1. Quantification of Bar Strength and the Structure of Galaxies
7/1/2018
Quantification of Bar Strength and the Structure of Galaxies
Ron Buta
University of Alabama

2. Why study bar properties?
7/1/2018
Why study bar properties?
Bars are pervasive among disk galaxies
Bars are common to spirals and S0s
Bars have been linked to a variety of interesting phenomena:
- circumnuclear starbursts
- resonance rings
- active galactic nuclei
- secular evolution and pseudobulge growth
- Bars have cosmological significance

3. Questions - How frequent are bars in disk galaxies?
7/1/2018
Questions
- How frequent are bars in disk galaxies?
- What determines bar strength?
- To what extent are the features seen in barred galaxies dependent on bar strength?
- What is the distribution of bar strengths in disk galaxies?
- What does the distribution tell us about galaxy evolution?

4. 7/1/2018
Hubble 1936

5. 7/1/2018
De Vaucouleurs 1959

6. NGC 1433 NGC 4340 NGC 4596 NGC 4754 NGC 4608 IC 4290 NGC 5850 NGC 5921
7/1/2018
NGC 4340
NGC 4596
NGC 4754
NGC 4608
IC 4290
NGC 1433
NGC 5850
NGC 5921
NGC 1073
NGC 4519
NGC 4027
NGC 4618
The de Vaucouleurs Atlas of Galaxies (Buta, Corwin, & Odewahn 2007): B-band images

7. Bar strength as a continuous property
7/1/2018
Bar strength as a continuous property
NGC SB
NGC 210 SAB
IC 1993 SA

8. Various Samples used to study:
7/1/2018
Various Samples used to study:
- bar strengths in spirals (OSUBGS- Ohio State bright galaxy survey)
- bar strengths in S0 galaxies (NIRS0S- near-IR S0 Survey)
- Fourier properties of bars in context of Athanassoula models
- bulge properties as function of Hubble type

9. OSUBGS Sample characteristics
7/1/2018
OSUBGS Sample characteristics
Buta, Laurikainen, & Salo 2004
OSUBGS consists of typical high luminosity galaxies

10. Frequency of barred galaxies: visual studies
7/1/2018
OSUBGS (Eskridge et al. 2000):
- H-band
- 186 spiral galaxies
- 56 % “strongly-barred”
- 16 % “weakly-barred”
- 27 % “non-barred”
Note: Near-IR imaging does not necessarily change the rankings of bars.
Optical ---> near-IR
SA > SAB, SAB > SB, SB > SB
Also see Knapen et al. 2000; Laurikainen et al. 2004; Menendez-Delmestre et al. 2007; Marinova and Jogee 2007

11. Or declining with increasing z:
7/1/2018
Bar frequency versus redshift: constant to z~1? (Jogee et al. 2004; Elmegreen et al. 2004)
Or declining with increasing z:
At a lookback time of 7Gyr, about 20% of spiral galaxies “matured” enough to form prominent bars.
Most massive galaxies in highest z bin have comparable bar fraction to present day, implying “downsizing” effects.
Sheth et al. 2007: Cosmos 2 square degree sample-Bar fraction declines with increasing redshift

12. What determines bar strength?
7/1/2018
What determines bar strength?
- in a relatively closed system, depends on effectiveness with which a bar can transfer angular momentum to other galactic components, such as the halo (Athanassoula 2003)
- in a relatively open system, external gas accretion and tidal interactions can cause bar growth and destruction (e.g., Bournaud & Combes 2002)

13. Quantifying bar strength: bar ellipticity
7/1/2018
Quantifying bar strength: bar ellipticity
Marinova & Jogee no evidence for bimodality in bar ellipticities
Abraham & Merrifield (2000): Bar ellipticity parameter vs concentration parameter suggest bimodal distribution and rapid evolution between SB and SA, SAB (see Whyte et al for refined analysis).

