WIYN Open Cluster Study LXXIX. M48 (NGC 2548) I. Radial Velocities, Rotational Velocities, and Metallicities of Stars in the Open Cluster M48 (NGC 2548)
Qinghui Sun, Constantine P. Deliyannis, Aaron Steinhauer, Bruce A. Twarog, Barbara J. Anthony-Twarog
aa r X i v : . [ a s t r o - ph . S R ] A p r Draft version April 16, 2020
Typeset using L A TEX twocolumn style in AASTeX63
WIYN Open Cluster Study LXXIX. M48 (NGC 2548) I. Radial Velocities, Rotational Velocities,and Metallicities of Stars in the Open Cluster M48 (NGC 2548)
Qinghui Sun , Constantine P. Deliyannis , Aaron Steinhauer, Bruce A. Twarog, andBarbara J. Anthony-Twarog Department of Astronomy, Indiana University, Bloomington, IN 47405, [email protected]; [email protected] Department of Physics and Astronomy, State University of New York, Geneso, NY 14454, [email protected] Department of Physics and Astronomy, University of Kansas, Lawrence, KS 660045, [email protected]; [email protected]
ABSTRACTWIYN/Hydra spectra (R ∼ − = 50–1000) of a 400 ˚A region aroundLi 6708 ˚A are used to determine radial and rotational velocities for 287 photometrically selectedcandidate members of the open cluster M48. The sample ranges from turnoff A stars to late-K dwarfsand eight giants. We combine our V RAD measurements and power spectrum analysis with parallaxand proper motion data from Gaia DR2 to evaluate membership and multiplicity. We classify 152stars as single cluster members, 11 as binary members, 16 as members of uncertain multiplicity, 56 assingle nonmembers, 28 as single “likely” nonmembers, two as single “likely” members, one as a binary“likely” member, five as binary nonmembers, 10 as “likely” members of uncertain multiplicity, threeas nonmembers of uncertain multiplicity, and three as “likely” nonmembers of uncertain multiplicity.From a subsample of 95 single members, we derive V RAD = 8.512 ± − ( σ µ , and σ = 0.848km s − ). Using 16 isolated Fe I lines for a subsample of 99 single members (that have σ T eff <
75 K(from 10 colors from
U BV RI ), v sin i <
25 km s − , and well-behaved Fe I lines), [Fe/H] M48 = -0.063 ± σ µ ). [Fe/H] is independent of T eff over an unprecedentedly large range of 2500 K. Theminimum cluster binary fraction is 11%–21%. M48 exhibits a clear but modest broadening of themain-sequence turnoff, and there is no correlation between color and v sin i . Keywords: open clusters and associations: individual (M48) stars: abundances technique: spectro-scopic INTRODUCTIONM48 (NGC 2548; α h m s , δ ◦ ′ )is a moderately rich, nearby ( D = 729 ±
26 pc), low-reddening ( E ( B − V ) = 0.05 ± ±
30 Myr, Deliyannis et al.(2020a; in preparation, Paper II)) intermediate to thatof the Pleiades ( ∼
100 Myr) and the Hyades ( ∼
650 Myr). Visiting Astronomer, Kitt Peak National Observatory, NationalOptical Astronomy Observatory, which is operated by the Asso-ciation of Universities for Research in Astronomy (AURA) undercooperative agreement with the National Science Foundation. The WIYN Observatory is a joint facility of the University ofWisconsin-Madison, Indiana University, the National Optical As-tronomy Observatory and the University of Missouri.
These characteristics make it a very interesting targetfor studying the rotational evolution and lithium (Li) de-pletion of stars, among many other topics. Of particularimportance for nearby clusters younger than the Hyadesis the ability to separate the often poor-to-moderatelypopulated main-sequence cooler than the sun from therising tide of field stars at fainter magnitudes encom-passed by the large areal coverage of a nearby cluster,making evolutionary studies of lower-mass stars as afunction of age a challenge. Equally critical for discern-ing any underlying link between fundamental stellar pa-rameters (e.g. T eff , mass, v sin i and evolutionary state,as defined by position within the color-magnitude dia-gram (CMD), and internal evolution, as defined by at-mospheric abundance changes) is the ability to separatesingle stars from binaries. As an example for Li studies,among the mechanisms proposed to create the severeF-dwarf lithium depletion (the “Li Dip,” Boesgaard &Tripicco 1986), mass loss and diffusion act closer to theage of the Hyades, whereas rotational mixing acts closerto the age of the Pleiades (Deliyannis et al. (1998), Cum-mings et al. (2017)), so M48 should help delineate theevolution of the Li Dip and may help distinguish be-tween proposed mechanisms. As another example, M48can help delineate the post-Pleiades main-sequence de-pletion of Li in G dwarfs, which requires a mechanism(s)beyond the realm of “standard” theory (Deliyannis etal. (1990), Cummings et al. (2017)). Finally, the age ofM48 provides an important link in understanding thespindown of main-sequence stars.Following a few early studies (Ebbighausen (1939); Li(1954)), and excepting studies limited to bright stars(e.g. Baumgardt et al. 2000), the only modern propermotion study of M48 was that of Wu et al. (2002). Withthe evolution to Gaia DR2 (2016, 2018), this aspect ofthe cluster’s database has changed dramatically, a pointwe will return to in Section 3. Spectroscopically, ra-dial velocity studies have been restricted to the cluster’sfew giants or brightest main-sequence stars (Wallersteinet al. (1963), Geyer & Nelles (1985), Mermilliod et al.(2008a)). Spectroscopic abundance analysis has beenlimited to one giant (Wallerstein & Conti 1964).Photolelectric photometry was published by Pesch(1961; U BV , 37 upper main-sequence and giant stars)and Claria (1985; DDO, five giants). CCD photometryof thousands of stars in the direction of M48 has beenreported in Wu et al. (2005; BATC 13-color), Rider etal. (2004; u ′ g ′ r ′ i ′ z ′ ), Balaguer-Nunez et al. (2005; ubvy- Hβ ), and Paper II.The present study is the first in a series of studiesof M48. Here, we report radial velocities and v sin i for nearly 300 candidate members of M48. Togetherwith Gaia DR2 data, we evaluate membership for eachstar, separate single stars from binaries/multiples, anddiscuss the binary fraction of the cluster. Finally, weconduct the first detailed spectroscopic metallicity of thecluster and discuss the result in the context of propertiesof open clusters in the solar neighborhood. Paper IIpresents U BV RI photometry in the direction of M48and reevaluates the basic cluster parameters. Paper III(C.P. Deliyannis et al. 2020b; in preparation) presentsLi abundances in M48 giants and from the turnoff to Kdwarfs and