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Register a new userEvolution of spatio-kinematic structures in star-forming regions: are Friends of Friends worth knowing?
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The Friends of Friends algorithm identifies groups of objects with similar spatial and kinematic properties, and has recently been used extensively to quantify the distributions of gas and stars in young star-forming regions. We apply the Friends of Friends algorithm to $N$-body simulations of the dynamical evolution of subvirial (collapsing) and supervirial (expanding) star-forming regions. We find that the algorithm picks out a wide range of groups (1 -- 25) for statistically identical initial conditions, and cannot distinguish between subvirial and supervirial regions in that we obtain similar mode and median values for the number of groups it identifies. We find no correlation between the number of groups identified initially and either the initial or subsequent spatial and kinematic tracers of the regions evolution, such as the amount of spatial substructure, dynamical mass segregation, or velocity dispersion. We therefore urge caution in using the Friends of Friends algorithm to quantify the initial conditions of star formation.
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The Q-parameter is used extensively to quantify the spatial distributions of stars and gas in star-forming regions as well as older clusters and associations. It quantifies the amount of structure using the ratio of the average length of a minimum spanning tree, mbar, to the average length within the complete graph, sbar. The interpretation of the Q-parameter often relies on comparing observed values of Q, mbar and sbar to idealised synthetic geometries, where there is little or no match between the observed star-forming regions and the synthetic regions. We measure Q, mbar, and sbar over 10 Myr in N-body simulations which are compared to IC 348, NGC 1333, and the ONC. For each star-forming region we set up simulations that approximate their initial conditions for a combination of different virial rations and fractal dimensions. We find that dynamical evolution of idealised fractal geometries can account for the observed Q, mbar, and sbar values in nearby star-forming regions. In general, an initially fractal star-forming region will tend to evolve to become more smooth and centrally concentrated. However, we show that initial conditions, as well as where the edge of the region is defined, can cause significant differences in the path that a star-forming region takes across the mbar-sbar plot as it evolves. We caution that the observed Q-parameter should not be directly compared to idealised geometries. Instead, it should be used to determine the degree to which a star-forming region is either spatially substructured or smooth and centrally concentrated.
We model the dynamical evolution of star forming regions with a wide range of initial properties. We follow the evolution of the regions substructure using the Q-parameter, we search for dynamical mass segregation using the Lambda_MSR technique, and we also quantify the evolution of local density around stars as a function of mass using the Sigma_LDR method. The amount of dynamical mass segregation measured by Lambda_MSR is generally only significant for subvirial and virialised, substructured regions - which usually evolve to form bound clusters. The Sigma_LDR method shows that massive stars attain higher local densities than the median value in all regions, even those that are supervirial and evolve to form (unbound) associations. We also introduce the Q-Sigma_LDR plot, which describes the evolution of spatial structure as a function of mass-weighted local density in a star forming region. Initially dense (>1000 stars pc^{-2}), bound regions always have Q >1, Sigma_LDR > 2 after 5Myr, whereas dense unbound regions always have Q < 1, Sigma_LDR > 2 after 5Myr. Less dense regions (<100 stars pc^{-2}) do not usually exhibit Sigma_LDR > 2 values, and if relatively high local density around massive stars arises purely from dynamics, then the Q-Sigma_LDR plot can be used to estimate the initial density of a star forming region.
We present a catalogue of galaxy groups and clusters selected using a friends-of-friends algorithm with a dynamic linking length from the 2dF-SDSS and QSO (2SLAQ) luminous red galaxy survey. The linking parameters for the code are chosen through an analysis of simulated 2SLAQ haloes. The resulting catalogue includes 313 clusters containing 1,152 galaxies. The galaxy groups and clusters have an average velocity dispersion of sigma_v = 467.97 km/s and an average size of R_clt = 0.78 Mpc/h. Galaxies from regions of one square degree and centred on the galaxy clusters were downloaded from the Sloan Digital Sky Survey Data Release 6 (SDSS DR6). Investigating the photometric redshifts and cluster red-sequence of these galaxies shows that the galaxy clusters detected with the FoF algorithm are reliable out to z~0.6. We estimate masses for the clusters using their velocity dispersions. These mass estimates are shown to be consistent with 2SLAQ mock halo masses. Further analysis of the simulation haloes shows that clipping out low richness groups with large radii improves the purity of catalogue from 52% to 88%, while retaining a completeness of 94%. Finally, we test the two-point correlation function of our cluster catalogue. We find a best-fitting power law model with parameters r0 = 24pm4 Mpc/h and gamma = -2.1pm 0.2, which are in agreement with other low redshift cluster samples and consistent with a {Lambda}CDM universe.
Barter exchange studies the setting where each agent owns a good, and they can exchange with each other if that gives them more preferred goods. This exchange will give better outcomes if there are more participants. The challenge here is how to get more participants and our goal is to incentivize the existing participants to invite new participants. However, new participants might be competitors for the existing participants. Therefore, we design an exchange mechanism based on the classical Top Trading Cycle (TTC) algorithm to solve their conflicts. Our mechanism is truthful in terms of revealing their preferences and also guarantees that inviting all their neighbors is a dominant strategy for all participants. The mechanism can be applied in settings where more participants are preferred but no extra budget to reach new participants.
We present the galaxy group catalogue for the recently-completed 2MASS Redshift Survey (2MRS, Macri2019) which consists of 44572 redshifts, including 1041 new measurements for galaxies mostly located within the Zone of Avoidance. The galaxy group catalogue is generated by using a novel, graph-theory based, modified version of the Friends-of-Friends algorithm. Several graph-theory examples are presented throughout this paper, including a new method for identifying substructures within groups. The results and graph-theory methods have been thoroughly interrogated against previous 2MRS group catalogues and a Theoretical Astrophysical Observatory (TAO) mock by making use of cutting-edge visualization techniques including immersive facilities, a digital planetarium, and virtual reality. This has resulted in a stable and robust catalogue with on-sky positions and line-of-sight distances within 0.5 Mpc and 2 Mpc, respectively, and has recovered all major groups and clusters. The final catalogue consists of 3022 groups, resulting in the most complete whole-sky galaxy group catalogue to date. We determine the 3D positions of these groups, as well as their luminosity and comoving distances, observed and corrected number of members, richness metric, velocity dispersion, and estimates of $R_{200}$ and $M_{200}$. We present three additional data products, i.e. the 2MRS galaxies found in groups, a catalogue of subgroups, and a catalogue of 687 new group candidates with no counterparts in previous 2MRS-based analyses.
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