The Distance to the Stars

The Distance to the Stars | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Physical Sciences - Article The Distance to the Stars Ralf Siebenmorgen, Rolf Chini This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3279464/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted You are reading this latest preprint version Abstract The vastness of a clear night sky evokes for most people curiosity about the distance to the stars. There are two primary methods for estimating stellar distances – parallax and luminosity. In this study, we present a new analysis revealing a noteworthy discrepancy between these two methods. Due to the accuracy of GAIA, parallaxes can directly be converted into distances. In contrast, luminosity distances require – apart from the determination of apparent and absolute brightness of a star – the reddening value that allows a correction for interstellar extinction. Using 47 stars with non-peculiar reddening curves from the high-quality sample 1 we find here that the luminosity distance overestimates the parallactic distance for most (79%) of these stars. This puzzling discrepancy can only be removed when incorporating a new population of large dust grains – so-called dark dust – with our model 2 that respects contemporary constraints of the interstellar dust 3 and is updated to scope for the first time with the absolute reddening. The model provides a visual extinction which unifies the conflicting distances. Another far-reaching consequence of the flat absorption and scattering properties of dark dust is that it broadens the light curves 4 of SNIa, which serve as a measure of the quantity of dark energy 5 . Physical sciences/Astronomy and planetary science/Astronomy and astrophysics/Astrophysical dust Physical sciences/Astronomy and planetary science/Astronomy and astrophysics/Interstellar medium Figures Figure 1 Figure 2 Parallax and luminosity distance The distance measurement to stars has long intrigued astronomers, prompting the exploration of various estimation techniques. Parallax, based on geometric principles, provides a straightforward approach but is limited to nearby stars whereas luminosity distance D L estimates enable the assessment of distances of several kpc. However, the extinction by dust diminishes the apparent brightness of stars and requires a precise determination. We examine 47 prominent OB stars within a distance of 2.5 kpc with the most superior sample of reddening curves currently accessible 1 . These stars have undergone precise spectral classifications through high-resolution spectroscopy with UVES 6 at resolving power λ/Δλ ~ 75,000) and their accurate distances have been obtained using the unprecedented precision of the GAIA 7 parallax at σ < 0.1mas. For many stars, our investigation uncovers a substantial inconsistency between both classical derivations of stellar distances. The paradox in the distance estimates remained undetected until now and its detection required the unprecedented resolution of the GAIA data release three 7 . By introducing the photometric equation nearly 100 years ago it was speculated that an additional non-selective or grey extinction term in the form of very large grains – at that time called 'meteoritic' bodies – might exist 8 . For a few stars it was hypothesized 9,10 that incorporating such an additional dust component could reconcile the disparity between distance estimates; however, this remained unverified due to the lack of a physical dust model. To reconcile the observed discrepancy, we introduce a new method to determine the visual extinction. It considers both the influence of micron-sized grains as a new population in the ISM and the distance provided by GAIA as a so far unused constraint in dust models. The sample The reddening curves were scrutinized by excluding stars with composite spectra in the IUE 11,12 /FUSE 13 aperture due to multiple bright stellar systems, inconsistent parallaxes between data releases two 14 and three 7 from Gaia, uncertain spectral type designations or photometric variability. In addition, the current investigation requires precise absolute stellar brightness Mv. Therefore, we dropped three Be stars due to possible variability. Another three stars with peculiarities in their reddening curves were also omitted decreasing the