Modeling the gravitational potential of a cosmological dark matter halo with stellar streams

Stellar streams result from the tidal disruption of satellites and star clusters as they orbit a host galaxy, and can be very sensitive probes of the gravitational potential of the host system. We select and study narrow stellar streams formed in a Milky-Way-like dark matter halo of the Aquarius suite of cosmological simulations, to determine if these streams can be used to constrain the present day characteristic parameters of the halo's gravitational potential. We find that orbits integrated in static spherical and triaxial NFW potentials both reproduce the locations and kinematics of the various streams reasonably well. To quantify this further, we determine the best-fit potential parameters by maximizing the amount of clustering of the stream stars in the space of their actions. We show that using our set of Aquarius streams, we recover a mass profile that is consistent with the spherically-averaged dark matter profile of the host halo, although we ignored both triaxiality and time evolution in the fit. This gives us confidence that such methods can be applied to the many streams that will be discovered by the Gaia mission to determine the gravitational potential of our Galaxy.Comment: ApJ sub

Action-space clustering of tidal streams to infer the Galactic potential

We present a new method for constraining the Milky Way halo gravitational potential by simultaneously fitting multiple tidal streams. This method requires full three-dimensional positions and velocities for all stars to be fit, but does not require identification of any specific stream or determination of stream membership for any star. We exploit the principle that the action distribution of stream stars is most clustered when the potential used to calculate the actions is closest to the true potential. Clustering is quantified with the Kullback-Leibler Divergence (KLD), which also provides conditional uncertainties for our parameter estimates. We show, for toy Gaia-like data in a spherical isochrone potential, that maximizing the KLD of the action distribution relative to a smoother distribution recovers the true values of the potential parameters. The precision depends on the observational errors and the number of streams in the sample; using KIII giants as tracers, we measure the enclosed mass at the average radius of the sample stars accurate to 3% and precise to 20-40%. Recovery of the scale radius is precise to 25%, and is biased 50% high by the small galactocentric distance range of stars in our mock sample (1-25 kpc, or about three scale radii, with mean 6.5 kpc). About 15 streams, with at least 100 stars per stream, are needed to obtain upper and lower bounds on the enclosed mass and scale radius when observational errors are taken into account; 20-25 streams are required to stabilize the size of the confidence interval. If radial velocities are provided for stars out to 100 kpc (10 scale radii), all parameters can be determined with 10% accuracy and 20% precision (1.3% accuracy in the case of the enclosed mass), underlining the need for ground-based spectroscopic follow-up to complete the radial velocity catalog for faint halo stars observed by Gaia.Comment: Accepted versio

Building an Acceleration Ladder with Tidal Streams and Pulsar Timing

We analyze stellar streams in action-angle coordinates combined with recent local direct acceleration measurements to provide joint constraints on the potential of our Galaxy. Our stream analysis uses the Kullback-Leibler divergence with a likelihood analysis based on the two-point correlation function. We provide joint constraints from pulsar accelerations and stellar streams for local and global parameters that describe the potential of the Milky Way (MW). Our goal is to build an ``acceleration ladder", where direct acceleration measurements that are currently limited in dynamic range are combined with indirect techniques that can access a much larger volume of the MW. To constrain the MW potential with stellar streams, we consider the Palomar 5, Orphan, Nyx, Helmi and GD1 streams. Of the potential models that we have considered here, the preferred potential for the streams is a two-component Staeckel potential. We also compare the vertical accelerations from stellar streams and pulsar timing, defining a function $f(z) = \alpha_{1pulsar}z - \frac{\partial\Phi}{\partial z}$, where $\Phi$ is the MW potential determined from stellar streams, and $\alpha_{1~\rm pulsar}z$ is the vertical acceleration determined from pulsar timing observations. Our analysis indicates that the Oort limit determined from streams is consistently (regardless of the choice of potential) lower than that determined from pulsar timing observations. The calibration we have derived here may be used to correct the estimate of the acceleration from stellar streams.Comment: 8 pages, 4 figures, 1 table. Submitted to ApJ Letter

