SLIDE 1 HIGH RE SOL UT ION 2D VE L OCIT Y F IE L DS IN DISK GAL AXIE S: F E AT HE RS, SPURS, AND INT E RL OCKING RE SONANCE S
AC, T e ne rife , Spain, 2. De pt. Astro físic a, U. L a L ag una, Spain, 3. CSI C,Spain, 4. MPI A, He ide lb e rg , Ge rmany, .
J.E .Be c kma n1,2,3, J. F
- nt1,2, M. Que re je ta 1,4,
SLIDE 2
GHaFaS (Galaxy Ha Fabry-Perot Spectrometer) Gafas in Spanish means spectacles
GHaFaS is an approved visitor instrument on the 4.2m William Herschel Telescope, La Palma aided by the astronomer support group of the Instituto de Astrofísica de Canarias
SLIDE 3 GHaFaS can be installed on the optical table
- f the Nasmyth focus of the WHT. It can be
taken out of its crates and set up in one
- morning. In spite of its simplicity it is very
- potent. We can obtain a complete velocity map
- f a galaxy which fits within its field of 3.4x3.4 arcsec2, with seeing limited
angular resolution (~1-1.5 arcsec) and velocity resolution of ~7 km s-1 in a period
- f around 4 hours (some 2 galaxies per night with overheads). The map is like
a 21 cm map: giving surface brightness, velocity, and velocity dispersion.
SLIDE 4
From a GHαFaS map of thevelocity field of NGC 5427 (part of Arp 271, the other, lower galaxy is NGC 5426) we found velocity and density jumps across feathered structures perpendicular to the spiral arms (c) (a) (b) (d) (e) (a ) and (b) are visible light images, (c) shows the pixels with zero radial velocity (see later); this distribution picks out arms and also feathers, almost perpendicular to them. (d) shows the cross-cut to a system of feathers, and the jumps in velocity and density along this path are shown in (e).
SLIDE 5
Interpretation of the density and velocity tracks shown in the previous slide in terms of a model for the formation of feathers by Woong-Tae Kim. We were too ambitious and tried to use the spacing and the amplitude of the observed jumps to try to measure the magnetic field. Woong-Tae asked us to give him a value for the pattern speed and while obtaining our value for this parameter we developed the method I will describe below.
SLIDE 6 I NT RODUCT I ON: Dynamic al Re so nanc e s
COROTATION Ω* = ΩP
INNER LINDBLAD RESONANCE (ILR) Ω* = ΩP + κ/2 OUTER LINDBLAD RESONANCE (OLR) Ω* = ΩP - κ/2
- Re so na nc e s: Co nse q ue nc e o f Spir
al De nsity Wave T he or y
- Multiple pa tte rn spe e ds (Se llwo o d & Sparke ’ 88; Rautiaine n & Salo ’ 99, Me idt+ ’ 08)
- Ba r c o ro t. Ba r le ng th: implic a tio ns fo r da rk ma tte r ha lo
In barred galaxies the earliest predictions, based purely on stellar dynamics, suggested that the bar (formed via the “bar instability”) drives the density wave system, in such a way that the pattern speed should be the angular velocity of the stars at the tip of the bar, i.e. the tip of the bar should be at corotation.Later simulations, incorporating gas and star formation put corotation a bit further
- ut, at some 1.2 times the bar length. More recently, as “·live” dark matter haloswere incorporated into
dynamical models, the halo was predicted to act as along-term brake on the bar, slowing it down so that its pattern speed is reduced and corotation moves to larger radii. These models suggested that present day bars should be “slow” so that corotation should always be at radii >1.4 times the bar length.
SLIDE 7 I NT RODUCT I ON: Patte rn spe e d me asure me nts
Me tho d Re quir e me nts
re ma ine -We inb e rg 2D ve lo c ity me a sure me nts, pre fe ra b ly ste lla r line s, plus ma p o f ste lla r c o ntinuum e missio n.