total number of the sample to 47 stars. To compensate for the binarity of five stars 15–19 we added the absolute brightness of the corresponding two components. Dark dust model Our study utilizes a dust model that aligns with current observational constraints of dust in the diffuse ISM of the Milky Way. It accounts for representative solid-phase element abundances and explains accurately phenomena such as wavelength-dependent reddening, extinction, star-light polarization, and the emission of polarized and unpolarized light. In addition, it accounts for the increased submm/mm emission observed by Planck and explains the polarized emission seen by Planck 20 . The model 2 incorporates three dust populations: 1) nanoparticles of graphite, silicate, and polycyclic aromatic hydrocarbon (PAH), 2) sub-micrometre-sized spheroidal grains of amorphous carbon and silicate, using the latest optical constants for amorphous silicates 21 , and 3) micrometre-sized dust particles. The latter dust component, proposed by 10 has been labelled as dark dust. The micrometre-sized grains are primarily composed as a composite of porous amorphous carbon and silicate particles. Micrometre sized grains have been detected in scattering-light haloes around X-ray sources 22,23 from submillimeter emission of evolved giants 24 . They preferentially survive the interaction regions between the asymptotic giant branch and the ISM 25 . Micrometre-sized particles from the diffuse ISM were also measured in situ from the Ulysses, Galileo, and Stardust space probes 26–28 . This hidden dust component appears in sightlines that are connected to the cold ISM 10 . Micrometre sized grains absorb a fraction of the interstellar radiation field, ISRF 29 . Because these grains are large, they are cold and will emit at long wavelengths. Originally very cold (10 K) dust emission was detected in our Galaxy towards high-density regions 30 and in non-active galaxies 31 . Such cold dust was confirmed with ISO 32,33 , and more recently, observed excess emission at 0.5\,mm with Herschel that cannot be explained by a single modified black-body temperature component 34–36 ; these results were confirmed with ALMA 37 and LABOCA 38 at even longer wavelengths. Distance discrepancy We observed a discrepancy between the distances obtained from luminosity and from parallax. In Fig. 1 we show the distance ratios D L /D Gaia vs. D Gaia for our sample. For the same star the luminosity distance D L generally overpredicts the distance D GAIA derived from the GAIA parallax. The luminosity distance is computed using Hipparcos photometry 39 and spectral types from UVES 1 . Absolute magnitudes M V were calculated from our spectral types and the conversion tables 40, 41 . Visual extinctions A V were extracted from published reddening curves 11–13 . A dependency of D L on the spectral types and luminosity classes of the stars is not observed. The (sub)millimetre excess emission observed in the Milky Way has gained explanation only recently. In alternative models, this phenomenon is attributed to the adjustment of grain emissivity at these wavelengths 3,20 . These authors avoid a population of micrometre-sized cold dust. However, these models fail short resolving the distance discrepancy observed in this work towards individual stars (Fig. 1 ). Absolute reddening By analysing the spectral type and luminosity class of a star one finds the absolute magnitude M V and with available photometry, one establishes the reddening E(B-V). We calculate the visual extinction A V necessary to align the luminosity distance precisely with the distance D GAIA derived from GAIA data using the photometric equation: A V = V - M V − 5 log D GAIA + 5. ( 1 ) The optical depth τ V = A V /1.086 is related to the column densities of nanoparticles and submicrometre-sized particles N n and to the column density of the new dust component of micrometre-sized grains N µ , with corresponding mass extinction cross-section K n and K µ (g/cm 3 ) based on the dust model 2 : τ V = N n K n V + N µ K µ V < |E(H)|/1.086. ( 2 ) The extinction cross-section 42–44 diminishes at infinite wavelengths, K(oo) = 0. To prevent negative optical depths, we assume that the reddening at infinite wavelengths is smaller than in the H-band, hence A V = -E(oo) > -E(H). The reddening E(B-V) = 1.086 (τ B - τ V ) provides a second constraint: (τ B - τ V ) = N n (K n B - K n V ) + N µ (K µ B – K µ V ), ( 3 ) These two equations enable us to derive the specific mass of each component, specifically m n =N n / (N n + N µ ) of the nano- and submicrometre grains and m µ =N µ / (N n + N µ ) of the micrometre-sized particles. The normalized reddening curves are converted into absolute reddening by multiplying E(B-V). The extrapolated reddening at infinitely long wavelengths is substituted with the visual extinction A V (Eq. 1). Notably, our approach obviates the requirement for the extrapolated parameter R V = A V / E(B-V) (45) . By adjusting grain sizes and abundances within the three populations, we achieve the best fit for the absolute reddening of each star, surpassing previous models that solely addressed relative reddening or extinction curves. Distance unification The proposed model effectively resolves the distance discrepancy brought here to light utilizing the unprecedented resolution of the GAIA data release three. Recent investigations 46 were still not able to detect any discrepancy within the errors of the GAIA data release two 14 . In this manner, we achieve a consistent estimate of the absolute reddening E( \(\lambda\) -V) going beyond previous models that only discussed normalized reddening E( \(\lambda\) -V) / E(B-V). In Fig. 2 we compute the luminosity distance D L by determining A V from the photometric equation with D GAIA as input. The reliability of our Av estimate (Eq. 1) is confirmed by fitting the absolute reddening curve towards the stars using our dust model, which incorporates micrometre-sized grains (see Online Material). Only for seven sightlines, a satisfactorily fit can be achieved without the new population of micrometre-sized particles. The scatter in our distance ratio (Fig. 2 ) is reduced by a factor 5.5 when compared to the literature values and compensates for the overprediction of previous estimates (Fig. 1 ). Conclusion Our distance analysis for bright stars uncovers a significant discrepancy between parallax and luminosity distance measurements for 79% of the objects. To resolve this distance paradox, we propose a physically consistent dust model incorporating micrometre-sized grains as a new, so far hidden population of dust particles in the general field of the ISM, and an estimate of the visual extinction towards the star derived from the GAIA parallax. By accounting for these aspects, we successfully reconcile the observed disagreement and present a unified approach for stellar distance estimation. This study emphasizes the significance of considering the absolute reddening of individual sightlines when deriving parameters like R V and underscores the necessity for further investigations of large dust particles in stellar distance determination. Dark dust induces a wavelength-independent extinction from the far-UV to the near-infrared which makes it invisible for standard photometric methods to determine interstellar extinction. This new dust component significantly influences various aspects of the grain physics of the ISM. Along with its scattering properties 47,48 , such a dust component in the vicinity of SNIa progenitors will contribute to the broadening of SNIa light curves 4, 49 , which has even implications for our understanding of the quantity of dark energy present in the universe 5 . References Siebenmorgen, R., Smoker, J., Krełowski, J., Gordon, K., Chini, R. Dark Dust III: The high-quality single-cloud reddening curve sample. 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Scicluna, P., Siebenmorgen, R. Extinction and dust properties in a clumpy medium, Astronomy and Astrophysics, 584, A108 (2015). Wang, L. Dust around Type Ia Supernovae, The Astrophysical Journal, 635, L33-L36 (2005). Additional Declarations There is NO Competing Interest. Cite Share Download PDF Status: Under Review Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-3279464","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Physical Sciences - Article","associatedPublications":[],"authors":[{"id":227953930,"identity":"24a0e01d-b6aa-45dc-afc9-8e9bdebe1fc4","order_by":0,"name":"Ralf