Constraining the Tilt of the Milky Way's Dark Matter Halo with the Sagittarius Stream

Recent studies have suggested that the Milky Way (MW)'s Dark Matter (DM) halo may be significantly tilted with respect to its central stellar disk, a feature that might be linked to its formation history. In this work, we demonstrate a method of constraining the orientation of the minor axis of the DM halo using the angle and frequency variables. This method is complementary to other traditional techniques, such as orbit fitting. We first test the method using a simulated tidal stream evolving in a realistic environment inside an MW-mass host from the FIRE cosmological simulation, showing that the theoretical description of a stream in the action-angle-frequency formalism still holds for a realistic dwarf galaxy stream in a cosmological potential. Utilizing the slopes of the line in angle and frequency space, we show that the correct rotation frame yields a minimal slope difference, allowing us to put a constraint on the minor axis location. Finally, we apply this method to the Sagittarius stream's leading arm. We report that the MW's DM halo is oblate with the flattening parameter in the potential $q\sim0.7-0.9$ and the minor axis pointing toward $(\ell,b) = (42^{o},48^{o})$. Our constraint on the minor axis location is weak and disagrees with the estimates from other works; we argue that the inconsistency can be attributed in part to the observational uncertainties and in part to the influence of the Large Magellanic Cloud.Comment: 16 pages, 12 figure

Reconciling observed and simulated stellar halo masses

We use cosmological hydrodynamical simulations of Milky-Way-mass galaxies from the FIRE project to evaluate various strategies for estimating the mass of a galaxy's stellar halo from deep, integrated-light images. We find good agreement with integrated-light observations if we mimic observational methods to measure the mass of the stellar halo by selecting regions of an image via projected radius relative to the disk scale length or by their surface density in stellar mass . However, these observational methods systematically underestimate the accreted stellar component, defined in our (and most) simulations as the mass of stars formed outside of the host galaxy, by up to a factor of ten, since the accreted component is centrally concentrated and therefore substantially obscured by the galactic disk. Furthermore, these observational methods introduce spurious dependencies of the estimated accreted stellar component on the stellar mass and size of galaxies that can obscure the trends in accreted stellar mass predicted by cosmological simulations, since we find that in our simulations the size and shape of the central galaxy is not strongly correlated with the assembly history of the accreted stellar halo. This effect persists whether galaxies are viewed edge-on or face-on. We show that metallicity or color information may provide a way to more cleanly delineate in observations the regions dominated by accreted stars. Absent additional data, we caution that estimates of the mass of the accreted stellar component from single-band images alone should be taken as lower limits.Comment: Version accepted by Ap

On the stability of tidal streams in action space

In the Gaia era it is increasingly apparent that traditional static, parameterized models are insufficient to describe the mass distribution of our complex, dynamically evolving Milky Way (MW). In this work, we compare different time-evolving and time-independent representations of the gravitational potentials of simulated MW-mass galaxies from the FIRE-2 suite of cosmological baryonic simulations. Using these potentials, we calculate actions for star particles in tidal streams around three galaxies with varying merger histories at each snapshot from 7 Gyr ago to the present day. We determine the action-space coherence preserved by each model using the Kullback-Leibler Divergence to gauge the degree of clustering in actions and the relative stability of the clusters over time. We find that all models produce a clustered action space for simulations with no significant mergers. However, a massive (mass ratio prior to infall more similar than 1:8) interacting galaxy not present in the model will result in mischaracterized orbits for stars most affected by the interaction. The locations of the action space clusters (i.e. the orbits of the stream stars) are only preserved by the time-evolving model, while the time-independent models can lose significant amounts of information as soon as 0.5--1 Gyr ago, even if the system does not undergo a significant merger. Our results imply that reverse-integration of stream orbits in the MW using a fixed potential is likely to give incorrect results if integrated longer than 0.5 Gyr into the past