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The Nearly Perfect Correlationbetween the Diffuse Interstellar Bands
λλ6196.0 and 6613.6
Ben McCallDepartment of Chemistry and Department of Astronomy
University of Illinois at Urbana-Champaign
Collaborators:
Meredith M. Drosback (Virginia), Julie Thorburn Dahlstrom (Carthage College), Don York (Chicago), Scott Friedman (STScI), Lew Hobbs (Yerkes), Brian Rachford (Embry Riddle), Ted Snow (Colorado),
Paule Sonnentrucker (STScI), Dan Welty (Illinois)
Discovery of the DIBs
5780, 5797 seen as unidentified bands Per, Leo (Mary Lea Heger, Lick, 1919)
• Broad (“diffuse”)
• “Stationary” (interstellar)
A Growing Problem
Heg
er 1
919
Mer
rill
& W
ilso
n 19
38
Mer
rill
& W
ilso
n 19
60
Her
big
1966
Her
big
1975
Her
big
1988
Jenn
iske
ns &
Des
ert 1
994
Tua
iris
g et
al.
2000
Hob
bs e
t al.
2008
Hob
bs e
t al.
2009
Greatest unsolved mystery in spectroscopy!
The APO DIB Survey• Apache Point Observatory 3.5-meter• 3,600–10,200 Å ; / ~ 37,500 (8 km/s)• 119 nights, from Jan 1999 to Jan 2003• S/N (@ 5780Å) > 500 for 160 stars (114 reddened)• Measurements & analysis still very much underway
Search for a Common Carrier
• Assumptions:– gas phase molecules– DIBs are vibronic bands– low temperature
• carriers all in v=0
– relative intensities fixed• Franck-Condon factors• independent of T, n
• Method:– look for DIBs with tight
correlations in intensity
• Prospect:– identify vibronic spectrum of
single carrier– spacings may suggest ID X
v=0
Av=0
DIB Correlations
r=0.55 r=0.986
Statistics of Correlations
• 1218 pairs of DIBs observed in >40 stars
• 58 DIBs included• Histogram of r• Few very good
correlations– 19 with r > 0.95
• Most strong DIBs have distinct carriers
Still much work to do, especially on weaker bands!
Example APO DIB Spectra
Correlation
114 SightlinesfH2 = 2.6×10-6 – 0.76EB-V = 0.02 – 3.31
29% O, 68% B, 3% AK I components: 1 – 17
Ordinary Least Squares
• Assume a relationship y=α+βx
• Minimize sum of squared residuals
• Compute Pearson’s correlation coefficient
• α = -5.0±2.2, β = 3.96±0.06
• r = 0.986, r2 = 0.971
• 97.1% of variance in 6613.6 explained by 6196.0
• Problems with least squares:– asymmetric treatment of two variables– ignores any knowledge of uncertainties
Error Estimates
• Statistical errors → easy to calculate from rms of “continuum” nearby
• Systematic errors → larger, harder to quantify– we don’t know the bandshape (limits of integration)– we don’t know the background (continuum)– there could be overlapping transitions
(we know at least one!)– we adopt rms uncertainty in continuum fit
(~10× the statistical errors)
twice the rms continuum shift
Maximum Likelihood Functional Relationship
• Used to compare different analytical techniques
• Equivalent to:– “heteroscedastic errors-in-variables model”– FITEXY from Numerical Recipes
• Assume functional relationship vi = α+βui
– vi, ui “true” values, contaminated by errors → yi, xi
– errors independent, normal, stdev’s σxi & σyi
– minimize the quantity:
MFLR Results• Expect ΣSi
2/(N-2) ~1; we get 3.35
• Chi-square probability function [p-value or Q(χ2|ν)] = 3.9×10-30 !!
• This is the probability that observed sum-of-squares would exceed this value based on chance alone, if underlying model is correct.
• Either not a perfect relationship, or we’ve underestimated our errors.
What if true errors are twice our estimates? ΣSi
2/(N-2) = 0.84, p-value = 0.89perfect linear relationship!
Comparison with Other Correlations
r=0.821
r=0.953(w/o outliers)
CH+ A-X 1-0 R(0)
CH
+ A
-X 0
-0 R
(0)
r=0.985
Two Possibilities
A
B
CGal
azut
dino
v et
al.
A&
A 3
84, 2
15 (
2002
) Ueda &
Shimanouchi
JMS 28, 350 (1968)
• λλ6196.0 and 6613.6 have the same carrier– first ID of two DIBs from same molecule– ratio of Franck-Condon factors ~1:4– excited state vibrational spacing 1018.9 cm-1 – search for other (weak) DIBs from this carrier!– need to explain differences in width & shape
• λλ6196.0 and 6613.6 don’t share a carrier– two molecules are amazingly well correlated– best correlation ever between molecules– what kind of chemical pathways can maintain
abundance ratio so constant, over such a wide range of conditions?
Future Work Needed
1) More thorough investigation of potential error sources → better estimates of uncertainties?
2) Search for some parameter that correlates with residuals → clues to interfering lines?
3) Observations with higher S/N, resolving power → help resolve interfering lines
4) Theoretical explanation of how two vibronic bands could (or could not) produce such different profiles → plausibility/disproof of conclusion of common carrier
http://dibdata.org
• Reasonable correlation with dust extinction– but “level off” at high AV → diffuse clouds only?
– for a long time, solid state carriers favored
• Several characteristics argue against dust:– constancy of – lack of emission– fine structure!
• Present consensus:– gas-phase molecules– probably large– likely carbon-based– reservoir of organic material
• Greatest unsolved mystery in spectroscopy!
What are the DIBs?
Sarre et al., MNRAS 277, L41 (1995)
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