Siebenmorgen","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAv0lEQVRIiWNgGAWjYFACxgZmEMVPuhbJBlLsAWsxOECscvP+w42PCyruRBsfb3/4gKHinh1B22RuJDYbzzjzLHfbmTPGBgxnipMJapGQYGyT5m07nLvtRg4bkJ2QTNBhEvwH23/z/jucu3n+82dEamFIbGPmbTicu0GCwQykxY6wFonEZukZxw7nzjiTY2yQcCYhgQiHHX/4uaDmcG5/+/GHDz5UJNgT1IIKgFYkNpCoh4GBVFtGwSgYBaNgBAAA72k+kSy78esAAAAASUVORK5CYII=","orcid":"https://orcid.org/0000-0002-9788-672X","institution":"European Southern Observatory","correspondingAuthor":true,"prefix":"","firstName":"Ralf","middleName":"","lastName":"Siebenmorgen","suffix":""},{"id":227953931,"identity":"cbd69392-f16e-4de3-8c4b-2d28f6265309","order_by":1,"name":"Rolf Chini","email":"","orcid":"","institution":"Ruhr University Bochum, Faculty of Physics and Astronomy, Astronomical Institute (AIRUB)","correspondingAuthor":false,"prefix":"","firstName":"Rolf","middleName":"","lastName":"Chini","suffix":""}],"badges":[],"createdAt":"2023-08-20 10:25:33","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-3279464/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-3279464/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":47217720,"identity":"c3590a67-f51b-4ede-a242-4dc9860cf128","added_by":"auto","created_at":"2023-11-28 18:41:40","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":98900,"visible":true,"origin":"","legend":"\u003cp\u003eSee image above for figure legend.\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-3279464/v1/3888a11e1bb48ce9ba348267.png"},{"id":47217721,"identity":"9f85e197-ba93-4b7a-b9af-755fdbcb41d9","added_by":"auto","created_at":"2023-11-28 18:41:40","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":78423,"visible":true,"origin":"","legend":"\u003cp\u003eThe unification of luminosity and parallax distances. Our estimate of the luminosity distances D\u003csub\u003eL\u003c/sub\u003e agrees with the parallax distances D\u003csub\u003eGAIA\u003c/sub\u003e\u003csup\u003e(7)\u003c/sup\u003e for 37 out of 47 stars to better than 1%. The distance ratio D\u003csub\u003eL\u003c/sub\u003e/D\u003csub\u003eGAIA\u003c/sub\u003e ranges between 0.75 and 1.0 and shows a 1 sigma scatter of 6% around a median of 1.\u0026nbsp;Spectral types and luminosity classes are denoted as in Fig. 1.\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-3279464/v1/1c26f7e368cf487813fd582b.png"},{"id":47219235,"identity":"010f19c4-b217-48e8-8f8f-4be566762b26","added_by":"auto","created_at":"2023-11-28 18:49:41","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":323951,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3279464/v1/9554072b-c793-40f1-b276-60c03e3db1ae.pdf"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"The Distance to the Stars","fulltext":[{"header":"Parallax and luminosity distance","content":"\u003cp\u003eThe distance measurement to stars has long intrigued astronomers, prompting the exploration of various estimation techniques. Parallax, based on geometric principles, provides a straightforward approach but is limited to nearby stars whereas luminosity distance D\u003csub\u003eL\u003c/sub\u003e estimates enable the assessment of distances of several kpc. However, the extinction by dust diminishes the apparent brightness of stars and requires a precise determination. We examine 47 prominent OB stars within a distance of 2.5 kpc with the most superior sample of reddening curves currently accessible\u003csup\u003e1\u003c/sup\u003e. These stars have undergone precise spectral classifications through high-resolution spectroscopy with UVES\u003csup\u003e6\u003c/sup\u003e at resolving power λ/Δλ\u0026thinsp;~\u0026thinsp;75,000) and their accurate distances have been obtained using the unprecedented precision of the GAIA\u003csup\u003e7\u003c/sup\u003e parallax at σ\u0026thinsp;\u0026lt;\u0026thinsp;0.1mas. For many stars, our investigation uncovers a substantial inconsistency between both classical derivations of stellar distances. The paradox in the distance estimates remained undetected until now and its detection required the unprecedented resolution of the GAIA data release three\u003csup\u003e7\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eBy introducing the photometric equation nearly 100 years ago it was speculated that an additional non-selective or grey extinction term in the form of very large grains \u0026ndash; at that time called 'meteoritic' bodies \u0026ndash; might exist\u003csup\u003e8\u003c/sup\u003e. For a few stars it was hypothesized\u003csup\u003e9,10\u003c/sup\u003e that incorporating such an additional dust component could reconcile the disparity between distance estimates; however, this remained unverified due to the lack of a physical dust model. To reconcile the observed discrepancy, we introduce a new method to determine the visual extinction. It considers both the influence of micron-sized grains as a new population in the ISM and the distance provided by GAIA as a so far unused constraint in dust models.