Research Programme: -rich subdwarfs and connections in

Summary. The chemical structure of early-type is susceptible to atomic diffusion driven by radiative levitation and gravitational settling on timescales comparable with stellar evolution. Such diffusion can lead to chemical stratification of the stellar atmosphere and envelope, to the formation of extremely chemically peculiar stars and to the existence of undiscovered classes of pulsating stars. This is particularly true for evolved stars and especially hot subdwarfs and related objects. Most remarkable are the heavy-metal subdwarfs, which present extreme surface chemistries, undetectable surface rotation, pulsations indicative of a C+O dominated interior, and galactic halo-like orbits. Challenges lie in identifying and characterising new classes of chemically peculiar and/or pulsating stars, in creating self-consistent models of the stellar atmosphere, envelope and pulsations with appropriate atomic data, and, most significantly, in placing these stars in the broader context of their origin, evolution and their relationship to other classes of evolved . The goals of this project and the associated work packages (WP) are to: i) better characterise the hot helium-rich (He-rich) subdwarfs and related objects (WP1); ii) build new models for their atmospheres and envelopes including self-consistent atomic diffusion theory and new atomic data (WP2); iii) explain the distribution of chemical peculiarities and how these align with new classes of pulsating star (e.g. -rich pulsators) (WP2+3); iv) identify the origin of the most exotic classes of He-rich subdwarf and their connections with other evolved stars (WP3); and v) develop new models to better exploit information from pulsating subdwarfs (WP4).

Background

Early calculations of stellar opacities demonstrated the possible existence of a high temperature bump (Carson+ 1981). Whilst premature (Carson+ 1984), major efforts to recalculate stellar opacities (OP 1987, OPAL 1992) revealed a significant contribution from - elements at temperatures of ≈ 2 × 105 K. This ‘iron bump’ provided the long- searched for explanation of pulsation observed in many B stars, (β Cep: Moskalik & Dziembowski 1992, V652 Her: Saio 1993) and led to the prediction of pulsation in hot subdwarfs (Charpinet+ 1997). The many classes of pulsating early type variable (Fig. 1) include p- and g-mode pulsations in subdwarf B stars (EC14026: Kilkenny+ 1997, PG1716: Green+ 2003), low-amplitude pulsations in low-mass pre-white dwarfs (WDs) (EL CVn: Maxted+ 2014), He-rich subdwarfs (V366Aqr: Ahmad & Jeffery 2005, Green+ 2011), and large amplitude pulsations in faint blue stars (BLAPs: Pietrukowicz+ 2017, Kupfer+ 2019). In all cases, significant features in opacity are responsible for driving the pulsations (Jeffery & Saio 2006, 2013, 2016, Saio & Jeffery 2019, Byrne & Jeffery 2020). For low-mass hot stars, the opacity bump from iron and (in particular) provides the driving mechanism, with carbon and oxygen opacity driving pulsations in the hottest stars. In most cases the opacity bump is only effective as a pulsation driver if coupled with either depletion of background opacity from hydrogen or high concentrations of specific elements.

Radiative opacities in faint blue stars also mediate gravitational settling and radiative levitation, with increased opacity due to ionisation providing a nett upward force on specific ions. The maximum value of this force occurs at the same temperature as the peak in

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Figure 1: Hertzsprung–Russell diagram showing locations of principal classes of pulsating star. Normal stellar evolution from the main-sequence is illustrated, tracks labelled by mass. Classes are coloured roughly by spectral type. Shadings represent opacity-driven p modes (\), g modes (/) and strange modes (|) and acoustically driven modes (−) [after J. Christensen- Dalsgard]. opacity and, if undisturbed, leads to high concentrations of these elements, effectively amplifying the local opacity. Conversely, low specific opacities lead to low concentrations. These phenomena are enhanced at high surface gravities, i.e. in hot WDs and subdwarfs. The latter dominate the ultraviolet component of evolved stellar systems including globular clusters and giant elliptical galaxies (Brown+ 2003). The largest class of hot subdwarf, the subluminous B (sdB) stars, are conventionally core-burning helium stars of ≈ 0.5 M⊙which have helium- poor atmospheres; settling dominates, but the surface helium fraction increases with Teff(Heber , Edelmann+ 2003). Meanwhile, multiple classes of helium- enriched hot subdwarf (Drilling+ 2013) merit special attention, despite the extreme rarity of