addresses physical mechanisms that act toalter the surface Li abundances of stars. OBSERVATIONS AND DATA REDUCTIONS Observations of M48 candidate members were madeusing the WIYN 3.5m telescope and Hydra multi-fiberspectrograph during four runs in 2017 October, 2017December, 2018 March, and 2018 April. We used [email protected] echelle grating in order 8 with the X19 filter,the blue cable, and the STA1 detector. The spectra span6450–6850 ˚A and have a dispersion of 0.205 ˚Apixel − ,and a resolution of R ∼ U BV RI photometry (Paper II) as fol-lows. For stars with B − V ≤ B − V > B − V , were kept; all five filters were usedin defining this fiducial, which helps increase the frac-tion of members (see Paper II). In total, 287 stars wereobserved with Hydra using seven distinct configurations,which were made based on the V magnitude and posi-tion of the star on the CMDs. For each configuration,Table 1 shows the configuration’s name, approximate V and B − V ranges for most stars in the configuration,and the number of stars observed.To help minimize errors, for each configuration, thefollowing calibrations were taken in the same configura-tion as the object spectra: multiple Th Ar lamp spectra(both long and short), at least 11 dome flats, and day-time sky spectra (except for m48rg). Table 2 providesthe nightly log of observations. In total, we observed 4hrfor m48vb1, 5.2hr for m48vb2, 8hr for m48b, 14.8hr form48m1, 9.7hr for m48m2, 14.5hr for m48f, and 0.17hrfor m48rg.For each configuration, the raw spectra were bias-subtracted, flat-fielded, daytime sky spectra corrected,and wavelength-calibrated using IRAF. For the radialvelocity ( V RAD ) work, cosmic-rays were eliminated withL.A. Cosmic (van Dokkum 2001). We first combinedall of the reduced spectra of the same configuration foreach night separately. For those configurations observedon more than one night, we shifted the night’s averagewavelength to match the cluster average, and then com-bined the spectra from different nights; for details andfinal membership and multiplicity results, see Section 3.We then normalized the combined spectra for each sin-gle member by fitting an eighth-order polynomial to thecontinuum, and used the normalized spectra to measureequivalent widths of iron lines to determine the stellarand cluster metallicities.
Table 1.
Hydra Configurations
Description Name V range (mag) B − V range (mag) red giant m48rg 8.108 1.233 1very bright 1 m48vb1 9.119–11.671 0.029–1.313 55very bright 2 m48vb2 10.986–13.960 0.105–0.599 59bright m48b 10.958–15.184 0.121–0.808 54medium 1 m48m1 15.042–17.059 0.768–1.226 47medium 2 m48m2 14.439–15.925 0.668–0.981 23faint m48f 16.015–17.392 0.982–1.311 53 Note —1. Configurations m48b and m48m2 both included star 2213; config-urations m48vb2 and m48b both included star 2157; configurations m48m1and m48m2 both included stars 2210, 2212, and 2221. RADIAL VELOCITY, BINARITY, CLUSTERMEMBERSHIP, AND CLUSTER BINARYFRACTIONTo determine a cluster average V RAD and metallicity,we used a suitably constrained subset of cluster membersingle stars. The following subsections describe how wedetermined the multiplicity and membership status ofeach star in our sample.3.1.
Radial Velocity
We ran the IRAF task fxcor which calculates V RAD and v sin i directly on the heliocentric-corrected, linear,and continuum subtracted spectra.We took spectra of V RAD standards on each night toperform an external check on the wavelength calibra-tion, with the exception of 1712n5 due to bad weather,as noted in Table 2. Reassuringly, with only a few excep-tions like 1712n1, the large majority of measured V RAD are within 2 σ of the literature values for the vast major-ity of nights. For M48 stars observed on more than onenight, we measured V RAD independently on each night.As an example, Figure 1 shows the V RAD distributionof the m48f stars from night 1712n3. Typical errorsfor individual stars are 0.5–0.9 km s − . A Gaussian fit(dashed line) to the data yields a mean V RAD of 8.53 ± − ( σ µ , and σ =0.31 km s − ). Table 2 showsthe results from similar fits to all configurations on allnights. 3.2. Binarity
Binarity can lead to misleading measurement of rota-tional velocity ( v sin i ) and equivalent width and, thus,abundance. For example, an indeterminate amount ofcontaminating flux from a secondary may lead to an in-determinate underestimation of equivalent width. So wehave attempted to identify binaries and then eliminatethem from subsequent analysis, where appropriate to doso. As discussed in Section 2, stars with B − V >
RAD (km s −1 )024681012 nu m b e r o f s t a r s µ=8.53σ=0.31σ µ =0.05 Figure 1.
Radial velocity of m48f stars on night 1712n3.The mean and standard deviation of the Gaussian fit are8.53 km s − and 0.31 km s − , respectively. mag were selected initially for spectroscopic follow-up ifthe U BV RI photometry placed them on the apparentcluster single-star fiducial sequence. We have appliedtwo additional criteria to help us determine binarity.First, we compared V RAD of the same configurationfrom different nights. All configurations were observedon at least two nights, and a few were observed on threenights, except m48rg, which was observed just once (seeTable 2). If both (or all three) V RAD measures for agiven star agree to within 2 σ , defined using the largest σ , we marked the star as a single star; if at least onemeasure disagreed by more than 2 σ , we marked it asa binary; if there were ambiguities, we left a questionmark. The second criterion evaluates the power spec-trum from fxcor . Spectroscopic binaries have two peaks(or more) in the power spectrum. We did this separatelyfor each night, so each star has binarity information forat least two nights. This also precludes confusion dueto co-addition of binary spectra after orbital motion hasshifted the spectra.Under most circumstances, the second criterion agreedwith the first. However, if the secondary is much fainterthan the primary, the power spectrum might not be ableto see enough flux to create a second peak. So, if the V RAD are robustly different, i.e. the individual V RAD errors were small compared to the differences in V RAD ,we labeled the star as a binary.3.3.
Membership and Final Cluster Radial Velocity
To identify stars consistent with single-star member-ship, we compared the V RAD of individual stars to theaverage V RAD of M48 as follows. For each configurationfor each night, we chose a subsample that satisfied the
Table 2.