\u003c/p\u003e"},{"header":"The sample","content":"\u003cp\u003eThe reddening curves were scrutinized by excluding stars with composite spectra in the IUE\u003csup\u003e11,12\u003c/sup\u003e/FUSE\u003csup\u003e13\u003c/sup\u003e aperture due to multiple bright stellar systems, inconsistent parallaxes between data releases two\u003csup\u003e14\u003c/sup\u003e and three\u003csup\u003e7\u003c/sup\u003e from Gaia, uncertain spectral type designations or photometric variability. In addition, the current investigation requires precise absolute stellar brightness Mv. Therefore, we dropped three Be stars due to possible variability. Another three stars with peculiarities in their reddening curves were also omitted decreasing the total number of the sample to 47 stars. To compensate for the binarity of five stars\u003csup\u003e15\u0026ndash;19\u003c/sup\u003e we added the absolute brightness of the corresponding two components.\u003c/p\u003e"},{"header":"Dark dust model","content":"\u003cp\u003eOur study utilizes a dust model that aligns with current observational constraints of dust in the diffuse ISM of the Milky Way. It accounts for representative solid-phase element abundances and explains accurately phenomena such as wavelength-dependent reddening, extinction, star-light polarization, and the emission of polarized and unpolarized light. In addition, it accounts for the increased submm/mm emission observed by Planck and explains the polarized emission seen by Planck\u003csup\u003e20\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eThe model\u003csup\u003e2\u003c/sup\u003e incorporates three dust populations: 1) nanoparticles of graphite, silicate, and polycyclic aromatic hydrocarbon (PAH), 2) sub-micrometre-sized spheroidal grains of amorphous carbon and silicate, using the latest optical constants for amorphous silicates\u003csup\u003e21\u003c/sup\u003e, and 3) micrometre-sized dust particles. The latter dust component, proposed by\u003csup\u003e10\u003c/sup\u003e has been labelled as dark dust. The micrometre-sized grains are primarily composed as a composite of porous amorphous carbon and silicate particles. Micrometre sized grains have been detected in scattering-light haloes around X-ray sources\u003csup\u003e22,23\u003c/sup\u003e from submillimeter emission of evolved giants\u003csup\u003e24\u003c/sup\u003e. They preferentially survive the interaction regions between the asymptotic giant branch and the ISM\u003csup\u003e25\u003c/sup\u003e. Micrometre-sized particles from the diffuse ISM were also measured in situ from the Ulysses, Galileo, and Stardust space probes\u003csup\u003e26\u0026ndash;28\u003c/sup\u003e. This hidden dust component appears in sightlines that are connected to the cold ISM\u003csup\u003e10\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eMicrometre sized grains absorb a fraction of the interstellar radiation field, ISRF\u003csup\u003e29\u003c/sup\u003e. Because these grains are large, they are cold and will emit at long wavelengths. Originally very cold (10 K) dust emission was detected in our Galaxy towards high-density regions\u003csup\u003e30\u003c/sup\u003e and in non-active galaxies\u003csup\u003e31\u003c/sup\u003e. Such cold dust was confirmed with ISO\u003csup\u003e32,33\u003c/sup\u003e, and more recently, observed excess emission at 0.5\\,mm with Herschel that cannot be explained by a single modified black-body temperature component\u003csup\u003e34\u0026ndash;36\u003c/sup\u003e; these results were confirmed with ALMA\u003csup\u003e37\u003c/sup\u003e and LABOCA\u003csup\u003e38\u003c/sup\u003e at even longer wavelengths.