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# An 18.9 min blue large-amplitude pulsator crossing the ‘Hertzsprung gap’ of hot subdwarfs

## Abstract

Blue large-amplitude pulsators (BLAPs) represent a new and rare class of hot pulsating stars with unusually large amplitudes and short periods. The evolutionary path that could give rise to such kinds of stellar configurations is unclear. Here we report a comprehensive study of the peculiar BLAP discovered by the Tsinghua University–Ma Huateng Telescopes for Survey (TMTS), namely, TMTS J035143.63+584504.2 (TMTS-BLAP-1). This new BLAP has an 18.9 min pulsation period and is similar to the BLAPs with a low surface gravity and extended helium-enriched envelope, suggesting that it is a low-gravity BLAP at the shortest-period end. In particular, the long-term monitoring data reveal that this pulsating star has an unusually large rate of period change, namely, $$\dot{P}/P$$ = 2.2 × 10–6 yr–1. Such a significant and positive value challenges its origins from both helium-core pre-white-dwarfs and core helium-burning subdwarfs, but is consistent with that derived from shell helium-burning subdwarfs. The particular pulsation period and unusual rate of period change indicate that TMTS-BLAP-1 is at a short-lived (~106 yr) phase of shell helium ignition before the stable shell helium burning; in other words, TMTS-BLAP-1 is going through a ‘Hertzsprung gap’ of hot subdwarfs.

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## Data availability

The ZTF r- and g-band photometry can be obtained from the NASA/IPAC Infrared Science Archive (https://irsa.ipac.caltech.edu). The ATLAS o- and c-band magnitudes can be obtained from the ATLAS forced photometry server (https://fallingstar-data.com/forcedphot). All the reduced light curves and spectra used for this work, as well as some evolutionary tracks, are available via Zenodo at https://doi.org/10.5281/zenodo.6425425. Source data are provided with this paper.

## Code availability

The codes of Tlusty (v. 207) and Synspec (v. 53) that are used for generating (non-local thermodynamic equilibrium) model atmospheres and producing synthetic spectra are available at https://www.as.arizona.edu/h̃ubeny, and the services of online spectral analyses (XTgrid) are provided from Astroserver (www.astroserver.org). The Python package libwwz (v. 1.2.0) for WWZ analysis can be obtained from https://pypi.org/project/libwwz. The general tools for timing analysis are provided from Python package gatspy (v. 0.3) (http://www.astroml.org/gatspy or https://zenodo.org/record/47887). The software MESA (v. 12115) used for stellar evolutionary calculations is available at http://mesastar.org.

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## Author information

Authors

### Contributions

J.L., C.W., X.W. and P.N. drafted the manuscript. A.V.F., T.W. and Y.C. also helped with the manuscript, and A.V.F. edited it in detail. X.W. is the PI of TMTS and SNOVA. J.L. discovered this source by analysing the large-volume data from TMTS observations and performed the timing analysis to determine its rate of period change. C.W. computed the stellar evolution models for helium-burning stars and helium-core pre-WDs, and H.X. provided some key ideas for these models. T.W. contributed to the asteroseismic theory and analysis. P.N. determined the atmospheric parameters from Keck I LRIS spectra. Y.C., S.Y., Y.L. and D.X. assisted in the spectral analysis. The Keck I LRIS spectra were provided by A.V.F.’s group (including A.V.F, T.G.B., W.-K.Z. and Y.Y.). A.I., A.E. and Jujia Zhang contributed to the observations with SNOVA and the Lijiang 2.4 m telescope, and X. Zeng reduced these data. X.W., J.M., G.X., J.Z. and J.L. contributed to the building, pipeline and database of TMTS. G.X., J.M., X.J., H.S., Z.W., L.C., F.G., Z.C., W. Li, W. Lin, H.L. and X. Zhang contributed to the operations of TMTS.

### Corresponding author

Correspondence to Xiaofeng Wang.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

## Peer review

### Peer review information

Nature Astronomy thanks Conor Byrne, Marco Lam and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## Extended data

### Extended Data Fig. 1 TMTS L-band (close to white-light) light curves of TMTS-BLAP-1 taken on December 24 and 25, 2020 (UT).

The red solid lines represent the best-fitting models of Fourier series truncated at fourth harmonic.

### Extended Data Fig. 2 Phase-folded light curves for every subset of ATLAS, ZTF, TMTS, and SNOVA data.

Every subset of ATLAS and ZTF data covers up to 20 ~ days, while each subset of TMTS and SNOVA data covers only one night. The observed time of maximum light ($${{{{\rm{T}}}}}_{\max }^{{{{\rm{O}}}}}-2,450,000$$) for every subset is shown above the plots. Since the phases here were all calculated using the ephemeris of Eq. (1), the pulsation phases ϕ = 0 (the vertical dot-dashed lines) here correspond to the calculated times of maximum light, namely $${{{{\rm{T}}}}}_{\max }^{{{{\rm{C}}}}}$$.

### Extended Data Fig. 3 Folded light curve and surface parameters against pulsation phase.

a, corrected ZTF r-band folded light curve with a best-fitting 3-harmonic Fourier model overplotted (red solid line); b,c,d, radial velocity (RV), effective temperature (Teff) and surface gravity (log g) against pulsation phase. The red solid curves are the best-fitting sinusoidal curves, and the purple dashed line in panel d represents the prediction from the time-derivative of the best-fitting model of radial velocity3.

### Extended Data Fig. 4 O-C diagram for the pulsation period of ZGP-BLAP-09.

The observed time of maximum light ($${{{{\rm{T}}}}}_{\max }^{{{{\rm{O}}}}}$$) was obtained from the 20 ~ day subsets of ATLAS and ZTF. The O-C values were calculated following the the ephemeris $${{{{\rm{T}}}}}_{\max }^{{{{\rm{C}}}}}={{{{\rm{BJD}}}}}_{{{{\rm{TDB}}}}}\,2,458,218.5012+0.0161558353\times {{{\rm{E}}}}$$. Because ZGP-BLAP-09 lacks similar cyclic behavior in the diagram, the O-C variability is modeled only by assuming the linear period change.

### Extended Data Fig. 5 Phase-folded light curves of TMTS-BLAP-1.

The folded light curves are derived from ZTF r-band (panels a,b) and ATLAS o-band (panels c,d) observations. a,c, The light curves are folded using a constant period inferred from the Lomb–Scargle periodogram. b,d, The light curves are folded using the new ephemeris derived from the O-C diagram. The red solid lines represent the best-fitting 3-harmonic Fourier models.

## Supplementary information

### Supplementary Information

Supplementary Figs. 1 and 2 and Tables 1–3.

## Source data

### Source Data Fig. 1

Statistical source data.

### Source Data Fig. 5

Statistical source data.

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Lin, J., Wu, C., Wang, X. et al. An 18.9 min blue large-amplitude pulsator crossing the ‘Hertzsprung gap’ of hot subdwarfs. Nat Astron (2022). https://doi.org/10.1038/s41550-022-01783-z

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• DOI: https://doi.org/10.1038/s41550-022-01783-z