Spectral appearance of the planetary-surface accretion shock: Global spectra and hydrogen-line profiles and fluxes

Abstract

Hydrogen-line emission, thought to come from an accretion shock, has recently been observed at planetarymass objects, and current and upcoming dedicated instruments should reveal many more sources. Previous work predicted the shock spectrum in the case of a shock on the circumplanetary disc. However no extensive investigation has been done on the planet-surface shock. Our main goals are to calculate the global spectral energy distribution (SED) of an accreting planet by combining our model emission spectra with photospheric SEDs, and to predict the line-integrated flux for different hydrogen lines, focusing on H 𝛼 but including also H 𝛽, Pa 𝛼, Pa 𝛽, Pa 𝛾, Br 𝛼, and Br 𝛾. We apply our non-equilibrium emission calculations to the surface accretion shock for the relevant large parameter space of accretion rate 𝑀 and mass 𝑀 p . In contrast to our previous model, fits to formation calculations provide radii and effective temperatures. We do not consider extinction by the preshock material in this work. We find that the H 𝛼 line luminosity increases monotonically with 𝑀 and 𝑀 p , ranging from 10 −8 to 10 −4 𝐿 , depending mostly on the accretion rate and weakly on the mass for the relevant range of parameters. We apply the result to the observed planets around PDS 70 and demonstrate that the estimated accretion rate is consistent with previous studies. The Lyman, Balmer, and Paschen continua can be visible above the photosphere. The H 𝛽 line ranges between 0.1 and ≈ 1 times the H 𝛼 flux, whereas other lines are weaker (∼ 0.001-0.1). Based on spectroscopic observations, a shock on the planetary surface and on the CPD surface can be distinguished at very high spectral resolution. The planet surface shock however likely dominates in total intensity if both are present. These predictions of the luminosity in H 𝛼 and other lines serve as a baseline prediction or conversely as a tool for interpreting observations of accreting planets.

Hubble Space Telescope UV and H$α$ Measurements of the Accretion Excess Emission from the Young Giant Planet PDS 70 b

“…Therefore, these nondetections are most likely due to our sensitivity limits. The F336W and F656N bands constrain hydrogen Balmer continuum and H emission, both of which are accretion indicators (Aoyama et al 2020). As shown in the UV, optical, and IR spectral energy distribution (SED) of PDS 70 b (Figure 7), our observed F336W and F656N flux densities are more than three orders of magnitude higher than the bestfit blackbody to the infrared (IR) observations.…”

“…Because line emission accounts for a greater amount of accretion luminosity in the substellar regime (Herczeg et al 2009;Rigliaco et al 2012;Zhou et al 2014), excluding other lines may introduce greater errors in ̇ for PDS 70 b compared to similar measurements in the stellar regime (e.g., Herczeg & Hillenbrand 2008). Based on a planetary accretion shock model, Aoyama et al (2018Aoyama et al ( , 2020 found that the Ly emission can be more than one order of magnitude more energetic than the H emission in accretion onto PDS 70 b-like planets. In this case, the hydrogen line emission will dominate PDS 70 b's accretion excess emission.…”

“…In addition, Christiaens et al (2019), Stolker et al (2020), and Uyama et al (2021) placed upper limits on infrared accretion tracers, such as the Br-and Palines. Based on these observations, accretion rates of PDS 70 b and c are estimated to be in the range of 1 × 10 −8 to 5 × 10 −7 Jup yr −1 (e.g., Wagner et al 2018;Haffert et al 2019;Aoyama & Ikoma 2019;Thanathibodee et al 2019;Hashimoto et al 2020;Aoyama et al 2020).…”

“…The accretion process is usually modeled as material falling onto the star or planet at nearly freefall velocity (e.g., Hartmann et al 2016;Aoyama et al 2018Aoyama et al , 2020. As the accretion flow hits the stellar/planetary surface, its kinetic energy is converted into thermal energy, forming a hot shock front.…”

“…So far, mass accretion rate measurements for the PDS 70 planets have been solely based on observations of the H line (e.g., Wagner et al 2018;Haffert et al 2019;Aoyama & Ikoma 2019;Thanathibodee et al 2019;Hashimoto et al 2020;Aoyama et al 2020). Wagner et al (2018) and Haffert et al (2019) estimated the mass accretion rates by extrapolating the empirical relations between total accretion luminosity and the H luminosity (Rigliaco et al 2012) or the line width (Natta et al 2004) calibrated from young stars and brown dwarfs.…”