\u003c/p\u003e"},{"header":"Distance discrepancy","content":"\u003cp\u003eWe observed a discrepancy between the distances obtained from luminosity and from parallax. In Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e we show the distance ratios D\u003csub\u003eL\u003c/sub\u003e/D\u003csub\u003eGaia\u003c/sub\u003e vs. D\u003csub\u003eGaia\u003c/sub\u003e for our sample. For the same star the luminosity distance D\u003csub\u003eL\u003c/sub\u003e generally overpredicts the distance D\u003csub\u003eGAIA\u003c/sub\u003e derived from the GAIA parallax. The luminosity distance is computed using Hipparcos photometry\u003csup\u003e39\u003c/sup\u003e and spectral types from UVES\u003csup\u003e1\u003c/sup\u003e. Absolute magnitudes M\u003csub\u003eV\u003c/sub\u003e were calculated from our spectral types and the conversion tables\u003csup\u003e40, 41\u003c/sup\u003e. Visual extinctions A\u003csub\u003eV\u003c/sub\u003e were extracted from published reddening curves\u003csup\u003e11\u0026ndash;13\u003c/sup\u003e. A dependency of D\u003csub\u003eL\u003c/sub\u003e on the spectral types and luminosity classes of the stars is not observed.\u003c/p\u003e \u003cp\u003eThe (sub)millimetre excess emission observed in the Milky Way has gained explanation only recently. In alternative models, this phenomenon is attributed to the adjustment of grain emissivity at these wavelengths\u003csup\u003e3,20\u003c/sup\u003e. These authors avoid a population of micrometre-sized cold dust. However, these models fail short resolving the distance discrepancy observed in this work towards individual stars (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"Absolute reddening","content":"\u003cp\u003eBy analysing the spectral type and luminosity class of a star one finds the absolute magnitude M\u003csub\u003eV\u003c/sub\u003e and with available photometry, one establishes the reddening E(B-V). We calculate the visual extinction A\u003csub\u003eV\u003c/sub\u003e necessary to align the luminosity distance precisely with the distance D\u003csub\u003eGAIA\u003c/sub\u003e derived from GAIA data using the photometric equation:\u003c/p\u003e \u003cp\u003eA\u003csub\u003eV\u003c/sub\u003e = V - M\u003csub\u003eV\u003c/sub\u003e \u0026minus;\u0026thinsp;5 log D\u003csub\u003eGAIA\u003c/sub\u003e + 5. (\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e)\u003c/p\u003e \u003cp\u003eThe optical depth τ\u003csub\u003eV\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;A\u003csub\u003eV\u003c/sub\u003e/1.086 is related to the column densities of nanoparticles and submicrometre-sized particles N\u003csup\u003en\u003c/sup\u003e and to the column density of the new dust component of micrometre-sized grains N\u003csup\u003e\u0026micro;\u003c/sup\u003e, with corresponding mass extinction cross-section K\u003csup\u003en\u003c/sup\u003e and K\u003csup\u003e\u0026micro;\u003c/sup\u003e (g/cm\u003csup\u003e3\u003c/sup\u003e) based on the dust model\u003csup\u003e2\u003c/sup\u003e:\u003c/p\u003e \u003cp\u003eτ\u003csub\u003eV\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;N\u003csup\u003en\u003c/sup\u003e K\u003csup\u003en\u003c/sup\u003e\u003csub\u003eV\u003c/sub\u003e + N\u003csup\u003e\u0026micro;\u003c/sup\u003e K\u003csup\u003e\u0026micro;\u003c/sup\u003e\u003csub\u003eV\u003c/sub\u003e \u0026lt; |E(H)|/1.086. (\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e)\u003c/p\u003e \u003cp\u003eThe extinction cross-section\u003csup\u003e42\u0026ndash;44\u003c/sup\u003e diminishes at infinite wavelengths, K(oo)\u0026thinsp;=\u0026thinsp;0. To prevent negative optical depths, we assume that the reddening at infinite wavelengths is smaller than in the H-band, hence A\u003csub\u003eV\u003c/sub\u003e = -E(oo) \u0026gt; -E(H). The reddening E(B-V)\u0026thinsp;=\u0026thinsp;1.086 (τ\u003csub\u003eB\u003c/sub\u003e - τ\u003csub\u003eV\u003c/sub\u003e) provides a second constraint:\u003c/p\u003e \u003cp\u003e(τ\u003csub\u003eB\u003c/sub\u003e - τ\u003csub\u003eV\u003c/sub\u003e)\u0026thinsp;=\u0026thinsp;N\u003csup\u003en\u003c/sup\u003e (K\u003csup\u003en\u003c/sup\u003e\u003csub\u003eB\u003c/sub\u003e - K\u003csup\u003en\u003c/sup\u003e\u003csub\u003eV\u003c/sub\u003e)\u0026thinsp;+\u0026thinsp;N\u003csup\u003e\u0026micro;\u003c/sup\u003e (K\u003csup\u003e\u0026micro;\u003c/sup\u003e\u003csub\u003eB\u003c/sub\u003e \u0026ndash; K\u003csup\u003e\u0026micro;\u003c/sup\u003e\u003csub\u003eV\u003c/sub\u003e), (\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e)\u003c/p\u003e \u003cp\u003eThese two equations enable us to derive the specific mass of each component, specifically m\u003csub\u003en\u003c/sub\u003e=N\u003csup\u003en\u003c/sup\u003e / (N\u003csup\u003en\u003c/sup\u003e \u003csub\u003e+\u003c/sub\u003e N\u003csup\u003e\u0026micro;\u003c/sup\u003e ) of the nano- and submicrometre grains and m\u003csub\u003e\u0026micro;\u003c/sub\u003e=N\u003csup\u003e\u0026micro;\u003c/sup\u003e / (N\u003csup\u003en\u003c/sup\u003e \u003csub\u003e+\u003c/sub\u003e N\u003csup\u003e\u0026micro;\u003c/sup\u003e ) of the micrometre-sized particles.