Interstellar extinction at high galactic latitude from photometric surveys Oleg Malkov Institute of Astronomy Rus. Acad. Sci. (INASAN) Faculty of Physics, Moscow State University malkov@inasan.ru MSA 2017

The task Fundamental scientific problem: investigation of galactic structure and interstellar medium distribution in the Galaxy Current goal: determination of stellar parameters and interstellar extinction value from photometric observations; construction of a 3D Galactic extinction map Data: multicolor photometry (2MASS, SDSS, GALEX, UKIDSS). Method: cross-matching objects in large surveys, simulation of observational photometry, parameterization of stars. MSA 2017

Molecular cloud Barnard 68 Light absorption Molecular cloud Barnard 68 MSA 2017

Absorption and reddening SED is deformed MSA 2017

Previous 3D models demonstrate contradictory results MSA 2017

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Today: large surveys are on hand While previous 3D models, using spectral and photometric data, were based on 104 – 105 stars..... ..... modern surveys (2MASS, DENIS, SDSS, GALEX, UKIDSS, ...) contain photometric (3 to 5 bands) data for 107 – 109 stars. However, one needs to cross-match objects in surveys MSA 2017

Cross-matching: a general problem The aim is to reliably link the same object data in different surveys, having different sky coverage different detection limits different object densities Which one is correct?.. MSA 2017

Cross-matching: finding reliable matches Positional match all objects from one catalogue within given radius from each object of second catalogue Parametric filtering nearby bands = nearby magnitudes similar objects = similar colors Postfactum filtering rejection of outliers after final spectral fitting MSA 2017

Cross-matching: technology Extraction of data for selected fields VO tools: ConeSearch, … Indexing to speed-up spatial queries HTM — Hierarchical Triangular Mesh Matching and filtering Python + ATPy + NumPy Visual checking Topcat, Python + MatplotLib MSA 2017

Surveys for matching DENIS IS NOT USED HERE MSA 2017

Step 1. Parameterization process σ2 = ∑ {[mobs,i – mcalc,i(d, Mi[SpT], Ai[Av])]/Δmobs,i}2 Summation goes over all photometric bands (N=13 at most) Here mobs,i is apparent magnitude from a survey Δmobs,i is its observational error Ai[Av] : Ai=kiAv, interstellar extinction law Mi is absolute magnitude, taken from calibration tables Mi[SpT] mcalc,i = Mi[SpT] + 5log(d) – 5 + Ai[Av] Distance d, spectral type SpT and interstellar extinction Av vary, to minimize σ i=1 MSA 2017

Parameters limits We deal with area located at relatively high galactic latitudes (|b|>45o), consequently: Av is assumed to be within 0.5 mag distance d is assumed to be within 8000 pc Spectral type range (B8-L0) is taken from available calibration tables MSA 2017

Calibration tables Mi[SpT] are taken from Krauss and Hillenbrand 2007, Findeisen et al. 2011. Data available for MS-stars only GALEX (FUN,NUV) photometry is not available for K7 and later spectral types UKIDSS photometry is calculated from 2MASS photometry with relations given by Hodgkin et al. 2009, Eqs (4-8) Interstellar extinction law is taken from (Schlafly and Finkbeiner 2011) and (Yuan et al. 2013) R ≡ Av/EB-V = 3.1 MSA 2017

Excursus: on the limiting distance Z R Hakkila et al. 1997: the maximum distance to which the absorbing material extends: dmax (kpc) = {cos(l)cos(b) + [cos2(l)cos2(b) + 2.114]-2} * 8.5, assuming R = 15 kpc Rastorguev 2016: Z = 3 kpc, R = 20 kpc However, the most distant stars, belonging to our Galaxy (ULAS J0744+25, ULAS J0015+01), are found to be at d > 270 kpc (five times the MW-LMC distance) MSA 2017

An example of σ(d, Av) plot: (l=333,b=+61)-area, object #41, SpT=G0 Matching solution: Av = 0.26 mag, d = 6900 pc MSA 2017

Error budget σAv2 = ∑ (Δmobs,i)2 σlog(d) = 0.2 σAv To calculate errors more correctly, one should take into account also calibration tables errors and relations errors MSA 2017

