arXiv subjects

P. C. Schneider

Publications and source records attributed to P. C. Schneider.

At least 55 records · Page 3Linked to original sources

arXiv2020

An X-ray activity cycle on the young solar-like star $ε\ \rm Eridani$

In 2015 we started the XMM-Newton monitoring of the young solar-like star Epsilon Eridani (440 Myr), one of the youngest solar-like stars with a known chromospheric CaII cycle. By analyzing the most recent Mount Wilson S-index CaII data of this star, we found that the chromospheric cycle lasts 2.92 +/- 0.02 yr, in agreement with past results. From the long-term X-ray lightcurve, we find clear and systematic X-ray variability of our target, consistent with the chromospheric CaII cycle. The average X-ray luminosity results to be 2 x 10^28 erg/s, with an amplitude that is only a factor 2 throughout the cycle. We apply a new method to describe the evolution of the coronal emission measure distribution of Epsilon Eridani in terms of solar magnetic structures: active regions, cores of active regions and flares covering the stellar surface at varying filling fractions. Combinations of these magnetic structures can describe the observed X-ray emission measure of Epsilon Eridani only if the solar flare emission measure distribution is restricted to events in the decay phase. The interpretation is that flares in the corona of Epsilon Eridani last longer than their solar counterparts. We ascribe this to the lower metallicity of Epsilon Eridani. Our analysis revealed also that the X-ray cycle of Epsilon Eridani is strongly dominated by cores of active regions. The coverage fraction of cores throughout the cycle changes by the same factor as the X-ray luminosity. The maxima of the cycle are characterized by a high percentage of covering fraction of the flares, consistent with the fact that flaring events are seen in the corresponding short-term X-ray lightcurves predominately at the cycle maxima. The high X-ray emission throughout the cycle of Epsilon Eridani is thus explained by the high percentage of magnetic structures on its surface.

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arXiv2020

Probing UV-Sensitive Pathways for CN and HCN Formation in Protoplanetary Disks with the Hubble Space Telescope

The UV radiation field is a critical regulator of gas-phase chemistry in surface layers of disks around young stars. In an effort to understand the relationship between photocatalyzing UV radiation fields and gas emission observed at infrared and sub-mm wavelengths, we present an analysis of new and archival HST, Spitzer, ALMA, IRAM, and SMA data for five targets in the Lupus cloud complex and 14 systems in Taurus-Auriga. The HST spectra were used to measure LyA and FUV continuum fluxes reaching the disk surface, which are responsible for dissociating relevant molecular species (e.g. HCN, N2). Semi-forbidden C II] 2325 and UV-fluorescent H2 emission were also measured to constrain inner disk populations of C+ and vibrationally excited H2. We find a significant positive correlation between 14 micron HCN emission and fluxes from the FUV continuum and C II] 2325, consistent with model predictions requiring N2 photodissociation and carbon ionization to trigger the main CN/HCN formation pathways. We also report significant negative correlations between sub-mm CN emission and both C II] and FUV continuum fluxes, implying that CN is also more readily dissociated in disks with stronger FUV irradiation. No clear relationships are detected between either CN or HCN and LyA or UV-H2 emission. This is attributed to the spatial stratification of the various molecular species, which span several vertical layers and radii across the inner and outer disk. We expect that future observations with JWST will build on this work by enabling more sensitive IR surveys than were possible with Spitzer.

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arXiv2019

Rapid escape of ultra-hot exoplanet atmospheres driven by Hydrogen Balmer absorption

Atmospheric escape is key to explaining the long-term evolution of planets in our Solar System and beyond, and in the interpretation of atmospheric measurements. Hydrodynamic escape is generally thought to be driven by the flux of extreme ultraviolet photons that the planet receives from its host star. Here, we show that the escape from planets orbiting hot stars proceeds through a different yet complementary process: drawing its energy from the intense near ultraviolet emission of the star that is deposited within an optically thin, high-altitude atmospheric layer of hydrogen excited into the lower state of the Balmer series. The ultra-hot exoplanet KELT-9b likely represents the first known instance of this Balmer-driven escape. In this regime of hydrodynamic escape, the near ultraviolet emission from the star is more important at determining the planet mass loss than the extreme ultraviolet emission, and uncertainties in the latter become less critical. Further, we predict that gas exoplanets around hot stars may experience catastrophic mass loss when they are less massive than 1--2 Jupiter masses and closer-in than KELT-9b, thereby challenging the paradigm that all large exoplanets are stable to atmospheric escape. We argue that extreme escape will affect the demographics of close-in exoplanets orbiting hot stars.

