1. Shu Wang and Biwei Jiang
Beijing Normal University
Department of Astronomy
Universality of the Near-Infrared Extinction Law Based on the APOGEE Survey
Shu Wang and Biwei Jiang
(Department of Astronomy, Beijing Normal University)
Wang & Jiang 2014 ApJL 788, L12

2. Outline Background Intrinsic colors of K-type giants
I will discuss from these three aspects.
Background
The Near-infrared interstellar extinction
Intrinsic colors of K-type giants
APOGEE project
Teff – Color Relation
The Red Clump Stars
The Near-Infrared Extinction Law
Color Excess Ratio
Dependence of E(J-H)/E(J-KS) on E(J-KS)
Discussion
compare with previous work and model results
Summary

3. The Near-Infrared Interstellar Extinction
Near-IR
α ≈1.61 (Rieke & Lebofsky 1985)
α ≈ 1.70 (Whittet 1988), α ≈ 1.75 (Draine 1989)
α ≈ 1.8 (Martin & Whittet 1990; Whittet et al. 1993)
The infrared extinction law is dependent on wavelength and interstellar environments.
The figure shows the infrared relative extinction A_lambda to A_Ks varies with lambda:
The near-infrared extinction appears to be an approximately uniform power law. The index is between 1.6 and 1.8. For example
β ≈ 1.61 (Rieke & Lebofsky 1985), 1.70 (Whittet 1988), 1.75 (Draine et al. 1989b), 1.8 (Martin & Whittet 1990, Whittet et al. 1993).
Recently, Nishiyama et al. (2009)explored the extinction law toward the Galactic center
(GC), they derived the power-law slope β ≈ 1.99, and Fritz et al. (2011) found β ≈ 2.11.)
Indebetouw et al. (2005): α ≈ 1.65
Nishiyama et al. (2009): α ≈ 1.99

4. Fritz et al. (2011)
Wang et al. 2013

5. Uncertainties in Determining the Power Law Index
Individual stars that are usually very luminous in the infrared
the difficulty in accurately determining the infrared intrinsic colors
uncertainty in determining the spectral type
light variation of red giants
Statistical method that uses a group of stars of the presumably same spectral type
completely relies on the photometric criteria
impurity of the sample
eg. red giants
unavoidably mix with other stars (YSOs, AGBs)
circumstellar dust
The effective wavelength of the filters
Stead & Hoare (2009)

6. Our work Based on APOGEE project Purity K-type giants sample
determination of intrinsic color indexes for individual stars
statistical method to study the near-IR extinction law

7. Data from the APOGEE Project
APOGEE (The Apache Point Observatory Galaxy Evolution Experiment)
a large scale, high-resolution NIR spectroscopic survey of the Galactic stars, one of the four experiments in SDSS-III (Eisenstein et al. 2011)
targeted about 100,000 giants with 2MASS H magnitude down to 13 mag with S/N > (Allende Prieto et al. 2008; Zasowski et al. 2013)
stellar parameters
effective temperature Teff (accuracy of 150K)
surface gravity log g (accuracy of 0.2 dex)
metal abundance Z (accuracy of 0.1 dex)

8. Class
Teff
log g
[M/H] K
3500 to 5000
0 to 5
-2.5 to 0.5 G
4750 to 6500
1 to 5 F
6000 to 10000
2 to 5 A
8000 to 15000
3 to 5
-2.5 to 0.0

9. Locations of sources in galactic plane

10. Teff – Intrinsic Color Relation
Concentrating only on K-type giants improves the reliability of the derived CIs thanks to a relatively narrow range of Teff . To study the extinction,
the K-type giants already penetrate to deep extinction sightlines
with the color excess (CE) EJKS (≡ E(J − KS))∼4.0 (about
24 mag in AV). In comparison, G-type giants trace shallower
extinction (cf. blue dots in Figure 1 with EJKS mostly < 1.5),
and the stellar parameters of late M-type giants have not been
accurately determined for the APOGEE survey partly due to
difficulty in modeling.
Method
similar to that by Ducati et al. (2001)
Teff vs. color (J−H), (H−KS), and (J−KS) diagrams
The bluest stars are considered to have little or no extinction
the blue envelope
a quadratic fitting
The near-IR intrinsic colors can derived
Concentrating only on K-type giants

11. K-type giant stars located in the Galactic plane | b |≤ 5◦
classified as 'K' type in APOGEE
3500K ≤ Teff ≤ 4800K
log g ≤ 3.0
metallicity ＞ -1
photometric quality
J_err ≤ 0.05
H_err ≤ 0.05
Ks_err ≤ 0.05
snr ≥ 100
Sample: 6074 giants
K & G type
3500K-5200K

