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CAPÍTULO 4. ANÁLISIS DE LA PREFERENCIA DE AHORRO EN

4.2 FACTORES ECONÓMICOS FINANCIEROS

4.2.1 Tasas de Interés

During regional site selection and atmospheric characterization campaigns for the ALMA experiment in the early 2000s, 220 and 225 GHz tipping radiometers were used to verify the atmospheric transparency above the Chajnantor Plateau, as reported in (Radford 2001). These radiometers were used to measure the atmospheric brightness temperature viewed at various zenith angles (e.g. through a variety of airmasses) as the radiometer is tipped from zenith to horizon. With this resultant data, atmospheric transparency could be calculated using the formula for atmospheric temperature brightness as a model, given here asTB(z),

defined in Equation 2.1

TB(z) = [Tatm](1−e−τ A) (2.1)

where Tatm is defined as the effective atmospheric radiation temperature, A is the air-

mass at a given zenith angle z in which the atmosphere is simplified to be considered isothermal with plane-parallel geometry such that A =sec(z), and finally, τ is the calcu- lated atmospheric optical depth at zenith. These results have a direct physical implication

of the operational design and ultimate operational sensitivity of a given experimental cos- mology system, in which (Radford 2001) describes the integration time needed to reach a given operational sensitivity going as the square of the receiver system noise, which itself is dependent on optical depth τ and receiver temperatureTrec, given in Equation 2.2 as

t∝Tsys2 =e2τ A[Trec+Tatm(1−e−τ A)]2 (2.2)

Additionally, the brightness temperature measured at any given time is also dependent on the instantaneous value of what is referred to as precipitable water vapor (PWV), in which periods of higher PWV correspond to higher observed atmospheric brightness tem- perature (and thus increased observational integration times necessary to reach a given sensitivity during CMB observations). As defined by the American Meteorological Soci- ety (AMS), PWV is the “total atmospheric water vapor contained in a vertical column of unit cross-sectional area extending between any two specified levels, commonly expressed in terms of the height to which that water substance [vapor] would stand if completely con- densed and collected in a vessel of the same unit cross section” (Society 2015). Throughout this manuscript, PWV is measured in mm. Given that experimental cosmology systems ob- serve radiation originating entirely outside of Earth’s atmosphere, PWV can be considered as the entire atmospheric column between the point of observation throughout the entirety of the atmospheric height. AMS thus defines PWV for the entire column of observation, represented in Equation 2.3 as

P W V = [1/(ρ)(g)] ∫ p2

p1

xdp (2.3)

where p1 and p2 are the atmospheric pressures bounding the defined column, x(p) the mixing ratio at a pressure p, ρ is the water density, and g is the acceleration due to grav- ity. Described in detail during our discussion of ACTPol observation operations later in this manuscript, operation of ACT+MBAC and ACT+ACTPol relied on radiometer results pro- vided by the Atacama Pathfinder EXperiment (APEX) weather monitor platform, acquired

at APEX’s nearby site on the Chajnantor Plateau. In particular, real-time APEX PWV monitoring led to decisions to observe (e.g. for significantly high PWV levels over a given ob- serving period, observations may be suspended), and the APEX PWV data was fed into the ACTPol housekeeping data stream to aid in decision making for ACTPol science data cuts. Figure 2.17 illustrates the real-time data stream of APEX radiometer PWV data accessible from the APEX online weather monitor platform (acquired for the 24-hour period ending Saturday, 19 August 2017, 23:00:00 UTC 2017) (Collaboration 2017a). Additionally, Figure 2.18 provides APEX historic radiometer data results for PWV levels recorded between 2007 and 2015, roughly encapsulating the near-entirety of ACT+MBAC and ACT+ACTPol ob- serving operations, as well as historic data indicating the fraction of days between 2006 and 2015 below a given PWV level (Collaboration 2017b). Generally, a PWV level of less than 1.5 is considered acceptable for ACTPol observing operations, while PWV less than 1.0 is considered optimal. APEX, like ACT, seeks to target an operational season in times of his- torically lower PWV - thus on an annual basis ACT+MBAC and ACT+ACTPol targeted a period of non-observation during the so-called ’Bolivian Winter’ between late-December and early-March each year when PWV levels are historically highest during the year (in which prevailing winds force humid continental-tropical airmasses from South America’s Amazon Basin into the Atacama), further non-observation site upgrades and receiver in- stallation are generally completed between March and May as PWV levels decline, before principal observing operations take place between June and December, when PWV levels roughly reach their annual nadir. As APEX is just over 7 kilometers removed from the ACT site, and also roughly 100 meters lower in elevation on the Chajnantor Plateau, while it is reasonable to expect that PWV levels at the ACT site would differ slightly than the APEX site, and that APEX atmospheric transparency results slightly underestimated in comparison to the ACT site given its lower elevation, APEX atmospheric monitoring results are assumed to be reasonably representative of real-time conditions at the ACT site.

