Searching for Low-mass Population III Stars Disguised as White Dwarfs
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Searching for Low-mass Population III Stars Disguised as White Dwarfs
Vedant Chandra and Kevin C. Schlaufman Department of Physics and AstronomyJohns Hopkins University3400 N Charles StBaltimore, MD 21218, USA (Received October 15, 2020; Revised January 29, 2021; Accepted February 9, 2021)
Submitted to the Astronomical JournalABSTRACTIt is uncertain whether or not low-mass Population III stars ever existed. While limits on the numberdensity of Population III stars with M ∗ ≈ . M (cid:12) have been derived using Sloan Digital Sky Survey(SDSS) data, little is known about the occurrence of Population III stars at lower masses. In the absenceof reliable parallaxes, the spectra of metal-poor main sequence (MPMS) stars with M ∗ (cid:46) . M (cid:12) can easily be confused with cool white dwarfs. To resolve this ambiguity, we present a classifier thatdifferentiates between MPMS stars and white dwarfs based on photometry and/or spectroscopy withoutthe use of parallax information. We build and train our classifier using state-of-the-art theoreticalspectra and evaluate it on existing SDSS-based classifications for objects with reliable Gaia DR2parallaxes. We then apply our classifier to a large catalog of objects with SDSS photometry andspectroscopy to search for MPMS candidates. We discover several previously unknown candidateextremely metal-poor (EMP) stars and recover numerous confirmed EMP stars already in the literature.We conclude that archival SDSS spectroscopy has already been exhaustively searched for EMP stars.We predict that the lowest-mass primordial-composition stars will have redder optical-to-infrared colorsthan cool white dwarfs at constant effective temperature due to surface gravity-dependent collision-induced absorption from molecular hydrogen. We suggest that the application of our classifier to dataproduced by next-generation spectroscopic surveys will set stronger constraints on the number densityof low-mass Population III stars in the Milky Way. Keywords:
Chemically peculiar stars (226) — Low mass stars (2050) — Population II stars (1284) —Population III stars (1285) — Sky surveys (1464) — White dwarf stars (1799) INTRODUCTIONThe first generation of stars formed in the Universewas made of only the stable products of Big Bang nu-cleosynthesis: hydrogen, helium, and a tiny amountof lithium. These Population III stars are predictedto start forming around 100 Myr after the Big Bang(e.g., Bromm 2013; Glover 2013; Greif 2015). The earli-est Population III star formation calculations suggestedthat inefficient cooling would require large Jeans massesand therefore that Population III stars would form with
Corresponding author: Vedant [email protected] a characteristic stellar mass M ∗ ∼ M (cid:12) (e.g., Silk1983; Tegmark et al. 1997; Bromm et al. 1999, 2002;Abel et al. 2000, 2002). However, more recent simu-lations have shown that fragmentation in the accretiondisks around massive Population III protostars could po-tentially form pristine stars at much lower masses (e.g.,Stacy et al. 2010, 2012, 2016; Clark et al. 2011a,b; Greifet al. 2011, 2012; Stacy & Bromm 2013, 2014; Dopckeet al. 2013; Riaz et al. 2018; Wollenberg et al. 2020).While it is theoretically uncertain if these fragments sur-vive or merge with the more massive protostar growingat the center of their parent accretion disk (e.g., Hi-rano & Bromm 2017), there is at least circumstantialobservational evidence to suggest that they might sur- a r X i v : . [ a s t r o - ph . S R ] F e b Chandra & Schlaufman vive (Schlaufman et al. 2018). If these fragments doavoid merging, then low-mass Population III stars mightpersist to the present day in the local Universe.While no Population III star has been directly ob-served to date, according to the latest Stellar Abun-dances for Galactic Archaeology (SAGA) database ob-servational searches have instead found more than 500extremely metal-poor (EMP) stars with metallicity[Fe/H] (cid:46) − T eff and surface gravity log g inferences, only 199 or2.3% have T eff (cid:46) g (cid:38) . ≈ − . T eff (cid:38) . (cid:46) log g (cid:46) . T eff (cid:46) g (cid:38) . T eff (cid:46) earching for Low-mass Population III Stars DATAOur goal is to differentiate MPMS stars from whitedwarfs on the basis of photometry and spectroscopyalone. While there is enough observational data forMPMS stars and white dwarfs with T eff (cid:38) T eff (cid:46) Theoretical Spectra
We first construct grids of theoretical spectra for whitedwarfs and MPMS stars using state-of-the-art mod-els. We consider temperatures in the range 4000 K ≤ T eff ≤ ≤ log g ≤ . ≤ log g ≤ . T eff (cid:46) − . ≤ [Fe/H] ≤ +1 . α abundances − . ≤ [ α /Fe] ≤ +1 .