F inds c o ro ta tio n using the ve lo c ity fie ld lumino sity-we ig hte d b y a c o ntinuum c o mpo ne nt. Ne e ds hig h re so lutio n lo ng -slit. T ime -c o nsuming . So fa r o n ~20 g a la xie s.
2D ve lo c ity ma p with wide c o ve r (e .g . VL A 21c m)
L
- o ks fo r a c ha ng e in symme try fro m two fo ld to thre e fo ld a t the c o ro ta tio n ra dius. E
le g a nt b ut in pra c tic e a pplic a b le to ve ry fe w g a la xie s. Co ro ta tio n ra dius no t ve ry we ll de fine d, a t le a st in the o rig ina l 21 c m a pplic a tio n o f the me tho d
- 3. Dire c t simula tio ns
Ba ryo n-do mina te d inne r ste lla r po te ntia l (fro m b ro a d -b a nd o ptic a l ima g ing + g a s ve lo c ity)
Applie d b y a numb e r o f a utho rs to so me 40 o b je c ts.
- 4. Po te ntia l pha se -shift
Re q uire s dust-fre e (i.e . I R) mo rpho lo g y
Buta & Zha ng (2009): 150+ g a la xie s. Mo re tha n o ne c o ro ta tio n ra dius. No e rro r b a rs.
SLIDE 8 An example, using the strongly barred galaxy NGC 1530, of how we handle the observations, in order to obtain the required residual velocity field. Upper left. Integrated Ha emission produced by summing the line map over velocity Upper right the velocity field , produced using the peak velocity of the complete set of emission lines across the disk Lower left. Map of the circular velocity component, obtained by rotating the velocity curve of the galaxy about its axis Lower right. Map of the residual non- circular velocity field, obtained by subtracting
- ff the circular velocity map (lower left)
from the measured velocity field (upper right). We use these residual velocity maps for
The basis for our novel technique for finding resonances, starting with the output
- f a Fabry-Perot scanning spectrometer: a
high resolution (spatial and velocity) 2D map
- f the velocity field of a complete galaxy.
SLIDE 9 Our me tho d to lo c a te re so na nc e s(F
- nt, Be c kma n, Que re je ta e t a l. (2014)
F a br y- Pe r
ume nts: GHαSP. Ob se rva to ire de Ha ute Pro ve nc e .
GHαF
a S. Willia m He rsc he l T
e le sc o pe , L a Pa lma .
Inte nsity Ve l. fie ld Ro t. c urve No n-c irc . ve l
Co nstruc t e lliptic a l a nnuli Pla c e a ra dia l slit
Alo ng the slit, id e ntify tho se ze ro s whe re the re a re c hange s in sign
c ular ve loc ity with a n
a mplitud e a t le a st twic e the me a sure me nt unc e rta intie s Histo g ra m o f numb e r o f sig n c ha ng e s a s a func tio n o f g a la c to c e ntric ra d ius [”] Co ro ta tio n (31 ± 4 )”
de l Río & Ce pa (1998, 1999)
c or
E xample : NGC 753
First map all the zeros of non-circular velocity across face
This method eliminates false zeros of various kinds
SLIDE 10 The method, by assuring a strong detectable phase change across any valid pixel, eliminates not only noise but also changes of sign due to possible projection effects along curved arm structures
We applied this technique to a set of 104 galaxies for which we had complete Ha velocity fields, some from the GHASP Fabry-Perot others from GHaFaS. To our surprise, and initial worry, we found that the histograms for all the galaxies showed multiple peaks, ranging up to 7, with a mode of 4. Initially we were not sure whether to assign all the peaks to corotations. Later
- ur simulations programme helped us to make valid assignations (I will deal
with this point in a few minutes). The first step was to compare our results with those of the literature obtained using
- ther methods. The comparison was encouraging..