\u003c/p\u003e \u003cp\u003eThe normalized reddening curves are converted into absolute reddening by multiplying E(B-V). The extrapolated reddening at infinitely long wavelengths is substituted with the visual extinction A\u003csub\u003eV\u003c/sub\u003e (Eq.\u0026nbsp;1). Notably, our approach obviates the requirement for the extrapolated parameter R\u003csub\u003eV\u003c/sub\u003e = A\u003csub\u003eV\u003c/sub\u003e / E(B-V) \u003csup\u003e(45)\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eBy adjusting grain sizes and abundances within the three populations, we achieve the best fit for the absolute reddening of each star, surpassing previous models that solely addressed relative reddening or extinction curves.\u003c/p\u003e"},{"header":"Distance unification","content":"\u003cp\u003eThe proposed model effectively resolves the distance discrepancy brought here to light utilizing the unprecedented resolution of the GAIA data release three.\u003c/p\u003e \u003cp\u003eRecent investigations\u003csup\u003e46\u003c/sup\u003e were still not able to detect any discrepancy within the errors of the GAIA data release two\u003csup\u003e14\u003c/sup\u003e. In this manner, we achieve a consistent estimate of the absolute reddening E(\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\lambda\\)\u003c/span\u003e\u003c/span\u003e-V) going beyond previous models that only discussed normalized reddening E(\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\lambda\\)\u003c/span\u003e\u003c/span\u003e-V) / E(B-V).\u003c/p\u003e \u003cp\u003eIn Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e we compute the luminosity distance D\u003csub\u003eL\u003c/sub\u003e by determining A\u003csub\u003eV\u003c/sub\u003e from the photometric equation with D\u003csub\u003eGAIA\u003c/sub\u003e as input. The reliability of our Av estimate (Eq.\u0026nbsp;1) is confirmed by fitting the absolute reddening curve towards the stars using our dust model, which incorporates micrometre-sized grains (see Online Material). Only for seven sightlines, a satisfactorily fit can be achieved without the new population of micrometre-sized particles. The scatter in our distance ratio (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e) is reduced by a factor 5.5 when compared to the literature values and compensates for the overprediction of previous estimates (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"Conclusion","content":"\u003cp\u003eOur distance analysis for bright stars uncovers a significant discrepancy between parallax and luminosity distance measurements for 79% of the objects. To resolve this distance paradox, we propose a physically consistent dust model incorporating micrometre-sized grains as a new, so far hidden population of dust particles in the general field of the ISM, and an estimate of the visual extinction towards the star derived from the GAIA parallax. By accounting for these aspects, we successfully reconcile the observed disagreement and present a unified approach for stellar distance estimation. This study emphasizes the significance of considering the absolute reddening of individual sightlines when deriving parameters like R\u003csub\u003eV\u003c/sub\u003e and underscores the necessity for further investigations of large dust particles in stellar distance determination.\u003c/p\u003e \u003cp\u003eDark dust induces a wavelength-independent extinction from the far-UV to the near-infrared which makes it invisible for standard photometric methods to determine interstellar extinction. This new dust component significantly influences various aspects of the grain physics of the ISM. Along with its scattering properties\u003csup\u003e47,48\u003c/sup\u003e, such a dust component in the vicinity of SNIa progenitors will contribute to the broadening of SNIa light curves \u003csup\u003e4, 49\u003c/sup\u003e, which has even implications for our understanding of the quantity of dark energy present in the universe\u003csup\u003e5\u003c/sup\u003e.