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)