Linear perturbation theory for tidal streams and the small-scale CDM power spectrum

Abstract

Tidal streams in the Milky Way are sensitive probes of the population of low-mass dark-matter subhalos predicted in cold-dark-matter (CDM) simulations. We present a new calculus for computing the effect of subhalo fly-bys on cold streams based on the action-angle representation of streams. The heart of this calculus is a lineof-parallel-angle approach that calculates the perturbed distribution function of a stream segment by undoing the effect of all relevant impacts. This approach allows one to compute the perturbed stream density and track in any coordinate system in minutes for realizations of the subhalo distribution down to 10 5 M , accounting for the stream's internal dispersion and overlapping impacts. We study the statistical properties of density and track fluctuations with large suites of simulations of the effect of subhalo fly-bys. The one-dimensional density and track power spectra along the stream trace the subhalo mass function, with higher-mass subhalos producing power only on large scales, while lower mass subhalos cause structure on smaller scales. We also find significant density and track bispectra that are observationally accessible. We further demonstrate that different projections of the track all reflect the same pattern of perturbations, facilitating their observational measurement. We apply this formalism to data for the Pal 5 stream and make a first rigorous determination of 10 +11 −6 dark-matter subhalos with masses between 10 6.5 M and 10 9 M within 20 kpc from the Galactic center (corresponding to 1.4 +1.6 −0.9 times the number predicted by CDMonly simulations or to f sub (r < 20 kpc) ≈ 0.2 %) assuming that the Pal 5 stream is 5 Gyr old. Improved data will allow measurements of the subhalo mass function down to 10 5 M , thus definitively testing whether dark matter is clumpy on the smallest scales relevant for galaxy formation.

A closer look at the spur, blob, wiggle, and gaps in GD-1

“…Most interestingly, the stream has significant residuals in the stream track which line up with the location of the gaps in the density. These correlated signals will be crucial for fitting the perturbations to the stream, both by fitting each feature as suggested by Erkal & Belokurov (2015b) and for fitting the perturbations statistically while taking these correlations into account as suggested by Bovy, Erkal & Sanders (2017). Equipped with this data set, we also showed that the stars in GD-1 are moving along the stream and do not have a significant velocity perpendicular to the stream.…”

“…Carlberg 2009;Yoon, Johnston & Hogg 2011;Carlberg 2012;Erkal & Belokurov 2015a), which are not observable by conventional methods (Ikeuchi 1986;Rees 1986). Indeed, tentative evidence for a disturbance by low mass subhaloes has been found in the Pal 5 stream (Bovy, Erkal & Sanders 2017;Erkal, Koposov & Belokurov 2017). One of the difficulties in uncovering the origin of details in the stream morphology is related to the uniqueness of the signature left by an encounter with a dark subhalo (Yoon, Johnston & Hogg 2011;Carlberg 2012;Erkal & Belokurov 2015a;.…”

Stellar Streams Discovered in the Dark Energy Survey

“…Observations of stellar streams can provide important constraints on the formation of the Milky Way stellar halo (e.g., Johnston 1998; Bullock & Johnston 2005;Bell et al 2008), the shape of the Galactic gravitational field (e.g., Johnston et al 2005;Koposov et al 2010;Law & Majewski 2010;Bonaca et al 2014;Bovy 2014;Gibbons et al 2014;PriceWhelan et al 2014;Sanders 2014;Bowden et al 2015;Küpper et al 2015;Erkal et al 2016b;Bovy et al 2016), and the abundance of low-mass dark matter substructure (e.g., Ibata et al 2002;Johnston et al 2002;Carlberg 2009;Yoon et al 2011;Carlberg 2012;Ngan & Carlberg 2014;Erkal & Belokurov 2015a;Carlberg 2016;Sanderson et al 2016;Sanders et al 2016;Bovy et al 2017;Erkal et al 2017;Sandford et al 2017). In addition, stellar streams are a direct snapshot of hierarchical structure formation (Peebles 1965;Press & Schechter 1974;Blumenthal et al 1984) and support the standard ΛCDM cosmological model (Diemand et al 2008;Springel et al 2008).…”

“…However, this prediction depends on the length and orbital trajectory of the ATLAS stream; therefore, given the increased length of the ATLAS stream detected in this work and in Pan-STARRS (Bernard et al 2016), as well as the uncertainty in its trajectory, the predicted number of gaps is likely an underestimate. If the underdensity is confirmed, then the gap can be used to infer the properties of the subhalo that created the gap (Erkal & Belokurov 2015b), and the statistical properties of the stream density can be used to place constraints on the number of subhalos in the Milky Way (Bovy et al 2017). …”

Shaken and stirred: the Milky Way's dark substructures

“…They show that the improved photometry, greater depth and more precise radial velocity and proper motion measurements of upcoming surveys such as Gaia (Perryman et al 2001;Gilmore et al 2012), DES (The Dark Energy Survey Collaboration 2005) and LSST (LSST Science Collaboration et al 2009) should allow a characterization of perturbers in terms of mass, concentration, impact time and 3D velocity, for subhaloes above 10 7 M , albeit with an irreducible degeneracy between mass and velocity. Recently, Bovy, Erkal & Sanders (2017) have used the density data of Pal-5 to infer the number of subhaloes in the mass range M = 10 6.5 -10 9 M inside the central 20 kpc of the Milky Way to be 10 +11 −6 . However, they also noted the uncertainty due to unaccounted baryonic effects and required assumptions in the subhalo velocity distribution.…”