in Paper III, although the current work extends the GSMFs to a much smaller stellar mass. Based on the GSMFs and the SHMRs, we derive the stellar mass completeness and halo occupation distributions for the LOWZ and CMASS samples, which are useful for correctly interpreting their cosmological measurements, such as galaxy–galaxy lensing and redshift space distortion.

79 ASTRONOMY AND ASTROPHYSICS↗

Correlations between the Neutron Star Mass–Radius Relation and the Equation of State of Dense Matter

We develop an analytic method of inverting the Tolman–Oppenheimer–Volkoff relations to high accuracy. In principle, a specified energy density–pressure relation gives a unique mass–radius (M–R) relation and vice versa. Our method is developed from the strong correlations that are shown to exist between the neutron star mass–radius curve and the equation of state (EOS) or pressure–energy density relation. Selecting points that have masses equal to fixed fractions of the maximum mass, we find a semi-universal power-law relation between the central energy densities, pressures, sound speeds, chemical potentials, and number densities of those stars, with the maximum mass and the radii of one or more fractional maximum mass points. Rms fitting accuracies, for EOSs without large first-order phase transitions, are typically 0.5% for all quantities at all mass points. The method also works well, although less accurately, in reconstructing the EOS of hybrid stars with first-order phase transitions. These results permit, in effect, an analytic method of inverting an arbitrary M–R curve to yield its underlying EOS. We discuss applications of this inversion technique to the inference of the dense matter EOS from measurements of neutron star masses and radii as a possible alternative to traditional Bayesian approaches.

Bayesian statistics↗

Reconciling dwarf galaxies with ΛCDM cosmology: simulating a realistic population of satellites around a Milky Way-mass galaxy

Low-mass “dwarf” galaxies represent the most significant challenges to the cold dark matter (CDM) model of cosmological structure formation. Because these faint galaxies are (best) observed within the Local Group (LG) of the Milky Way (MW) and Andromeda (M31), understanding their formation in such an environment is critical. We present first results from the Latte Project: the Milky Way on Feedback in Realistic Environments (FIRE). This simulation models the formation of an MW-mass galaxy to z=0 within ΛCDM cosmology, including dark matter, gas, and stars at unprecedented resolution: baryon particle mass of 7070 M{sub ⊙} with gas kernel/softening that adapts down to 1 pc (with a median of 25--60 pc at z=0). Latte was simulated using the GIZMO code with a mesh-free method for accurate hydrodynamics and the FIRE-2 model for star formation and explicit feedback within a multi-phase interstellar medium. For the first time, Latte self-consistently resolves the spatial scales corresponding to half-light radii of dwarf galaxies that form around an MW-mass host down to M{sub star}≳10{sup 5} M{sub ⊙}. Latte’s population of dwarf galaxies agrees with the LG across a broad range of properties: (1) distributions of stellar masses and stellar velocity dispersions (dynamical masses), including their joint relation; (2) the mass–metallicity relation; and (3) diverse range of star formation histories, including their mass dependence. Thus, Latte produces a realistic population of dwarf galaxies at M{sub star}≳10{sup 5} M{sub ⊙} that does not suffer from the “missing satellites” or “too big to fail” problems of small-scale structure formation. We conclude that baryonic physics can reconcile observed dwarf galaxies with standard ΛCDM cosmology.

79 ASTRONOMY AND ASTROPHYSICS↗

The influence of environment on the chemical evolution in low-mass galaxies

The mean alpha-to-iron abundance ratio ([α/Fe]) of galaxies is sensitive to the chemical evolution processes at early time, and it is an indicator of star formation timescale (τ{sub SF}). Although the physical reason remains ambiguous, there is a tight relation between [α/Fe] and stellar velocity dispersion (σ) among massive early-type galaxies (ETGs). However, no work has shown convincing results as to how this relation behaves at low masses. We assemble 15 data sets from the literature and build a large sample that includes 192 nearby low-mass (18<σ<80 km s{sup −1}) ETGs. We find that the [α/Fe]–σ relation generally holds for low-mass ETGs, except in extreme environments. Specifically, in normal galaxy cluster environments, the [α/Fe]–σ relation and its intrinsic scatter are, within uncertainties, similar for low-mass and high-mass ETGs. However, in the most massive relaxed galaxy cluster in our sample, the zero point of the relation is higher and the intrinsic scatter is significantly larger. By contrast, in galaxy groups the zero point of the relation offsets in the opposite direction, again with substantial intrinsic scatter. The elevated [α/Fe] of low-mass ETGs in the densest environments suggests that their star formation was quenched earlier. For the low-mass ETGs in the lowest-density environments, we suggest that their more extended star formation histories suppressed their average [α/Fe]. The large scatter in [α/Fe] may reflect stochasticity in the chemical evolution of low-mass galaxies.

