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Y. C. Unruh

Publications and source records attributed to Y. C. Unruh.

At least 19 recordsLinked to original sources

Effect of surface magnetic fields on limb darkening in main-sequence stars

Context.Stellar limb darkening encodes the thermal and radiative structure of stellar photospheres and is a key ingredient in modeling transit light curves and transmission spectra. It was recently shown that stellar surface magnetic fields modify limb darkening in stars with near-solar fundamental parameters, and that only magnetic models can reproduce high-precision transit observations for such stars. However, for stars with non-solar fundamental parameters, the magnitude of the magnetic effect on limb darkening remain unconstrained. Aims.We aim to investigate how surface magnetism affects stellar limb darkening across a range of fundamental parameters and to provide the community with center-to-limb spectra of stars at different magnetization levels. Methods. We use the MPS-ATLAS code to compute synthetic spectra from 3D radiative magnetohydrodynamic box-in-a-star simulations performed with the MURaM code. These simulations self-consistently capture photospheric magneto-convection without relying on ad hoc parameterizations. We perform calculations for main-sequence stars at solar metallicity with effective temperatures in the range Teff = 3200 - 6800 K. For stars with solar effective temperature we also consider metal-poor, M/H = -1.0, and metal-rich, M/H = 0.5, cases. Results. We show that the magnitude of the magnetic effect depends strongly on stellar fundamental parameters, increasing toward hotter and more metal-rich stars. Overall, limb darkening is significantly affected by magnetic fields in K, G, and F dwarfs, while the effect becomes negligible in M-dwarfs. We release a public database of synthetic spectra at 10 disk positions.

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Energy deposition in Saturn's equatorial upper atmosphere

We construct Saturn equatorial neutral temperature and density profiles of H, H$_2$, He, and CH$_4$, between 10$^{-12}$ and 1 bar using measurements from Cassini's Ion Neutral Mass Spectrometer (INMS) taken during the spacecraft's final plunge into Saturn's atmosphere on 15 September 2017, combined with previous deeper atmospheric measurements from the Cassini Composite InfraRed Spectrometer (CIRS) and from the UltraViolet Imaging Spectrograph (UVIS). These neutral profiles are fed into an energy deposition model employing soft X-ray and Extreme UltraViolet (EUV) solar fluxes at a range of spectral resolutions ($Δλ=4\times10^{-3}$ nm to 1 nm) assembled from TIMED/SEE, from SOHO/SUMER, and from the Whole Heliosphere Interval (WHI) quiet Sun campaign. Our energy deposition model calculates ion production rate profiles through photo-ionisation and electron-impact ionisation processes, as well as rates of photo-dissociation of CH$_4$. The ion reaction rate profiles we determine are important to obtain accurate ion density profiles, meanwhile methane photo-dissociation is key to initiate complex organic chemical processes. We assess the importance of spectral resolution in the energy deposition model by using a high-resolution H$_2$ photo-absorption cross section, which has the effect of producing additional ionisation peaks near 800 km altitude. We find that these peaks are still formed when using low-resolution ($Δλ=1$ nm) or mid-resolution ($Δλ=0.1$ nm) solar spectra, as long as high-resolution cross sections are included in the model.

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MPS-ATLAS: A fast all-in-one code for synthesising stellar spectra

Context. Stellar spectral synthesis is essential for various applications, ranging from determining stellar parameters to comprehensive stellar variability calculations. New observational resources as well as advanced stellar atmosphere modelling, taking three dimensional (3D) effects from radiative magnetohydrodynamics calculations into account, require a more efficient radiative transfer. Aims. For accurate, fast and flexible calculations of opacity distribution functions (ODFs), stellar atmospheres and stellar spectra we developed an efficient code building on the well-established ATLAS9 code. The new code also paves the way for an easy and fast access to different elemental compositions in stellar calculations. Methods. For the generation of ODF tables we further developed the well-established DFSYNTHE code by implementing additional functionality, and a speed-up by employing a parallel computation scheme. In addition, the line lists used can be changed from Kurucz's recent lists. In particular, we implemented the VALD3 line list. Results. A new code, the Merged Parallelised Simplified ATLAS is presented. It combines the efficient generation of ODF, atmosphere modelling and spectral synthesis in local thermodynamic equilibrium, therefore being an all-in-one code. This all-in-one code provides more numerical functionality and is substantially faster compared to other available codes. The fully portable MPS-ATLAS code is validated against previous ATLAS9 calculations, the PHOENIX code calculations, and high quality observations.