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arXiv2019

X-ray emission in the enigmatic CVSO 30 system

CVSO 30 is a young, active, weak-line T Tauri star; it possibly hosts the only known planetary system with both a transiting hot-Jupiter and a cold-Jupiter candidate (CVSO 30 b and c). We analyzed archival ROSAT, Chandra, and XMM-Newton data to study the coronal emission in the system. According to our modeling, CVSO 30 shows a quiescent X-ray luminosity of about 8e29 erg/s. The X-ray absorbing column is consistent with interstellar absorption. XMM-Newton observed a flare, during which a transit of the candidate CVSO 30 b was expected, but no significant transit-induced variation in the X-ray flux is detectable. While the hot-Jupiter candidate CVSO 30 b has continuously been undergoing mass loss powered by the high-energy irradiation, we conclude that its evaporation lifetime is considerably longer than the estimated stellar age of 2.6 Myr.

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arXiv2019

Swift UVOT near-UV transit observations of WASP-121 b

Close-in gas planets are subject to continuous photoevaporation that can erode their volatile envelopes. Today, ongoing mass loss has been confirmed in a few individual systems via transit observations in the ultraviolet spectral range. We demonstrate that the Ultraviolet/Optical Telescope (UVOT) onboard the Neil Gehrels Swift Observatory enables photometry to a relative accuracy of about 0.5% and present the first near-UV (200-270 nm, NUV) transit observations of WASP-121 b, a hot Jupiter with one of the highest predicted mass-loss rates. The data cover the orbital phases 0.85 to 1.15 with three visits. We measure a broad-band NUV transit depth of $2.10\pm0.29$%. While still consistent with the optical value of 1.55%, the NUV data indicate excess absorption of 0.55% at a 1.9$σ$ level. Such excess absorption is known from the WASP-12 system, and both of these hot Jupiters are expected to undergo mass loss at extremely high rates. With a CLOUDY simulation, we show that absorption lines of Fe II in a dense extended atmosphere can cause broad-band NUV absorption at the 0.5% level. Given the numerous lines of low-ionization metals, the NUV range is a promising tracer of photoevaporation in the hottest gas planets.

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arXiv2018

Detection of He I $\lambda10830$ Å absorption on HD 189733 b with CARMENES high-resolution transmission spectroscopy

We present three transit observations of HD 189733 b obtained with the high-resolution spectrograph CARMENES at Calar Alto. A strong absorption signal is detected in the near-infrared He I triplet at 10830 Å in all three transits. During mid-transit, the mean absorption level is $0.88\pm0.04$ % measured in a $\pm$10 km s$^{-1}$ range at a net blueshift of $-3.5\pm0.4$ km s$^{-1}$ (10829.84--10830.57 Å). The absorption signal exhibits radial velocities of $+6.5\pm3.1$ km s$^{-1}$ and $-12.6\pm1.0$ km s$^{-1}$ during ingress and egress, respectively; measured in the planetary rest frame. We show that stellar activity related pseudo-signals interfere with the planetary atmospheric absorption signal. They could contribute as much as 80% of the observed signal and might also affect the radial velocity signature, but pseudo-signals are very unlikely to explain the entire signal. The observed line ratio between the two unresolved and the third line of the He I triplet is $2.8\pm0.2$, which strongly deviates from the value expected for an optically thin atmospheres. When interpreted in terms of absorption in the planetary atmosphere, this favors a compact helium atmosphere with an extent of only 0.2 planetary radii and a substantial column density on the order of $4\times 10^{12}$ cm$^{-2}$. The observed radial velocities can be understood either in terms of atmospheric circulation with equatorial superrotation or as a sign of an asymmetric atmospheric component of evaporating material. We detect no clear signature of ongoing evaporation, like pre- or post-transit absorption, which could indicate material beyond the planetary Roche lobe, or radial velocities in excess of the escape velocity. These findings do not contradict planetary evaporation, but only show that the detected helium absorption in HD 189733 b does not trace the atmospheric layers that show pronounced escape signatures.

