Precision kinematics Demonstration on Bootes dsph. Sergey Koposov Matt Walker, Vasily Belokurov, Gerry Gilmore, Jorge Pennarubia and others

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1 Precision kinematics Demonstration on Bootes dsph Sergey Koposov Matt Walker, Vasily Belokurov, Gerry Gilmore, Jorge Pennarubia and others

2 Stellar kinematics in dwarfs Dwarfs most dark matter dominated systems. The only way to find the DM mass in dwarf galaxies stellar kinematics (velocity dispersion). The number of dwarfs of given mass test of CDM Dark matter annihilation Radial velocity Diemand et al. (2005)

3 Brief intro on dwarf galaxies By 2000, around 15 dwarf galaxies were known Kinematics high M/L large dark matter masses Grebel(1999) Mateo (1998)

4 Reasons to be interested in the dwarf galaxy kinematics Number of dwarfs can be a check of small scale power spectrum of DM Can be sensitive to the exact nature of DM (CDM, WDM) Moore et al.(1999)

5 Multiple discoveries of new dwarf galaxies Courtesy of Vasily Belokurov Tens new galaxies discovered: Willman et al(2005), Belokurov et al( ), Walsh et al (2007), Irwin et al. (2007), Zucker et al. (2006)

6 Substructure crisis solved? Simon & Geha (2007) Need precise kinematics for mass measurements.

7 Other reasons to be interested in the masses of dwarfs Dark matter annihilation. Need to be sure in the DM mass if you point large satellite at it. Diemand et al. (2005)

8 Problems with dwarf kinematics Dynamical equilibrium (embedded in streams)? Binary stars Underestimated errors Small number of stars (faint) Most effects only increase the observed velocity dispersions main reason to try to measure the velocities precisely.

9 Strangeness of ultra-faints Coleman et al. (2007) Niederste-Ostholt et al. (2009) Kinematic evidence: Willman et al. (2010), Aden et al. (2009), Martin et al. (2010)

10 Problems with dwarf kinematics Dynamical equilibrium (embedded in streams)? Binary stars Underestimated errors Small number of stars (faint) Most effects only increase the observed velocity dispersions main reason to try to measure the velocities precisely.

11 Effect of binaries Binaries effectively smear out the distribution of velocities Binaries studied to some extend in the field in the GCs. Odenkirchen et al. (2002) (see also Minor et al. 2010)

12 Problems with dwarf kinematics Dynamical equilibrium (embedded in streams)? Binary stars Underestimated errors Small number of stars (faint) Most effects only increase the observed velocity dispersions main reason to try to measure the velocities precisely.

13 Simon & Geha (2007) Martin et al. (2007)

14 The general idea of dwarf kinematics

15 Bootes dsph Bootes dsph Discovery: Belokurov et al. (2006) Luminosity: Mv ~ -6.6 Half-light radius ~ 230 pc Distance ~ 66 kpc Belokurov et al (2007) MV Boo Size, [pc] Martin et al.(2007) Belokurov et al (2006)

16 Bootes dsph Deep imaging (courtesy of Sakurako Okamoto). Stellar distribution smooth Stellar population consistent with single old M92-like SP The simplicity of the system seems to be good for kinematics. Okamoto (2010; PhD thesis)

17 Multiple epoch spectroscopy Purposes: Reduce and calibrate errors Assess binarity (radial velocity variability) Assess dynamic equilibrium

18 Previous measurements First measurement: Munoz et al (2006) ~ WYIN data, 1015 member stars. Measured velocity dispersion 6-14 km/s Munoz et al. (2006) Martin et al(2007) Keck data, 30 members. Measured velocity dispersion 6 km/s Martin et al. (2007)

19 Spectroscopy: data VLT GIRAFFE fiber spectrograph Medium resolution mode R~8000, CaT region 120 targets ~20 Observations during one Month period

20 Data demonstration 120 spectra Most visible features belong to sky-lines

21 A little bit of data reduction Data reduction boring, but important. Special care proper error-bars. Error-bar is key for velocity dispersion measurements. i. Check the errorbars produced by latest ESO (giraf-3.8.1) pipeline apparently wrong. Scaling incorrect. We have fixed that. ii. The more interpolation you do, the more correlated noise you introduce. iii. Self calibrate the spectra using sky-lines. Offsets from 1 to 3 km/s were detected and corrected for.

22 Radial velocity determination More or less standard here cross-correlation IRAF routine fxcor Disadvantages: Usually additional interpolation to log(lambda) + fourier filtering Does not provide proper error-bars Not clear how to treat multiple templates Requires continuum subtraction Galaxy kinematics is done by direct spectral fitting istead of cross-correlation for a long time Rix&White(1992); Cappellari&Emsellem(2006); Chilingarian (2007); Koleva et al. (2008)

23 Spectral fitting Fitting analogous to galaxy spectra fitting Koleva et al. (2009) Spectral library: Munari et al. (2010) Spectral resolution: Parameters: -2.5<[Fe/H]<0.5; Teff=3000K K 1<log(g)<5; [α/fe]=0,0.4; Vrot; v Model,i, p j, v =P T i 1 c j P = j 2 i, v, p j = i Model k, i, p j, v Spec k ESpec k 2 We derive probability distribution for radial velocites and best fit templates for each spectra.

24 Results of spectral fitting I show the fitting of the coadded spectra. We determine best fit template + rad. Vel. Estimate. Best fit templates are very different for different stars (e.g. MW dwarfs, Bootes giants, BHBs)

25 Parameters of best fit templates All contamination with [Fe/H]<~-1, log(g)>4 Teff is correlated with color

26 Radial velocity errors We have multiple measurements can compare the scatter with the measured error-bars; check the consistency of error-bars. Conclusions: Our error-bars are correct within 10% level. The precision floor of one exposure is ~ m/s (averaged over multiple exposures 50 m/s) Several stars are clear outliers: repeated fit

27 Stellar variability How to assess it? From Each exposure Probability(RV) (20 exposures) For each star two hypothesis Hypothesis 1: There is intrinsic RV variability. Hypothesis 2: The star is stationary. Derive the bayes factors for these hypothesis relative plausibility of them. Conclusions: Several stars clearly identified as variable.

28 Looking at objects with variable radial velocities Lets look at one particular object RRlyra Phased with the period from Siegel (2006)

29 Binaries or variable stars Short period fluctuation in disk dwarf. Possible Bootes long periodic binaries

30 Binary detectability We have detected radial velocity variability in 10% We can create simple models assuming P(separation), P(eccentricity) P(mass ratios) Vel, km/s What can we say about binary fraction, and how the velocity dispersion can be affected by binaries? Period, yrs

31 Measuring the velocity dispersion Velocities distribution from individual epochs (without combining them) RV distribution for the high probability members and stars with σ(v)<2km/s

32 Best sample All the stars in the sample

33 Conclusions Careful analysis and good data(multiple epochs + VLT GIRAFFE) lead to significantly better precision. Precise measurements lower the velocity dispersion of Bootes down to ~2.5+/-0.7km/s (mass goes down by factor of 4). There maybe a secondary high velocity dispersion component (stream, binaries, non-gaussianity of the velocity distribution) It is hard to correct for the effect of binaries Ultra-faints are tricky systems for kinematics and mass measurements. All the possible systematic effects on velocity dispersions make them higher. Such big difference to previous measurements suggest we should be careful in interpreting results of kinematic analyses.