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Readdressing the UV solar variability with SATIRE-S: non-LTE effects

Context. Solar spectral irradiance (SSI) variability is one of the key inputs to models of the Earth's climate. Understanding solar irradiance fluctuations also helps to place the Sun among other stars in terms of their brightness variability patterns and to set detectability limits for terrestrial exo-planets. Aims. One of the most successful and widely used models of solar irradiance variability is SATIRE-S. It uses spectra of the magnetic features and surrounding quiet Sun computed with the ATLAS9 spectral synthesis code under the assumption of Local Thermodynamic Equilibrium (LTE). SATIRE-S has been at the forefront of solar variability modelling, but due to the limitations of the LTE approximation its output SSI has to be empirically corrected below 300 nm, which reduces the physical consistency of its results. This shortcoming is addressed in the present paper. Methods. We replace the ATLAS9 spectra of all atmospheric components in SATIRE-S with the spectra calculated using the non-LTE Spectral Synthesis Code (NESSY). We also use Fontenla et al. (1999) temperature and density stratification models of the solar atmosphere to compute the spectrum of the quiet Sun and faculae. Results. We compute non-LTE contrasts of spots and faculae and combine them with the SDO/HMI filling factors of the active regions to calculate the total and spectral solar irradiance variability during solar cycle 24. Conclusions. The non-LTE contrasts result in total and spectral solar irradiance in good agreement with the empirically corrected output of the LTE version. This suggests that empirical correction introduced into SATIRE-S output is well judged and that the corrected total and spectral solar irradiance obtained from the SATIRE-S model in LTE is fully consistent with the results of non-LTE computations.

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Effect of stellar flares on the upper atmospheres of HD 189733b and HD 209458b

Stellar flares are a frequent occurrence on young low-mass stars around which many detected exoplanets orbit. Flares are energetic, impulsive events, and their impact on exoplanetary atmospheres needs to be taken into account when interpreting transit observations. We have developed a model to describe the upper atmosphere of Extrasolar Giant Planets (EGPs) orbiting flaring stars. The model simulates thermal escape from the upper atmospheres of close-in EGPs. Ionisation by solar radiation and electron impact is included and photochemical and diffusive transport processes are simulated. This model is used to study the effect of stellar flares from the solar-like G star HD209458 and the young K star HD189733 on their respective planets. A hypothetical HD209458b-like planet orbiting the active M star AU Mic is also simulated. We find that the neutral upper atmosphere of EGPs is not significantly affected by typical flares. Therefore, stellar flares alone would not cause large enough changes in planetary mass loss to explain the variations in HD189733b transit depth seen in previous studies, although we show that it may be possible that an extreme stellar proton event could result in the required mass loss. Our simulations do however reveal an enhancement in electron number density in the ionosphere of these planets, the peak of which is located in the layer where stellar X-rays are absorbed. Electron densities are found to reach 2.2 to 3.5 times pre-flare levels and enhanced electron densities last from about 3 to 10 hours after the onset of the flare. The strength of the flare and the width of its spectral energy distribution affect the range of altitudes that see enhancements in ionisation. A large broadband continuum component in the XUV portion of the flaring spectrum in very young flare stars, such as AU Mic, results in a broad range of altitudes affected in planets orbiting this star.

astro-ph.EP

Solar Irradiance Variability is Caused by the Magnetic Activity on the Solar Surface

The variation in the radiative output of the Sun, described in terms of solar irradiance, is important to climatology. A common assumption is that solar irradiance variability is driven by its surface magnetism. Verifying this assumption has, however, been hampered by the fact that models of solar irradiance variability based on solar surface magnetism have to be calibrated to observed variability. Making use of realistic three-dimensional magnetohydrodynamic simulations of the solar atmosphere and state-of-the-art solar magnetograms from the Solar Dynamics Observatory, we present a model of total solar irradiance (TSI) that does not require any such calibration. In doing so, the modeled irradiance variability is entirely independent of the observational record. (The absolute level is calibrated to the TSI record from the Total Irradiance Monitor.) The model replicates 95% of the observed variability between April 2010 and July 2016, leaving little scope for alternative drivers of solar irradiance variability at least over the time scales examined (days to years).