2. In our theoretical grid of MPMSstar spectra, we use the [Fe/H] = − . α abundances. The spectroscopic classifier we de-scribe in Section 3 relies on Balmer lines, so the assumedmetallicity has only a negligible impact on our analyses.For both the MPMS and WD grids of theoretical spec-tra spanning T eff and log g , we tri-linearly interpolate F l u x ( a r b i t r a r y ) DA WD F l u x ( a r b i t r a r y ) [Fe/H] = -4.0 MPMS Effective Temperature (K)
Figure 1.
Sample theoretical white dwarf and MPMSstar spectra from the Blouin et al. (2018a) and PHOENIX(Husser et al. 2013) libraries, respectively. We plot spec-tra spanning the range 4000 K ≤ T eff ≤ g = 8 and log g = 4 . − . T eff = 4000 K white dwarf in thetop panel. the logarithm of the fluxes with respect to effective tem-perature, surface gravity, and the logarithm of wave-length. We convolve all theoretical spectra to matchan instrumental resolution of 1 . SDSS Data
Our empirical data for warmer MPMS stars and whitedwarfs come mostly from SDSS DR16 (Ahumada et al.2020). They were collected during the first four phases ofthe SDSS (York et al. 2000; Eisenstein et al. 2011; Blan-ton et al. 2017), including its Sloan Extension for Galac-tic Understanding and Exploration (SEGUE), BaryonOscillation Spectroscopic Survey (BOSS), and extendedBOSS (eBOSS) programs (Yanny et al. 2009; Dawsonet al. 2013, 2016). The data were collected using the
Chandra & Schlaufman
Sloan Foundation 2.5 m Telescope and its imager andoptical spectrographs (Gunn et al. 1998, 2006; Doi et al.2010; Smee et al. 2013) then placed on the SDSS photo-metric system using the methods described in Fukugitaet al. (1996), Smith et al. (2002), and Padmanabhanet al. (2008). We also make use of Gaia DR2 astrome-try (Gaia Collaboration et al. 2016, 2018; Salgado et al.2017; Arenou et al. 2018; Lindegren et al. 2018; Luriet al. 2018; Marrese et al. 2019). We de-redden the SDSS ugriz magnitudes using the mwdust utility (Bovy et al.2016) and the combined dust maps of Drimmel et al.(2003), Marshall et al. (2006), and Green et al. (2019).We focus on the MPMS star and white dwarf classifi-cations provided by Kepler et al. (2019). Those authorsexamined 500,000 SDSS spectra plausibly produced bywhite dwarfs. They provide classifications for 37,053spectra based on 11 criteria, of which 15,716 were clas-sified as DA white dwarfs and 15,855 were classifiedas subdwarf A or sdA stars (i.e., likely MPMS stars).Among the white dwarfs, over 78% were classified as DAwhite dwarfs with hydrogen-rich atmospheres on the ba-sis of broad Balmer absorption lines with no other strongspectral features. Kepler et al. (2019) visually differen-tiated these DA white dwarfs from subdwarf A starsbased on the fact that DA white dwarfs have broaderBalmer lines at a given photometric color due to theirhigh surface gravities and increased pressure broaden-ing. Together these two classes comprise more than 85%of the classifications provided in Kepler et al. (2019).We use in our analysis only those white dwarfs orMPMS stars classified by Kepler et al. (2019) as mem-bers of their “DA”, “sdA”, or “sdA/F” classes. The class“DA” designates hydrogen-atmosphere white dwarfs,the class “sdA” refers to subdwarf A stars, and the class“sdA/F” indicates ambiguous subdwarf A or F stars.This limits our sample to 14,522 spectra with promi-nent Balmer lines and no strong metal features. It alsoremoves other white dwarf spectral types like helium-rich DB white dwarfs. While most of the stars classifiedas “sdA” or “sdA/F” stars are likely MPMS stars (e.g.,Brown et al. 2017; Pelisoli et al. 2018b,a), a very smallfraction could also be extremely low-mass (ELM) whitedwarfs (e.g., Kosakowski et al. 2020).As we argued above, visually separating MPMS starsfrom white dwarf is prone to error, especially at cooltemperatures where MPMS star and white dwarf spec-tra are visually similar. For that reason, Kepler et al.(2019) appealed to Gaia DR2 parallaxes to distinguishMPMS stars and DA white dwarfs. At a given color,white dwarfs are far less luminous than MPMS starsdue to their smaller radii. A high-quality parallax mea-surement therefore provides accurate classifications via M g [ m a g ] Unreliable ParallaxReliable Parallax o f s t a r s Figure 2.