SLIDE 11
Co mpa riso n to the L ite ra ture
Studies based on morphology Velocity fields (TW, Canzian…) Numerical simulations
NGC 753 CR ✔ NGC 1530 CR ✔ ILR ✔ CR ✔ NGC 2336 CR ✘ CR ✔ NGC 3504 CR ✔ ILR,OLR ✘ ILR ✔ NGC 3344 ILR ✘ CR ✔ NGC 3893 CR ✔ CR ✔ NGC 5055 ILR ✔ NGC 6946 CR ✔ ILR,OLR... ✔ NGC 7217 ILR ✘ CR,OLR ✔ NGC 7479 CR ✔ CR ✔
SLIDE 12 Re sults
Inte r loc king of the r e sonanc e s we fo und: fro m ro ta tio n c urve a nd κ2 = 4Ω2 { 1+(R/2Ω)dΩ/ dR } plo t:
Ω Ω ± κ/ 4 Ω ±κ/ 2
Assuming e a c h o f the pe a ks is c o ro ta tio n, we c a n pr
e dic t whe r e IL R/ OL R wo uld fa ll, a nd
c he c k c o mpa tibility with
linke d r e sonanc e patte r ns in ove r 70% of the galaxie s!
We find a distinctive rrelation between pairs of corotations CR1 and CR2: The OLR of CR1 falls on CR2, and the inner 4:1 resonance of CR2 falls on
- CR1. This pattern as such was not
really predicted by the modelers.
SLIDE 13
The resonance pattern procedure applied to UGC 11861 A further example of the procedure, this time for a galaxy which has yielded a histogram with 5 peaks. We find the pattern of linked resonances explained for the previous object between the innermost corotation peak and the fourth peak from the centre. In this case, there is no such pattern connecting the fifth peak outwards with any of the other peaks, but it does lie at the OLR corresponding to the third corotation peak. We conclude that peak five is just an OLR, and not a corotation. There are a number of cases like this Which have allowed us to identify OLR´s and occasionally ILR´s at the radii of the histogram peaks, but they are a minority of cases.
SLIDE 14 As a check on whether our a maximum in the number of phase changes (zero crossings in the non-circular velocity field) is really giving us the corotation radius we used a model to simulate the velocity field of a disc galaxy, and to derive the relevant parameters, which we could compare qualitatively with our observational results. Left panel. Velocity field derived from our numerical model, projected as if
Right panel. Residual velocity field of the model galaxy, found by subtracting off the 2D rotational velocity field from the complete field.
The results of our model fits can be seen in the above diagrams. They show: (a) The peaks are found, and indeed occur at corotation. A much smaller peak is also found at the ILR, and a very small peak is found at the OLR. We have used these results in
- ur article (submitted!) to select a a small
subset of the peaks as showing ILR´s. (b) We can assign error bars to the corotation radii if we know the measurement errors in the centre position, the position angle, and the inclination angle. In practice the measurement uncertainties for the 2D velocity maps obtained using an FP are acceptably small, leading to errors in corotation of order 10%.
SLIDE 15 Using literature data
HI, 21 cm,(a complete VLA velocity map) we could show that the resonance peaks found In Ha lie at the same radii as those found in
thatthe technique using Hα gave much better spatial resolution. However the method is applicable in principle using any ISM gas emitter, e.g. CO or HI.
Velocity field maps for M100 (NGC 4321). These are produced by subtracting off the rotation curve (rotated through 180º) from the observed velocity map. The maps show the residual velocity field. Map (c) is from our Hα observations with GHαFaS, Map (d) is from equivalent observations in HI, 21cm, with the VLA, clearly at lower angular resolution.
- Fig. (a) shows the radial plot of the zero crossings in non-circular velocity with Ha
- Fig. (b) shows the equivalent in HI. Peaks are assigned to corotation radii.
SLIDE 16
This is the first part of the table presenting the resonance radii for our sample of 104 galaxies. In bold face are the peaks which we have identified as either ILR´s or OLR´s only; the remaining peaks are corotations, often coincident with the ILR´s the OLR´s or the 4:1 (ultraharmonic) resonances of other corotations. SUPERSCRIPTS (1, 2 etc) SHOW RESONANCES LINKED IN THE PATTERN CR- OLR- I4:1 DESCRIBED IN THIS TALK, FOUND IN OVER 70% OF ALL THE GALAXIES (IN ONE THIRD OF THESE MORE THAN ONCE!)