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Reconstruction of spectral solar irradiance since 1700 from simulated magnetograms

We present a reconstruction of the spectral solar irradiance since 1700 using the SATIRE-T2 (Spectral And Total Irradiance REconstructions for the Telescope era version 2) model. This model uses as input magnetograms simulated with a surface flux transport model fed with semi-synthetic records of emerging sunspot groups. We used statistical relationships between the properties of sunspot group emergence, such as the latitude, area, and tilt angle, and the sunspot cycle strength and phase to produce semi-synthetic sunspot group records starting in the year 1700. The semisynthetic records are fed into a surface flux transport model to obtain daily simulated magnetograms that map the distribution of the magnetic flux in active regions (sunspots and faculae) and their decay products on the solar surface. The magnetic flux emerging in ephemeral regions is accounted for separately based on the concept of extended cycles whose length and amplitude are linked to those of the sunspot cycles through the sunspot number. The magnetic flux in each surface component (sunspots, faculae and network, and ephemeral regions) was used to compute the spectral and total solar irradiance between the years 1700 and 2009. This reconstruction is aimed at timescales of months or longer although the model returns daily values. We found that SATIRE-T2, besides reproducing other relevant observations such as the total magnetic flux, reconstructs the total solar irradiance (TSI) on timescales of months or longer in good agreement with the PMOD composite of observations, as well as with the reconstruction starting in 1878 based on the RGO-SOON data. The model predicts an increase in the TSI of 1.2[+0.2, -0.3] Wm-2 between 1700 and the present. The spectral irradiance reconstruction is in good agreement with the UARS/SUSIM measurements as well as the Lyman-alpha composite.

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The Sun as a planet-host star: Proxies from SDO images for HARPS radial-velocity variations

The Sun is the only star whose surface can be directly resolved at high resolution, and therefore constitutes an excellent test case to explore the physical origin of stellar radial-velocity (RV) variability. We present HARPS observations of sunlight scattered off the bright asteroid 4/Vesta, from which we deduced the Sun's activity-driven RV variations. In parallel, the HMI instrument onboard the Solar Dynamics Observatory provided us with simultaneous high spatial resolution magnetograms, Dopplergrams, and continuum images of the Sun in the Fe I 6173A line. We determine the RV modulation arising from the suppression of granular blueshift in magnetised regions and the flux imbalance induced by dark spots and bright faculae. The rms velocity amplitudes of these contributions are 2.40 m/s and 0.41 m/s, respectively, which confirms that the inhibition of convection is the dominant source of activity-induced RV variations at play, in accordance with previous studies. We find the Doppler imbalances of spot and plage regions to be only weakly anticorrelated. Lightcurves can thus only give incomplete predictions of convective blueshift suppression. We must instead seek proxies that track the plage coverage on the visible stellar hemisphere directly. The chromospheric flux index R'_HK derived from the HARPS spectra performs poorly in this respect, possibly because of the differences in limb brightening/darkening in the chromosphere and photosphere. We also find that the activity-driven RV variations of the Sun are strongly correlated with its full-disc magnetic flux density, which may become a useful proxy for activity-related RV noise.

astro-ph.EP

EUV-driven ionospheres and electron transport on extrasolar giant planets orbiting active stars

The composition and structure of the upper atmospheres of Extrasolar Giant Planets (EGPs) are affected by the high-energy spectrum of their host stars from soft X-rays to EUV. This emission depends on the activity level of the star, which is primarily determined by its age. We focus upon EGPs orbiting K- and M-dwarf stars of different ages. XUV spectra for these stars are constructed using a coronal model. These spectra are used to drive both a thermospheric model and an ionospheric model, providing densities of neutral and ion species. Ionisation is included through photo-ionisation and electron-impact processes. We find that EGP ionospheres at all orbital distances considered and around all stars selected are dominated by the long-lived H$^+$ ion. In addition, planets with upper atmospheres where H$_2$ is not substantially dissociated have a layer in which H$_3^+$ is the major ion at the base of the ionosphere. For fast-rotating planets, densities of short-lived H$_3^+$ undergo significant diurnal variations, with the maximum value being driven by the stellar X-ray flux. In contrast, densities of longer-lived H$^+$ show very little day/night variability and the magnitude is driven by the level of stellar EUV flux. The H$_3^+$ peak in EGPs with upper atmospheres where H$_2$ is dissociated under strong stellar illumination is pushed to altitudes below the homopause, where this ion is likely to be destroyed through reactions with heavy species. The inclusion of secondary ionisation processes produces significantly enhanced ion and electron densities at altitudes below the main EUV ionisation peak, as compared to models that do not include electron-impact ionisation. We estimate infrared emissions from H$_3^+$, and while, in an H/H$_2$/He atmosphere, these are larger from planets orbiting close to more active stars, they still appear too low to be detected with current observatories.