M48 observing logs
Nights Configurations Exposure Time Standards < σ σ > σ V RAD (km s − ) σ V RAD (km s − ) Note —1. Dates of the observation, e.g., 1710n4 means the data were taken on the fourth night of the oserving run that began during 2017 Octoberobserving run, and the UT date is 2017 October 31. Afternoon calibrations may have begun on the previous UT date. 2. The total exposure forthe given configuration(s). 3. Whether radial velocity standards were observed during the night. 4. The number of radial velocity standards thatfall within 1 σ , between 1 σ and 2 σ , and above 2 σ compared to the literature. 5. Average radial velocity of each configuration determined by fittinga Gaussian profile to all of the observed stars of that configuration, and 1 σ error of the Gaussian fit. following criteria: 1) single star according to the abovecombined binarity criteria, 2) v sin i <
20 km s − , and3) σ V RAD < − . To this subsample, we then fita Gaussian to the V RAD distribution and calculated theaverage V RAD and standard deviation. We initially ig-nored nights where our standard measurements did notagree well with literature and the m48vb1 and m48vb2configurations because the luminous stars at the main-sequence turnoff have very high v sin i , leading to largeuncertainties in the stellar V RAD . The weighted mean V RAD from all of the considered configurations from thenights is 8.399 ± − ( σ µ , and σ = 0.099 kms − ). We adopted this value temporarily as the aver-age V RAD for M48 ( < V
RAD > ). We then shifted theaverage V RAD from each and every configuration fromthe full sample to match this initial cluster < V
RAD > ,and combined the spectra from separate nights to gethigher signal-to-noise ratio (S/N) spectra for each con-figuration. We then ran the fxcor task once again on thecombined spectra. As in section 3.1, we then fit a Gaus-sian in the V RAD distribution for each configuration butonly to the single stars. Finally, treating each configu-ration separately, we marked the stars within 2 σ of themean as members, those between 2 and 3 σ as uncer-tain (“?”), and those outside 3 σ as not-single members.They could be nonmembers, or member binaries whosebinarity was not detected by the above techniques (notethat these stars all lie less than 0.75 mag brighter thanthe left-edge fiducial).For further evidence of membership, we also consid-ered the Gaia data, using proper motion ( P µ R . A . & P µ decl . ) and parallax from the Gaia DR2 (Gaia Col- −2.0 −1.5 −1.0 −0.5PM RA (mas yr −1 )0.60.81.01.21.41.6 P M D E C ( m a s y r − ) M48 Gaia DR2 Proper Motion
Figure 2.
M48 proper motion (PM) membership determina-tion using PM in both R.A. and decl. directions (mas yr − )),for our full Hydra sample. We define the center red circlesas M48 PM members, the yellow circles as stars of uncertainPM membership, and the blue circles as PM nonmembers. laboration 2016) full degree that covers the Hydra fieldwith a G magnitude cut at G = 17.2 mag, slightly fainterthan the faint limit of our Hydra sample, and matchedwith our U BV RI photometry. Figure 2 shows HydraM48 proper motion members selected using
P µ R . A . and P µ decl . criteria. Parallax ( π ) was considered indepen-dently of proper motion. Figure 3 shows a histogram ofthe number of stars versus π , where the cluster mem-bers clearly stand out from the other stars. Based ona Gaussian fit, we marked stars within 2 σ as members, nu m b e r o f s t a r s M48 Gaia DR2 G < 16 mag µ=1.285σ=0.055σ µ =0.004 Figure 3.
The parallax (mas) distribution for our full Hydrasample. We define stars that fall within 2 σ of the Gaussianfit as parallax members, those between 2 σ and 3 σ as havingundetermined membership from parallax, and those beyond3 σ as nonmembers. The mean and standard deviation of theparallax for M48 Hydra stars are 1.285 mas and 0.055 masfrom the Gaussian fit. V ( m a g ) mm?n?nHydra Gaia Dr2 M48 all data
Figure 4.
Color-magnitude diagram of M48 stars with Gaiamembership. The blue circles are Gaia members, the greensquares are uncertain members, the cyan triangles are uncer-tain nonmembers, and the yellow dots are nonmembers. Thered circles are our observations of M48 stars using Hydra. between 2 σ and 3 σ as stars with uncertain membership,and stars outside 3 σ as nonmembers. We also consid-ered two stars falling outside the 3 σ region that hadunusually large astrometric errors; neither has convinc-ing evidence of membership, either from Gaia data orour V RAD data, and are designated “sn” below. Giventhe frequency of stars outside the π interval 1.05–1.50mas, we estimate that the group identified as membersmay contain of the order of three nonmembers. V ( m a g ) Gaia m & m?Hydra m & m?0.75 mag brighter than Hydra m & m?
Figure 5.
A comparison of M48 Gaia members and likelymembers (blue circles) to Hydra members and likely mem-bers (red circles). The green line is 0.75 mag brighter thanHydra fiducial.
