1. Interstellar extinction at high galactic latitude from photometric surveys
Oleg Malkov
Institute of Astronomy Rus. Acad. Sci. (INASAN)
Faculty of Physics, Moscow State University
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2. 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.
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3. Molecular cloud Barnard 68
Light absorption
Molecular cloud Barnard 68
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4. Absorption and reddening
SED is deformed
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5. Previous 3D models demonstrate contradictory results
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6. MSA 2017

7. 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
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8. 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?..
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9. 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
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10. 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
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11. Surveys for matching
DENIS IS NOT USED HERE
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12. 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
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13. 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
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14. Calibration tables
Mi[SpT] are taken from Krauss and Hillenbrand 2007, Findeisen et al 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
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15. Excursus: on the limiting distanceZ 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} * 8.5, assuming R = 15 kpc
Rastorguev 2016: Z = 3 kpc, R = 20 kpc
However, the most distant stars, belonging to our Galaxy (ULAS J , ULAS J ), are found to be at d > 270 kpc (five times the MW-LMC distance)
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16. 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
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17. 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
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18. 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|
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19. Area (l=333,b=+61): Av – d
All objects/solutions
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20. Area (l=333,b=+61): Av – d
All objects/solutions. MS-stars are indicated
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21. Area (l=333,b=+61): Av – d
MS-stars only
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22. Area (l=333,b=+61): Av – d
MS-stars only. Approximation by cosecant law
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23. 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 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)
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24. 333, +61
Results for four areas
256, +48
129, -58
301, +62
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25. Number of objects used
In the current study: 4-10 objects per 5’-circle
In the previous models: on average objects per 5’-circle
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26. Why we have selected these four areas (actually there were six)?
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27. MSA 2017

28. MSA 2017

29. 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
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30. - 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
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31. Comparison with other maps
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32. 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
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33. 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
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34. 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
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35. 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)
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36. Acknowledgements Co-authors LAMOST survey staff RFFR 17-52-45076
Audience for your attention
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