Color–magnitude diagram of the stars classi-fied by Kepler et al. (2019) as white dwarfs or subdwarfA stars based on SDSS spectroscopy. Stars with unreliableparallaxes—75% of the sample—are not included in the 2Dhistogram and are plotted in gray. There is a clear separa-tion between the white dwarf track on the bottom left andthe more luminous stellar main sequence at the top. Whileit is trivial to discriminate between white dwarfs and MPMSstars when parallaxes are available, most of the Kepler et al.(2019) sample lacks reliable parallaxes in Gaia DR2. absolute magnitudes. However, only about 15% of the14,522 stars in this sample have reliable parallaxes (i.e., π/σ π > parallax over error> 10 , (2) visibility periods used > 8 , and (3) astrometric sigma5d max < 1 . This results in an em-pirical validation sample of 1807 stars with reliableMPMS star/white dwarf classifications. Of these, 65%are classified as DA white dwarfs and the remaining 35%are classified as MPMS stars. We illustrate this em-pirical validation sample in the Sloan color–magnitudediagram depicted in Figure 2. METHODSEven though visual classifications have been sufficientto separate MPMS stars from white dwarfs in the past,the volume of data expected to be produced by ongoingand next-generation spectroscopic surveys will make thetraditional approach impractical. We therefore use thegrids of theoretical spectra described in Section 2.1 tobuild an automated process to differentiate MPMS stars earching for Low-mass Population III Stars
Balmer Lines
Both relatively warm MPMS stars and white dwarfsexhibit strong Balmer lines in their spectra. On thisbasis, in the absence of high-quality parallaxes MPMSstars have usually been differentiated from white dwarfsbased on Balmer lines for temperatures T eff (cid:38) α , H β , H γ , and H δ with a Voigt profile . From eachprofile we derive two summary statistics: the full-widthat half-maximum (FWHM) in angstroms and the min-imum of the profile in continuum-normalized flux unitsthat we define as the line amplitude. For each spectrumwe therefore derive eight line statistics in total whichtogether quantify the phase space of the Balmer lines.This results in a vector of eight Balmer features per spec-trum plus a “label” identifying it as the spectrum of aMPMS star or white dwarf. Our classifier then makesuse of all eight features to differentiate MPMS stars fromwhite dwarfs. We focus on H α , H β , H γ , and H δ in thisstudy because Balmer lines bluer than H δ occur in lowersignal-to-noise ratio regions of the SDSS spectra of coolstars.We illustrate in Figure 3 two 2D “slices” through theBalmer line phase space that demonstrate why Balmerline features are useful for classification. Because of thefaintness of cooler white dwarfs, most white dwarfs tar-geted by the SDSS have T eff (cid:38) T eff (cid:46) α pro-files than white dwarfs.Figure 3 is representative of the relationship betweenBalmer line features as a function of T eff and log g .Above T eff ≈ A Voigt profile is a convolution of Gaussian and Lorentzianprofiles that well-approximates the pressure-broadened wings ofthe Balmer lines (e.g., Tremblay & Bergeron 2009). H A m p li t u d e H A m p li t u d e WDMPMS4000 4500 5000 5500 6000 6500 7000 7500 8000Effective Temperature (K)
Figure 3.