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Figure2: The distribution of heavy metal (filled symbols; Zr:maroon, Pb:blue and yellow), metal- normal(open symbols), He-rich and normal hot subdwarfs with effective temperature (Teff), surface gravity (g: left) and surface He/H ratio (y: right)

some species. In about 10% of hot subdwarfs, hydrogen is so deficient there is insufficient to conceal the helium; an origin that destroys hydrogen seems probable (Zhang & Jeffery 2012). In the gap between helium- poor and hydrogen-poor subdwarfs (Fig. 2) lies a sparse group of intermediate helium subdwarfs (Naslim+ 2012). This group consistently displays remarkable properties. Their surfaces are super-abundant in trans-iron elements and form two groups, the cooler zirconium-rich and the hotter lead-rich (heavy-metal subdwarfs; Naslim+ 2011, Naslim+ 2013, Jeffery+ 2017a, Dorsch+ 2019, Latour+ 2019, Jeffery & Miszalski 2019, Naslim+ 2020). All show very sharp absorption lines indicative of low surface rotation (ibid.). The zirconium stars pulsate in g-modes driven by carbon and oxygen opacities at ≈ 106 K (Saio & Jeffery 2019). The majority are in high-energy galactic (halo?) orbits (Martin 2018).

These remarkable stars form the primary focus of this proposal; why are their surfaces hydrogen/helium poor? why are they chemically peculiar? how did they form? what is their internal structure? do they have C+O-rich cores? what gave them their high velocities? why do they lie at the upper Teff boundary of normal sdB stars? how are they connected with other classes of hot subdwarfs and hydrogen-deficient stars?

WP1. The SALT survey of chemically peculiar subdwarfs: PI Year 1 - 2. The PI is leading a spectroscopic survey of all southern He-rich hot ‘subdwarfs’ using SALT with resolution and S/N sufficient to measure atmospheric properties (mV ≤ 16) and detailed surface composition (mV ≤ 14.5). The survey has discovered several new extreme helium stars, a heavy-metal subdwarf and other stars of interest (Fig. 3: Jeffery 2017, Jeffery+ 2017b, Jeffery & Miszalski 2019). This WP covers classification, parameterization and a spectroscopic atlas of the entire sample (≈ 200 stars), together with follow-up analyses of interesting objects and will be carried out by the PI and an STFC-PhD student (Ted Snowdon). The PI is also a LAMOST consortium member and will extend the survey to the northern hemisphere using data already available.

WP2. Stratified model atmospheres for heavy-metal subdwarfs: PDRA Year 1 – 2.

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Current abundance analyses of heavy-metal subdwarfs indicate surface abundances of trans-iron elements which are ≈ 104 times solar. Surface enrichment of material produced by the s-process is possible but unlikely; these are not post-AGB stars. Alternatively, the enriched material forms a thin layer supported by radiative levitation. If centered at the line- forming depth in the photosphere, Figure 3: Surface properties of selected SALT an abundance measurement would subdwarfs (red), extreme helium stars (black reflect the abundance in that layer, squares), extreme helium subdwarfs (black diamonds) but not the mean abundance in the and intermediate helium subdwarfs (violet photosphere. diamonds). The Eddington limit, LM contours (solar Two tests will be made using model units), zero-age helium main-sequence, a He+He WD atmospheres with a non-uniform post-merger track (Zhang & Jeffery 2012) (maroon), chemical distribution; i) the and a ’late hot flasher’ track (Miller Bertolami et al. distribution will be assigned 2008) (orange) are also shown. parametrically assuming discontinuities above and/or below the enriched layer. Theoretical line profiles will be compared with observed profiles to established the allowed range at which these discontinuities might occur. ii) our existing model atmosphere code (sterne: Behara+ 2006) includes provision for self-consistent radiative levitation and gravitational settling (Behara 2007). We will upgrade this code to incorporate additional opacities for trans-iron species (Fernandez-Menchero+ 2020, in prep) and hence determine whether radiative levitation can produce the observed concentrations. A key test will be to demonstrate how effective temperature affects different species; the peak concentration temperatures or Pb3+ and Zr3+ should reflect Pb- rich subdwarfs occurring at higher Teff than Zr-rich subdwarfs (Fig. 2).

Data for these tests exist in the form of high signal-to-noise échelle spectra of several Zr- and Pb-rich subdwarfs. Information about stratification of less exotic elements will be equally important. Atomic data are being generated through a collaboration with Queens University Belfast. Fine analyses will be supplemented by analyses of spectral energy distributions and Gaia distances to determine radii and masses more precisely than hitherto, and to confront the origin and evolution questions in WP3.

WP3. Evolution and pulsation models for heavy-metal subdwarfs: PDRA Year 1 – 3

So far, the origin and internal structure of heavy-metal subdwarfs has not been securely established. Several possible models need to be investigated and tested more closely.

