On the Zero Point Constant of the Bolometric Correction Scale

Arbitrariness attributed to the zero point constant of the V band bolometric corrections (BCV) and its relation to “bolometric magnitude of a star ought to be brighter than its visual magnitude” and “bolometric corrections must always be negative” was investigated. The falsehood of the second assertion became noticeable to us after IAU 2015 General Assembly Resolution B2, where the zero point constant of bolometric magnitude scale was decided to have a definite value CBol(W) = 71.197 425 ... . Since the zero point constant of the BCV scale could be written as C2 = CBol − CV, where CV is the zero point constant of the visual magnitudes in the basic definition BCV = MBol − MV = mbol − mV, and CBol > CV, the zero point constant (C2) of the BCV scale cannot be arbitrary anymore; rather, it must be a definite positive number obtained from the two definite positive numbers. The two conditions C2 > 0 and 0 < BCV < C2 are also sufficient for LV < L, a similar case to negative BCV numbers, which means that “bolometric corrections are not always negative”. In sum it becomes apparent that the first assertion is misleading causing one to understand bolometric corrections must always be negative, which is not necessarily true.

Light and colour variations of Mira variables in the Small Magellanic Cloud

ABSTRACT The goal of this paper is to characterize the light variation properties of Mira variables in the Small Magellanic Cloud. We have investigated a combined optical and near-infrared multi-epoch data set of Mira variables based on our monitoring data obtained over 15 yr. Bolometric correction relations are formulated for various near-infrared colours. We find that the same bolometric correction equation holds for both the bolometricly brightest and faintest pulsation phases. Period–bolometric magnitude relations and period–colour relations were derived using time-averaged values. Phase lags between bolometric phase and optical and near-infrared phases were detected from the O-rich (the surface C/O number ratio is below unity) Mira variables, while no significant systematic lags were observed in most of the C-rich (the C/O ratio is over unity) ones. Some Miras show colour phase inversions, e.g. H–Ks at its bluest while J–H and J–Ks are at their reddest values at about the bolometricly brightest phase. Their occurrence conditions were studied but no clear direct or indirect trigger was found. A large NIR colour change unassociated with stellar pulsation was observed in Miras with long secondary periods, and its possible explanation is described.

Empirical bolometric correction coefficients for nearby main-sequence stars in the Gaia era

ABSTRACT Nearby detached double-lined eclipsing binaries with most accurate data were studied and 290 systems were found with at least one main-sequence component having a metallicity of 0.008 ≤ Z ≤ 0.040. Stellar parameters, light ratios, Gaia Data Release 2 trigonometric parallaxes, extinctions and/or reddening were investigated and only 206 systems were selected as eligible to calculate empirical bolometric corrections. NASA/IPAC Galactic dust maps were the main source of extinctions. Unreliable extinctions at low Galactic latitudes |b| ≤ 5° were replaced with individual determinations, if they exist in the literature, else associated systems were discarded. The main-sequence stars of te remaining systems were used to calculate the bolometric corrections (BCs) and to calibrate the BC–Teff relation, which is valid in the range 3100–36 000 K. De-reddened (B − V)0 colours, on the other hand, allowed us to calibrate two intrinsic colour–effective temperature relations; the linear one is valid for $T_{\rm eff}\gt 10\, 000$ K, while the quadratic relation is valid for $T_{\rm eff}\lt 10\, 000$ K; that is, both are valid in the same temperature range in which the BC–Teff relation is valid. New BCs computed from Teff and other astrophysical parameters are tabulated, as well.

Evolved massive stars at low metallicity

We present the most comprehensive red supergiant (RSG) sample for the Small Magellanic Cloud (SMC) to date, including 1239 RSG candidates. The initial sample was derived based on a source catalog for the SMC with conservative ranking. Additional spectroscopic RSGs were retrieved from the literature, and RSG candidates were selected based on the inspection of Gaia and 2MASS color-magnitude diagrams (CMDs). We estimate that there are in total ∼1800 or more RSGs in the SMC. We purify the sample by studying the infrared CMDs and the variability of the objects, though there is still an ambiguity between asymptotic giant branch stars (AGBs) and RSGs at the red end of our sample. One heavily obscured target was identified based on multiple near-IR and mid-IR (MIR) CMDs. The investigation of color-color diagrams shows that there are fewer RSGs candidates (∼4%) showing PAH emission features compared to the Milky Way and LMC (∼15%). The MIR variability of RSG sample increases with luminosity. We separate the RSG sample into two subsamples (risky and safe), and identify one M5e AGB star in the risky subsample based on simultaneous inspection of variabilities, luminosities, and colors. The degeneracy of mass loss rate (MLR), variability, and luminosity of the RSG sample is discussed, indicating that most of the targets with high variability are also the bright ones with high MLR. Some targets show excessive dust emission, which may be related to previous episodic mass loss events. We also roughly estimate the total gas and dust budget produced by entire RSG population as ∼1.9−1.1+2.4 × 10−6 M⊙ yr−1 in the most conservative case, according to the derived MLR from IRAC1–IRAC4 color. Based on the MIST models, we derive a linear relation between Teff and observed J − KS color with reddening correction for the RSG sample. By using a constant bolometric correction and this relation, the Geneva evolutionary model is compared with our RSG sample, showing a good agreement and a lower initial mass limit of ∼7 M⊙ for the RSG population. Finally, we compare the RSG sample in the SMC and the LMC. Despite the incompleteness of LMC sample in the faint end, the result indicates that the LMC sample always shows redder color (except for the IRAC1–IRAC2 and WISE1–WISE2 colors due to CO absorption) and higher variability than the SMC sample, which is likely due to a positive relation between MLR, variability and the metallicity.