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arXiv2018

Spectro-astrometry of the pre-transitional star LkCa 15 does not reveal an accreting planet but extended H$α$ emission

(Abridged) The detection of forming planets in disks around young stars remains elusive, and state-of-the-art observational techniques provide somewhat ambiguous results. It has been reported that the pre-transitional T Tauri star LkCa 15 could host three planets; candidate planet b is in the process of formation, as inferred from its H$α$ emission. However, a more recent work casts doubts on the planetary nature of the previous detections. We have observed LkCa 15 with ISIS/WHT. The spectrograph's slit was oriented towards the last reported position of LkCa 15 b (parallel direction) and 90degr from that (perpendicular). The photocenter and full width half maximum (FWHM) of the Gaussians fitting the spatial distribution at H$α$ and the adjacent continuum were measured. A well-known binary (GU CMa) was used as a calibrator to test the spectro-astrometric performance of ISIS/WHT, recovering consistent photocenter and FWHM signals. However, the photocenter shift predicted for LkCa 15 b is not detected, but the FWHM in H$α$ is broader than in the continuum for both slit positions. Our simulations show that the photocenter and FWHM observations cannot be explained simultaneously by an accreting planet. In turn, both spectro-astrometric observations are naturally reproduced from a roughly symmetric Halpha emitting region centered on the star and extent comparable to the orbit originally attributed to the planet at several au. The extended H$α$ emission around LkCa 15 could be related to a variable disk wind, but additional multi-epoch data and detailed modeling are necessary to understand its physical nature. Spectro-astrometry in H$α$ is able to test the presence of accreting planets and can be used as a complementary technique to survey planet formation in circumstellar disks.

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arXiv2018

Optical dimming of RW Aur associated with an iron rich corona and exceptionally high absorbing column density

RW Aur is a binary system composed of two young, low-mass stars. The primary, RW Aur A, has undergone visual dimming events ($ΔV =2-3$~mag) in 2011, 2014-16, and 2017-2018. Visual and IR observations indicate a gray absorber that moved into the line-of-sight. This dimming is also associated with changes in the outflow. In 2017, when the optical brightness was almost 2~mag below the long-term average we triggered a Chandra observation to measure the absorbing column density $N_\mathrm{H}$ and to constrain dust properties and the gas-to-dust ratio of the absorber. In 2017, the X-ray spectrum is more absorbed than it was in the optically bright state ($N_\mathrm{H} = (4\pm 1) \times 10^{23}\;\mathrm{cm}^{-2}$) and shows significantly more hot plasma than in X-ray observations taken before. Also, a new emission feature at $6.63\pm0.02$ keV (statistic) $\pm0.02$ keV (systematic) appeared indicating an Fe abundance an order of magnitude above Solar, in contrast with previous sub-Solar Fe abundance measurements. Comparing X-ray absorbing column density $N_\mathrm{H}$ and optical extinction $A_V$, we find that either the gas-to-dust ratio in the absorber is orders of magnitude higher than in the ISM or the absorber has undergone significant dust evolution. Given the high column density coupled with changes in the X-ray spectral shape, this absorber is probably located in the inner disk. We speculate that a break-up of planetesimals or a terrestrial planet could supply large grains causing gray absorption; some of these grains would be accreted and enrich the stellar corona with iron which could explain the inferred high abundance.

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arXiv2018

Multiepoch, multiwavelength study of accretion onto T Tauri: X-ray versus optical and UV accretion tracers

Classical T Tauri stars (CTTSs) accrete matter from the inner edge of their surrounding circumstellar disks. The impact of the accretion material on the stellar atmosphere results in a strong shock, which causes emission from the X-ray to the near-infrared (NIR) domain. Shock velocities of several 100 km s$^{-1}$ imply that the immediate post shock plasma emits mainly in X-rays. Indeed, two X-ray diagnostics, the so-called soft excess and the high densities observed in He-like triplets, differentiate CTTSs from their non-accreting siblings. However, accretion shock properties derived from X-ray diagnostics often contradict established ultraviolet (UV)-NIR accretion tracers and a physical model simultaneously explaining both, X-ray and UV-NIR accretion tracers, is not yet available. We present new XMM-Newton and Chandra grating observations of the CTTS T Tauri combined with UV and optical data. During all epochs, the soft excess is large and the densities derived from the O VII and Ne IX He-like triplets are compatible with coronal densities. This confirms that the soft X-ray emission cannot originate in accretion funnels that carry the bulk of the accretion rate despite T Tauri's large soft excess. Instead, we propose a model of radially density stratified accretion columns to explain the density diagnostics and the soft excess. In addition, accretion rate and X-ray luminosity are inversely correlated in T Tauri over several epochs. Such an anti-correlation has been observed in samples of stars. Hence the process causing it must be intrinsic to the accretion process, and we speculate that the stellar magnetic field configuration on the visibile hemisphere affects both the accretion rate and the coronal emission, eventually causing the observed anti-correlation.