SLIDE 17
This is the first part of the table showing the pattern speeds associated with each determined corotation radius. It is interesting that the concept of a pattern speed, which has been recently extended to cover multiple resonances, does a useful job in defining annular behaviour of the gas in the disc
SLIDE 18 Left panel. Histogram showing the number of peaks in the plot of the observed frequency of the phase changes in radial velocity measured on the residual velocity maps of the galaxies in the
- sample. We assign almost all of these to corotation radii detected in the gas component, apart
from a specific few which mark Inner or Outer Lindblad Resonances.. Right panel. Histogram showing the frequency with which we detect the pattern of interaction between two of the resonances (the Outer Lindblad resonance of the internal corotation coincides with the external corotation, while the Inner 4:1 resonance of the external corotation coincides with the internal corotation) in a given galaxy of the sample. Note that the number of non- detections is certainly an upper limit, since we cannot measure the residual velocities adequately if the galaxy is close to edge-on or close to face-on. Note that the pattern occurs more than once in almost one third of the galaxies in the sample.
SLIDE 19 Application of the technique to double barrred galaxies. Are the pattern speeds different? ..Yes! (Every time, so decoupled systems). What are the ratios of the two pattern speeds? (see table below) First column. Maps of the residual velocity across the face
- f the galaxies observed, produced by subtracting off a 2D
projection of the rotation curve from the original velocity map after performing the iterative procedure to optimize the circular and radial velocity components. Second column. Histograms of the radial distribution of the measured phase reversals obtained using the residual velocity maps. Third column. Projected circles corresponding to the peaks in the number of phase reversals, projected into the planes
- f the galaxy disks, showing how the peaks relate to
morphological structure, and which peaks can be taken as bar corotations (in red ). A key general result: The ratios of the corotation radii to the bar lengths for the main bars are of order 1-1.4 (“fast” bars) but the ratios of the corotation radii to the bar lengths for the inner bars are of order 2-2.5 (“slow” bars). The latter is a predicted result.
SLIDE 20
The striking result here is that the ratio of the pattern speeds is invariant, even though there are major differences between the values of the individual pattern speeds among this set of galaxies
SLIDE 21 CONCLUSIONS
- 1. We have devised a new method for determining the radial locations of resonances in disc galaxies
based on a straightforward application of linear density wave theory
- 2. We have shown, using simulations, that the method should allow us to detect and locate the resonance radii.
It should respond most strongly to the presence of corotations, and more weakly to the presence of ILR´s and OLR´s.
- 3. The method is particularly suited to the use of emission line maps of whole galaxies at high spatial and
velocity resolutions. We have used it with Hα data cubes from Fabry-Perot interferometric maps, but it should be practical to use with maps in HI or CO at sufficiently high spatial resolution.
- 4. Applying it to 104 galaxies using data from the GHASP and GHαFaS systems, we find multiple resonances
in all of them with corotations ranging in number up to 7 in a single galaxy. The mode value is 4. 5.We find a pattern of linked resonance between pairs of corotations, CR1 and CR2, such that the OLR of CR1 coincides with CR2 , and the inner 4:1 ultraharmonic resonance of CR2 coincides with CR1. This pattern has been partly, but not fully predicted. The pattern occurs in over 70% of the galaxies. It occurs more than
- nce in ~one third of these, and 4 times in a specific object!
- 6. The ratio of the radius of corotation associated with a bar, to the bar length, has a mean value of 1.3, with a
slight trend to larger values in later-type galaxies. Thus bars are generally “fast”.
- 7. The ratio of the corotation radius to the bar length for the inner (“nuclear”) has a mean value of 2.25; these
bars are, as predicted, “slow”
- 8. The ratio of the pattern speeds of the two bars in double-barred galaxies is close to 3.5 even though there is
considerable varation in the bar length ratios (this sample is still quite small!)
SLIDE 22
END .
Thank you all for your attention!
QUESTIONS?
