# General description

The GRAVITY Exposure Time Calculator is a software tool to prepare observations. The objective of this software tool is to estimate the feasibility of an observation and the necessary telescope time at Phase 1 (before the proposal is submitted), as well as determine the suitable instrument parameters at Phase 2 (to be input to P2PP for the preparation of the OBs). Thanks to the fringe tracking capability of the instrument, it will be possible to integrate the spectrally dispersed signal from the Science Combiner. Therefore, the GRAVITY ETC will provide:

1. An evaluation of the feasibility of fringe tracking on the specified Fringe Tracker and Science Targets.
2. [Work in Progress!!!] An estimate if the necessary integration times for the science combiner as a function of the brightness and SED of the observed object and instrument configuration. This will provide the user with the resulting photometric S/N of the foreseen observation, or alternatively, estimate the necessary number of exposures (NDIT) considering a goal SNR and a specified individual exposure time (DIT).

# Instrument configuration

## Instrument mode

GRAVITY has two principal observing modes:

• Single field (Fringe Tracker and Science targets are the same object).
• Dual field (Fringe Tracker and Science targets are different objects, located within the GRAVITY FOV of 2” for UTs and 6” for ATs).

## Beam Combiner settings

### Scientific beam combiner spectral resolution

Two spectral resolution settings are available for the Science combiner:

• Low resolution (R=22) only for Dual Field mode
• Medium resolution (R=500)
• High resolution (R=4000).
In all cases, the covered spectral domain will be the K band (1.9-2.5 μm).

### Polarization splitting

Two polarization settings will be available for each of the spectral resolutions of the Science target:

• Non-split polarizations
• Split polarizations (using a Wollaston prism).
This corresponds to a total of 4 spectral/polarimetric configurations (2 spectral resolutions x 2 polarization settings).

# Science Object Properties

## Target spectrum

The following options are available to describe the spectrum of the science target.

• ### Template Spectrum

The target model can be defined by a template spectrum which is scaled to the provided magnitude and filter. References: Pickles (1998, PASP 110, 863); Coleman et al.: 1980ApJS; Kinney at al.: 1996ApJ.

• ### Blackbody

The target model is a blackbody defined by its temperature, expressed in Kelvin. The intensity distribution is scaled to the object magnitude.

• ### Uploaded spectrum

User-defined spectrum.

• ### Single line

The input spectrum is a single emission line. It is an analytical Gaussian, centered on the Wavelength parameter, defined by its total Flux and full-width at half-maximum FWHM. Line flux is given in 10-16 erg.cm-2.s-1.

NB: When requesting a single line as input spectrum, the magnitude parameter is not taken into account. Only the line flux will be used to determine the signal magnitude. The FWHM of a single line is limited by the sampling. If the requested FWHM is too narrow, it will be replaced by the minimum supported value, and a warning will be issued in the beginning of the result page.

## Target geometry

Together with the declination of the target on sky and the chosen baseline quadruplet, the ETC evaluates the fringe visibility and photometric flux measured at the detector. It also checks that the fringe tracking is possible in this configuration. The Science Target may be used to calibrate the zero point of the metrology by switching the two fields of GRAVITY. Considering the small maximum separation of the GRAVITY dual field observations, the angular distance between the two objects is considered negligible for the computation of the projected baselines, hence the user will specify only a single set of coordinates.

The available target geometries for the users are:

• ### Uniform disc

The target is represented by a single disc with uniform intensity.

• ### Gaussian

The target intensity is represented by a gaussian model.

• ### Elliptical Gaussian

The target intensity is represented by a elliptical gaussian model.

• ### Binary

The target is represented by a couple of uniform discs with the specified sizes, separation and relative fluxes.

## Target coordinates

To define the target locationm the user can directly give the coordinates of use the Simbad service:
• ### Right Ascension and Declination (2000.0)

• RA: Given in hours, minutes, and seconds, or in decimal degrees
• Dec: Given in degrees, arc-minutes, and arc-seconds, or in decimal degrees between -90 and +90 degrees.

The target name is resolved by Simbad. This service determines the coordinates of the target automatically.

## Time constraints

The user defines the science target hour angle during the observation (beginning, end, and step).

# Fringe Tracking Object Properties

## Fringe Tracking Object spectrum

The following options are available to describe the spectrum of the fringe tracker:

• ### Template Spectrum

The target model can be defined by a template spectrum which is scaled to the provided magnitude and filter. References: Pickles (1998, PASP 110, 863); Coleman et al.: 1980ApJS; Kinney at al.: 1996ApJ.

• ### Blackbody

The target model is a blackbody defined by its temperature, expressed in Kelvin. The intensity distribution is scaled to the object magnitude.

• ### Uploaded spectrum

User-defined spectrum.