Step 2. Approximation of Av(d) in a given area by cosecant law (Parenago formula) Cosecant law seems to be a good approximation for such high galactic latitudes: A (d,b) = (a0β/sin|b|) * (1 - e-d*sin|b|/β) d – distance, b – galactic latitude, a0, –magnitude of the absorption per kpc, β – vertical scale of absorbing matter distribution When d → infinity: A (b) → a0β/sin|b| MSA 2017

Area (l=333,b=+61): Av – d All objects/solutions MSA 2017

Area (l=333,b=+61): Av – d All objects/solutions. MS-stars are indicated MSA 2017

Area (l=333,b=+61): Av – d MS-stars only MSA 2017

Area (l=333,b=+61): Av – d MS-stars only. Approximation by cosecant law MSA 2017

Reasons to disregard some objects Original surveys contain various flags: Binary object (2MASS, UKIDSS) Non-stellar/extended object (2MASS, SDSS, GALEX, UKIDSS) Observation of low quality (SDSS) Rough parameterization (based on 2MASS+SDSS photometry, with Covey et al. 2007 tables) shows that there is a high probability for a given star to be a non-MS star (giant or supergiant) Too bright object Large observational error Minimization of σ(d, Av) function produces marginal value for Av (0 or 0.5 mag) or d (0 or 8000 pc) MSA 2017

333, +61 Results for four areas 256, +48 129, -58 301, +62 MSA 2017

Number of objects used In the current study: 4-10 objects per 5’-circle In the previous models: on average 0.0025 objects per 5’-circle MSA 2017

Why we have selected these four areas (actually there were six)? MSA 2017

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Six most distant SNs were taken from Perlmutter et al. 1999 Two of the six areas are not covered by UKIDSS, one of those two is not also covered by SDSS The four remaining are: SN 1997ap (Vir), SN 1996cl (Leo), SN 1996ck (Vir), SN 1995at (Psc) We check the correctness of Av values, used by Perlmutter et al. 1999 Six most distant SNs were taken from Perlmutter et al. 1999 MSA 2017

- Av, interstellar extinction value to SN (Perlmutter et al. 1999) 333, +61 0.17 0.24 256, +48 - Av, interstellar extinction value to SN (Perlmutter et al. 1999) Three of four areas demonstrate an excellent agreement 129, -58 301, +62 0.17 0.09 MSA 2017

Comparison with other maps MSA 2017

Comparison with LAMOST data Axes range is due to SpT range (B8-L0) used in calibration tables LAMOST uses a smaller scale SpT grid than one, used in calibration tables Errors are about 0.1 and 0.3 mag on X- and Y-axes, respectively Left bottom point represents two objects MSA 2017

Possible reasons for disagreement Star is unresolved binary/multiple system Star is variable Star belongs to a marginal luminosity class (sub-giant, white dwarf, sub-dwarf, …) Non-stellar object Non-standard interstellar extinction law in the area (R ≠ 3.1) Non-uniform extinction behavior within the area (a part of the area comprises a cloud) Observational error, misprint in catalogue or cross-matching error MSA 2017

Conclusions The presented method allows us to construct Av(d) relations at least for high galactic latitudes, to approximate them by the cosecant law and estimate (a0, β) parameters. Our results are confirmed by LAMOST data and by interstellar extinction values for SNs, used for the Universe accelerating expansion study (Perlmutter et al. 1999) Results of previous studies (Sharov, 1963; Arenou et al. 1991) contradict our results 2MASS data can be ignored if other three surveys cover the area MSA 2017

Future plans Add modern UV data (UVIT) Verify our results with GAIA DR1/DR2 data Extend calibration tables (M – SpT): to hotter and cooler spectral (temperature) classes to other luminosity classes (III, I, …) to YJHK UKIRT photometry (currently it is re-calculated from 2MASS photometry) Interpolate calibration tables Add other surveys: WISE, DENIS, … Vary R (check R ≠ 3.1) MSA 2017

Acknowledgements Co-authors LAMOST survey staff RFFR 17-52-45076 Audience for your attention MSA 2017