How well did our photometric selection procedure pickout members? Figure 4 shows the stars observed withHydra (red dots) with membership status using onlyGaia membership information (no V RAD information;blue dots are Gaia members, “m”; green squares leaningtoward membership, “m?”; inverted triangles leaning to-ward nonmembership, “n?”; and yellow dots nonmem-bers, “n”). Reassuringly, the few instances of m? arenear the fiducial sequence, while the vast majority ofn? and n are scattered away from it. Our photometricmethod eliminated a good number of n that lie on thefiducial, but it also threw out of the order of 50 m on orvery near the fiducial. This compares favorably to thenumber of stars observed with Hydra (192) whose finaldesignation (below) is m (163) or m? (29). Although thephotometric method also (deliberately) ignored poten-tial high-q binary members, the number of such starsthat were not observed with Hydra (15) is vastly out-numbered by the number of n? and n that lie up to 0.75mag brighter than the fiducial. We can see the lack of asignificant high-q binary sequence in Figure 5.We combined all of the V RAD , P µ R . A . , P µ decl . , and π information to make a final decision on placing each starinto one of the following categories: single-star mem-ber (sm), single-star nonmember (sn), binary member(bm), binary nonmember (bn), uncertain multiplicity(?m, ?n), and uncertain membership (“likely” member:sm?, ?m?, bm?; “likely” nonmember: n? etc.). Thisresults in 152 sm, 11 bm, 16 ?m, 56 sn, 28 sn?, 2 sm?, 1bm?, 5 bn, 10 ?m?, 3 ?n, and 3 ?n?. Figure 6 ( V versus B − V CMD) and Table 3 show the final M48 member-ship and multiplicity determinations.In more detail, our final determination of membershipwas carried out as follows. As discussed above, for eachstar, we assigned a membership status of “y,” “n,” or“?” to each of the following four criteria: photometry, V RAD , P µ , and parallax. (Recall that all stars have sta-tus “y” for photometry, since they were selected this wayto begin with.) Then, membership status was treated abit differently for each of the three binarity cases (s,b,?).For single stars, status “sm” was assigned if all four cri-teria had a “y” (130 stars) or if three criteria had a“y” and one had a “?” (22 stars). Status “sm?” wasassigned if two criteria had a “?” (two stars). Status“sn?” was assigned if one criterion had an “n” and theother three were “y” (21 stars) or if one criterion had an“n,” one had a “?,” and the other two had a “y” (sevenstars). Finally, status “sn” was assigned if at least twocriteria had an “n” (56 stars). For binary (or multiple)stars, the radial velocity criterion was ignored. Status“bm” was assigned if all three (remaining) criteria had a“y” (11 stars), “bm?” if one criterion had a “?” and twohad a “y” (one star), and “bn” if at least one criterionhad an “n” (five stars). Binarity status “?” was treatedas an intermediate case, and radial velocities were againincluded for consideration. Status “?m” was assigned ifall four criteria had a “y” (15 stars) or if three had a “y”and the fourth had a “?” in a category other than radial velocity (one star). Status “?m?” was assigned if theradial velocity criterion had an “n” and the other threehad “y” (eight stars), or if for the other three criteria,one had a “?” and two had a “y” (one star); or if theradial velocity criterion had a “?” and the other threehad a “y” (one star). Status “?n?” was assigned if twocriteria had a “?” and two had a “y” (one star) or ifone criterion had an “n”, one had a “?,” and two had a“y” (three stars). Finally, status “n” was assigned if atleast two criteria had an “n” (two stars).To determine a final V RAD and v sin i for each star andto determine the final cluster average V RAD , we appliedthe procedure described at the beginning of section 3.3once again and used the same criteria: a) must be smbased upon our final determination, Gaia data included,b) v sin i <
20 km s − , and c) σ V RAD < − .Again, a Gaussian was fit to each configuration fromeach night. The weighted mean V RAD is 8.376 ± − ( σ µ , and σ = 0.137 km s − ). After shiftingeach configuration onto 8.376 km s − and combiningthe spectra from separate nights, we ran fxcor on thecombined spectra and reevaluated the V RAD and v sin i of each star. We fit a Gaussian distribution functionto all of the qualifying stars to arrive at a final clusteraverage V RAD of 8.512 ± − ( σ µ , and σ =0.848 km s − ; shown in Figure 7). Table 3 . Parameters and Metallicity for M48 stars
Star Id R.A. Decl. V B − V V σ V σ v sin i σ Hα ?5 ( B − V )6eff σ T σ g V
7t [Fe/H]8 σ µ S/N9 mem10h m s ◦ ′ ′′ mag mag km s − − − − − − − ∗ ∗ – – 29(31) ∗ ∗ no 0.072 0.009 – – – – – – 661 bm2016 8 12 58.57 -5 34 08.1 9.543 0.071 38.88, 19.34 2.32, 3.08 – – 20 4.8 no 0.084 0.009 – – – – – – 719 bm?2017 8 13 23.22 -5 45 23.0 9.777 0.071 11.69, 13.58 0.86, 4.05 10.63 3.29 23 2.5 no 0.066 0.007 – – – – – – 579 sm2018 8 13 39.66 -5 47 14.6 9.807 0.129 20.33, 4.90 4.79, 3.52 – – – – – 0.141 0.029 – – – – – – 664 bm2019 8 13 04.96 -5 53 04.8 9.935 0.094 20.67, 14.96 9.76, 7.88 11.48 8.09 250 – yes 0.089 0.006 – – – – – – 561 sm2020 8 13 49.00 -5 44 23.7 9.937 0.078 -12.97, -1.19 4.35, 6.92 -7.20 5.93 – – – 0.071 0.019 – – – – – – 571 ?n2021 8 13 26.60 -5 49 53.8 9.990 0.059 26.75, 6.46 5.49, 4.98 – – – – – 0.054 0.008 – – – – – – 554 bn2022 8 13 43.39 -5 41 33.7 10.002 0.032 18.85, 15.86 6.26, 9.34 12.95 9.06 230 – yes 0.047 0.006 – – – – – – 515 sm2023 8 13 40.40 -5 42 20.1 10.138 0.102 10.93, 7.13 4.81, 4.69 6.86 2.95 150 – yes 0.109 0.013 – – – – – – 570 sm2024 8 13 54.40 -5 58 47.6 10.160 0.060 11.47, 12.48 3.12, 9.77 8.60 5.86 – – – 0.060 0.003 – – – – – – 531 sn2025 8 14 03.19 -5 41 44.5 10.187 0.029 20.83, 1.83 3.02, 2.74 – – 40 6.0 no 0.042 0.008 – – – – – – 513 bm2027 8 13 12.17 -5 46 41.8 10.341 0.111 15.83, 10.39 4.55, 5.74 9.32 5.90 – – – 0.128 0.016 – – – – – – 453 sn?2028 8 13 45.99 -5 46 01.9 10.364 0.111 2.25, 2.2 2.02, 2.49 -0.48 2.18 46 5.2 no – – – – – – – – 492 sn2029 8 12 08.26 -6 03 16.0 10.483 0.051 17.78, 11.65 4.55, 6.35 11.18 6.60 230 – yes 0.063 0.008 – – – – – – 376 sm2030 8 14 20.28 -5 39 57.4 10.531 0.071 3.64, 1.93 4.24, 3.90 -0.39 3.12 42 6.5 no 0.068 0.008 – – – – – – 400 sm2031 8 13 17.60 -5 41 13.4 10.540 0.064 23.3, 22.13 6.94, 9.67 19.80 9.21 – – – 0.080 0.013 – – – – – – 458 sn?2032 8 14 02.41 -5 56 46.8 10.550 0.066 4.61, 1.09 2.00, 3.12 -0.28 2.84 20 1.9 no 0.074 0.006 – – – – – – 376 sm2033 8 13 43.25 -5 45 53.1 10.576 0.082 37.77, -19.73 2.46, 4.49 – – 52 8.3 no – – – – – – – – 433 bm2035 8 13 52.12 -5 54 20.3 10.596 0.148 20.95, 16.49 5.55, 9.10 14.44 7.34 280 – yes 0.149 0.014 – – – – – – 404 sm2036 8 13 13.82 -5 56 38.2 10.614 0.091 21.40, 14.18 9.01, 5.75 14.56 8.34 230 – yes 0.092 0.012 – – – – – – 447 sm2037 8 13 19.73 -5 33 37.2 10.617 0.063 -0.07, 30.72 2.35, 2.33 – – 24 2.1 no 0.085 0.015 – – – – – – 437 bm2038 8 13 09.50 -5 27 01.1 10.625 9.999 18.78, 9.43 7.59, 5.49 8.86 6.05 – – – 0.136 0.013 – – – – – – 437 ?m... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... Note —1. V magnitude and B − V color from our M48 photometry. 2. Radial velocity ( V RAD) and errors in km s − V RAD and errorsin km s − v sin i ) and errors in km s −
