The Nearly Perfect Correlation
between the Diffuse Interstellar Bands
λλ6196.0 and 6613.6
Ben McCall
Department 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)
Greatest unsolved mystery
in spectroscopy!
Hobbs et al. 2008
Hobbs et al. 2009
Herbig 1988
Jenniskens & Desert 1994
Tuairisg et al. 2000
Herbig 1975
Merrill & Wilson 1960
Herbig 1966
Merrill & Wilson 1938
Heger 1919
A Growing Problem
The APO DIB Survey
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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
A
v=0
• 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
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 Sightlines
fH2 = 2.6×10-6 – 0.76
EB-V = 0.02 – 3.31
29% O, 68% B, 3% A
K I components: 1 – 17
Ordinary Least Squares
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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)
twice (continuum)
the rms continuum shift
– we don’t know the background
– there could be overlapping transitions
(we know at least one!)
– we adopt rms uncertainty in continuum fit
(~10× the statistical errors)
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 ΣSi2/(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-ofsquares 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?
ΣSi2/(N-2) = 0.84, p-value = 0.89
perfect linear relationship!
r=0.821
CH+ A-X 0-0 R(0)
Comparison with Other Correlations
r=0.985
CH+ A-X 1-0 R(0)
r=0.953
(w/o outliers)
Two Possibilities
• λλ6196.0 and 6613.6 have the same carrier
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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
A
– two molecules are amazingly well correlated
– best correlation ever between molecules
B
– what kind of chemical pathways can maintain
abundance ratio so constant, over such a wide
C
range of conditions?
Ueda & Shimanouchi
JMS 28, 350 (1968)
Galazutdinov et al.
A&A 384, 215 (2002)
• λλ6196.0 and 6613.6 don’t share a carrier
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
What are the DIBs?
• 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:
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gas-phase molecules
probably large
likely carbon-based
reservoir of organic material
Sarre et al., MNRAS 277, L41 (1995)
• Greatest unsolved mystery in spectroscopy!