Universal bolometric corrections for active galactic nuclei over seven luminosity decades

Context. The AGN bolometric correction is a key element for understanding black hole (BH) demographics and computing accurate BH accretion histories from AGN luminosities. However, current estimates still differ from each other by up to a factor of two to three, and rely on extrapolations at the lowest and highest luminosities. Aims. Here we revisit this fundamental question by presenting general hard X-ray (KX) and optical (KO) bolometric corrections, computed by combining several AGN samples spanning the widest (about 7 dex) luminosity range ever used for this type of studies. Methods. We analysed a total of ∼1000 type 1 and type 2 AGN for which we performed a dedicated SED-fitting. Results. We provide a bolometric correction separately for type 1 and type 2 AGN; the two bolometric corrections agree in the overlapping luminosity range. Based on this we computed for the first time a universal bolometric correction for the whole AGN sample (both type 1 and type 2). We found that KX is fairly constant at log(LBOL/L⊙) < 11, while it increases up to about one order of magnitude at log(LBOL/L⊙) ∼ 14.5. A similar increasing trend has been observed when its dependence on either the Eddington ratio or the BH mass is considered, while no dependence on redshift up to z ∼ 3.5 has been found. In contrast, the optical bolometric correction appears to be fairly constant (i.e. KO ∼ 5) regardless of the independent variable. We also verified that our bolometric corrections correctly predict the AGN bolometric luminosity functions. According to this analysis, our bolometric corrections can be applied to the whole AGN population in a wide range of luminosity and redshift.

YBC: a stellar bolometric corrections database with variable extinction coefficients

We present the YBC database of stellar bolometric corrections, in which we homogenise widely used theoretical stellar spectral libraries and provide BCs for many popular photometric systems, including Gaia filters. The database can easily be extended to additional photometric systems and stellar spectral libraries. The web interface allows users to transform their catalogue of theoretical stellar parameters into magnitudes and colours of selected filter sets. The BC tables can be downloaded or implemented into large simulation projects using the interpolation code provided with the database. We computed extinction coefficients on a star-by-star basis, hence taking into account the effects of spectral type and non-linearity dependency on the total extinction. We illustrate the use of these BCs in PARSEC isochrones. We show that using spectral-type dependent extinction coefficients is necessary for Gaia filters whenever AV ≳ 0.5 mag. Bolometric correction tables for rotating stars and tables of limb-darkening coefficients are also provided.

The X-ray properties of z > 6 quasars: no evident evolution of accretion physics in the first Gyr of the Universe

Context. X-ray emission from quasars (QSOs) has been used to assess supermassive black hole accretion properties up to z ≈ 6. However, at z > 6 only ≈15 QSOs are covered by sensitive X-ray observations, preventing a statistically significant investigation of the X-ray properties of the QSO population in the first Gyr of the Universe. Aims. We present new Chandra observations of a sample of 10 z > 6 QSOs, selected to have virial black-hole mass estimates from Mg II line spectroscopy $ \left(\log\frac{M_{\mathrm{BH}}}{M_\odot}=8.5{-}9.6\right) $. Adding archival X-ray data for an additional 15 z > 6 QSOs, we investigate the X-ray properties of the QSO population in the first Gyr of the Universe. In particular, we focus on the LUV − LX relation, which is traced by the αox parameter, and the shape of their X-ray spectra. Methods. We performed photometric analyses to derive estimates of the X-ray luminosities of our z > 6 QSOs, and thus their αox values and bolometric corrections (Kbol = Lbol/LX). We compared the resulting αox and Kbol distributions with the results found for QSO samples at lower redshift, and ran several statistical tests to check for a possible evolution of the LUV − LX relation. Finally, we performed a basic X-ray spectral analysis of the brightest z > 6 QSOs to derive their individual photon indices, and joint spectral analysis of the whole sample to estimate the average photon index. Results. We detect seven of the new Chandra targets in at least one standard energy band, while two more are detected discarding energies E > 5 keV, where background dominates. We confirm a lack of significant evolution of αox with redshift, which extends the results from previous works up to z > 6 with a statistically significant QSO sample. Furthermore, we confirm the trend of an increasing bolometric correction with increasing luminosity found for QSOs at lower redshifts. The average power-law photon index of our sample (⟨Γ⟩ = 2.20−0.34+0.39 and ⟨Γ⟩ = 2.13−0.13+0.13 for sources with < 30 and > 30 net counts, respectively) is slightly steeper than, but still consistent with, typical QSOs at z = 1 − 6. Conclusions. All of these results indicate a lack of substantial evolution of the inner accretion-disk and hot-corona structure in QSOs from low redshift to z > 6. Our data hint at generally high Eddington ratios at z > 6.