14. Quantifying bar strength: Relative Fourier Intensity Amplitudes and Bar Contrast A2
7/1/2018
SB( r)a
< A2
A2 is the maximum of relative Fourier amplitude I2/I0.
< A2
SB0

15. Athanassoula Bar Models
7/1/2018
Athanassoula Bar Models
- bar strength determined by transfer of angular momentum to halo
- effectiveness depends on halo properties
-relative Fourier mass profiles distinguish different halo properties
and effects of central mass concentration (CMC)
Massive halo with no CMC
Massive halo with increasing CMC >
Athanassoula, Lambert, & Dehnen 2005

16. Single and double-gaussian Fourier profiles of bars
7/1/2018
Single and double-gaussian Fourier profiles of bars
Buta et al. 2005

17. QT( r) = |FT( r )/F0R( r )|max
7/1/2018
Quantifying Bar Strength: the Gravitational Torque Method (GTM)
- near-IR image
- constant M/L ratio---> gravitational potential
FT=tangential force
F0R=mean radial force
Ratio map: Q(i,j)=FT(i,j)/F0R(i,j)
QT( r) = |FT( r )/F0R( r )|max
Sanders & Tubbs 1980; Combes & Sanders 1981; Quillen Frogel, & Gonzalez 1994; Buta & Block 2001; Laurikainen et al. 2004

18. Bar orbits versus solar system orbits
7/1/2018
Bar orbits versus solar system orbits

19. 7/1/2018
NGC 6951
Ks image
FT/F0R Force ratio map

20. 7/1/2018
Qg=maximum gravitational torque per unit mass per unit square of circular speed
NGC 6951

21. Bars and the Evolution of Galaxies
7/1/2018
Bars and the Evolution of Galaxies
Distribution of bar strengths (Sellwood 2000)
buildup of central mass concentration & bar destruction (Pfenniger & Norman 1990; Shen & Sellwood 2004)
bar destruction & reformation via gas accretion (Bournaud & Combes 2002)
bar regeneration and tidal interactions (Berentzen et al. 2004)
pseudobulge and lens formation (Kormendy & Kennicutt 2004)

22. 7/1/2018
Das et al. (2007, Ap&SS, submitted). Correlations of bar strength estimates with normalized nuclear velocity dispersion, implying bars weaken as their central components get hotter.

23. 7/1/2018
Fourier amplitude A2 correlates with relative radius of m=2 component, implying a bar transfers angular momemtum to other galactic components, and grows stronger and longer relative to disk radius.
Luminosity density in inner regions correlates with relative radius of m=2 component, implying galaxies with higher central densities evolve faster.
Elmegreen et al. (2007, ApJ 670, L97)

24. Bar ellipticity parameter (Whyte et al. 2002) vs Qg.
7/1/2018
Bar ellipticity parameter (Whyte et al. 2002) vs Qg.
Correlations between photometric parameters and type for 216 galaxies
Mean Qg vs Hubble type for spirals
Laurikainen et al. 2007, MNRAS

25. Gravitational Torques in Spiral Galaxies
7/1/2018
Gravitational Torques in Spiral Galaxies
Quantitative dust-penetrated bar classification (Buta & Block 2001)
distribution & type dependence of Qg values for OSUBGS sample (Buta, Laurikainen, & Salo 2004)
active vs nonactive galaxies (Laurikainen, Salo, & Buta 2004)
bar strength and inner ring shape (Buta 2002)
bar/spiral separation and correlations between bar and spiral arm strengths (Buta, Block, & Knapen 2003, Block et al. 2004)

26. Sequence of increasing bar strength (Buta & Block 2001)
7/1/2018
Sequence of increasing bar strength (Buta & Block 2001)

27. Inner ring shape does not correlate with bar strength
7/1/2018
R-band with Qg
H-alpha with (b/a)ring
R-band with Qg
H-alpha with (b/a)ring
Romero-Gomez et al. (2007) show that invariant manifolds related to periodic orbits around unstable Lagrangian points produce inner ring shapes sensitive to bar strength (mass) but not bar ellipticity.

