1. 1 High-z galaxy masses from spectroastrometry Alessio Gnerucci Department of Physics and Astronomy University of Florence 13/12/2009- Obergurgl Collaborators: A. Marconi, R. Maiolino, F. Mannucci, G. Cresci and many others High-z galaxy masses from spectroastrometry Galaxy dynamical masses at high redshift set important constraints on galaxy formation and evolutionary models. However, the principal limitations for measuring dynamical masses for z>2 galaxies are given by the low S/N ratio and the poor spatial resolution achievable even with AO assisted observations. Virial mass estimates are difficult because the galaxy continuum emission is rarely detectable and the galaxy size cannot be reliably estimated. In this talk I will present an improved virial mass estimator based on spectroastrometry. When detecting the shift between the photocenters of the red and blue side of emission lines, it is possible to obtain a "kinematical" estimate of the galaxy size which is then used to obtain a virial mass. Taking advantage of the dynamical masses we have measured accurately for a sample of galaxies at z~3 from the AMAZE project, we will assess the reliability and accuracy of these improved virial mass estimates, and we will apply that to galaxies for which the standard kinematical analysis is not feasible. Although based on SINFONI data, this method is instrument-independent and indeed has been used many times by radio and submm astronomers.

2. 2 High redshift galaxies dynamics and masses Galaxies formation ad cosmological evolution Structures formation Dark matter Star formation history Many theoretical models that need to be constrained with data. Dynamics is directly related to the models of galaxy formation and it is the most direct way to probe the content of dark matter. Dynamical studies are important for assessing the cases of mergers, rotating disk or turbulence dominated object. 3D spectroscopy is a key technique for these studies. In literature there are few dynamical studies of high-z galaxies ( z~2: Genzel+06,08, Forster-Schreiber+06,09, Cresci+09, Erb+06 ) ( z>2.5: Nesvabda+06,07,08, Jones+09, Law+09, Lemoine-Busserolle+09,Swimbank+07,09 ) importanza degli ifu data above z~3 the model predictions diverge significantly Dynamics is directly related to the models of galaxy formation and it is the most direct way to probe the content of dark matter. 3D spectroscopy is a key technique for these studies as it allows to derive the full velocity field of the galaxies, without the need to restrict the study to a slit. Forster-Schreiber+09

3. 3 Gas dynamics on z~3 galaxies Gas dynamics from Integral field spectra Projects AMAZE (PI: R.Maiolino) and LSD (PI: F.Mannucci) z~3 galaxies sample deep SINFONI (VLT) Integral field spectra ~ 6 Rotating objects (~21%) ~13 Non rotating objects (~47%) ~9 Unresolved objects (~32%) AMAZE sample: 28 objects

4. 4 Gas dynamics on z~3 galaxies Dynamical modeling LINE OF NODES LINE OF SIGTH SKY PLANE DISK AXIS i DISK PLANE Model (Marconi et al. 2006, Cresci et al. 2009) Rotating thin disk. Mass distribution modeled as “exponential disk”. Instrumental effects (beam smearing, pixel size, spectral resolution).

5. 5 Gas dynamics on z~3 galaxies Some examples of the fit for the rotating objects

6. 6 Gas dynamics on z~3 galaxies In the case of unresolved objects it is not possible to perform the dynamical modeling.

7. 7 Virial mass estimates Virial Theorem Characteristic radius estimated as half light radius of the continuum (or line) emission (corrected for beam smearing) Vc FWHM Wavelength Intensity Integrated source spectrum V_{circ}(r)=\sqrt{\frac{GM(r)}{r}} V_{circ}(r)\equiv FWHM M(r_e)=f \frac{r_e V^2_{circ}}{G} M(r_e)=f \frac{r_e^{sp} FWHM^2}{G} (corrected for instrumental response)

8. 8 log\left[\frac{M_{dyn}sin^2i}{M_{\odot}}\right]=log(f)+log\left(\frac{r_e FWHM^2}{G}\right) M_{dyn}=f'\ M^{sp} log(f)=-0.16\pm 0.08 0.16301439 +- 0.076925067 vir M_{dyn}sin^2i=0.7^{+0.1}_{-0.1}\ \frac{r_e V^2_{circ}}{G}M_{\odot} Virial mass estimates