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– The discovery that pulsations in Zr-rich subdwarfs are driven by C+O opacities (Saio & Jeffery 2019) confronts the conventional hot subdwarf model because it requires these stars to be C+O enriched by ≥ 50% through al- most their entire mass; in other words, they appear to be the stripped cores of massive stars. This idea resonates with their high space velocities and suggests they could have been ejected from a binary following several mass transfer episodes and a . Whilst binary-star population synthesis has not yet demonstrated a plausible pathway (Jeffery et al. in preparation), there are parts of binary- star parameter space which need to be explored in more detail using full stellar evolution calculations.

A second model to investigate is the conventional sdB model with a negligible hydrogen- envelope. Similar models were used to investigate early evolution onto the helium main- sequence (Byrne & Jeffery 2018). Whilst unable to explain heavy-metal subdwarfs directly (see WP2), they can account for partially helium-enriched surfaces if the hydrogen envelope is removed well before helium ignition. This is because the helium-flash is delayed and accompanied by a strong hydrogen shell-flash which mixes helium to the surface (cf. Brown+ 2001, Miller Bertolami+ 2008). Our models with radiative levitation successfully explain the evolutionary status and pulsation properties of pulsating low-mass pre-WDs. Iron-group elements switch pulsations on at exactly the right time to explain the loci of all known BLAPs (Fig. 4; Byrne & Jeffery 2019, 2020). We will make similar calculations to study whether radiative levitation can produce a sufficient concentration of carbon and oxygen in the driving zone to excite pulsations without requiring nearly the entire star to be C+O enriched.

The third model to consider is a hybrid He+He WD merger. Normal He+He WD mergers produce extremely He-rich hot subdwarfs (Zhang & Jeffery 2012). However, if at least one He WD retains sufficient hydrogen which survives on the surface of the merged star, the range of He/H ratios observed could be accounted for. Again radiative levitation in both photosphere and C+O driving zone will be required. We will build and test appropriate models.

In all three cases, the high space velocities and low rotation velocities must also be accounted for, but a major break- through would be to account for both surface chemistries and pulsations with a single model.

WP4. Evolution and Pulsation in other He-rich and Faint Blue Stars: PI Year 2 – 3

Owing to the number of He-rich subdwarf classes, the range of other observational and theoretical work required is extensive and varied. The SALT survey (Fig. 3, WP1) has demonstrated a sequence of He-rich stars running from the loci of pulsating extreme helium stars V652 Her and BX Cir to the helium main- sequence. A limited analysis shows considerable variety in surface helium, as well as carbon, nitrogen and other species. The preferred theory for the origin of both V652 Her and extreme helium subdwarfs is a He+He WD merger (Saio & Jeffery 2000, Zhang & Jeffery 2012). Additional calculations will verify whether a merger can account for all the observed stars, especially the extremely metal-poor EC19529-4430. – With completion of the SALT

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survey and additional statistics from LAMOST, we will derive space densities for many classes of He-rich subdwarf. Lifetime estimates from evolution models and birth rates from binary-star population syn- thesis will allow us to test theories of origin and evolutionary connections.

– Whilst V652 Her and BX Cir are well-known pulsating variables (P ≈ 0.11d), their near twin GALEX J1845-4138 shows no variability in TESS photometry. We will examine all known He-rich subdwarfs Figure 4: log g − log Teff diagram showing evolution of pre- observed with TESS for WDs with masses 0.18 − 0.38 M⊙. Colour indicates the mass variability. Predicted pulsation 5 periods range from 5 minutes fraction of iron present around T = 2 × 10 K. Filled (open) to 5 hours. Stability strips symbols indicate models with an unstable (stable) depend on composition in the fundamental mode. Black crosses indicate observed BLAPs driving zone, as well as on Teff (Byrne & Jeffery 2020) and L/M (Jeffery & Saio 2016). We shall follow-up any detections with both linear and, where appropriate, non-linear models, to obtain constraints on internal structure. Perfect candidates for such non-linear modelling include V652 Her and BLAPS.

Methods. Spectroscopic analyses will be carried out using our in-house stellar atmosphere codes sterne, spectrum and sfit upgraded to include chemical diffusion and stratification and augmented in some cases to allow for a hybrid LTE/non-LTE approach through collaboration with Bamberg/Potsdam teams. Stellar evolution experiments will be carried out using the mesa toolkit, with which we have > 5 years experience. Where necessary, we will introduce additional opacities in order to model diffusion for some species. Pulsation calculations will be carried out using elements within the mesa toolkit (e.g. gyre). The non- linear pulsation tool will be modified in order to treat models with chemically inhomogeneous envelopes. We also have a well-established toolkit for modelling radial pulsations.

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