28. 7/1/2018
Grouchy et al. 2008
Star formation rates in rings do not depend much on bar strength or deprojected ring shape.
Open circles=SA, filled circles=SB
< new result showing deprojected inner ring shapes are also not sensitive to bar strength.

29. The Distribution of Maximum Relative Bar Torques in Galaxies
7/1/2018
The Distribution of Maximum Relative Bar Torques in Galaxies

30. 7/1/2018
Bournaud & Combes 2002
- examined impact of external gas accretion on distribution of bar strengths
- competing issues: bar transports gas into center; this builds up central mass concentration, which destroys or weakens bar. Disk heats up and becomes more stable. External gas accretion cools disk, making it susceptible to new bar instability.
- distribution of bar strengths tells relative amount of time galaxies spend in different bar states.
- examine this observationally for statistically well-defined samples of spirals and S0s.

31. With external gas accretion, get bar dissolution and reformation
7/1/2018
With external gas accretion, get bar dissolution and reformation
Without external gas accretion, get only bar dissolution
Bournaud & Combes 2002

32. Distribution of Qg Values: Spirals
7/1/2018
Distribution of Qg Values: Spirals
_____ observed
with gas accretion
……..without gas accretion Qg
Block et al. 2002, with preliminary GTM
Note extended “tail” in distribution
These values are affected by spiral arm torques.

33. Bar/Spiral Separation Buta, Block, & Knapen 2003
7/1/2018
Bar/Spiral Separation Buta, Block, & Knapen 2003
Use Fourier techniques to separate bars and spirals
plots of Im/I0 versus radius r
symmetry assumption
construction of bar+disk and spiral+disk images

34. m=2 and 4 relative intensity amplitudes for NGC 6951 in Ks band
7/1/2018
crosses show “symmetry assumption”

35. Separation for NGC 6951
7/1/2018

36. Qb = bar strength Qs = spiral strength
7/1/2018
Qb = bar strength
Qs = spiral strength
Strong bars, weak spirals: Qb ~ Qg
Strong spirals, weak bars: Qs ~ Qg
NGC 6951

37. 7/1/2018
When spiral arm torques are removed, there are more weak bars >

38. 7/1/2018
Bar-spiral separation for various samples suggests that spirals are generally NOT driven by their associated bars.
Buta et al. (2008)

39. Is this a genuine bar-driven spiral?
7/1/2018
Is this a genuine bar-driven spiral?
Potential-density phase shift distribution for NGC 986
Ks-band image of NGC 986 showing corotation circle
Zhang and Buta 2007

40. Gravitational Torques in S0-Sa Galaxies
7/1/2018
Gravitational Torques in S0-Sa Galaxies
“Near-IR S0 Survey” (NIRS0S, Laurikainen, Buta, Salo, et al.)
Ks band, 2.2 microns
Goal: ~200 S0, S0/a, and Sa in well-defined sample similar to OSUBGS
2D three-component decompositions

41. Deprojected Ks-band images
7/1/2018
NGC 936
NGC 4596
NGC 4608
NGC 4643

42. Force ratio maps for two early-type barred galaxies
7/1/2018
Force ratio maps for two early-type barred galaxies
NGC 4596
NGC 4643

43. 7/1/2018
The distribution of bar strengths in S0 galaxies differs from spirals in lacking an extended “tail” of strongly-barred cases. This is expected if they are not accreting any external gas. Also, S0 bar torques are diluted by significant bulges and larger vertical thicknesses than later type spirals.

44. 7/1/2018
Conclusions
- GTM is a promising way of quantifying bar strength in galaxies
- SA, SAB, SB represent a continuous sequence of increasing bar strength
- Qg, Qb, Qs are well-defined parameters
- distribution of nonaxisymmetry strengths Qg for spirals favors external gas accretion
- distribution of bar strengths for S0s favors no accretion
- bars and spirals may be independent features
- on average, early Hubble types have weaker bars than late Hubble types.
This work was supported by NSF grants AST and AST