9. 9 Wavelength Position along the slit Fixed slit position 1D image Fixed wavelength (velocity) 1D image Wavelength centroid Position centroid Rotation curve Spectroastrometric curve A. Gnerucci, A. Marconi et al.: Spectroastrometry of rotating gas disks and the detection of supermassive black holes in galactic nuclei. (A&A accepted) Spectroastrometry in principle

10. 10 Spectroastrometry in principle Wavelength Y direction X direction Integral field spectrum Fixed wavelength 2D image Image: Stephen Todd (ROE) and Douglas Pierce-Price (JAC)

11. 11 Overcoming the spatial resolution D HWHM PSF SLIT Two unresolved point sources Position along the slit Intensity SLIT HWHM PSF D V1 V2 It is possible to get the centroid position with an accuracy better than the PSF FWHM D Position along the slit Intensity

12. 12 Spectroastrometry and virial mass estimates “Classical” virial mass estimator Characteristic radius estimated as half light radius of the continuum (or line) emission D (Xr,Yr) (Xb,Yb) Vc FWHM Wavelength Intensity Integrated source spectrum Velocity map V_{circ}(r)=\sqrt{\frac{GM(r)}{r}} V_{circ}(r)\equiv FWHM M(r_e)=f \frac{r_e V^2_{circ}}{G} M(r_e)=f \frac{r_e^{sp} FWHM^2}{G} “Spectroastrometric” virial mass estimator Blue side Red side

13. 13 Spectroastrometric mass estimator Blue image Red image M^{sp}=\frac{r_e^{sp} \sigma^2}{G} M(r_e^{sp})=f\ M^{sp} M_{dyn}=f’\ M^{sp} M^{sp}=\frac{r_e^{sp} \sigma^2}{G} M(r_e^{sp})=f\ M^{sp} M_{dyn}=f’\ M^{sp} PSF size ~0.6”(FWHM) pixel size ~0.125”

14. 14 Calibration of the mass estimator log\left[\frac{M_{dyn}sin^2i}{M_{\odot}}\right]=log(f’’)+log(M^{sp}) M_{dyn}=f'\ M^{sp} log(f'')=-0.82\pm 0.05 -1.0950514 +- 0.073154733 vir M_{dyn}sin^2i=6.6^{+0.8}_{-0.7}\ M^{sp}

15. 15 stesso discorso con le masse viriali classiche log\left[\frac{M_{dyn}sin^2i}{M_{\odot}}\right]=log(f’’)+log(M^{sp}) M_{dyn}=f'\ M^{sp} log(f'')=-0.90\pm 0.05 - 0.89780255 +- 0.049442287 M_{dyn}sin^2i=7.9^{+1.0}_{-0.9}\ \frac{r_e V^2_{circ}}{G}M_{\odot} This method is instrument-independent, it needs only the “cube” data format. Useful with ALMA!

16. 16 We study the gas kinematics of the AMAZE and LSD objects from VLT SINFONI data. For a subsample of “rotating” objects we perform a complete dynamical modeling. We introduce the spectroastrometry technique and observe that the power of spectroastrometry is the capability to overcome the spatial resolution. We use of spectroastrometry to improve the virial mass estimate. We calibrate the spectroastrometric mass estimator using dynamical masses for some AMAZE object obtained by complete dynamical modeling, observing a better correlation between fitted dynamical mass and the estimator on respect of classical virial estimate. We introduced an estimator of the dynamical mass of high z galaxies, based on the “spectroastrometric” technique, that can be useful in the cases of poor spatial resolution or signal to noise ratio. This estimator correlate very well with more robust estimates of the dynamic mass. Although based on SINFONI data, this method is instrument-independent and indeed has been used many times by radio and sub-mm astronomers. It can be useful even with ALMA data. Summary and conclusion

17. 17 Gas dynamics on z~3 galaxies Gas turbulence