Two “slices” of the Balmer line phase space forMPMS stars (solid lines colored by effective temperature)and white dwarfs (dashed lines). The thickness of each lineis proportional to surface gravity log g = 4, 4.5, 5 for MPMSstar models and log g = 7.5, 8, 8.5 for white dwarf models. spectra are visually differentiable on many 2D slicesthrough Balmer line phase space. Below T eff ≈ (cid:46) T eff (cid:46) T eff ≈ T eff ≈ Chandra & Schlaufman [mag]0.00.20.40.60.81.01.21.41.6 ( u g ) [ m a g ] White Dwarfs[Fe/H] = -1.5, 10 Gyr[Fe/H] = -4.0, 13.5 GyrSDSS DA & sdATypical Uncertainties
Figure 4.
Synthetic color–color diagram using SDSS bands.The blue line corresponds to white dwarfs with log g = 8while the shaded region indicates the locus of white dwarfswith surface gravities in the range 7 < log g <
9. We alsoplot MIST isochrones for MPMS stars with [Fe/H] = − . − . Synthetic Photometry
In addition to the Balmer features we extract fromeach theoretical spectrum, we also calculate syntheticphotometry in several photometric systems using the pyphot utility (Fouesneau 2020). We calculate syntheticabsolute magnitudes in the SDSS ugriz , Pan-STARRS grizy (Chambers et al. 2016), SkyMapper uvgriz (Bessellet al. 2011), DECam ugrizY (Flaugher et al. 2015), andVera Rubin Observatory ugrizy (Ivezic et al. 2019) sys-tems. While the software accompanying this paper canbe used with any of these photometric systems, we fo-cus on SDSS photometry colors in this paper since wevalidate our method on SDSS data.We plot in Figure 4 a comparison between MPMSstars and white dwarfs in Sloan color–color space. Sloan u − g color is strongly affected by the Balmer jump, a sen-sitive probe of surface gravity. A u − g versus g − r color–color plot can therefore be used to cleanly differentiaterelatively warm MPMS stars and white dwarfs. At lowertemperatures the difference becomes less pronounced, sothis color–color diagram can only differentiate MPMSstars and white dwarfs when T eff (cid:38) N -dimensional color spacedistribution at once rather than relying on individual2D slices through that space.3.3. Logistic Regression Classifier
To map the spectroscopic and photometric featuresdescribed above to a MPMS star or white dwarf classi-fication, we use a logistic regression classifier. A logisticregression is a model that assumes a linear relationshipbetween the input features and the log-odds of a binary(i.e., Bernoulli) random variable taking on the value 1(or “true”). Given input features x = [ x , x , x , . . . ],fitting a logistic regression involves solving for the coef-ficients β = [ β , β , β , . . . ] such that β (cid:124) x = log (cid:18) p − p (cid:19) , (1)where p is the probability that the Bernoulli randomvariable is 1 (or “true”). A logistic regression model istypically fit to data with known labels (i.e., where p isknown to be either zero or one), and the coefficients β are subsequently used to estimate ˆ p for new input data.There is no closed-form solution to determine β , so aniterative gradient descent algorithm is often used to findthe optimal coefficients.We define the underlying Bernoulli variable to havevalue 0 if an object is a confirmed white dwarf and 1 ifan object is a confirmed metal-poor main-sequence star.The associated probability in the model can thereforebe defined as p = P MPMS , the probability that a givenobject is a MPMS star as opposed to a white dwarf.We demonstrate three possible input configurations: theBalmer line summary statistics (eight features), ugriz photometric colors (ten features), and griz photomet-ric colors (six features). We also consider a combinedclassifier that uses ugriz colors and Balmer features si-multaneously.We use a logistic regression model due to its simplic-ity and ease of interpretation. The classification prob-ability P MPMS returned by a logistic regression is well-calibrated by default (Yu et al. 2011), providing confi-dence in the classification. We found that using a morecomplex classification algorithm like a random forest orsupport vector machine increased the complexity of the earching for Low-mass Population III Stars Model Validation with Objects that have SecureEmpirical Classifications
