33 New Stellar Angular Diameters from the NPOI, and Nearly 180 NPOI Diameters as an Ensemble

We present new angular diameter measurements for 33 stars from the Navy Precision Optical Interferometer, reaching uncertainties on the limb-darkened diameter of 2% or less for 21 targets. We also determined the physical radius, bolometric flux, luminosity, and effective temperature for each star. Our sample is a mix of giant, subgiant, and dwarf stars, and span spectral classes from mid-A to to mid-K. We combined these 33 stars with samples from previous publications to analyze how the NPOI diameters compare to those obtained using other means, namely (V − K) color, the JMMC Stellar Diameters Catalog, and Gaia predictions.


Introduction
In one sense, the story of astronomy can be told as the quest for better resolution: in its simplest form, the larger the telescope, the more detail you can see on a celestial object.At a certain point, extremely large telescope mirrors become incredibly complicated and prohibitively expensive to build, so we use telescope arrays to provide the ever-increasing resolution required.Optical and infrared interferometry has been used for some exciting explorations, including an expanding fireball from a nova explosion (Schaefer et al. 2014), observations of the dust sublimation region of a bright AGN Kishimoto et al. (2022), determining the size and thermal properties of an asteroid (Matter et al. 2013), supporting theoretical descriptions of a Mira variable star's atmosphere (Wittkowski et al. 2016), and so on.Since its inception, optical and infrared interferometry has been used to measure stellar angular diameters (Michelson & Pease 1921;Wittkowski et al. 2001;van Belle et al. 2009;Boyajian et al. 2012a;Kervella et al. 2017, and many more), though these measurements are more generally the exception rather than the rule.
Stellar diameters have historically been determined using indirect methods, with photometry and spectroscopy being the most common.However, both of these techniques rely upon models of stellar interiors and atmospheres that cannot fully describe the complexity of the stars themselves.To make the models feasible, a number of simplifications and/or assumptions are required that we hope are mostly right, but some evidence shows they are not always accurate (e.g., Boyajian et al. 2012a showed that models overestimate cooler stellar temperatures by ∼3% and underestimate radii by ∼5% for small stars; this paper also includes a discussion about the discrepancy between model predictions and direct measurements).Interferometric measurements are key to testing stellar models and acting as benchmarks (e.g., Karovicova et al. 2020;Perraut et al. 2020), which is particularly important in high signal-to-noise stellar spectroscopic studies and the Gaia survey.A collection of reliably calibrated stellar radii and effective temperatures based on accurate diameters is vital for their use in determining evolutionary state, understanding any planets orbiting the star, and calibrating empirical relationships such as the photometric color-temperature scale (Rains et al. 2020).
The angular diameter measurements presented here are a continuation of the survey project in Baines et al. (2018) and Baines et al. (2021), where we presented the angular diameters and other fundamental stellar properties for a total of 131 stars.This paper is organized as follows: Section 2 discusses the Navy Precision Optical Interferometer and the data reduction process; Section 3 describes interferometric visibility and calibration; Section 4 details how we determined various stellar parameters, including the radius, bolometric flux, extinction, luminosity, and effective temperature for each target; Section 5 provides notes on individual stars, when required; Section 6 considers Navy Precision Optical Interferometer (NPOI) angular diameters as an ensemble; and Section 7 is the conclusion.