1. 5. Whether v sin i are measured using Hα or by averaging lines between 6600 ˚Aand 6800 ˚A. 6. Averaged ( B − V ) and standard deviation by using all 10 possible color combinationsfrom UBV RI . 7. Stellar atmosphere parameters derived from section 4.1: T eff & σT eff in K, log g , and V t in km s −
1. 8. [Fe/H] and σµ ([Fe/H]) for individual starsbased on calculations in section 4.2, for single-member stars that satisfy the v sin i and σT eff criteria only. 9. Signal-to-noise ratio of the combined spectra of all nightsof the star. 10. Binarity & membership determination from section 3. sm: single member; bm: binary member; ?m: member of uncertain multiplicity; sn: single starnonmember; sn?: single star likely non-member; sm?: single star likely member; bm?: binary likely member; bn: binary nonmember; ?m?: likely member of uncertainmultiplicity; ?n: nonmember of uncertain multiplicity; ?n?: likely nonmember of uncertain multiplicity. ∗ V RAD and v sin i for secondary star measured from fxcor. To determine final V RAD and v sin i for each star, weshifted V RAD from each and every configuration onto thenew cluster average of 8.512 km s − (these final V RAD from each individual night are reported in Table 3), com-bined spectra from the same configuration, and deter-mined the final V RAD and v sin i for each star (reportedin Table 3). The reader should be cautious about the V RAD of those stars that have multiplicity status “?”.Similarly, v sin i may not be accurate for stars that arenot single. Furthermore, even though we report the v sin i produced by fxcor , values far below our resolutionlimit of roughly 10–12 km s − are uncertain, even forsingle stars. A conservative interpretation might treatvalues less than 10–12 km s − as upper limits of 12 kms − . Star 2015 has two clear peaks from fxcor and weare able to measure the V RAD and v sin i for each sepa-rate peak, so we report V RAD and v sin i for both starsin Table 3 (secondary shown in parentheses). For somevery hot and/or rapidly rotating stars, fxcor was unableto determine v sin i . In these cases, we obtained a roughestimate of v sin i (to within roughly 10–20 %) by syn-thesizing the H α line from 6515 to 6610 ˚A (indicatedas “yes” in column H α of Table 3) using MOOG (Sne-den et al. 1973). In choosing the best-fitting value of v sin i , we were guided by similar syntheses of the mostrapidly rotating stars of similar spectral type that had fxcor -determined values of v sin i . We do not report v sin i from H α for stars of uncertain binarity or member-ship. Figure 8 presents the v sin i of M48 members andlikely members (m, m?) in the V versus B − V CMD,with the symbol size proportional to √ v sin i , where v sin i ranges from 6 to 300 km s − . Note that for con-figurations observed on more than one night, Table 3shows final V RAD s and errors from the combined spec-tra of multiple nights only for single stars and stars withuncertain multiplicity. The shifts of final V RAD from in-termediate V RAD are very small, always less than 0.2 kms − for all single stars.We compare our cluster radial velocity to three previ-ous reports of V RAD in M48. We are in good agreementwith Wallerstein et al. (1963), who report 8.9 km s − (no error reported) based on three giants, and who sus-pect their V RAD are systematically too high by up to 1- 2 km s − . Our value is just slightly higher than thatof Mermilliod et al. (2008a), who report 7.70 ± − (“error”) from four giants of which two are SB. Notethat of the eight giants observed by us, two are sm, oneis sm?, and five are sn. Geyer & Nelles (1985) report 5.7 ± − (m.e.) from 21 stars, which have a rangein V RAD of -20 to 42 km s − with errors ranging from2.6 to 6.8 km s − (two stars have larger errors). Their V RAD distribution peaks at 6–10 km s − , in agreementwith our result.Finally, we comment on the possible relation betweenthe broadening of the turnoff and stellar rotation. Ev-idence that cluster turnoffs in the CMD can be muchwider than the single-star fiducial at lower mass hasbeen around for a very long time; compare, for exam-ple, the very thin single star fiducial in Praesepe to themuch wider cluster turnoff (Johnson 1952). Such “ex-tended” (broadened) main-sequence turnoffs (eMSTOs)have been observed in many more clusters, such as inmost massive clusters in the Large and Small Magel-lanic Clouds (MC) with age < <
700 Myr) show “split”(bimodal) main-sequences (Milone et al. (2013); Goud-frooij et al. (2014); Li et al. (2017)). Aided by Gaia DR2membership information and photometry, increasingly,Milky Way (MW) open clusters are also found to ex-hibit eMSTOs (Cordoni et al. 2018), even though theygenerally are much less massive than the MC clusters.Deciphering the origin of eMSTOs is thus becoming ofincreasing interest.One contributor could be binarity, but binaries shouldbroaden the entire main-sequence, not just the turnoff,so unless the binary fraction is much larger for moremassive stars (see also Section 3.4), other contributorsmay be important. In fact, M48 exhibits a modest eM-STO even among stars identified as single (red disks inFigure 8). Another posited contributor among clusterswith ages 1–3 Gyr has been variability (Salinas et al.2016); however, the number of variable stars in the MCcluster NGC 1846 may not be sufficiently large (Salinaset al. 2018). Another possibility is age spreads due toprolonged star formation or multiple epochs of star for-mation, in which case, the MC clusters could be youngeranalogs of MW globular clusters that show multiplepopulations (Keller et al. 2011). However, it is expectedthat only very massive star clusters can create multiplepopulations (e.g. D’Ercole et al. 2008), which would ex-clude almost all MW open clusters, and evidence suchas the existence of multiple main-sequences that attestto the multiple populations in MW globular clusters hasyet to be discovered in open clusters. Furthermore, theimplied age spreads can be absurdly large; for example,up to 500 Myr in an open cluster (NGC 5822) with anage of 900 Myr (Figure 3 of Sun et al. 2019). By con-trast, evidence suggests an absence of primordial clus-ter gas after 4 Myr (Hollyhead et al. 2015) and no starformation in clusters older than 10 Myr (Elmegreen &Efremov (1997); Niederhofer et al. (2016)). Other ex-planations include metallicity variations (Milone et al. avg (mag)81012141618 V ( m a g ) Membership for all M48 Hydra data smsm??m?m?bmbm?n&n?