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Classical T Tauri stars with VPHAS$+$: I: H$α$ and $u$-band accretion rates in the Lagoon Nebula M8

We estimate the accretion rates of 235 Classical T Tauri star (CTTS) candidates in the Lagoon Nebula using $ugri$H$α$ photometry from the VPHAS+ survey. Our sample consists of stars displaying H$α$-excess, the intensity of which is used to derive accretion rates. For a subset of 87 stars, the intensity of the $u$-band excess is also used to estimate accretion rates. We find the mean variation in accretion rates measured using H$α$ and $u$-band intensities to be $\sim$ 0.17 dex, agreeing with previous estimates (0.04-0.4 dex) but for a much larger sample. The spatial distribution of CTTS align with the location of protostars and molecular gas suggesting that they retain an imprint of the natal gas fragmentation process. Strong accretors are concentrated spatially, while weak accretors are more distributed. Our results do not support the sequential star forming processes suggested in the literature.

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UV solar irradiance in observations and the NRLSSI and SATIRE-S models

Total solar irradiance and UV spectral solar irradiance have been monitored since 1978 through a succession of space missions. This is accompanied by the development of models aimed at replicating solar irradiance by relating the variability to solar magnetic activity. The NRLSSI and SATIRE-S models provide the most comprehensive reconstructions of total and spectral solar irradiance over the period of satellite observation currently available. There is persistent controversy between the various measurements and models in terms of the wavelength dependence of the variation over the solar cycle, with repercussions on our understanding of the influence of UV solar irradiance variability on the stratosphere. We review the measurement and modelling of UV solar irradiance variability over the period of satellite observation. The SATIRE-S reconstruction is consistent with spectral solar irradiance observations where they are reliable. It is also supported by an independent, empirical reconstruction of UV spectral solar irradiance based on UARS/SUSIM measurements from an earlier study. The weaker solar cycle variability produced by NRLSSI between 300 and 400 nm is not evident in any available record. We show that although the method employed to construct NRLSSI is principally sound, reconstructed solar cycle variability is detrimentally affected by the uncertainty in the SSI observations it draws upon in the derivation. Based on our findings, we recommend, when choosing between the two models, the use of SATIRE-S for climate studies.

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New OB star candidates in the Carina Arm around Westerlund 2 from VPHAS+

O and early B stars are at the apex of galactic ecology, but in the Milky Way, only a minority of them may yet have been identified. We present the results of a pilot study to select and parametrise OB star candidates in the Southern Galactic plane, down to a limiting magnitude of $g=20$. A 2 square-degree field capturing the Carina Arm around the young massive star cluster, Westerlund 2, is examined. The confirmed OB stars in this cluster are used to validate our identification method, based on selection from the $(u-g, g-r)$ diagram for the region. Our Markov Chain Monte Carlo fitting method combines VPHAS+ $u, g, r, i$ with published $J, H, K$ photometry in order to derive posterior probability distributions of the stellar parameters $\log(\rm T_{\rm eff})$ and distance modulus, together with the reddening parameters $A_0$ and $R_V$. The stellar parameters are sufficient to confirm OB status while the reddening parameters are determined to a precision of $σ(A_0)\sim0.09$ and $σ(R_V)\sim0.08$. There are 489 objects that fit well as new OB candidates, earlier than $\sim$B2. This total includes 74 probable massive O stars, 5 likely blue supergiants and 32 reddened subdwarfs. This increases the number of previously known and candidate OB stars in the region by nearly a factor of 10. Most of the new objects are likely to be at distances between 3 and 6 kpc. We have confirmed the results of previous studies that, at these longer distances, these sight lines require non-standard reddening laws with $3.5<R_V<4$.