12. measurement error of the color index
Two factors
measurement error of the color index
Photometric error ~ 0.05 mag
~ 0.1mag error in color index
non-sharp edge
bluest star actually bluer than the true intrinsic color
To compensate for this under-estimation of the color
redward shift
0.02 mag to (J-H)0
0.03 mag to (H-KS)0
consistency between the three color indexes
only two independent at a given Teff
在得到内禀颜色与有效温度关系的时候，我们考虑了两个因素。
测光误差会使最蓝段低于真实的内禀颜色。为了弥补内禀颜色的低估，我们用眼睛判断，认为的移动了拟合线大概0.01, 0.02mag
三个内禀颜色中实际只有两个是独立于有效温度的，所以三个内禀颜色要一致

13. The near-IR intrinsic color indexes for K-type giants

14. Comparison with Previous Results: the Red Clumps Stars
Choosing them from the contour of Teff vs. log g
Standard candle & tracers for IR interstellar extinction
Constant luminosity with small color scattering
RC stars clumpy distribute in H-R diagram 14

15. Absolute magnitude of K band MK -1.54 mag (Groenewegen et al. 2008)
-1.61 mag (Alves 2000)
-1.65mag (Wainscoat et al. 1992)
The (J−KS)0 centers
around (Wainscoat et al. 1992)
0.65± (Girardi et al. 2002)
Our RCs 0.65 ≤ (J−KS)0 ≤ 0.75
Teff =4750±160K (Puzeras et al. 2010)
Our RCs 4550K ≤ Teff ≤ 4800K
Consistency with previous results
0.65 ≤ (J−KS)0 ≤ 0.75, 0.11 ≤ (H−KS)0 ≤ 0.14, 0.52 ≤ (J−H)0 ≤ 0.61

16. The Near-Infrared Extinction Law
The CER depends much less on the filter wavelength than the power law index because the photometry is performed in wide bands.
color excess ratio (CER) as the measure of the NIR extinction law
avoid the uncertainty in the choice of the filter wavelength
effective or isophotal
Compare with previous works
convert a CER to a power law index

17. Color Excess Ratio the color excess ratio for all K-type giant stars
APOGEE Teff → the intrinsic color index
2MASS data → the observed color index
E(J−H), E(H−KS), and E(J−KS) are derived for every sample star
statistical fitting Color excess vs. Color eccess
alleviate the uncertainty of individuals
the intercept between any two CEs
rarely taken into account in previous studies
In previous statistical studies of interstellar extinction,
this constraint is rarely taken into account, very often because
only the slope of the linear fitting of the observed CIs, rather
than the CER itself, is calculated.

18. the lines are forced to pass through (0,0)
Although any one of the three ratios can be taken to be the indicator of the NIR extinction law, the EJH/EJKS ratio is favored because of its large wavelength interval leading to stability against uncertainty. On the other hand, EJH/EHKS is very weak against the error, since EHKS is only about a third of EJKS . This weakness stands out particularly at small EHKS . Nonetheless, this ratio was very often cited as the measure of the NIR extinction law, possibly for its sensitivity to the variation of the NIR extinction power law index.
the lines are forced to pass through (0,0)
three ratios are independently calculated
very good internal consistency

19. Dependence of E(J− H)/E(J− KS) on E(J- KS)
E(J− KS) vs. E(J− H)/E(J− KS) diagram for K-type stars
stars around the red line → no clear systematic tendency
correlation analysis of E(J− H)/E(J− KS) on E(J- KS)
a Pearson correlation coefficient of 0.03 → no relation
0 ≤ E(J − KS) ≤ 1 large dispersions
take into account the error
This work takes the stars from all the fields surveyed by APOGEE with the Galactic longitude 0◦< l < 220◦, and has no bias toward any specific environment. Nonetheless, the magnitude of the CE represents in general the environment because of its proportionality to the density of dust. Therefore, we investigate the variation of the CER EJH/EJKS along the CE EJKS to determine whether the NIR extinction law is universal.
It can be seen that all stars are apparently around the red line. There is no clear systematic tendency toward either an increase or decrease as EJKS changes from very small values representative of diffuse interstellar medium (ISM) to E(J-KS) ∼ 5mag, which is equivalent to a visual extinction of∼30 mag attainable only in dense regions. A correlation analysis results in a Pearson correlation coefficient of 0.03, indicative of no relation between EJH/EJKS and EJKS . On the other hand, the dispersion in EJH/EJKS is apparent and presents a tendency to increase when EJKS gets small. Whether this dispersion is genuine needs to take into account the error.
Red lines: color excess ratio derived from fitting , E(J− H)/E(J− KS) = 0.641

20. Error Analysis
error of the E(J− H)/E(J− KS) originate from that of photometry and Teff
JHKS bands photometry uncertainties ≤ 0.05 mag
average photometric error ∼ 0.02
observed color index error is ∼ 0.04 (< 1% of stars have observed color error ∼ 0.1)
The average error of APOGEE stellar parameter Teff ∼ 100K
Teff → NIR intrinsic color
the errors of (J−H)0, (H− KS)0, (J− KS)0 are 0.05, 0.02, 0.07
the uncertainties of color excess
E(J − H)err∼0.09,
E(H − KS)err∼0.06
E(J − KS)err∼0.11.
The error of the EJH/EJKS values comes from a few contributors.
The primordial errors originate from that of Teff and photometry.