We now further validate our classifier with the empir-ical validation sample of 1807 objects described in Sec-tion 2.2. These objects were classified by Kepler et al.(2019) based on spectroscopic features with Gaia DR2-confirmed classifications as either MPMS stars or whitedwarfs. We confirm that the Kepler et al. (2019) clas-sifications for these objects are accurate based on ourinspection of their locations in a color–magnitude dia-gram. We use the available SDSS photometry and spec-troscopy for this empirical validation sample to computeBalmer features and ugriz colors. We then run the logis-tic regression classifier described in Section 3.3 on thesefeatures to predict based solely on SDSS photometryand spectroscopy the probability that each object is aMPMS star.Receiver operating characteristic (ROC) curves areone way to graphically evaluate classifiers. ROC curvesdescribe the relationship between the true-positive andfalse-positive rates of a classifier as a function of its ac-ceptance threshold (i.e., the output probability abovewhich a “positive” classification is made). ROC curvesprovide a high-level summary of the sensitivity (i.e.,probability of detection) and specificity (i.e., probabil-ity of false alarm). Precision-recall (PR) curves providean alternative graphical classifier diagnostic. They areparticularly useful for our application, as precision (i.e., https://github.com/vedantchandra/mpms the probability that a MPMS star is accurately classi-fied by our classifier) is the most important metric forour scientific goal. PR curves are also more agnostic tothe possible existence of class imbalance in a data set, asis the case in our empirical validation sample in whichthere are twice as many white dwarfs as MPMS stars.Together, ROC and PR curves provide an overview ofthe performance of a classifier.We illustrate in Figure 5 ROC and PR curves for theapplication of our classifiers to our empirical validationdata. We evaluate our logistic regression classifier inseveral scenarios: only the eight Balmer-line-summary-based features, only the ten ugriz colors, only the six griz colors, and both the Balmer-line-summary-basedfeatures and ugriz colors. As expected, the Balmerspectroscopic features provide the most discriminatingpower. The inclusion of u − g color greatly improves thequality of classifications compared to griz colors alone,as u − g color is sensitive to log g via the Balmer break.In terms of precision, the classifier using both photo-metric and spectroscopic features far outperforms thespectroscopy-only classifier. This implies that a de-generacy in spectroscopic features in MPMS star andwhite dwarf spectra can be overcome by including pho-tometric features. That natural interpretation is thatthe photometric colors provide a strong constraint ontemperature, breaking the T eff –log g degeneracy of theabsorption line features. We validate the naive expec-tation that classifiers using more than one Balmer lineare superior to any classifier based on a single line. Wefind that classification performance is most enhancedwhen lower-order Balmer lines like H α are combinedwith higher-order lines like H δ and confirm that thebest performance is achieved when all four Balmer linesare included. We conclude that our combined photo-metric and spectroscopic classifier has the accuracy andprecision necessary to separate MPMS stars from whitedwarfs using SDSS data or equivalent LAMOST or DESIdata.While our photometry-only classifier can be used toseparate MPMS stars from white dwarfs, it is suscep-tible to many of the issues with traditional color–colorselections. For example, the colors of white dwarfs withheavily metal-polluted photospheres will change due toline blanketing and changes in continuum opacity. Whilemetal-polluted white dwarfs could be misclassified byour photometry-only classifier, they are easy to removefrom a joint photometric/spectroscopic search for metal-poor stars due to their prominent metal absorption lines.Our classifier is therefore most powerful when spectro-scopic data are available. Chandra & Schlaufman T r u e P o s i t i v e R a t e AUC P r e c i s i o n AUC
Figure 5.
Receiver operating characteristic (ROC)and precision-recall (PR) curves for the photometry-only,spectroscopy-only, and combined logistic regression classi-fiers trained on theoretical models and validated with clas-sifications confirmed by high-quality Gaia DR2 parallaxes.The classifier that uses both spectroscopic and photometricfeatures achieves the best performance, followed closely bythe classifier that uses only spectroscopic features. Classi-fiers that use only photometric features achieve acceptableperformance but lag behind classifiers that utilize spectro-scopic features.