Interferometry with the NPOI
As mentioned previously, one of the advantages that interferometry brings is its outstanding resolution, which can be an order of magnitude better than the largest telescopes equipped with adaptive optics (Rains et al. 2020).NPOI is located on Anderson Mesa near Flagstaff, AZ (Armstrong et al. 1998;Benson et al. 2003;Hummel et al. 2003).It consists of three main arms, designated north, east, and west, and incorporates two subarrays: the four fixed astrometric stations concentrated near the center of the array (AC, AE, AW, and AN, which stand for astrometric center, east, west, and north, respectively), and the imaging stations.The latter are labeled according to which arm they are on and their relative distance from the array center.For example, E1 is the station nearest the center on the east arm, while E10 is the station farthest away.We can combine light from the astrometric and imaging stations at will, and "baseline" refers to the distance between the two imaging elements.In this paper, we used 21 unique baselines, and Table 1 lists the baselines used and their average length.The minimum length of baseline used here was just under 9 m, while the longest was just over 79 m.
For the earliest data from 1996 to 2001, we used the original version of the "Classic" beam combiner that recorded data on one baseline per spectrograph, of which there were three, and the light was dispersed into 32 spectral channels spanning 450-950 nm.The data reduction for these early years follows procedures described in Hummel et al. (1998).For data from 2002 on, we used the updated "Classic" beam combiner that records data over 16 spectral channels across 550-850 nm (Hummel et al. 2003;Hutter et al. 2016).Every observation produced a pair of scans: a 30 s coherent (on the fringe) scan where the fringe contrast was measured every 2 ms, and an incoherent (off the fringe) scan that was used to estimate the additive bias affecting fringe measurements.
The NPOI's data reduction package OYSTER was developed by C. A. Hummel3 and automatically edits data as described in Hummel et al. (2003).In addition to this process, we edited out individual data points and/or scans that showed large scatter, on the order of 5σ or higher.This was more common in shorter-wavelength channels where the channels are narrower, atmospheric effects are more pronounced, and the avalanche photodiode detectors have lower quantum efficiency.We removed the points because while the diameter was not affected, the error determined using these points was unfairly biased by the lower-quality shorter-wavelength channels.
We made two assumptions about the stars at the outset: they are effectively single, and they do not rotate rapidly and therefore do not have asymmetrical profiles.Some of the targets measured here may have stellar companions, but almost all are comfortably outside of the detection sensitivity of the NPOI: Hutter et al. (2016) showed that the NPOI can detect binaries with separations from 3 to 860 mas with magnitude differences (Δm) of 3.0 for most binary systems, and up to 3.5 when the component spectral types differ by less than two.There are a few exceptions to these assumptions, which are discussed in Section 5.
Our end goal is to obtain angular diameters on the order of 2% or less, which is considered the minimal standard of astrophysically useful measurements (Booth 1997).Our sample consists of 30 stars with previously unpublished data in the NPOI data archive, and three stars observed solely in 2021, which were chosen for their large angular sizes (4 mas) due to the short baselines available at the time.The dates of observations range from 1996 to 2021, and the entire data set totals more than 56,000 data points.The smallest number of measurements for a given star is 102, and the largest is 6529.Table 2 includes each target's identifiers, spectral type, parallax, and metallicity ([Fe/H]), and Table 3 is the observing log.