## Fringe Tracking Object geometry

In addition to the spectral energy distribution of the Fringe Tracking (FT) target, another useful parameter for the estimation of the feasibility of the fringe tracking is its geometry. The fringe tracking object is represented by a uniform disc. The user can specify the diameter of the disc and the separation from the science target.

# Baseline configuration

GRAVITY will be usable either with four Unit Telescopes or with four Auxiliary Telescopes. For reasons of optical efficiency, it will not be possible to use a combination of both UTs and ATs sim- ultaneously (e.g. 2 UTs + 2 ATs). As a consequence, the user will be given only the choice of four UTs with fixed (x,y,z) positions or four ATs. For an AT configuration, the user will select the quadruplet of stations in a list of the available VLTI configurations for the considered observing period. See below the available stations.

Light Collector Possible Stations
Unit Telescopes U1, U2, U3, U4
Auxiliary Telescopes A0, A1, B0, B1, B2, B3, B4, B5 C0, C1, C2, C3, D0, D1, D2, E0, G0, G1, G2, H0, I1, J1, J2, J3, J4, J5, J6, K0, L0, M0

The list of offered AT configurations is available at: VLTI Configurations

# Sky Conditions

## Seeing and Image Quality

Since version 6.0.0, the definitions of seeing and image quality used in the ETC follow the ones given in Martinez, Kolb, Sarazin, Tokovinin (2010, The Messenger 141, 5) originally provided by Tokovinin (2002, PASP 114, 1156) but corrected by Kolb (ESO Technical Report #12):

Seeing is an inherent property of the atmospheric turbulence, which is independent of the telescope that is observing through the atmosphere; Image Quality (IQ), defined as the full width at half maximum (FWHM) of long-exposure stellar images, is a property of the images obtained in the focal plane of an instrument mounted on a telescope observing through the atmosphere.

The IQ defines the S/N reference area for non-AO point sources in the ETC.

With the seeing consistently defined as the atmospheric PSF FWHM outside the telescope at zenith at 500 nm, the ETC models the IQ PSF as a gaussian, considering the gauss-approximated transfer functions of the atmosphere, telescope and instrument, with s=seeing, λ=wavelength, x=airmass and D=telescope diameter:

Image Quality
 $${ $$\mathit{FWHM}_{\text{IQ}} = \sqrt{\mathit{FWHM}_{\text{atm}}^2(\mathit{s},x,\lambda)+\mathit{FWHM}_{\text{tel}}^2(\mathit{D},\lambda)+\mathit{FWHM}_{\text{ins}}^2(\lambda)}$$ }$$

For fibre-fed instruments, the instrument transfer function is not applied.

The diffraction limited PSF FWHM for the telescope with diameter D at observing wavelength λ is modeled as:
 \begin{aligned} \mathit{FWHM}_{\text{tel}} & = 1.028 \frac{\lambda}{D} \text{, } & \text{ with } \lambda \text{ and D in the same unit}\\ & = 0.000212 \frac{\lambda}{D} \text{arcsec, } & \text{ with } \lambda \text{ in nm and D in m}. \end{aligned}
For point sources and non-AO instrument modes, the atmospheric PSF FWHM with the given seeing $$s$$ (arcsec), airmass $$x$$ and wavelength $${ \lambda }$$ (nm) is modeled as a gaussian profile with:
 $${\mathit{FWHM}}_{\text{atm}}(\mathit{s},\mathit{x},\lambda) = \mathit{s} \cdot x^{0.6} \cdot (\frac {\lambda} {500})^{-0.2} \cdot \sqrt{[1+F_{\text{Kolb}} \cdot 2.183 \cdot ({r_0}/L_{0})^{0.356})]}$$ Note: The model sets $${ \mathit{FWHM}}_{\text{atm}}$$=0 if the argument of the square root becomes negative $${ [1+F_{\text{Kolb}} \cdot 2.183 \cdot ({r_0}/L_{0})^{0.356}] < 0 }$$ , which happens when the Fried parameter $${ {r_0} }$$ reaches its threshold of $${ r_{\text{t}} = L_{0} \cdot [1/(2.183 \cdot F_{\text{Kolb}})]^{1/0.356}}$$. For the VLT and $${ L_{0} = 46m}$$ , this corresponds to $${ r_{\text{t}} = 5.4m}$$.
$${ L_{0} }$$ is the wave-front outer-scale. We have adopted a value of $${ L_{0} }$$=46m (van den Ancker et al. 2016, Proceedings of the SPIE, Volume 9910, 111).

$$F_{\text{Kolb}}$$ is the Kolb factor (ESO Technical Report #12):
 $$F_{\text{Kolb}} = \frac {1}{1+300 {\text{ }} D/L_{0}}-1$$ For the VLT and $${ L_{0} }$$=46m, this corresponds to $$F_{\text{Kolb}} = -$$0.981644.
$${r_0}$$ is the Fried parameter at the requested seeing $$s$$, wavelength $${ \lambda }$$ and airmass $$x$$:
 $$r_0 = 0.100 \cdot s^{-1} \cdot (\frac{\lambda}{500})^{1.2} \cdot x^{-0.6} \text{ m, } \text{ } \text{ } \text{ } \text{ with } s \text{ in arcsec } \text{and } \lambda \text{ in nm.}$$

For AO-modes, a model of the AO-corrected PSF is used instead.

