First Temperature Profile of a Stellar Flare using Differential Chromatic Refraction

TL;DR

The authors present the first measurement of a stellar flare color temperature evolution derived from differential chromatic refraction (DCR) in single-band photometry. Using DECam data from a bright, high-air-mass flare, they model the flare as a blackbody with a filling factor, propagating uncertainties through a forward-model that links observed $\\Delta m_g$ and $\\lambda_{eff}$ to $T_{BB}$ and $X_{BB}$, while accounting for instrumental DCR and emission-line contributions. Their analysis shows that emission features can bias temperature estimates high or low depending on line strength, and that constraining the temporal evolution of the flare area ($X_{BB}$) materially affects inferred temperatures and post-peak behavior. This method enables population-scale flare temperature studies with upcoming surveys like LSST and highlights key modeling improvements, such as incorporating time-dependent line evolution, to better capture flare physics.

Abstract

We present the first derivation of a stellar flare temperature profile from single-band photometry. Stellar flare DWF030225.574-545707.45129 was detected in 2015 by the Dark Energy Camera as part of the Deeper, Wider, Faster Programme. The brightness ($Δm_g = -6.12$) of this flare, combined with the high air mass ($1.45 \lesssim X \lesssim 1.75$) and blue filter (DES $g$, 398-548 nm) in which it was observed, provided ideal conditions to measure the zenith-ward apparent motion of the source due to differential chromatic refraction (DCR) and, from that, infer the effective temperature of the event. We model the flare's spectral energy distribution as a blackbody to produce the constraints on flare temperature and geometric properties derived from single-band photometry. We additionally demonstrate how simplistic assumptions on the flaring spectrum, as well as on the evolution of flare geometry, can result in solutions that overestimate effective temperature. Exploiting DCR enables studying chromatic phenomena with ground-based astrophysical surveys and stellar flares on M-dwarfs are a particularly enticing target for such studies due to their ubiquity across the sky, and the heightened color contrast between their red quiescent photospheres and the blue flare emission. Our novel method will enable similar temperature constraints for large sample of objects in upcoming photometric surveys like the Vera C. Rubin Legacy Survey of Space and Time.

Figures (7)

• Figure 1: Number of reference stars detected in each frame. Empty circles are pre-flare, filled circle are after the start of the flare (see \ref{['sec:astrometry']}). Between 72 and 94 stars are detected and used as reference in each frame.
• Figure 2: Panel A: Light curve of the DWF030225.574-545707.45 flare expressed as $g$ magnitudes in excess of the quiescent stellar brightness. Hollow points indicate pre-flare epochs and solid points indicate flaring epochs. We define the start of the flare as the first measurement to exceed the quiescent magnitude by $3\sigma$, where the quiescent magnitude is taken to be the mean magnitude of the first 1000 seconds of observation, and $\sigma$ is the standard deviation of all points within the first 1000 seconds. As noted in webb2021, the lightcurve does not return to pre-flare brightness before the end of the observing period. Panel B: Raw $d_\parallel$ measured on the images, relative to source position at $t_0$. The weighted average $d_\parallel$ of 91 reference stars, weighted by the stars' astrometric standard deviation across the entire time series, is shown as a grey line and the standard deviation of their relative position itself is shown as a filled region. Panel C: detrended $d_\parallel$ of the flare star generated by subtracting the weighted average $d_{\parallel}$ of the reference stars shown in Panel B. A 9-point rolling median is shown by the dashed black line. Panel D: Rolling median over an 9-point window of the detrended data shown in Panel C, and the time series used for subsequent analysis in this work.
• Figure 3: Left: Change in $g$ magnitude relative to the quiescent stellar magnitude as a function of flare temperature and filling factor. Right: Effective wavelength of the model flare spectrum in the $g$ band as a function of flare temperature and filling factor. Each grid consists of 400x400 cells, giving a resolution of 170 K in temperature and 0.005% in filling factor.
• Figure 4: Top left: Flare lightcurve as shown in the top panel of \ref{['fig:dpar']}. Top right: $d_\parallel$ as shown in the bottom panel of \ref{['fig:dpar']}. Bottom: the evolution of temperature ($T_\mathrm{BB}$, left) and filling factor (right) from our most simplistic model described in \ref{['sec:weffs']}: a blackbody flare on top of a dM SED and no constraints on the filling factor evolution. The peak of the flare is marked in each panel with a vertical line. The uncertainties are derived by bootstrapping over the observable uncertainties 1,000 times.
• Figure 5: The effect of emission lines on the effective wavelength $\lambda_\mathrm{eff}$ in a stellar flare. In red, the quiescent spectrum of an active dM7 star (see \ref{['sec:quiescent']}). The quiescent spectrum has been magnified by a factor of 60 for visibility. In green, the blackbody-only flaring spectrum with $T_\mathrm{BB} = 14,000$ K and $X_\mathrm{BB} = 0.25\%$. In blue, the flaring spectrum with $T_\mathrm{BB} = 14,000$ K and $X_\mathrm{BB} = 0.25\%$, as well as enhanced Ca H & K, H$\beta$, H$\gamma$, and H$\delta$ lines. The transmission function of the DES $g$ filter is shown in grey. The vertical dashed lines correspond to the effective wavelength in $g$ for each model: $\lambda_\mathrm{eff, quiescent}=5,035 \rm\AA$, $\lambda_\mathrm{eff, flare}=4,721 \rm\AA$, $\lambda_\mathrm{eff, flare+lines}=4,677 \rm\AA$. While this is a simplistic model for the inclusion of emission lines, it illustrates the effect lines have on $\lambda_\mathrm{eff}$: for the same blackbody temperature, the effective wavelength decreases. Conversely, a smaller temperature is needed to explain the DCR if emission features are enhanced during the flare.