Visibility and Calibrators
Interferometric diameter measurements use visibility squared (V 2 ).For a point source, V 2 is 1 and it is defined as completely unresolved, while a star is completely resolved when its V 2 reaches zero.Atmospheric turbulence and instrumental effects can reduce the signal strength, significantly affecting V 2 .In order to address this, we used calibrator stars that are small, i.e., significantly less than the resolution of the NPOI, so that V 2 would be at or close to 1 and is only weakly dependent on the star's angular diameter.This means we can calibrate the atmospheric and instrumental variations out of the science target measurements as we observe calibrators and science targets alternately.The observations taken during a given night were obtained using the same configuration, and the time  Alonso et al. (1996).θ est is the estimated angular diameter calculated using the method described in Section 3.
(This table is available in machine-readable form.) between data collection was generally on the order of a few minutes to 10 minutes.
To estimate the calibrators' diameters, we created spectral energy distribution (SED) fits to published UBVRIJHK photometry.We used plane-parallel model atmospheres from Castelli & Kurucz (2003) based on effective temperature (T eff ), surface gravity (log g), and E(B − V ).Stellar models were fit to observed photometry after converting the magnitudes to fluxes using Colina et al. (1996) for UBVRI and Cohen et al. (2003) for JHK.Table 4 lists the photometry, T eff , log g, and E(B − V ) used, and the resulting angular diameters. 4nce the visibilities are calibrated, we fit angular diameters to the data.For a uniformly illuminated disk, , where J 1 is the Bessel function of the first order, x = πBθ UD λ −1 , B is the projected baseline toward the star's position, θ UD is the apparent uniform disk angular diameter of the star, and λ is the effective wavelength of the observation (Shao & Colavita 1992).θ UD results for our program stars are listed in Table 5.The data are freely available in OIFITS form (Duvert et al. 2017) upon request.
We did not stop with the uniform disk diameter, though.A more realistic model of a star's disk includes limb darkening.When a linear limb-darkening coefficient μ λ is used, then ´-+ l l l l where x LD = πBθ LD λ −1 and θ LD is the limb-darkened diameter (Hanbury Brown et al. 1974a).We gathered published T eff , log g, and [Fe/H] values, and assigned a microturbulent velocity of 2 km s −1 to select μ λ from Claret & Bloemen (2011).We used  Robin et al. (2012).Max SF is the maximum spatial frequency for that star's diameter measurement, # scans is the total number of scans used, and # pts is the number of data points in the angular diameter fit.
a The diameter fit for this target may not be of significant value without knowledge of the pulsation phase of the star, as described in Section 5.
(This table is available in machine-readable form.) Figure 1.An example probability density solution for the diameter fit to HD 3712/α Cas visibilities as described in Section 3. the ATLAS stellar model5 in the R-band, the wave band most closely matched to the central wavelength of the NPOI's bandpass.We note that a more refined analysis would include limb darkening's nonlinear dependence on wavelength, but believe the treatment described here is fair.Limb-darkening effects are related to the height of the second maximum of the visibility curve (Wittkowski et al. 2001) and we deal almost entirely with measurements before the first minimum in this paper.
We calculated angular diameter uncertainties using the modified bootstrap Monte Carlo method developed by Tycner et al. (2010) where a large number of synthetic data sets are created by selecting entire scans at random, as opposed to a single data point within that scan.The width represents the standard deviation of the Gaussian distribution of diameters fit to these data sets, and it becomes our measure of the uncertainty for the diameter (see Figure 1).
For each target's data set, Table 5 shows the T eff , log g, [Fe/H], and μ λ used, the resulting θ LD , the maximum spatial frequency (SF), the number of scans, and the number of data points in the angular diameter fit. Figure 2 shows the θ LD fit for HD 3712/α Cas as an example.The remaining plots are included as an online-only figure set.

Stellar Radius, Luminosity, and Effective Temperature
When available, we converted parallax from Gaia DR3 (Gaia Collaboration 2022) into a distance and combined it with our measured diameters to calculate the physical radius R. Otherwise, parallaxes from the Hipparcos Astrometric Catalog (van Leeuwen 2007), Mamajek & Hillenbrand (2008), and Gaia DR2 (Gaia Collaboration et al. 2018) were used, which was the case for 10 stars (see Table 2).
In order to determine each star's luminosity (L) and T eff , we created SED fits using photometric and spectrophotometric values published in the sources listed in Table 6.The assigned uncertainties for the 2MASS infrared measurements are as reported in Cutri et al. (2003), and an uncertainty of 0.05 mag was assigned to the optical measurements.We did not use the R-and I-band data from (Ducati 2002) because they were always significant outliers.
We fit stellar spectral templates, interpolating when necessary, to the photometry from the flux-calibrated stellar spectral atlas of Pickles (1998) using the χ 2 minimization technique (Press et al. 1992;Wall & Jenkins 2003).This produced the bolometric flux (F BOL ) and extinction (A V ) for each star with the wavelength-dependent reddening relations of Cardelli et al. (1989).Next, we combined our F BOL values with the stars' distances (d) to estimate L using L = 4πd 2 F BOL .We also combined the F BOL with θ LD to determine each star's T eff using the equation from van Belle et al. (1999): where σ is the Stefan-Boltzmann constant and θ LD is in radians (von Braun et al. 2014).The resulting R, F BOL , A V , T eff , and L are listed in Table 7.
Because T eff is an input to select μ λ , we performed an iterative process to arrive at the final θ LD .Table 5 shows the results of this process, including the initial θ LD and subsequent Note.These are the sources used in the SED fitting procedure described in Section 4.
T eff , the recalculated μ λ , and the final θ LD and T eff .For six stars, μ λ and θ LD did not change, and all of the remaining targets converged after just two iterations.Overall, μ λ did not change much, with an average of 0.01 and a maximum of 0.06.The θ LD changed by an average of 0.4% (0.012 mas) and a maximum of 2.3% (0.055 mas).Similarly, T eff changed an average of 9 K, and at most 46 K. Eight stars in this sample have never been measured before using interferometry (see Table 8), and Figure 3 compares our measurements with those that came before using a variety of instruments: the Two-Telescope Stellar Interferometer at CERGA, the Mark III, the NPOI, the Center for High Angular Resolution Astronomy (CHARA) Array, the Infrared Optical Telescope Array, the Stellar Intensity Interferometer at Narrabri, the Palomar Testbed Interferometer, and the Very Large Telescope Interferometer.There is generally good agreement across instruments and the wave bands they use.