21. calculate under the error propagation theory
The error of the color excess ratio [E(J − H)/E(J − KS)]err dependence on both E(J − H) and E(J − KS)
calculate under the error propagation theory
The error amplitude and its tendency both agree very well with the dispersion of EJH/EJKS in Figure 3(a, upper).
E(J − H)/E(J − KS)=0.641
If a star have E(J − KS)=0.3
[E(J − H)/E(J − KS)]err = 0.38
If a star have E(J − KS)=3
[E(J − H)/E(J − KS)]err = 0.038
At E(J − KS)=0.1
error reaches 1.14
the dispersion can be fully explained by the error

22. Discussion
Calculate the corresponding power law index α and AJ/AKS from the CERs
Adopting the 2MASS effective wavelengths
E(J − H)/E(J − KS) =0.641 ± 0.001, α = 1.95, AJ/AKS = 2.88
E(H − KS)/E(J − KS) = ± 0.001, α = 1.95, AJ/AKS = 2.88

23. Comparison with Previous Results
our result agrees with the average of previous works for different sightlines toward diversified environments
The discrepancy in using different wavelengths of the filters
For a given AJ/AKS=2.88
the unavailable parameters are calculated for previous works using the provided information on CER or the power law index and the α value is re-calculated from CER, as shown inTable 2,where the boldface denotes the values from the reference and the normal font denotes the values we converted using λeff of 2MASS. It can be seen that our result agrees with the average of previous works for different sightlines toward diversified environments. The α value of thiswork, 1.95, is larger than the widely derived values 1.6–1.8 in the 1980s, but agrees with the recent works from this century.
E(J − H)/E(J − KS) =0.641
alpha
AJ/AKS
Filter system
J 1.25， H 1.65， KS 2.15
1.95
2.88
Effective wavelength
J 1.24， H 1.66， KS 2.16
1.65
2.51
Isophotal wavelength
AJ/AKS = 2.88
alpha
Filter system
J 1.25， H 1.65， KS 2.15
1.95
Effective wavelength
J 1.25， H 1.65， KS 2.2
2.15
Johnson system

24. The Effect of Metallicity
E(J − H)/E(J − KS) = 0.64
E(H − KS)/E(J − KS) = 0.36
E(J − H)/E(H − KS) = 1.78
The Effect of Metallicity
LMC NIR extinction Gao et al. (2013)
E(J − H)/E(J − KS) = 0.64 coincides very well
E(J − H)/E(H − KS) = 1.25 is significantly lower
A metal-poor Z < −1.0 sample of 735 giants in the whole APOGEE sky
located in the halo with low extinction E(J − KS) < 1
Results E(J − H)/E(J − KS) = 0.73, E(J − H)/E(H − KS) = 2.03
low extinction
small number of stars
Uncertainy stellar parameters for metal < -1.0 stars in APOGEE
the LMC is not as poor as the sample stars
needs further investigation
Gao et al. (2013) obtained a value of EJH/EHKS = 1.25 for the LMC NIR extinction which agrees well with previous studies but is significantly lower than the Galactic value.
Whether and how the metallicity affects the NIR extinction law needs further investigation.

25. Model Explanations The Weingartner & Draine (2001, WD01) dust model
The Weingartner & Draine (2001, WD01) dust model produces an invariant NIR extinction law when RV changes from 3.1 to 5.5, corresponding to the power law index from 1.62 to 1.60 as shown in Table 2. This can explain the universality of the NIR extinction law even though the change of dust size distribution leads to apparent variation in the optical extinction law. Their results are consistent with ours when using the standard deviations as uncertainties for α. On the other hand, if we assume the dust size distribution conforms to classical power law with an index of 3.5 (Mathis et al. 1977), our model calculation (Wang et al. 2013) yields EJH/EJKS = 0.65 when amax, the maximum cutoff radius of the spherical dust grains, occurs at 0.25μm. This means the dust size distribution of the MRN model better matches our result.
The Weingartner & Draine (2001, WD01) dust model
an invariant NIR extinction law
RV changes from 3.1 to 5.5, alpha from 1.62 to 1.60
This can explain the universality of the NIR extinction law even though the change of dust size distribution leads to apparent variation in the optical extinction law.
assume classical power law dust size distribution with an index of 3.5 (Mathis et al. 1977) and amax = 0.25μm
E(J − H)/E(J − KS) = 0.65
The results are consistent with the MRN dust size distribution

26. Summary Based on the NIR APOGEE project
the relations between the effective temperature and three NIR intrinsic colors
K-type giants with 3500K ≤ Teff ≤ 4800K
the color excess ratio E(J−H)/E(J−KS), represented the NIR extinction law, show no apparent variation.
E(J − H)/E(J − KS)=0.64
E(H − KS)/E(J − KS)=0.36
E(J−H)/E(H−KS)=1.78
The corresponding power law index α = 1.95 and AJ/AKS = 2.88
consisted with MRN dust size distribution

27. Thank you