Figure 6.
Color-magnitude diagram of M48 stars with membership and multiplicity information. The red circles are singlemembers, the blue circles are likely single members, the green squares are members with unknown binarity, the light bluesquares are likely members with unknown binarity, the black triangles are binary members, the magenta triangles are binariesof uncertain membership, and the small yellow dots are nonmembers and likely nonmembers.
RAD (km s −1 )0246810 nu m b e r o f s t a r s µ=8.512σ=0.848σ µ =0.087 Figure 7.
Final Radial Velocity of M48. The mean andstandard deviation of the Gaussian fit are 8.512 km s − and0.848 km s − , respectively. . v sin i (Brandt & Huang 2015; BH15). For detailed discussionof the various issues and complexities we refer the readerto BH15, and comment here only on the interesting pre-diction listed above, and one more. In particular, BH15find that in an observational color-magnitude diagram,the thickness (in color) of the eMSTO is small at youngerages ( <
500 Myr), then grows and peaks between 1 and1.5 Gyr, and becomes thin at older ages. Consistentwith both predictions, Figure 8 shows a clear eMSTO ofrather modest thickness and no discernible correlationbetween color and v sin i . We interpret the data of Sunet al. (2019) for open cluster NGC 5882 in a similar way:at the turnoff ( G = 11–12 mag) the two most rapid rota-tors are redder and have v sin i = 230–250 km s − , butthe next six most rapidly rotating stars are bluer androtate only slightly less rapidly, with v sin i = 150–220km s − .0 avg (mag)81012141618 V ( m a g ) Hydra membership & v sini smsm??m?m?bm?
Figure 8.
Color-magnitude diagram of M48 members and likely members with rotational velocity. The marker size is propor-tional to √ v sin i . Cluster Binary Fraction
The combination of our photometric data, our spec-troscopic data, and the Gaia data enable us to examinethe binary/multiple fraction of M48. None of the threem or m? giants showed evidence of binarity, but fx-cor could have missed such evidence if the companionis much fainter, so we restrict attention to the main-sequence and turnoff stars. Since the analysis of rapidrotators is more challenging, we separate the sample intoa “hot” subsample of stars rotating more rapidly thatincludes dwarfs with B − V ≤ B − V > B − V > B − V , there is some evidence that rapid rotation is nota possible cause of such displacement: single rapid rota-tors in the Pleiades fall on the fiducial (Soderblom et al.1993a,b). Note also the caveat that we might misiden-tify a binary as single if it has a sufficiently long periodso that its radial velocity did not vary significantly be-tween the dates of the two (or three) measurements andif the secondary flux is sufficiently low so as not to bedetected by fxcor .Summing up the numbers of the cool sample, of205 members, 180 are single (87.8%), 22 are binaries(10.7%), and three are ? (1.5%). Given our very lim-ited number of epochs (two or three) it is impossibleto attach errors to these numbers, as do a number ofother studies that have multiple epochs of observationsand determine binary orbits, and they are often able tomake estimates of incompleteness (below).Rapid rotation complicates analysis of the hot sampleof more massive stars. In contrast to the cool sample,hot rapid rotators can be photometrically either on oroff of the left-edge fiducial sequence (Figure 8). So welimit analysis to the 66 Hydra members and ignore theadditional 16 Gaia members not observed with Hydra.Of the 66 Hydra members, 32 are single (48.5%), 10are binaries (15.2%), and 24 are ? (36.4%). If the ?are all binaries, then the hot binary fraction could beas high as 51.6% and the combined hot+cold fractionwould be 21%. However, given the various uncertaintiesintroduced by rapid rotation, it is difficult to ascertainwhether these results truly differ from those of the coolsample. For example, it is also possible that all hot? are single, in which case, the results of the cool andhot samples would be fairly similar. A mass-dependentbinary fraction is sometimes seen; for example, Bohm-Vitense (2007) reports that the binary fraction in theHyades increases from 26% in K dwarfs to 87% in Adwarfs. However, we can neither claim nor preclude asimilar trend of increasing binary fraction with mass inM48.The binary fractions in open clusters vary signifi-cantly. For the 100 Myr-old Pleiades, using 144 G andK dwarfs, Bouvier et al. (1997) report a fraction of 28%based on 22 binaries with separations 11–910 au andcorrected for incompleteness, and Richichi et al. (2012)report 29% from a smaller number of dwarfs of morevaried spectral type. Bouvier et al. (1997) point outthe much higher binary fraction in some star formingregions such as Taurus-Auriga and Ophiuchus (Leinertet al. (1993), Ghez et al. (1993), Simon et al. (1995)),and they suggest that cluster formation environmentrather than cluster evolution is a more important fac- tor: Pleiades is a dense cluster whereas the clouds areloose T Tauri associations. Mermilliod et al. (2008b) re-port a fraction of 20% in FGK dwarfs of the 100 Myr-oldBlanco 1, and Geller et al. (2010; WOCS study) reportan incompleteness-corrected fraction of 24% in the 150Myr-old M35 for binaries with periods < P <
P <
P <
P < might be 12–20%. In its younger days, NGC 188may have had a smaller binary fraction, perhaps morecomparable to that of M67, if evaporation favors singlestars instead of binaries, as suggested by the models ofHurley et al. (2005). On the other hand, destructionof binaries through internal cluster dynamics may alsoplay an important role. Finally, Raghavan et al. (2010)studied several hundred field stars and found a binaryfraction of 19% for
P < METALLICITYTo determine stellar and cluster metallicities, we fol-low procedures very similar to those in Cummings et al.(2017), which we briefly summarize here. These proce-dures include deriving precision cluster [Fe/H] based onas many isolated Fe I lines as possible in our spectralrange, using as many carefully selected stars as possiblecovering as wide a range in T eff as possible, and ensuringthat we use only the range in T eff for each line in whichthat line is well behaved. Cummings et al. (2017) wereable to use Praesepe stars covering a range of 1700 K in T eff . For M48, we extend the range to 2500 K.4.1. Effective Temperature, Log g, and Microturbulence
We have adopted the following cluster input param-eters, as derived from our
U BV RI photometric study(Paper II): distance ( m − M ) v = 9 . ± .
