====== Science case difference between 2Hz cut-off and 10Hz cut-off ======

main selling points for as low frequencies as possible:

  - **early warning** with sky localization for EM followup thanks to early SNR buildup. ~1000s-10ks
  - IMBHs/IMRIs with higher total masses (>1000Msun) and up to high redshifts -> **cosmic history of SMBH seeds**
  - Long inspiral gives highly improved CBC parameter estimation even with just small SNR gains, breaking degeneracies with **precession** and **higher modes**, constraining **ellipticity** before it is completely radiated away. -> formation channels and environments
  - **No other observatory** will look at this range, except maybe DECIGO on even longer timescales -> unique discovery potential for unknown unknowns.

For many more analyses low frequencies yield improved rates/sensitivity/precision, but it can usually be offset with increased bucket sensitivity instead; the three above seem to be the main drivers for low-freq specifically.


====== CBC ======

===== early warning and sky localization =====

  * Lifetime in the detector window: ignoring SNR buildup for the moment, total BNS track length increases from ~10 minutes for 10Hz lower cutoff to ~1 day at 2Hz cutoff. [Plot: M. Chan]
{{ :et_update_2017:col.png?direct&400 |}}
  * For a useful early warning alert, we also want good sky localisation early enough. See below.
  * More specifically, we want the //time before coalescence that some SNR (or false-alarm rate) threshold is crossed//. Using universal SNR distribution and an estimated merger rate (or fancier: redshift-dependent distribution+rate), can predict number of events as a function of pre-alert time.
  * This FoM, from Adhikari et al, LIGO-P1700208 for LIGO Voyager, red is the only Voyager variant with some sensitivity below 10Hz. Note the localization panel assumes 2x Voyager + 1x aVirgo.
{{:et_update_2017:ligo_p1700208-v1_fig6.png?500|}}
  * Localisation accuracy also improves when starting at lower frequency, and can actually be done surprisingly well with a single-site ET for sources that are close enough. (The daily rotation of the detector gives "synthetic aperture", i.e. equivalent to a network. 
  * Below is a plot showing the localisation by an L-shape ET or CE for the same source at a location randomly selected but at three different distances.
  * The signal starts at 1Hz, and the two detectors (ET and CE) are assumed to be at the same location for a fair comparison.
  * The top panel of the plot is for ET and the bottom panel is for CE.
  * {{:et_update_2017:shortintegrated1.png?1200|}}
  * It can be seen that although CE accumulates much higher SNR, the localistion by L-shape ET is much smaller because ET's improvement in the low frequency band provides a long in-band duration of the signal.
  * Thus, if with the early alerts to EM followers, we need low-frequency sensitivity.
  * In addition, given the localization, polarization measurement from ET topology gives you source inclination too.

===== going to high BH masses and redshifts =====

  * The lower the frequency, the higher the BH masses we probe. fLSO ~ 4400 / ( Mtot[Msun] * (1+z) )
  * We measure redshifted detector frame masses. -> meaning higher cosmological reach
  * Intermediate mass black holes (IMBHs) could be observed both as IMBH-IMBH binaries and as IMRIs with stellar-mass BHs or NSs.
  * Observing IMBH/BBH at higher redshifts probes the BBH formation history and mass function evolution --> cosmology, galaxy formation!
{{ :et_update_2017:et-10hz-range.png?direct&400 |}}
the arows indicate the highest masses we woud detect if we reduced the sensitivity to 10Hz. [Sathya et al 2012]
  * IMRIs have rich waveforms, allowing e.g. additional TGR opportunities.

===== Parameter Estimation from long inspirals =====

  * Already for a basic quantity like chirp mass, low freqs may contribute only few % of SNR, but large improvements in PE. From Salvo's talk this week, how well CE can do, need to quantify low-freq ET in comparison:
{{:et_update_2017:screenshot_mchirp_salvo.png?400|}}
  * Higher order effects in BBH that might be much better observable with very long inspirals:
    * precession
    * eccentricity (gets radiated away until late inspiral, really need as early as possible)
    * higher multipole modes (more prominent for higher mass ratio, profits from being able to see higher-Mtot systems)
    *  Observing BBH at higher redshifts. BBH formation history, mass function evolution -   need to quantify.

===== Testing GR =====

  * long inspiral will let us see some deviations from GR with higher sensitivity: //(references?)//
    * speed of gravity / LIV tests particularly helped by high-redshift sources, too
    * parametrized PN-violation tests should be helped by many cycles
    * though for many tests: do low-freq cycles help by themselves, or can be easily made up for by high SNR from bucket?
    * BNS: tidal deformability? Both intuition and Table 1 of Adhikari et al imply bucket/high-freq more relevant, but comparing the non-deformed early inspiral with the deformed late inspiral might be quite useful, at the very least to study degeneracies/systematics. Need an actual expert to look into whether this is relevant early enough in the inspiral for low freqs to matter at all.
  * remember tradeoffs with high-freq, interesting things like post-merger and BNS studies require high-freq as well!


====== Stochastic Backgrounds ======

  * cosmic background from BH/ and NS binaries: low frequencies are very important
{{ :et_update_2017:et-gw-background.png?direct&500 |}}
Lots of sensitivity for the GW background at low frequencies. The expected spectrum is a power law but the level 
is determined by the integrated  rate density. Probably by 2030 we will have a very good idea of 
the level of the background from binaries. 


====== Continuous Waves from Neutron Stars ======

  * Most of the bulk of known pulsars population is at low frequencies.
  * Including particularly glitchy ones that could make good transient emitters!
  * Preliminary estimate: could beat spindown upper limit for ~350 known pulsars from ATNF with full ET-D curve, ~150 left with hard cut at 10 Hz. ([[https://inspirehep.net/record/894489|Pitkin 2011]] estimated ~100--600 observable with ET-C)
  * We don't know of any //lower// limit of NS ellipticities or how GW emission really correlates with source properties, so we should just aim to have as many interesting objects in band as possible/
  * Blind searches are also potentially sensitive to EM-dark NSs, but unclear whether "horizontal" or "vertical" extension of search space is more promising.
  * CW ULs from known pulsars and glitches - quick work [D. Keitel], might be a few factors off, but right ballpark:
{{:et_update_2017:atnf_spindown_and_glitch_uls_aligo_et.png?direct&500}}


====== Supernovae ======

  * rare sources anyway
  * core collapse basically emit inside the LIGO band, not much from low freq
  * SNIa might have some emission at <1Hz, but very low local rate
  * for this source we actually want as much high-freq sensitivity as possible!

====== resources ======

  * LIGO Voyager blue/red/green: https://dcc.ligo.org/P1700208-v1
    {{:et_update_2017:ligo_p1700208-v1_table1.png?direct&600|table I with various FoMs}}
  * Sathya et al 2012 ET science objectives: https://inspirehep.net/record/1116935

====== to-do list ======

All of the following is basically quantitative comparisons that will be equally useful for any other 2G+/3G proposals, so it will be useful to distribute labor in the international 3G science case working group.

  * reproduce and extend Table 1 from P1700208:
    * IMBH maximum mass, range/horizon
    * sky localization (average/cumdist/..., time for early localization)
    * spins, precession, eccentricity parameter estimation
    * ...
  * stoch. background: update/verify plot above with current rate knowledge
  * full quantitative analysis of early warning / sky localization (Mervin; also do our version of Fig. 6 from P1700208)
  * study and quantify influence of many low-freq cycles on tidal estimates (vs. just more SNR overall)
  * our version of Salvo's Mchirp plot with low-freq
  * update / double-check CW estimates, compare with Matt's 2011 paper
  * testing GR: first step is to talk to experts