Approximate Determination of Metallicity
After differentiating MPMS stars from white dwarfs,another important task is to select the most metal-poorcandidates among the predicted MPMS stars. In orderto select the most metal-poor MPMS star candidates, weimplement a simple method to approximately quantifystellar metallicity from MPMS star spectra by fittingthem with theoretical spectra.We first use SDSS photometry and any available Gaiaparallax information to generate an initial set of spec-troscopic stellar parameters T eff , log g , and [Fe/H]. Wedefine a χ statistic by comparing the observed SDSS ugriz photometry dereddened as described in Section2.2 to MESA Isochrones & Stellar Tracks (MIST) ugriz photometry (Dotter 2016; Choi et al. 2016; Paxton et al.2011, 2013, 2015, 2018). To account for the low-precisionparallaxes available in most cases, we use an exponen-tially decreasing space density prior on parallax (Bailer-Jones 2015). We sample with emcee (Foreman-Mackeyet al. 2013; Foreman-Mackey et al. 2019) the posteriordistribution of the fundamental stellar parameters (e.g.,mass, age, and metallicity) conditioned on the data, tak-ing − . · χ as the log-likelihood of the data. We thenidentify the maximum-likelihood sample and interpolatethe MIST isochrone grid to define an initial set of spec-troscopic stellar parameters T eff , log g , and [Fe/H].Next, we fit PHOENIX theoretical spectra fromHusser et al. (2013) spanning the range 3000 K ≤ T eff ≤ . ≤ log g ≤ .
5, and − ≤ [Fe/H] ≤ α in each SDSS spectrum and thendivide the flux by that line to approximately normal-ize the spectrum in the vicinity of the line. We thenfit a Gaussian to H α and use its known wavelengthto correct each SDSS spectrum to the rest frame. Tospectroscopically infer T eff and log g , we assume a fixed[Fe/H] = − T eff and log g derived in theprevious step and fit the continuum-normalized Ca II Kabsorption line to infer [Ca/H] and thereby [Fe/H] as-suming [Ca/Fe] = 0. For each absorption line, we fitthe theoretical spectra using a non-linear least squaresalgorithm lmfit (Newville et al. 2014) that minimizesthe squared residual between the observed and theoret- earching for Low-mass Population III Stars T eff & log g and the Ca II K-based [Fe/H] inferences until the spec-troscopic stellar parameters are self-consistent. In prac-tice this only requires one or two iterations since theBalmer-based inference is quite independent of metal-licity.For the metal-poor main sequence stars with pub-lished spectroscopic stellar parameters from higher res-olution or signal-to-noise ratio (S/N) data, we find thatthe spectroscopically derived parameters are better thanthose based on photometry and astrometry. This islikely due to the low-quality parallaxes available in mostcases. Additionally, we note that spectroscopic Fe/Hinferences based on the Ca II K absorption line canbe overestimated if the star is carbon-enhanced, sincethe Ca II K line is blended with nearby carbon fea-tures on the mid-resolution spectra (e.g., Frebel et al.2015). Since our primary goal is to find the most metal-poor candidates (including those depleted in carbon), wedo not correct for this effect explicitly, but we cautionthat our spectroscopically-inferred metallicities shouldbe treated as indicative estimates only. RESULTSWith the accuracy and precision of our classifier nowestablished, we can now classify the entire sample of14,522 MPMS star/white dwarf candidates from Kepleret al. (2019) with SDSS photometry and spectroscopy.We fit the Balmer lines of these spectra to derive the linesummaries described in Section 3.1. We then apply ourcombined logistic regression classifier to the Balmer fea-tures and ugriz colors of these stars. The result of thisprocess is a prediction of the probability P MPMS that aspectrum was produced by a MPMS star as opposed toa white dwarf. Reassuringly, the distribution of proba-bilities is bimodal: most stars have probabilities close tozero or one. This distribution provides even more con-fidence that our classifier is both precise and accurate.We decide on decision threshold of 0.5 and classify allobjects with P MPMS > . P MPMS > . II K (3934.8 ˚A), Na I (5895.6˚A), and Mg I (5176.7 ˚A) lines in particular. We reportour most promising candidates in Table 1, along withour spectroscopically-inferred estimates of T eff , log g ,and [Fe/H].In addition, we use SIMBAD to search for literaturereferences to our candidate MPMS stars (Wenger et al.2000). While several of our MPMS star candidates haveno prior reference in the literature, we find that our se-lection turns up dozens of previously-known metal-poorstars with confirmed metallicities [Fe/H] < − .