79 ASTRONOMY AND ASTROPHYSICS↗

Find the Gap: Black Hole Population Analysis with an Astrophysically Motivated Mass Function

We introduce a novel black hole mass function that realistically models the physics of pair-instability supernovae with a minimal number of parameters. Applying this to all events in the LIGO-Virgo Gravitational-Wave Transient Catalog 2 (GWTC-2), we detect a peak at M BHMG = 46$^{+17}_{-6}$ M ⊙ . Repeating the analysis without the black holes from the event GW190521, we find this feature at M BHMG =54± 6 M ⊙ . These results establish the edge of the anticipated "black hole mass gap" at a value compatible with the expectation from standard stellar structure theory. The mass gap manifests itself as a discontinuity in the mass function and is populated by a distinct, less-abundant population of higher-mass black holes. We find that the primary black hole population scales with power-law index -1.95 ± 0.51 (-1.97 ± 0.44) with (without) GW190521, consistent with models of star formation. Using Bayesian techniques, we establish that our mass function fits a new catalog of black hole masses approximately as well as pre-existing phenomenological mass functions. We also remark on the implications of these results for constraining or discovering new phenomena in nuclear and particle physics.

79 ASTRONOMY AND ASTROPHYSICS↗

Inferring Type II-P Supernova Progenitor Masses from Plateau Luminosities

Abstract Connecting observations of core-collapse supernova explosions to the properties of their massive star progenitors is a long-sought, and challenging, goal of supernova science. Recently, Barker et al. presented bolometric light curves for a landscape of progenitors from spherically symmetric neutrino-driven core-collapse supernova (CCSN) simulations using an effective model. They find a tight relationship between the plateau luminosity of the Type II-P CCSN light curve and the terminal iron-core mass of the progenitor. Remarkably, this allows us to constrain progenitor properties with photometry alone. We analyze a large observational sample of Type II-P CCSN light curves and estimate a distribution of iron-core masses using the relationship of Barker et al. The inferred distribution matches extremely well with the distribution of iron-core masses from stellar evolutionary models and namely, contains high-mass iron cores that suggest contributions from very massive progenitors in the observational data. We use this distribution of iron-core masses to infer minimum and maximum masses of progenitors in the observational data. Using Bayesian inference methods to locate optimal initial mass function parameters, we find M min = 9.8 − 0.27 + 0.37 and M max = 24.0 − 1.9 + 3.9 solar masses for the observational data.

79 ASTRONOMY AND ASTROPHYSICS↗

Ablation and deceleration of mass-driver launched projectiles for space disposal of nuclear wastes

The energy cost of launching a projectile containing nuclear waste is two orders of magnitude lower with a mass driver than with a typical rocket system. A mass driver scheme will be feasible, however, only if ablation and deceleration are within certain tolerable limits. It is shown that if a hemisphere-cylinder-shaped projectile protected thermally with a graphite nose is launched vertically to attain a velocity of 17 km/sec at an altitude of 40 km, the mass loss from ablation during atmospheric flight will be less than 0.1 ton, provided the radius of the projectile is under 20 cm and the projectile's mass is of the order of 1 ton. The velocity loss from drag will vary from 0.4 to 30 km/sec, depending on the mass and radius of the projectile, the smaller velocity loss corresponding to large mass and small radius. Ablation is always within a tolerable range for schemes using a mass driver launcher to dispose of nuclear wastes outside the solar system. Deceleration can also be held in the tolerable range if the mass and diameter of the projectile are properly chosen.

Park, C.↗

Binary stars: Mass transfer and chemical composition

It is noted that mass exchange (and mass loss) within a binary system should produce observable changes in the surface chemical composition of both the mass losing and mass gaining stars as a stellar interior exposed to nucleosyntheses is uncovered. Three topics relating mass exchange and/or mass loss to nucleosynthesis are sketched: the chemical composition of Algol systems; the accretion disk of a cataclysmic variable fed by mass from a dwarf secondary star; and the hypothesis that classical Ba II giants result from mass transfer from a more evolved companion now present as a white dwarf.

Lambert, D. L.↗

Cepheid binaries with large mass ratios (M1/M2)

The IUE observations of 3 Cepheid systems (Polaris, FF Aql, and S Sge) are used to derive, or set limits on, the temperatures and masses of the companions. Light from the companions of FF Aql and S Sge from 1700 to 2000 A is consistent with an A5 to A7 main sequence companion for both Cepheids, with a mass of 1.8 solar mass. This mass for the companion of S Sge is smaller than required by the orbital mass function and an evolutionary mass of the Cepheid, suggesting that the companion may itself be a binary. For Polaris, the mass of the companion must be less than 1.8 solar mass.

Evans, Nancy Remage↗