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In this work, we focus on the period-luminosity relation (PLR) of $\delta$ Sct stars, in which mode excitation and selection mechanisms are still poorly constrained, and whose structure and oscillations are affected by rotation. We review the PLRs in the recent literature, and add a new inference from a large sample of $\delta$ Sct. We highlight the difficulty in identifying the fundamental mode and show that rotation-induced surface effects can impact the measured luminosities, explaining the broadening of the PLR. We derive a tight relation between the low-order large separation and the fundamental radial mode frequency (F0) that holds for rotating stars, thus paving the way towards mode identification. We show that the PLRs we obtain for different samples are compatible with each other and with the recent literature, and with most observed $\delta$ Sct stars when taking rotation effects into account. We also find that the highest-amplitude peak in the frequency spectrum corresponds to the fundamental mode in most $\delta$ Sct, thus shedding some light on their elusive mode selection mechanism., Comment: 10 pages, 5 figures, 1 table, IAU conference proceeding

Aims. The main goal of this work is to date young open clusters using $\delta$ Sct stars. Seismic indices such as the large separation and the frequency at maximum power can help to constrain the models to better characterise the stars. We propose a reliable method to identify some radial modes, which gives us greater confidence in the constrained models. Methods. We extract the frequency content of a sample of $\delta$ Sct stars belonging to the same open cluster. We estimate the low-order large separation by means of different techniques and the frequency at maximum power for each member of the sample. We use a grid of models built with the typical parameters of $\delta$ Sct stars, including mass, metallicity and rotation as independent variables, and determine the oscillation modes. We select the observed frequencies whose ratios match those of the models. Once we find a range of radial modes matching the observed frequencies, mainly the fundamental mode, we add it to the other seismic parameters to derive the stellar age. Assuming star groups have similar chemistry and age, we estimate their mean age by computing a weighted probability density function fit to the age distribution of the seismically constrained models. Results. We estimate the age of Trumpler 10 to be $30_{-20}{+30}$ Myr, and that of Praesepe to be $580 \pm 230$ Myr. In this latter case, we find two apparent populations of $\delta$ Sct stars in the same cluster, one at $510 \pm 140$ Myr and another at $890 \pm 140$ Myr. This may be due to two different formation events, different rotational velocities of the members in our sample of stars (as rapid rotation may modify the observed large separation), or to membership of unresolved binary systems., Comment: 20 pages, 25 figure, uses the open-source code MultiModes (see https://github.com/davidpamos/MultiModes). It will be published in A&A

The first population of X-ray binaries (XRBs) is expected to affect the thermal and ionization states of the gas in the early Universe. Although these X-ray sources are predicted to have important implications for high-redshift observable signals, such as the hydrogen 21-cm signal from cosmic dawn and the cosmic X-ray background, their properties are poorly explored, leaving theoretical models largely uninformed. In this paper we model a population of X-ray binaries arising from zero metallicity stars. We explore how their properties depend on the adopted initial mass function (IMF) of primordial stars, finding a strong effect on their number and X-ray production efficiency. We also present scaling relations between XRBs and their X-ray emission with the local star formation rate, which can be used in sub-grid models in numerical simulations to improve the X-ray feedback prescriptions. Specifically, we find that the uniformity and strength of the X-ray feedback in the intergalactic medium is strongly dependant on the IMF. Bottom-heavy IMFs result in a smoother distribution of XRBs, but have a luminosity orders of magnitude lower than more top-heavy IMFs. Top-heavy IMFs lead to more spatially uneven, albeit strong, X-ray emission. An intermediate IMF has a strong X-ray feedback while sustaining an even emission across the intergalactic medium. These differences in X-ray feedback could be probed in the future with measurements of the cosmic dawn 21-cm line of neutral hydrogen, which offers us a new way of constraining population III IMF., Comment: Accepted for publication in MNRAS, 17 pages, 9 figures

Properties of the first generation of stars (Pop III), such as their initial mass function (IMF), are poorly constrained by observations and have yet to converge between simulations. The cosmological 21-cm signal of neutral hydrogen is predicted to be sensitive to Lyman-band photons produced by these stars, thus providing a unique way to probe the first stellar population. In this paper, we investigate the impacts of the Pop III IMF on the cosmic dawn 21-cm signal via the Wouthuysen-Field effect, Lyman-Werner feedback, Ly-alpha heating, and CMB heating. We calculate the emission spectra of star-forming halos for different IMFs by integrating over individual metal-free stellar spectra, computed from a set of stellar evolution histories and stellar atmospheres, and taking into account variability of the spectra with stellar age. Through this study, we therefore relax two common assumptions: that the zero-age main sequence emission rate of a Pop III star is representative of its lifetime mean emission rate, and that Pop III emission can be treated as instantaneous. Exploring a bottom-heavy, a top-heavy, and intermediate IMFs, we show that variations in the 21-cm signal are driven by stars lighter than 20 solar masses. For the explored models we find maximum relative differences of 59% in the cosmic dawn global 21-cm signal, and 131% between power spectra. Although this impact is modest, precise modelling of the first stars and their evolution is necessary for accurate prediction and interpretation of the 21-cm signal., Comment: 20 pages, 16 figures. Accepted for publication in MNRAS, updated to accepted version