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arXiv2018

Long-term variations in the X-ray activity of HR 1099

Although timing variations in close binary systems have been studied for a long time, their underlying causes are still unclear. A possible explanation is the so-called Applegate mechanism, where a strong, variable magnetic field can periodically change the gravitational quadrupole moment of a stellar component, thus causing observable period changes. One of the systems exhibiting such strong orbital variations is the RS CVn binary HR 1099, whose activity cycle has been studied by various authors via photospheric and chromospheric activity indicators, resulting in contradicting periods. We aim at independently determining the magnetic activity cycle of HR 1099 using archival X-ray data to allow for a comparison to orbital period variations. Archival X-ray data from 80 different observations of HR 1099 acquired with 12 different X-ray facilities and covering almost four decades were used to determine X-ray fluxes in the energy range of 2-10 keV via spectral fitting and flux conversion. Via the Lomb-Scargle periodogram we analyze the resulting long-term X-ray light curve to search for periodicities. We do not detect any statistically significant periodicities within the X-ray data. An analysis of optical data of HR 1099 shows that the derivation of such periods is strongly dependent on the time coverage of available data, since the observed optical variations strongly deviate from a pure sine wave. We argue that this offers an explanation as to why other authors derive such a wide range of activity cycle periods based on optical data. We conclude that our analysis constitutes the longest stellar X-ray activity light curve acquired to date, yet the still rather sparse sampling of the X-ray data, along with stochastic flaring activity, does not allow for the independent determination of an X-ray activity cycle.

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arXiv2018

Multi-epoch monitoring of the AA Tau like star V354 Mon - Indications for a low gas-to-dust ratio in the inner disk warp

Disk warps around classical T Tauri stars (CTTS) can periodically obscure the central star for some viewing geometries. For these so-called AA Tau-like variables, the obscuring material is located in the inner disk and absorption spectroscopy allows one to characterize its dust and gas content. Since the observed emission from CTTS consists of several components (photospheric, accretion, jet, and disk emission), which can all vary with time, it is generally challenging to disentangling disk features from emission variability. Multi-epoch, flux-calibrated, broadband spectra provide us with the necessary information to cleanly separate absorption from emission variability. We applied this method to three epochs of VLT/X-Shooter spectra of the CTTS V354 Mon (CSI Mon-660) located in NGC 2264 and find that: (a) the accretion emission remains virtually unchanged between the three epochs; (b) the broadband flux evolution is best described by disk material obscuring part of the star, and (c) the Na and K gas absorption lines show only a minor increase in equivalent width during phases of high dust extinction. The limits on the absorbing gas column densities indicate a low gas-to-dust ratio in the inner disk, less than a tenth of the ISM value. We speculate that the evolutionary state of V354 Mon, rather old with a low accretion rate, is responsible for the dust excess through an evolution toward a dust dominated disk or through the fragmentation of larger bodies that drifted inward from larger radii in a still gas dominated disk.

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arXiv2018

Resolving the Inner Arcsecond of the RY Tau Jet With HST

Faint X-ray emission from hot plasma (T > 1 MK) has been detected extending outward a few arcseconds along the optically-delineated jets of some classical T Tauri stars including RY Tau. The mechanism and location where the jet is heated to X-ray temperatures is unknown. We present high spatial resolution HST far-ultraviolet long-slit observations of RY Tau with the slit aligned along the jet. The primary objective was to search for C IV emission from warm plasma at T(CIV) ~ 10$^{5}$ K within the inner jet (<1 arcsec) that cannot be fully-resolved by X-ray telescopes. Spatially-resolved C IV emission is detected in the blueshifted jet extending outward from the star to 1 arcsec and in the redshifted jet out to 0.5 arcsec. C IV line centroid shifts give a radial velocity in the blueshifted jet of -136 $\pm$ 10 km/s at an offset of 0.29 arcsec (39 au) and deceleration outward is detected. The deprojected jet speed is subject to uncertainties in the jet inclination but values >200 km/s are likely. The mass-loss rate in the blueshifted jet is at least 2.3 $\times$ 10$^{-9}$ M_sun yr$^{-1}$, consistent with optical determinations. We use the HST data along with optically-determined jet morphology to place meaningful constraints on candidate jet-heating models including a hot-launch model in which the jet is heated near the base to X-ray temperatures by an unspecified (but probably magnetic) process, and downstream heating from shocks or a putative jet magnetic field.