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XUV-driven mass loss from extrasolar giant planets orbiting active stars

Upper atmospheres of Hot Jupiters are subject to extreme radiation conditions that can result in rapid atmospheric escape. The composition and structure of the upper atmospheres of these planets are affected by the high-energy spectrum of the host star. This emission depends on stellar type and age, which are thus important factors in understanding the behaviour of exoplanetary atmospheres. In this study, we focus on Extrasolar Giant Planets (EPGs) orbiting K and M dwarf stars. XUV spectra for three different stars - epsilon Eridani, AD Leonis and AU Microscopii - are constructed using a coronal model. Neutral density and temperature profiles in the upper atmosphere of hypothetical EGPs orbiting these stars are then obtained from a fluid model, incorporating atmospheric chemistry and taking atmospheric escape into account. We find that a simple scaling based solely on the host star's X-ray emission gives large errors in mass loss rates from planetary atmospheres and so we have derived a new method to scale the EUV regions of the solar spectrum based upon stellar X-ray emission. This new method produces an outcome in terms of the planet's neutral upper atmosphere very similar to that obtained using a detailed coronal model of the host star. Our results indicate that in planets subjected to radiation from active stars, the transition from Jeans escape to a regime of hydrodynamic escape at the top of the atmosphere occurs at larger orbital distances than for planets around low activity stars (such as the Sun).

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The Second Data Release of the INT Photometric H-Alpha Survey of the Northern Galactic Plane (IPHAS DR2)

The INT/WFC Photometric H-Alpha Survey of the Northern Galactic Plane (IPHAS) is a 1800 square degrees imaging survey covering Galactic latitudes |b| < 5 deg and longitudes l = 30 to 215 deg in the r, i and H-alpha filters using the Wide Field Camera (WFC) on the 2.5-metre Isaac Newton Telescope (INT) in La Palma. We present the first quality-controlled and globally-calibrated source catalogue derived from the survey, providing single-epoch photometry for 219 million unique sources across 92% of the footprint. The observations were carried out between 2003 and 2012 at a median seeing of 1.1 arcsec (sampled at 0.33 arcsec/pixel) and to a mean 5σ-depth of 21.2 (r), 20.0 (i) and 20.3 (H-alpha) in the Vega magnitude system. We explain the data reduction and quality control procedures, describe and test the global re-calibration, and detail the construction of the new catalogue. We show that the new calibration is accurate to 0.03 mag (rms) and recommend a series of quality criteria to select the most reliable data from the catalogue. Finally, we demonstrate the ability of the catalogue's unique (r-Halpha, r-i) diagram to (1) characterise stellar populations and extinction regimes towards different Galactic sightlines and (2) select H-alpha emission-line objects. IPHAS is the first survey to offer comprehensive CCD photometry of point sources across the Galactic Plane at visible wavelengths, providing the much-needed counterpart to recent infrared surveys.

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Planets and Stellar Activity: Hide and Seek in the CoRoT-7 system

Since the discovery of the transiting super-Earth CoRoT-7b, several investigations have yielded different results for the number and masses of planets present in the system, mainly owing to the star's high level of activity. We re-observed CoRoT-7 in January 2012 with both HARPS and CoRoT, so that we now have the benefit of simultaneous radial-velocity and photometric data. This allows us to use the off-transit variations in the star's light curve to estimate the radial-velocity variations induced by the suppression of convective blueshift and the flux blocked by starspots. To account for activity-related effects in the radial-velocities which do not have a photometric signature, we also include an additional activity term in the radial-velocity model, which we treat as a Gaussian process with the same covariance properties (and hence the same frequency structure) as the light curve. Our model was incorporated into a Monte Carlo Markov Chain in order to make a precise determination of the orbits of CoRoT-7b and CoRoT-7c. We measure the masses of planets b and c to be 4.73 +/- 0.95 Mearth and 13.56 +/- 1.08 Mearth, respectively. The density of CoRoT-7b is (6.61 +/- 1.72)(Rp/1.58 Rearth)^(-3) g.cm^(-3), which is compatible with a rocky composition. We search for evidence of an additional planet d, identified by previous authors with a period close to 9 days. We are not able to confirm the existence of a planet with this orbital period, which is close to the second harmonic of the stellar rotation at around 7.9 days. Using Bayesian model selection we find that a model with two planets plus activity-induced variations is most favoured.