Bolometric corrections of stellar oscillation amplitudes as observed by the Kepler, CoRoT, and TESS missions

ABSTRACT A better understanding of the amplitudes of stellar oscillation modes and surface granulation is essential for improving theories of mode physics and the properties of the outer convection zone of solar-like stars. A proper prediction of these amplitudes is also essential for appraising the detectability of solar-like oscillations for asteroseismic analysis. Comparisons with models, or between different photometric missions, are enabled by applying a bolometric correction, which converts mission-specific amplitudes to their corresponding bolometric (full light) values. We derive the bolometric correction factor for amplitudes of radial oscillation modes and surface granulation as observed by the Kepler, CoRoT, and TESS missions. The calculations are done assuming a stellar spectrum given by a black-body as well as by synthetic spectral flux densities from 1D model atmospheres. We derive a power-law and polynomial relations for the bolometric correction as a function of temperature from the black-body approximation and evaluate the deviations from adopting a more realistic spectrum. Across the full temperature range from 4000 to 7500 K, the amplitudes from TESS are in the black-body approximation predicted to be a factor ∼0.83–0.84 times those observed by Kepler. We find that using more realistic flux spectra over the black-body approximation can change the bolometric correction by as much as ${\sim }30{{\ \rm per\ cent}}$ at the lowest temperatures, but with a change typically within ${\sim }5\!-\!10 {{\ \rm per\ cent}}$ around a Teff of 5500–6000 K. We find that after Teff, the bolometric correction most strongly depends on $\rm [M/H]$, which could have an impact on reported metallicity dependences of amplitudes reported in the literature.

Bolometric correction factors for active galactic nuclei

ABSTRACT The bolometric luminosity of active galactic nuclei (AGNs) is difficult to determine, and various approximations have been used to calibrate it against different observed properties. Here, I combine theoretical calculations of optically thick, geometrically thin accretion discs, and observed X-ray properties of AGN, to provide new bolometric correction factors (kBOL) over a large range of black hole (BH) mass, accretion rate, and spin. This is particularly important in cases where the mass accretion rate cannot be determined from the observed spectral energy distribution, and in cases where luminosity-independent correction factors have been used. Simple power-law approximations of kBOL are provided for L(5100 Å), L(3000 Å), L(1400 Å), L(2–10 keV), and L(narrow Hβ). In all cases, the uncertainties are large mostly due to the unknown BH spin. Prior knowledge of the BH mass reduces the uncertainty considerably.

Gaia Data Release 2

The second Gaia data release (Gaia DR2) contains, beyond the astrometry, three-band photometry for 1.38 billion sources. One band is the G band, the other two were obtained by integrating the Gaia prism spectra (BP and RP). We have used these three broad photometric bands to infer stellar effective temperatures, Teff, for all sources brighter than G = 17 mag with Teff in the range 3000–10 000 K (some 161 million sources). Using in addition the parallaxes, we infer the line-of-sight extinction, AG, and the reddening, E(BP − RP), for 88 million sources. Together with a bolometric correction we derive luminosity and radius for 77 million sources. These quantities as well as their estimated uncertainties are part of Gaia DR2. Here we describe the procedures by which these quantities were obtained, including the underlying assumptions, comparison with literature estimates, and the limitations of our results. Typical accuracies are of order 324 K (Teff), 0.46 mag (AG), 0.23 mag (E(BP − RP)), 15% (luminosity), and 10% (radius). Being based on only a small number of observable quantities and limited training data, our results are necessarily subject to some extreme assumptions that can lead to strong systematics in some cases (not included in the aforementioned accuracy estimates). One aspect is the non-negativity contraint of our estimates, in particular extinction, which we discuss. Yet in several regions of parameter space our results show very good performance, for example for red clump stars and solar analogues. Large uncertainties render the extinctions less useful at the individual star level, but they show good performance for ensemble estimates. We identify regimes in which our parameters should and should not be used and we define a “clean” sample. Despite the limitations, this is the largest catalogue of uniformly-inferred stellar parameters to date. More precise and detailed astrophysical parameters based on the full BP/RP spectrophotometry are planned as part of the third Gaia data release.