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arXiv2018

A UV-to-NIR Study of Molecular Gas in the Dust Cavity Around RY Lupi

We present a study of molecular gas in the inner disk $\left(r < 20 \, \text{AU} \right)$ around RY Lupi, with spectra from HST-COS, HST-STIS, and VLT-CRIRES. We model the radial distribution of flux from hot gas in a surface layer between $r = 0.1-10$ AU, as traced by Ly$α$-pumped H$_2$. The result shows H$_2$ emission originating in a ring centered at $\sim$3 AU that declines within $r < 0.1$ AU, which is consistent with the behavior of disks with dust cavities. An analysis of the H$_2$ line shapes shows that a two-component Gaussian profile $\left(\text{FWHM}_{broad, H_2} = 105 \pm 15 \, \text{km s}^{-1}; \, \text{FWHM}_{narrow, H_2} = 43 \pm 13 \, \text{km s}^{-1} \right)$ is statistically preferred to a single-component Gaussian. We interpret this as tentative evidence for gas emitting from radially separated disk regions $\left( \left \langle r_{broad, H_2} \right \rangle \sim 0.4 \pm 0.1 \, \text{AU}; \, \left \langle r_{narrow, H_2} \right \rangle \sim 3 \pm 2 \, \text{AU} \right)$. The 4.7 $μ$m $^{12}$CO emission lines are also well fit by two-component profiles $\left( \left \langle r_{broad, CO} \right \rangle = 0.4 \pm 0.1 \, \text{AU}; \, \left \langle r_{narrow, CO} \right \rangle = 15 \pm 2 \, \text{AU} \right)$. We combine these results with 10 $μ$m observations to form a picture of gapped structure within the mm-imaged dust cavity, providing the first such overview of the inner regions of a young disk. The HST SED of RY Lupi is available online for use in modeling efforts.

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arXiv2017

Coronal X-ray emission and planetary irradiation in HD 209458

HD 209458 is one of the benchmark objects in the study of hot Jupiter atmospheres and their evaporation through planetary winds. The expansion of the planetary atmosphere is thought to be driven by high-energy EUV and X-ray irradiation. We obtained new Chandra HRC-I data, which unequivocally show that HD 209458 is an X-ray source. Combining these data with archival XMM-Newton observations, we find that the corona of HD 209458 is characterized by a temperature of about 1 MK and an emission measure of 7e49 cm^-3, yielding an X-ray luminosity of 1.6e27 erg/s in the 0.124-2.48 keV band. HD 209458 is an inactive star with a coronal temperature comparable to that of the inactive Sun but a larger emission measure. At this level of activity, the planetary high-energy emission is sufficient to support mass-loss at a rate of a few times 1e10 g/s.

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arXiv2016

Violent environment of the inner disk of RW Aur A probed by the 2010 and 2015 dimming events

RW Aur is a young binary system showing strong signatures of a recent tidal encounter between the circumprimary disk and the secondary star. The primary star has recently undergone two major dimming events ($Δ$mag $\approx$ 2 in V-band), whose origin is still under debate. To shed light on the mechanism leading to the dimming events, we study the extinction properties, accretion variability, and gas kinematics using absorption lines from the material obscuring star RW Aur A. We compare our moderate resolution X-Shooter spectra of the dim state of RW Aur A with other spectral observations. In particular, we analyse archival high resolution UVES spectra obtained during the bright state of the system, in order to track the evolution of the spectral properties across the second dimming event. The spectrum obtained during the dim state shows narrow absorption lines in the Na and K optical doublets, where the former is saturated. With a velocity of -60 km/s these lines indicate that during the dim state the disk wind is either enhanced, or significantly displaced into the line of sight. The photometric evolution across the dimming event shows a gray extinction, and is correlated with a significant reduction of the EW of all photospheric lines. Emission lines tracing accretion do not vary significantly across the dimming. We conclude that the dimming event is related to a major perturbation on the inner disk. We suggest that the inner disk is occulting (most of) the star, and thus its photosphere, but is not occulting the accretion regions within a few stellar radii. Since observations of the outer disk indicate that the disk is modestly inclined (45 - 60 deg), we propose that the inner disk might be warped by a yet unseen (sub-)stellar companion, which may also explain the 2.77 day periodic variability of the spectral lines.