08 mag, age = 420 ±
30 Myr, interstellar reddening E ( B − V ) =0 . ± .
01 mag, and metallicity [Fe/H] = -0.05 ± B − V colors to determine the effective temper-ature of our M48 dwarfs. To incorporate atmosphericinformation contained outside the B and V spectralranges, and to reduce statistical and systematic errors,we use all 10 possible color combinations from U BV RI to derive an effective, average B − V for each star. Forinstance, we fit a polynomial to the U – V vs. B − V plotusing the members in the M48 fiducial sequence, andthen convert the U – V for each star to the corresponding B − V according to this relation. Similarly, we convertthe U – B , U – R , U – I , B – R , B – I , V – R , V – I , and R – I to B − V . Then we average the 10 B − V colors to de-rive the final effective B − V and σ ( B − V ) (See Table3). Some stars lack measurements in certain bands, sofor these stars we use only the measured colors to derive B − V .To remain consistent with our previous studies (forexample, Thorburn et al. (1993); Deliyannis et al.(1994), (2002), (2019); Steinhauer & Deliyannis (2004);Anthony-Twarog et al. (2009), (2010), (2018a); Maderaket al. (2013)), we have used the ( B − V ) − [ F e/H ] − T eff relation in equation (1) of Cummings et al. (2017). ForM48, we have assumed E ( B − V ) = 0 .
05 mag and [Fe/H]= -0.05 dex, and, as usual, for the Hyades we assume[Fe/H]
Hyades = +0 .
15 dex. σ T eff are calculated from σ ( B − V ) based on error propagation. This relationshipis valid for T eff = [3500 K, 7750 K], which excludes manyof our m48vb1 and m48vb2 stars that are hotter than7500 K. However, none of these hotter stars meet thestringent selection criteria for metallicity determinationdefined in section 4.2, so their exclusion does not affectthe results of this study. We determined the log g of each star from the Yonsei–Yale ( Y ; Demarque et al. (2004)) isochrones, adopting[Fe/H] = -0.05 dex, Z = 0.01618, Y = 0.26236, [ α /Fe]= 0.00, and an age of 420 Myr. Lastly, the microturbu-lence ( V t ) was calculated using the empirical relation fordwarfs of Edvardsson et al. (1993), or 0.8 km s − for thecoolest dwarfs, as discussed in Cummings et al. (2017).Stellar atmosphere models were created from theKurucz (1992) models with convective overshoot.4.2. M48 Metallicity
To derive a more robust cluster average metallicity,we have used a subsample of stars that obey the fol-lowing stringent criteria: a) must be a single (dwarf)member (Section 3), b) must have σ T eff <
75 K (larger σ T eff may indicate atmospheric problems or other errorsleading to unreliable [Fe/H]); and c) v sin i <
25 km s − (the broadened iron lines in stars with larger v sin i might be contaminated by nearby lines). We selected16 non-blended Fe I lines from the solar spectrum (Del-bouille et al. 1989) and measured the equivalent widthof each line for each star. Fe I lines with an equiv-alent width greater than 150 m˚A were not consideredto avoid possible nonlinearity issues. Table 4 shows thewavelength λ (˚A), excitation Potential (eV), and log (gf)values of the 16 Fe I lines. We started with the Kurucz(1992) atmosphere model grids with [Fe/H] = -0.05 dex,and then used an interpolator to construct model atmo-spheres using the T eff , log g , and V t derived in section4.1 for each star. Then, we derive A(Fe) by performinglocal thermal equilibrium (LTE) line analysis for eachFe I line using the abfind task of MOOG (Sneden et al.1973). The S/Ns per pixel were measured empiricallyusing the “line-free” region from Fe I (6678˚A) and Al I(6696˚A). For stars fainter than V = 14 mag, which allrotate slowly, the ratio of the Poisson-based S/N (fromthe number of counts) to this empirical S/N is slightlyhigher than 1, with little scatter from star to star. How-ever, stars with V <
14 mag rotate more rapidly, andthe ratio deviates from this value increasingly with v sin i , possibly because rotational broadening means the line-free region is increasingly less line-free. Table 3 showsthe empirical S/N for V >
14 mag, and the Poisson-based S/N divided by this ratio for
V <
14 mag.Following Cummings et al. (2017), Figure 9 showsA(Fe) for each line versus T eff . Four lines, namely6609.118 ˚A, 6677.997 ˚A, 6726.673 ˚A, and 6752.716 ˚A,not shown in the figure, show trends with T eff through-out the entire T eff range and were rejected from the cal-culations of [Fe/H], below. For the remaining 12 Fe Ilines (all shown in the figure), we also rejected regionswith possible trends in T eff and outliers (yellow dots).3 Table 4.
Selected Fe I lines
Wavelength (˚A) Excitation Potential (eV) log (gf)6597.560 4.80 -1.046608.044 2.28 -4.026609.118 2.56 -2.676627.540 4.55 -1.576653.910 4.15 -2.446677.997 2.69 -1.226703.576 2.76 -3.136710.320 1.49 -4.776725.364 4.10 -2.306726.673 4.61 -1.126733.153 4.64 -1.526750.164 2.42 -2.486752.716 4.64 -1.306806.856 2.73 -3.246810.267 4.61 -1.126820.374 4.64 -1.27 A ( F e ) ( d e x ) eff (K)7.07.58.08.59.0 6710.320 Å 4200490056006300700077006820.374 Å Figure 9.
Iron abundance by individual lines. We kept linesshown in red dots. Lines 6609.118˚A, 6677.997 ˚A, 6726.673 ˚A,and 6752.716 ˚A are not shown here because the abundancesdepend on T eff throughout the entire range in T eff . Most linesshow an upward trend toward cooler T eff , and these coolerstars and outliers were eliminated. A v e r a g e [ F e / H ] ( d e x ) Average [Fe/H] for each Fe I line
Figure 10.