Notes on Individual Stars
Some targets of interest include the following: 1. HD 62044/σ Gem: this is a highly active single-lined spectroscopic RS CVn binary (Cao et al. 2022) with imaged star spots (Roettenbacher et al. 2017).The companion was resolved by Roettenbacher et al. (2015) but the magnitude difference between the components is too large to be detected by the NPOI at Δm = 6.72 (Mason et al. 2001)   Note.The spectral types are those that provide the best SED fit as described in Section 4. The SED fits are also the source of F BOL and A V .The other parameters are derived as described in Section 4.
(This table is available in machine-readable form.)determine a θ LD of 1.43 ± 0.02 mas, versus our measurement of 1.479 ± 0.013 mas.
In addition to the dust components, β Leo is a δ Scuti variable and it shows pulsations, though of an unspecified type (Liakos & Niarchos 2017).It is also a multiple-star system, characterized by Rodriguez et al. (2015) as having an A-Ba pair with a separation of 1 91 and Δm = 3.9, and a Ba-Bb pair separated by 0 51 and Δm = 0.129.Between the magnitude difference of the A-B pair and the fact that van Belle & von Braun (2009) considered the star a reliable star against which to compare exoplanet hosts, we treat our diameter as a single-star measurement.3. HD 112185/ò UMa: Ludendorff (1913) identified ò UMa as a spectroscopic binary over a hundred years ago, and Roberts (2011) identified a possible companion with a separation of 0 11 and Δm = 2.31 ± 0.03 in the I-band.
We did not see any evidence of a binary companion in our data, but plan on observing the star in the future in the hope of detecting (or not) the companion.Given that this star is bright at V = 1.77, we would expect to see a companion with that separation easily.Note.
a No LD diameter was provided, so we list the UD diameter here.Figure 3 shows a graphical representation of this table.If more than one diameter was available in the literature, we used the most recent one when plotting the results.
(This table is available in machine-readable form.)The dotted line is the 1:1 ratio.When more than one measurement was available in the literature, we used the most recent measurement (see Table 8).Bottom panel: the residuals were calculated as follows: ( NPOI literature ) q q -× (combined error) −1 .Mermilliod (2006).K magnitudes are from Cutri et al. (2003) for all stars except HD 189319 and HD 192909, which are from Richichi et al. (2005) and have an assigned error of 0.01.A V is from Gontcharov & Mosenkov (2018), for all but nine stars.For those, we used: Salsi et al. (2020;HD 10700, HD 19373, HD 61421, and HD 114710), Neckel et al. (1980;HD 31964), Le Borgne et al. (2003;HD 187929), Famaey et al. (2005;HD 196094, HD 208816, and HD 213311).HD 224014 had no A V listed on Vizier.θ LD,Mozur is the angular diameter calculated using equations from Mozurkewich et al. (2003) Because the relations are limited to the color ranges for which they had data, we did not use all of our 178 stars: 54 of our stars were out of range while 124 were within the limits.We used the coefficients appropriate for the luminosity class of each star, and obtained a fit of f (x) = 1.039x − 0.014 (see Figure 6).Adams et al. (2018) provided a range of predicted fractional uncertainty, which we averaged and applied to the diameters: 3.6% for giant stars, and 3.0% for dwarf and subgiant stars.We also compared angular diameters from the JMMC Stellar Diameters Catalogue (Bourgés et al. 2014), and estimates from the Gaia catalog (Cruzalèbes et al. 2013; derived from radii and distances from Gaia Collaboration et al. 2018).Figure 7 shows this in graphical form, with the JSDC diameters compared in the top panel and the Gaia diameters in the bottom panel.The JSDC diameters show a reasonable fit overall, with a linear fit of f (x) = 0.969x + 0.088, while the Gaia comparison shows more scatter.The fit is good with a larger y-intercept at f (x) = 0.996x + 0.246, so the information could be useful for ensembles of stars, but not for an individual comparison.Cruzalèbes et al. note this issue as well, explaining that the diameters were determined using only three broad-band photometric measurements, which show strong degeneracies between T eff and extinction/reddening meaning "strong assumptions" are required.