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arXiv2015

Modelling telluric line spectra in the optical and infrared with an application to VLT/X-Shooter spectra

Earth's atmosphere imprints a large number of telluric absorption and emission lines on astronomical spectra, especially in the near infrared, that need to be removed before analysing the affected wavelength regions. These lines are typically removed by comparison to A- or B-type stars used as telluric standards that themselves have strong hydrogen lines, which complicates the removal of telluric lines. We have developed a method to circumvent that problem. For our IDL software package tellrem we used a recent approach to model telluric absorption features with the line-by-line radiative transfer model (LBLRTM). The broad wavelength coverage of the X-Shooter at VLT allows us to expand their technique by determining the abundances of the most important telluric molecules H2O, O2, CO2, and CH4 from sufficiently isolated line groups. For individual observations we construct a telluric absorption model for most of the spectral range that is used to remove the telluric absorption from the object spectrum. We remove telluric absorption from both continuum regions and emission lines without systematic residuals for most of the processable spectral range; however, our method increases the statistical errors. The errors of the corrected spectrum typically increase by 10% for S/N~10 and by a factor of two for high-quality data (S/N~100), i.e. the method is accurate on the percent level. Modelling telluric absorption can be an alternative to the observation of standard stars for removing telluric contamination.

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arXiv2015

Simulating the escaping atmospheres of hot gas planets in the solar neighborhood

Absorption of high-energy radiation in planetary thermospheres is believed to lead to the formation of planetary winds. The resulting mass-loss rates can affect the evolution, particularly of small gas planets. We present 1D, spherically symmetric hydrodynamic simulations of the escaping atmospheres of 18 hot gas planets in the solar neighborhood. Our sample only includes strongly irradiated planets, whose expanded atmospheres may be detectable via transit spectroscopy. The simulations were performed with the PLUTO-CLOUDY interface, which couples a detailed photoionization and plasma simulation code with a general MHD code. We study the thermospheric escape and derive improved estimates for the planetary mass-loss rates. Our simulations reproduce the temperature-pressure profile measured via sodium D absorption in HD 189733 b, but show unexplained differences in the case of HD 209458 b. In contrast to general assumptions, we find that the gravitationally more tightly bound thermospheres of massive and compact planets, such as HAT-P-2 b are hydrodynamically stable. Compact planets dispose of the radiative energy input through hydrogen Ly$α$ and free-free emission. Radiative cooling is also important in HD 189733 b, but it decreases toward smaller planets like GJ 436 b. The simulations show that the strong and cool winds of smaller planets mainly cause strong Ly$α$ absorption but little emission. Compact and massive planets with hot, stable thermospheres cause small absorption signals but are strong Ly$α$ emitters, possibly detectable with the current instrumentation. The absorption and emission signals provide a possible distinction between these two classes of thermospheres in hot gas planets. According to our results, WASP-80 and GJ 3470 are currently the most promising targets for observational follow-up aimed at detecting atmospheric Ly$α$ absorption signals.

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arXiv2015

Energy-limited escape revised

Gas planets in close proximity to their host stars experience photoevaporative mass loss. The energy-limited escape concept is generally used to derive estimates for the planetary mass-loss rates. Our photoionization hydrodynamics simulations of the thermospheres of hot gas planets show that the energy-limited escape concept is valid only for planets with a gravitational potential lower than $\log_\mathrm{10}\left( -Φ_{\mathrm{G}}\right) < 13.11~$erg$\,$g$^{-1}$ because in these planets the radiative energy input is efficiently used to drive the planetary wind. Massive and compact planets with $\log_\mathrm{10}\left( -Φ_{\mathrm{G}}\right) \gtrsim 13.6~$erg$\,$g$^{-1}$ exhibit more tightly bound atmospheres in which the complete radiative energy input is re-emitted through hydrogen Ly$α$ and free-free emission. These planets therefore host hydrodynamically stable thermospheres. Between these two extremes the strength of the planetary winds rapidly declines as a result of a decreasing heating efficiency. Small planets undergo enhanced evaporation because they host expanded atmospheres that expose a larger surface to the stellar irradiation. We present scaling laws for the heating efficiency and the expansion radius that depend on the gravitational potential and irradiation level of the planet. The resulting revised energy-limited escape concept can be used to derive estimates for the mass-loss rates of super-Earth-sized planets as well as massive hot Jupiters with hydrogen-dominated atmospheres.

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