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n \u003cli\u003eSiebenmorgen, R., Smoker, J., Krełowski, J., Gordon, K., Chini, R. Dark Dust III: The high-quality single-cloud reddening curve sample. Scrutinizing extinction curves in the Milky Way, arXiv e-prints, arXiv:2307.00367 (2023).\u003c/li\u003e\n \u003cli\u003eSiebenmorgen, R., Dark dust. II. Properties in the general field of the diffuse ISM, Astronomy and Astrophysics, 670, A115 (2023).\u003c/li\u003e\n \u003cli\u003eHensley, B. S., Draine, B. T. 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Galactic Environments, The Astrophysical Journal, 528, 799\u0026ndash;816 (2000).\u003c/li\u003e\n \u003cli\u003eScicluna, P., Siebenmorgen, R. Extinction and dust properties in a clumpy medium, Astronomy and Astrophysics, 584, A108 (2015).\u003c/li\u003e\n \u003cli\u003eWang, L. Dust around Type Ia Supernovae, The Astrophysical Journal, 635, L33-L36 (2005).\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"nature-portfolio","isNatureJournal":true,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"","title":"Nature Portfolio","twitterHandle":"","acdcEnabled":false,"dfaEnabled":false,"editorialSystem":"ejp","reportingPortfolio":"","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-3279464/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3279464/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe vastness of a clear night sky evokes for most people curiosity about the distance to the stars. There are two primary methods for estimating stellar distances – parallax and luminosity. In this study, we present a new analysis revealing a noteworthy discrepancy between these two methods. Due to the accuracy of GAIA, parallaxes can directly be converted into distances. In contrast, luminosity distances require – apart from the determination of apparent and absolute brightness of a star – the reddening value that allows a correction for interstellar extinction. Using 47 stars with non-peculiar reddening curves from the high-quality sample\u003csup\u003e1\u003c/sup\u003e we find here that\u0026nbsp;the luminosity distance overestimates the parallactic distance for most (79%) of these stars.\u0026nbsp;This puzzling discrepancy can only be removed when incorporating a new population of large dust grains – so-called dark dust –\u0026nbsp;with our model\u003csup\u003e2\u003c/sup\u003e that respects contemporary constraints of the interstellar dust\u003csup\u003e3\u003c/sup\u003e and is updated to scope for the first time with the absolute reddening. The model provides a visual extinction which unifies the conflicting distances. Another far-reaching consequence of the flat absorption and scattering properties of dark dust is that it broadens the light curves\u003csup\u003e4\u003c/sup\u003e of SNIa, which serve as a measure of the quantity of dark energy\u003csup\u003e5\u003c/sup\u003e.\u003c/p\u003e","manuscriptTitle":"The Distance to the Stars","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2023-11-28 18:41:35","doi":"10.21203/rs.3.rs-3279464/v1","editorialEvents":[],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"nature-astronomy","isNatureJournal":true,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"natastron","sideBox":"Learn more about [Nature Astronomy](http://www.nature.com/natastron/)","snPcode":"","submissionUrl":"","title":"Nature Astronomy","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"ejp","reportingPortfolio":"Nature Research","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"84488a9b-0801-4812-80cc-390d5d86b6a4","owner":[],"postedDate":"November 28th, 2023","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[{"id":24193437,"name":"Physical sciences/Astronomy and planetary science/Astronomy and astrophysics/Astrophysical dust"},{"id":24193438,"name":"Physical sciences/Astronomy and planetary science/Astronomy and astrophysics/Interstellar medium"}],"tags":[],"updatedAt":"2023-11-28T18:41:35+00:00","versionOfRecord":[],"versionCreatedAt":"2023-11-28 18:41:35","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-3279464","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-3279464","identity":"rs-3279464","version":["v1"]},"buildId":"_2-kVJe1T_tPrBINL-cwx","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}