0. A se-lection of these stars is included in Table 1. We thereforeconclude that SDSS data have already been exhaustivelysearched for extremely metal-poor stars. Nevertheless,this serves as a comprehensive validation of our method-ology to search for metal-poor stars in future spectro-scopic surveys.While the existence of low-mass Population III starsis still debated, we assert that it will be possible touniquely classify a featureless optical spectrum plausi-bly produced be either a low-mass Population III staror a cool white dwarf based on the optical-to-infraredcolors of the object. The lowest mass primordial-composition object that can burn hydrogen should have M ∗ ≈ . M (cid:12) . Stellar models therefore predict a lowerlimit on the effective temperature of Population III starsof T eff ≈ Chandra & Schlaufman
Table 1.
Extremely Metal-poor Candidates Identified in This StudyGaia DR2 R.A. Decl. Sloan g T eff log g [Fe/H] ReferenceSource ID (deg) (deg) Plate-MJD-Fiber (mag) (K)3724067121891339648 211.826 10.505 1703-53799-0013 16.9 6441 4.0 -4.0874891332185786752 116.953 26.762 2055-53729-0121 17.3 6450 3.7 -4.04465215302785008640 245.076 16.141 2188-54595-0026 18.5 6550 4.1 -3.91448863790892447744 203.103 27.516 2245-54208-0450 16.8 6435 4.0 -3.83958825597588943232 189.109 23.019 3374-54948-0220 18.2 6453 3.7 -3.83905214200892445184 184.325 8.870 5396-55947-0370 19.4 6560 4.5 -3.81493736818927192576 220.706 44.954 6046-56096-0550 18.8 6359 4.0 -3.83092216989574463616 126.339 4.059 1185-52642-0519 17.1 6441 4.0 -3.9 Aoki et al. (2013)290930261314166528 25.151 23.749 2044-53327-0515 15.8 6354 4.8 -3.5 Arentsen et al. (2019)1276882477044162688 230.509 30.924 1651-53442-0330 16.6 6333 4.7 -3.4 Aoki et al. (2013)4190837398756490112 301.306 -10.751 2303-54629-0377 17.0 6536 3.8 -3.6 Fran¸cois et al. (2018)1184737183522291712 221.669 12.822 1712-53531-0636 16.2 6445 4.0 -2.9 Aoki et al. (2013)3740963179636227968 207.345 14.127 1777-53857-0479 16.6 6340 3.8 -3.5 Bonifacio et al. (2018)3976087728282022272 175.848 20.349 2506-54179-0576 16.9 6426 4.0 -2.9 Yoon et al. (2016)3890626773968983296 157.313 17.491 2853-54440-0113 16.9 6047 4.7 -4.0 Caffau et al. (2011a)1609914447333432192 213.030 56.159 2447-54498-0274 16.0 6488 3.8 -4.0 Aoki et al. (2013)1195572458297534080 233.443 15.950 2782-54592-0411 16.9 6562 4.0 -4.0 Caffau et al. (2013)931227322991970560 123.976 47.496 3693-55208-0408 17.1 6523 4.6 -4.0 Aguado et al. (2018b)2548541852945056896 5.808 3.133 4299-55827-0002 17.9 6404 4.0 -4.0 Aguado et al. (2018a) Note —We indicate SIMBAD references for stars with confirmed [Fe/H] < − . T eff , log g and [Fe/H]are estimated from Sloan spectra with the spectroscopic fitting routine described in Section 3.5. At a given temperature (or g − r color), a white dwarfwill have more CIA than a low-mass Population III stardue to its higher surface gravity. White dwarfs will con-sequently be fainter than low-mass Population III starsin the red optical izy and infrared bands like JHK .Therefore, at constant temperature photometric colorscomparing optical to red optical or infrared bands (e.g., r − z , V − J , etc.) will be bluer for white dwarfs thanlow-mass Population III stars. This effect is expectedto be larger than the typical photometric uncertaintiesin ground-based surveys like the SDSS, Pan-STARRS,SkyMapper, or DES (Saumon et al. 1994; Blouin et al.2017).While future work on CIA opacities will enable a morequantitative comparison, current uncertainties in thetheoretical modeling of CIA make it challenging to pre-cisely quantify the expected difference between low-massPopulation III stars and white dwarfs, and thereby builda