Conclusion
We measured angular diameters for 33 stars from 0.715 mas to 10.144 mas.The former has an uncertainty of ±0.205 mas (29%), while the latter has an uncertainty of ±0.020 mas (0.2%).Of the 33 stars presented here, all but six targets have diameter uncertainties of 5%, and all but 12 stars have uncertainties of 2%.We present six stars close to 1.0 mas or smaller, which is under the formal resolution limit of the NPOI.It is therefore not surprising that those uncertainties are among the highest.
We also combined diameters from four other NPOI papers containing angular diameters to assess the collection as a  5, NPOI errors are often smaller than the open circle indicating the data point, as is the case for some of the diameters predicted using (V − K ) color.The dotted line is the 1:1 ratio, and the solid red line is the linear fit to the data ( f (x) = 1.039x − 0.014).Bottom panel: the residuals to the 1:1 line, calculated in the same way as described in Figure 3. whole, and compared our diameters to those obtained using other methods.

Figure 2 .
Figure 2. Top panel: the θ LD fit for HD 3712/α Cas.The solid red line represents the visibility curve for the best fit θ LD , the points are the calibrated visibilities, and the vertical lines are the measurement uncertainties.Bottom panel: the residuals (O − C) of the diameter fit to the visibilities.(The complete figure set (33 images) is available.)

Figure 3 .
Figure 3. Top panel: comparison of the angular diameters measured here vs. previously measured interferometric diameters from the literature.The error bars are included but are often smaller than the open circle indicating the measurement.The dotted line is the 1:1 ratio.When more than one measurement was available in the literature, we used the most recent measurement (see Table8).Bottom panel: the residuals were calculated as follows: ( NPOI literature ) q q -× (combined error) −1 .
, θ LD,Adams is fromAdams et al. (2018), θ LD,JSDC is from the JMMC Stellar Diameters Catalog(Bourgés et al. 2014), and θ LD,Gaia is from GaiaCollaboration et al. (2018).The Y/N in the "Star in range?" column indicates whether or not the particular star was within the color limits ofAdams et al. (2018) and is included in Figure6.See Section 6 for details.empirical relations of angular diameters to various colors, including (V − I C ), (V − H), (V − K ), (I C − H), and (I C − K ).

Figure 6 .
Figure6.Top panel: comparison of the angular diameters measured here vs. diameters predicted using the relations from theAdams et al. (2018) paper.As in Figure5, NPOI errors are often smaller than the open circle indicating the data point, as is the case for some of the diameters predicted using (V − K ) color.The dotted line is the 1:1 ratio, and the solid red line is the linear fit to the data ( f (x) = 1.039x − 0.014).Bottom panel: the residuals to the 1:1 line, calculated in the same way as described in Figure3.

Table 6
Photometry and Spectrophotometry Sources
Raghavan et al. (2012)n the question of whether ι Vir is single or binary, and concluded "single, candidate binary" and retained it as an object for future exploration.Raghavan et al. (2012)later used the CHARA Array to look for previously unknown companions to nearby solar-type stars to help fill the gap between spectroscopic and visual techniques.They explored the 8-80 mas range

Table 9
Current and Previous NPOI Diameters as an Ensemble Hutter et al. (2016)bit of P = 833.26±0.07days.He discussed the confusion arising due to the secondary's nature, considering it is bright in ultraviolet but its contribution to the total luminosity is very small in optical wavelengths, on the order of Δm = 4-5 in the Vband.Hutter et al. (2016)used the NPOI to detect the secondary component for the first time at precisely the Washington Double Star Catalog), Albireo was measured by Mozurkewich et al. (2003) as a single star with θ LD = 4.834 ± 0.048 mas.More recently, Drimmel et al. (2021) used spectroscopy to determine the all three stars in the system (Aa, Ac, and B) are likely coeval and in a hierarchical triple system with an orbital period of 121.65 2.90 3.34 -+ years.They speculated that