Smooth Expansion in the universe is "Hubble Flow" dictated by \(v_{hubble}=H_od\)   Deviation ->Peculiar Velocities: \(v_{obs}=v_{hubble}+v_{pec}\)\(v_{pec}=v_{obs}-H_od\) where d is units Mpc.
Distances used are redshift-independent (using Cepheids, Blue supergiants) based on several variables such as needed %uncertainty, object, and distance. Vhubble is expected recessional velocity. Observe H1 21cm profile for Vobs and Wobs (velocity width). Take image to: measure apparent total brightness, apparent axial ratio (major axis/semi-major axis). Make corrections to solve for Vrot and abs magnitude of brightness. Use TFR to get a distance.
Peculiar velocities encompass: Orbital motion in clusters, inflow/outflow based on densities in regions, "noise" on Hflow. Peculiar motion describes motion combination of Hflow, local flow, and inside-cluster motion. 
APPSS survey covers b/w 22h RA 3h and +23 Dec +35. Objectives of the survey are to use BTFR to measure distances and Vpecs of large sample of galaxies in PPS, look for infall/backlow onto overdensity regions in PPS, measurement m/L of supercluster and compare these to predictions made bynumerical sims to restrictresultsresults.
Since BTFR distances have a ~25%-30% uncertainty on them, large samples of galaxies must be collected and averaged to obtain more usable data. 
Source: http://egg.astro.cornell.edu/alfalfa/ugradteam/uat16talks/uat16_introAPPSS.pdf (Powerpoint by Martha Haynes of UAT, Cornell University)
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Observing Proposal:
The Pisces-Perseus  Supercluster is ideal for measuring peculiar velocities in galaxy clusters  because of its size, and perpendicularity to our telescopes. The project is  useful as a comparison in dark matter simulations as well as other cosmology  simulations. Began in Fall 2015, named the Arecibo Pisces-Perseus Supercluster  (APPS) Survey, in 2016 requests to be allocated further telescope time to  continue the survey and create the first robust measurement of infall onto the  PPS.
The telescopes are needed  to detect HI because this dominates the content of star forming galaxies and is  necessary for the BTFR calculations. The amount of data is necessary because  this process poorly localizes the peculiar velocity of individual galaxies.
The study will also for  the first time allow HI-rich galaxies within a filamentary structure to be  studied outside of the Local Volume. The APPSS may also confirm the tentative  finding of the slope of the HI mass function having a low-mass slope dependent  on the galaxy residing inside or outside a large-scale filament, because of its  relation to the effect of supercluster scale overdensity. Furthermore, the  APPSS will use the peculiar velocity dataset to make a constrained dark matter  simulation of formation of the PPS over time.    
Results:  The selection method for detection in programs A2941 (pilot) and A2982  (starting in Fall of 2015) had a high detection rates of 71% and 68%  respectively, making them more efficient than ALFA surveys. The findings so far  have shown a split in the velocity field into two around the main velocity  field. Further observations with the APPSS are necessary to make a robust  infall measurement.
Objective: To  continue the APPSS survey, detecting HI line emission, in hopes to make a  robust measurement of infall velocity, and measure the HI mass function’s slope  to logMHI~8. In the process, approximately 239 new redshifts of  objects in the PPS region will be cataloged, and with the total 500~ objects in  the final sample, the survey team will be able to assess whether the structural  environment here has an impact on the abundance of low-mass objects in the  region.
Strategy:  Continuing using L-Band Wide (measures b/w 1.15-1.73 Hz frequencies) observing  with the sources that SDSS and GALEX photometry have identified as low-mass,  gas-rich candidates is important as it will be much more time efficient.    
Request: Estimated  was about 250 hours of telescope time would be required for the whole survey,  requested now is the second half, 126.5 hrs of telescope time. UAT students and  faculty heavily involved.
Source: http://egg.astro.cornell.edu/alfalfa/ugradteam/apps/docs/jones+koopmann_APPSS2016.pdf (The Arecibo Pisces-Perseus Supercluster Survey (APPSS) Michael G. Jones (P.I.) & Rebecca A. Koopmann (Co-P.I.) for the ALFALFA team)
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TFR:
Correlation b/w spiral galaxy luminosities and rotational velocities. Larger galaxy = faster Vrot.
\(v_{rot}\) can be used to, through TF -> \(Intrinsic\ Brightness\ \left(L\right)\ =\ v_{rot}^4\) (use this when assuming m/L to be constant), to find intrinsic brightness. Comparing this and apparent brightness distance can be found through -> \(Apparent\ Brightness\ \left(B\right)\ =\ \frac{L}{4\pi d^2}\) (?).
Source: https://www.noao.edu/staff/shoko/tf.html 
Remember BTFR has 25%-30% uncertainty b/c of assumed m/L ratio
BTFR: 
Baryonic matter excludes matter that is not made up of Baryons, which is everything inside the nucleus of an atom (does not include things such as electrons and Essentially disregards electrons (.0005% of mass) and neutrinos. Source: http://astronomy.swin.edu.au/cosmos/B/Baryonic+Matter
BTFR is a relation b/w baryonic mass and \(v_{rot}\) in disk galaxies. The baryonic mass of galaxies is directly correlated to intrinsic brightness which can be used to find distance with the TFR (?)
BTFR is more accurate for more faint galaxies. Galaxies with \(M_{gas}<10^9\) are gas dominated, these are good candidates and with BTFR give a \(v_{pec}\) within 1500~km/s with distance of PPS.
Data Reduction Notes
The radiometer equation is  a relationship of signal to noise in the form of :