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 .Be c kma n 1,2,3 , J. F o nt 1,2 , M. Que re je ta 1,4 , J.E 1. I 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, .
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
GHaFaS can be installed on the optical table of 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 of a galaxy which fits within its field of 3.4x3.4 arcsec 2 , with seeing limited angular resolution (~1-1.5 arcsec) and velocity resolution of ~7 km s-1 in a period of 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.
(c) (d) (b) From a GH α FaS map of thevelocity field of NGC 5427 (part of Arp 271, the other, lower galaxy is NGC 5426) we found velocity and density (e) jumps across feathered structures perpendicular to the spiral arms (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). (a)
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.
I NT RODUCT I ON: Dynamic al Re so nanc e s - Re so na nc e s: Co nse q ue nc e o f Spir al De nsity Wave T he or y INNER LINDBLAD RESONANCE (ILR) Ω * = Ω P + κ /2 COROTATION Ω * = Ω P OUTER LINDBLAD RESONANCE (OLR) Ω * = Ω P - κ /2 - 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 out, 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.
I NT RODUCT I ON: Patte rn spe e d me asure me nts Me tho d Re quir e me nts 1 . T 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. 2 . Ca nzia n 2D ve lo c ity ma p with wide c o ve r (e .g . VL A 21c m) L o 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.
The basis for our novel technique for finding resonances, starting with the output of a Fabry-Perot scanning spectrometer: a high resolution (spatial and velocity) 2D map of the velocity field of a complete galaxy. 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 off the circular velocity map (lower left) from the measured velocity field (upper right). We use these residual velocity maps for our resonance analysis
Our me tho d to lo c a te re so na nc e s(F o nt, Be c kma n, Que re je ta e t a l. (2014) ume nts: GHαSP . Ob se rva to ire de Ha ute Pro ve nc e . F a br y- Pe r ot Instr GHα F a S . Willia m He rsc he l T e le sc o pe , L a Pa lma . First map all the zeros of non-circular velocity across face Inte nsity Ve l. fie ld Ro t. c urve No n-c irc . ve l of galaxy Co ro ta tio n (31 ± 4 ) ” Alo ng the slit, id e ntify tho se ze ro s whe re the re a re c hange s in sign ve loc ity with a n of non- c ir c ular a mplitud e a t le a st twic e the Pla c e a me a sure me nt unc e rta intie s ra dia l slit Co nstruc t Histo g ra m o f numb e r o f sig n c ha ng e s a s a e lliptic a l a nnuli func tio n o f g a la c to c e ntric ra d ius [ ” ] This method eliminates false zeros of E xample : NGC 753 de l Río & Ce pa (1998, 1999) various kinds otation at 30 ” c or
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 our 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 other methods. The comparison was encouraging..
Co mpa riso n to the L ite ra ture Studies based on Velocity fields Numerical morphology (TW, Canzian…) simulations CR ✔ NGC 753 CR ✔ ILR ✔ CR ✔ NGC 1530 CR ✘ CR ✔ NGC 2336 CR ✔ ILR,OLR ✘ ILR ✔ NGC 3504 ILR ✘ CR ✔ NGC 3344 CR ✔ CR ✔ NGC 3893 ILR ✔ NGC 5055 CR ✔ ILR,OLR... ✔ NGC 6946 ILR ✘ CR,OLR ✔ NGC 7217 CR ✔ CR ✔ NGC 7479
Re sults e sonanc e s we fo und: fro m ro ta tio n c urve a nd κ 2 = 4Ω 2 { 1+(R/2Ω)dΩ / dR } plo t: Inte r loc king of the r 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 R wo uld fa ll, a nd whe r e IL R/ OL c he c k c o mpa tibility with o the r pe a ks 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. linke d r e sonanc e patte r ns in ove r 70% of the galaxie s!
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.
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