Averaged [Fe/H] over all stars vs. wavelengthfor each line. Error bars are the standard deviation of themean. The line at 6609.118 ˚A was rejected as an outlier. eff (K)−0.6−0.4−0.20.00.20.40.6 [ F e / H ] ( d e x ) [ F e / H ] ( d e x ) t (km s −1 )−0.6−0.4−0.20.00.20.4 [ F e / H ] ( d e x ) Ave age [Fe/H] of each M48 sta
Figure 11. [Fe/H] for individual stars in M48. Error barsare the standard deviation of the mean. ≃ ± σ µ ), and σ = 0.1096 dex.) For each linefor each star, we subtracted the solar A(Fe) from thestellar A(Fe) to derive an [Fe/H] for that line for thatstar.Figure 10 shows A(Fe) for each line as averaged overall (kept) stars, plotted against wavelength. This illus-trates that the average abundances are consistent fromline to line, except for the 6608.044 ˚A line (red), whichwe rejected as a 2.6 σ outlier and and which we excludedfrom further analysis. For all surviving lines, we sub-tracted the solar A(Fe) from that line’s A(Fe) to derivethat line’s [Fe/H]. A linear (not log) average of eachstar’s lines produced a [Fe/H] for that star (as in Boes-gaard et al. (2005) and Cummings et al. (2017)). Fig-ure 11 shows the stellar [Fe/H] versus T eff (top panel),[Fe/H] versus log g (middle panel), and [Fe/H] versus V t (bottom panel) for all stars in our carefully selected sub-sample. Across nearly the entire range in T eff of 2500K, [Fe/H] shows no dependence on T eff . Similarly, notrends are found with log g or V t . Table 3 also liststhe stellar [Fe/H] for those stars included in the Fe-subsample, and their errors (standard deviation of themean).The overall cluster average [Fe/H] for M48 was deter-mined using the precepts discussed in Cummings et al.(2017) and our other works. In particular, the cluster[Fe/H] was derived by averaging linearly and in linear(not log) space all the lines surviving the cuts in Figures9 and 10. The result is [Fe/H] M48 = -0.063 ± σ µ , and σ = 0.151 dex), in excellent agreement withour photometric study. Table 5 shows how systematicchanges in ∆( E ( B − V )), ∆(log g ), and ∆( V t ) affect thederived [Fe/H].The only spectroscopic abundance (that we could find)comes from Wallerstein & Conti (1964), who observedone giant and report [Fe/H] = -0.51 dex. But theyalso indicate that the star is metal poor by a factor oftwo compared to γ T au of the Hyades, which suggests Table 5.
Possible systematic errors on [Fe/H] (dex)
Parameter Changes1 4300 K 2 5300 K 2 6300 K 2 M48 cluster3∆( E ( B − V )) = +0.01 mag -0.011 0.017 0.027 0.0089∆(log g ) = +0.2 0.033 -0.005 -0.005 0.0076∆( V t) = +0.2 km s − comb (∆( E ( B − V )) = +0.01 mag) -0.012 0.018 0.023 0.0012 Note —1. The first three lines show changes for each of the three parameters (E( B − V ), log g , V t) independently. For example, we change E ( B − V ) by +0.01 mag, but keep the log g and V t the same. The bottom line shows changes for all three parameters simultaneouslybased on ∆( E ( B − V )) = +0.01 mag: ∆( E ( B − V )) implies a certain ∆(log g ), and thesetwo imply a certain ∆( V t). 2. Change of [Fe/H] for a star at T eff = 4300 K, 5300 K, 6300K. 3. Change of [Fe/H] for the whole M48 cluster following the above procedure. [Fe/H] = -0.15 dex, assuming [Fe/H] = +0.15 dex forthe Hyades (Cummings et al. 2017). They quote an un-certainty in [Fe/H] by a factor of two, so their result isin agreement with ours. There are several photomet-rically based metallicities. From Claria’s (1985) DDOphotometry of three giants, we infer [Fe/H] = +0.14 ± ± ± u ′ g ′ r ′ i ′ z ′ )report a range of [Fe/H] = -0.1 to +0.1 dex, with a pre-ferred value of 0.0 dex. Wu et al. (2005; BATC) report[Fe/H] = 0.0 dex (no error). Finally, Balaguer-Nunez etal. (2005; uvby − H β ) report [Fe/H] = -0.24 ± SUMMARYWe present high signal-to-noise WIYN/Hydra spectrafor 287 stars that mainly fall on the single-star fiducialmain-sequence of our M48 CMD. We report radial ve-locities ( V RAD ) for all of the stars on at least two nights(except one possible red-giant star member, which wasobserved only once) and compare the V RAD from differ-ent nights along with the Fourier-transformed spectra todetermine binarity for all of the stars. Using only singlestars with rotational velocity ( v sin i ) less than 20 kms − and σ ( V RAD ) < − , we derive an initial esti-mate for the M48 cluster mean V RAD of 8.399 ± − ( σ µ , and σ = 0.099 km s − ). Stars within 2 σ of the M48 V RAD are defined as radial velocity mem-bers. We retrieve the proper motion in R.A. and decl.and parallax of stars from the Gaia DR2 (Gaia Collab-oration 2016, 2018) to determine independently a groupof highly probable M48 members. Combining both the V RAD data and the Gaia DR2 data, we designate 152stars as single members of M48 (sm), 11 stars as bi-5nary members (bm), 16 stars as members of uncertainmultiplicity (?m), 56 stars as single-star nonmembers(sn), 28 as single-star “likely” nonmembers (sn?), two assingle-star “likely” members (sm?), one star as a binary“likely” member (bm?), five stars as binary nonmembers(bn), 10 stars as “likely” members of uncertain multi-plicity (?m?), three stars as nonmembers of uncertainmultiplicity (?n), and three stars as “likely” nonmem-bers of uncertain multiplicity (?n?). Now, using a morerestricted sample of stars, namely, (1) it must be sm,(2) v sin i <
20 km s − , and (3) σ V RAD < − ,we evaluate our final M48 cluster mean V RAD as 8.512 ± − ( σ µ ).Using our spectroscopic data together with Gaia DR2data, we find a minimum binary fraction in M48 of 11–21%. This is similar to a number of other clusters thatspan a variety of ages and richness classes but not ashigh as some, such as the Hyades.To derive a more robust cluster average metallicity,we use a subsample of stars that obey the followingstringent criteria: must be a single (dwarf) member,must have σ T eff derived from 10 color index combina-tions of U BV RI photometry <
75 K, and v sin i <
25 km s − . Stellar parameters are evaluated as fol-lows. We use the averaged B − V color transformed fromall 10 possible color combinations of U BV RI to deter-mine the effective temperature ( T eff ) for each star fromour usual color–metallicity–temperature relation (Cum-mings et al. 2017). The log g values are derived from Y isochrones (Demarque et al. 2004) based on a cluster ageof 420 Myr and [Fe/H] = -0.05 dex, and we adopt therelationship from Edvardsson et al. (1993) to determine V t , with a lower limit of 0.8 km s − for the coolest stars.Using the Kurucz (1992) stellar atmospheres, we deriveA(Fe) for all Fe I lines. Solar A(Fe) are calculated basedon our high–S/N daytime sky spectra in a similar wayand are then subtracted to arrive at [Fe/H] for each linein each star. Examining each Fe I line separately for allstars as a function of T eff , we eliminate portions (or en-tire lines) that show trends with T eff , and outliers. 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