predictive model like the one we presented for warmerstars. Nevertheless, we predict that the photometric sig-nature of CIA should be detectable via infrared photom-etry and consequently able to differentiate between low- mass Population III stars and white dwarfs even withoutparallax information. DISCUSSIONWe have developed a classification framework that canbe used to differentiate low-mass Population III starsfrom white dwarfs in future spectroscopic surveys. Sinceour techniques primarily rely on Balmer lines and broad-band photometry, our methods naturally extend to theidentification of metal-poor stars including the sought-after EMP and ultra metal-poor (UMP) stars (i.e., starswith [Fe/H] (cid:46) − M ∗ ≈ . M (cid:12) , R ∗ ≈ R ⊕ ,and consequently log g ∼
8. Its surface gravity is there-fore orders of magnitude larger than the typical metal-poor main sequence star surface gravity log g (cid:46)
5. Asa result, our classifier gains most of its discriminatorypower from an object’s surface gravity. While MPMSstars are well separated from typical white dwarfs inlog g , MPMS stars can overlap in log g with ELM whitedwarfs produced by mass transfer in multiple systems earching for Low-mass Population III Stars g and much narrowerBalmer lines than typical white dwarfs. Their narrowBalmer lines could cause our classifier to misidentifythem as MPMS stars. While the identification of theserelatively rare ELM white dwarfs is a worthwhile goal inits own right, it is not the main objective of our currentanalysis. We argue that in future searches for MPMSor low-mass Population III stars, ELM white dwarfscan be filtered out by directly fitting theoretical spectrato Balmer lines to infer log g . Indeed, even the least-massive ELM white dwarfs should have log g (cid:38) M ∗ (cid:38) . M (cid:12) will have log g (cid:46) halo stars is required to rule out Popula-tion III survivors at the 95% confidence level. However,this is likely an overestimate since it only considers blindsurveys. In practice, searching for EMP and UMP starsis far more efficient. Magg et al. (2019) suggested in-stead to use the occurrence of EMP and UMP stars toconstrain the existence of Population III survivors. Thelargest uncertainty in this method by far is the totalnumber of EMP and UMP stars in the Milky Way’s stel-lar halo. As a result, a comprehensive search for suchstars is an important need. CONCLUSIONWhile it is trivial to separate metal-poor main se-quence stars and white dwarfs when high-quality par-allaxes are available, even post-Gaia many objects withDESI or Sloan spectroscopy will lack reliable parallaxes.For that reason, we developed a classifier capable of sep-arating metal-poor main sequence stars from cool whitedwarfs using a range of photometric and spectroscopicfeatures. We trained and validated our classifier us-ing theoretical spectra and synthetic photometry. Wealso validated the classifier using objects securely classi-fied as metal-poor main sequence stars or white dwarfsbased on Sloan spectroscopy and high-quality Gaia DR2parallaxes. We then applied our classifier to a sampleof candidate metal-poor main sequence stars and whitedwarfs with visual classifications and confirmed that ourautomated approach reproduces the human classifica- tions. We make our classifier and its underlying sourcecode publicly available Chandra & Schlaufman
Facilities:
Gaia, Sloan
Software: numpy (Harris et al. 2020), scipy (Vir-tanen et al. 2020), matplotlib (Hunter 2007), astropy (Robitaille et al. 2013), scikit-learn (Pedregosa et al.2011), lmfit (Newville et al. 2014), mwdust (Bovy et al.2016)REFERENCES
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