Figure 2.17: Example real-time data stream of APEX radiometer PWV data accessible from the APEX online weather monitor platform (acquired for the 24-hour period ending Saturday, 19 August 2017, 23:00:00 UTC 2017) (Collaboration 2017a)

Figure 2.18: Selected APEX historic radiometer Precipitable Water Vapor Data. (Left) APEX historic radiometer data results for PWV levels recorded between 2007 and 2015, roughly encap- sulating the near-entirety of ACT+MBAC and ACT+ACTPol observing operations. (Right) APEX radiometer historic data indicating the fraction of days between 2006 and 2015 below a given PWV level. (Collaboration 2017b)

the characterization of localized atmospheric conditions and related modeling to determine CMB channel band center. MBAC operated TES bolometer arrays with frequency centers at roughly 145, 220, and 280 GHz, while ACTPol operated TES polarimeter arrays with frequency centers at roughly 90 and 150 GHz. With these centers, both generations of receivers could make observations of CMB signal at these frequencies, while avoiding over- lap with, and resultant loading from (to the greatest extent possible) atmospheric oxygen emission line features centered at roughly 60 GHz and 117 GHz, as well as the 183 GHz and 325 GHz water emission line features. Figure 2.19 shows the median atmospheric brightness temperature spectrum at various times throughout the year, split by morning and night, corresponding to PWV values, as shown in (Marriage 2006), with MBAC observing bands centered at 147.2 GHz, 215 GHz, and 278.7 GHz indicated. In this case, winter is defined from June to November and Summer from December to May, while morning is defined as 0500-1700 UTC, and evening 1700-0500 UTC. In terms of PWV, Summer Evening corre- sponds to PWV = 2.15 mm, Summer Morning to PWV = 1.55 mm, Winter Evening to PWV = 0.94 mm, and Winter Morning to 0.69 mm. Figure 2.20 shows the median atmospheric brightness temperature spectrum for PWVs on the range of 0.0-2.0 mm, shown in PWV = 0.25 mm increments, with ACTPol bandpass results overlayed (discussion on the measure- ment and impact of these bandpass results will be given later in this manuscript) (Thornton et al. 2016). The MBAC-era brightness temperature spectra extrapolations were generated with the use of the atmospheric transmission modeling package Atmospheric Transmission at Microwaves (ATM), described in (Pardo 2001), while the ACTPol-era brightness tem- perature spectra extrapolations were generated with a repackaged ATM code, the ALMA Atmospheric Transmission Modeling package (Marriage 2006; Pardo 2001) From these fig- ures, the strong dependence between brightness temperature loading contributions from water at increasing PWV levels is clear, while brightness temperature loading contributions from oxygen are fairly consistent with changing PWV level. With these logistical and at- mospheric characterization site selection criterion taken into account, the development of

site logistical and scientific observational systems for the Atacama Cosmology Telescope on the southwestern face of Cerro Toco, adjacent to the Chajnantor Plateau, could thus commence, ushering in a permanent presence for ACT operating with three generations of receiver for the observation of CMB temperature, and then temperature and polarization anisotropy characteristics following site groundbreaking in 2007.

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