Seeing statistics:

The Paranal seeing statistics is based on the so-called UT seeing measurements obtained from the UT1 Cassegrain Shack-Hartmann wavefront sensor used for active optics.

The measurements are deconvolved in order to represent the seeing outside the dome (i.e. they are corrected for the instrument+telescope resolution).

The La Silla seeing statistics is based on the DIMM FWHM measurements corrected for the instrumental resolution.

These data come from http://www.eso.org/gen-fac/pubs/astclim/paranal/seeing/singcumul.html

## Sky Model

The sky background model is based on the Cerro Paranal Advanced Sky Model, also for instruments at la Silla, except for the different altitude above sea level. The observatory coordinates are automatically assigned for a given instrument.

Since version P101, the ETCs include a dynamic almanac widget to facilitate assignment of accurate sky model parameters for a given target position and time of observation. The sky radiation model includes the following components: scattered moonlight, scattered starlight, zodiacal light, thermal emission by telescope and instrument, molecular emission of the lower atmosphere, emission lines of the upper atmosphere and airglow continuum.

Alternatively, the almanac mode can be overridden to allow manual assignment of airmass and moon phase. In that case, the sky model will use fixed typical values for all remaining parameters (which can be seen in the output page by enabling the check box "show skymodel details").

The almanac is updated dynamically by a service on the ETC web server, without the need to manually update the web application.

Notes about the algorithms, resources and references for the almanac are available here

### Usage

Hovering the mouse over an input element in the almanac normally displays a pop-up "tooltip" with a short description.

### Time

The upper left part of the almanac box refers to the date and time of observation.
This can be done with a UT time or a MJD. A date/time picker widget will appear when the UT input field is clicked, but the UT can also be assigned manually. In any case, the UT and MJD fields are dynamically coupled to be mutually consistent.

The two +/- buttons can be used to step forward or backward in time by the indicated step and unit per click. The buttons can be held down to step continuously until released.

The third of night corresponding to the currently selected time is indicated. This is an input parameter to the airglow component in the sky model. Twilight levels (civil, nautical and astronomical) referring to the sun altitude ranges are also indicated in the dynamic text. These levels refer to the sun altitude:

• Astronomical Twilight −18° ≥ alt < −12°
• Nautical Twilight −12° ≥ alt < −6°
• Civil Twilight −6° ≥ alt < 0°

### Target

The target equatorial coordinates RA and dec can be assigned manually in the two input fields or automatically using the SIMBAD resolver to retrieve the coordinates.
If the lookup is successful, an "info" link will open a window in which the raw SIMBAD response can be inspected.
The units can be toggled between decimal degrees and hh:mm:ss [00:00:00 - 23:59:59.999] for RA and dd:mm:ss (or dd mm ss) for dec. A whitespace can be used as separator instead of a colon.

### Output Table

The table dynamically displays the output from the server back-end service, including temporal and spatial coordinates for the target, Moon and Sun. The bold-faced numbers indicate the parameters normally relevant in the phase 1 proposal for optical instruments. The numbers appear in red color if they are out of the range supported by the sky model.

### Visiblity Plot

The chart dynamically shows the altitude and equivalent airmass as function of time for the moon and target, centered on midnight for the currently selected date.
The green line, which refers to the currently selected time, can be dragged left and right to change the time, dynamically coupled with the sections in the Time section.

A more advanced version of the almanac is included in our SkyCalc web application, which provides more input and output options.

# Results

## Exposure time

The available parameters for the users are:

• Exposure time (DIT) in seconds,
• Number of DITs (NDIT)
The user must refer to the Gravity Template Manual for a more detailed description of the available DIT/NDIT/NEXP. In particular, one may check table 1 and table 2.

The minimum possible exposure time (min DIT) depends on the chosen spectral resolution. The higher the spectral resolution, the larger the number of pixels to be read out from the detector, and therefore the higher the min DIT. There is one min DIT value per spectral resolution setting. The selection of polarization splitting option does not result in an increase in min DIT, as the read out window on the detector does not change compared to the non-split setting. The min DIT values for the three different spectral resolution settings of the SC are listed below.

Spectral Resolution Number of Pixels Minimum DIT (ms)
22 640x10 1.5
500 640x256 30
4000 640x2048 300

 Send comments and questions to usd-help@eso.org