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The variability of Sun-like stars: reproducing observed photometric trends

The Sun and stars with low magnetic activity levels, become photometrically brighter when their activity increases. Magnetically more active stars display the opposite behaviour and get fainter when their activity increases. We reproduce the observed photometric trends in stellar variations with a model that treats stars as hypothetical Suns with coverage by magnetic features different from that of the Sun. The presented model attributes the variability of stellar spectra to the imbalance between the contributions from different components of the solar atmosphere, such as dark starspots and bright faculae. A stellar spectrum is calculated from spectra of the individual components, by weighting them with corresponding disc area coverages. The latter are obtained by extrapolating the solar dependences of spot and facular disc area coverages on chromospheric activity to stars with different levels of mean chromospheric activity. We have found that the contribution by starspots to the variability increases faster with chromospheric activity than the facular contribution. This causes the transition from faculae-dominated variability and direct activity--brightness correlation to spot-dominated variability and inverse activity--brightness correlation with increasing chromospheric activity level. We have shown that the regime of the variability also depends on the angle between the stellar rotation axis and the line-of-sight and on the latitudinal distribution of active regions on the stellar surface. Our model can be used as a tool to extrapolate the observed photometric variability of the Sun to Sun-like stars at different activity levels, which makes possible the direct comparison between solar and stellar irradiance data.

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The VST Photometric Halpha Survey of the Southern Galactic Plane and Bulge (VPHAS+)

The VST Photometric Halpha Survey of the Southern Galactic Plane and Bulge (VPHAS+) is surveying the southern Milky Way in u, g, r, i and Halpha at 1 arcsec angular resolution. Its footprint spans the Galactic latitude range -5 < b < +5 at all longitudes south of the celestial equator. Extensions around the Galactic Centre to Galactic latitudes +/-10 bring in much of the Galactic Bulge. This ESO public survey, begun on 28th December 2011, reaches down to 20th magnitude (10-sigma) and will provide single-epoch digital optical photometry for around 300 million stars. The observing strategy and data pipelining is described, and an appraisal of the segmented narrowband Halpha filter in use is presented. Using model atmospheres and library spectra, we compute main-sequence (u - g), (g - r), (r - i) and (r - Halpha) stellar colours in the Vega system. We report on a preliminary validation of the photometry using test data obtained from two pointings overlapping the Sloan Digital Sky Survey. An example of the (u - g, g - r) and (r - Halpha, r - i) diagrams for a full VPHAS+ survey field is given. Attention is drawn to the opportunities for studies of compact nebulae and nebular morphologies that arise from the image quality being achieved. The value of the u band as the means to identify planetary-nebula central stars is demonstrated by the discovery of the central star of NGC 2899 in survey data. Thanks to its excellent imaging performance, the VST/OmegaCam combination used by this survey is a perfect vehicle for automated searches for reddened early-type stars, and will allow the discovery and analysis of compact binaries, white dwarfs and transient sources.

astro-ph.GA

Recent variability of the solar spectral irradiance and its impact on climate modelling

The lack of long and reliable time series of solar spectral irradiance (SSI) measurements makes an accurate quantification of solar contributions to recent climate change difficult. Whereas earlier SSI observations and models provided a qualitatively consistent picture of the SSI variability, recent measurements by the SORCE satellite suggest a significantly stronger variability in the ultraviolet (UV) spectral range and changes in the visible and near-infrared (NIR) bands in anti-phase with the solar cycle. A number of recent chemistry-climate model (CCM) simulations have shown that this might have significant implications on the Earth's atmosphere. Motivated by these results, we summarize here our current knowledge of SSI variability and its impact on Earth's climate. We present a detailed overview of existing SSI measurements and provide thorough comparison of models available to date. SSI changes influence the Earth's atmosphere, both directly, through changes in shortwave (SW) heating and therefore, temperature and ozone distributions in the stratosphere, and indirectly, through dynamical feedbacks. We investigate these direct and indirect effects using several state-of-the art CCM simulations forced with measured and modeled SSI changes. A unique asset of this study is the use of a common comprehensive approach for an issue that is usually addressed separately by different communities. Omissis. Finally, we discuss the reliability of the available data and we propose additional coordinated work, first to build composite SSI datasets out of scattered observations and to refine current SSI models, and second, to run coordinated CCM experiments.

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