# Input Parameters

The model includes an input spectrum (e.g. a template star spectrum), atmospheric parameters , optical instrument path and an observation criterium. The model generates as default the spectral format in a table format reporting for each order number the wavelength of the central column, its y position in pixel units and arcseconds units, the Free Spectral Range (FSR) size, minimum and maximum wavelength, the order starting and ending wavelength and size (Template Spectra range). If required the ETC also calculates for each significative order (in the single line case only for the order where is detected the line) the total efficiency (% units), the Object, Sky and maximum expected counts (in electron units) and the Signal to Noise ratio for three points, the FSR minimum, central column and FSR maximum wavelength. For the wavelength of the central column it is reported also the wavelength value and the spectral bin size (over which the Object, Sky, Imax counts are integrated). The information contained in the spectral format table, relative to the central column wavelength value, can be displayed also in form of graph selecting the appropriate check button in the input page. In this case the ETC generate applet graphs and links to the corresponding data in ASCII format and in gif images format.

• ### Input Flux Spectral Distribution

• Template spectrum

The target model can be defined by a spectral template spectrum.

• MARCS

The target spectrum can also be selected from a subset of MARCS stellar model spectra, kindly provided by Bengt Edvardsson at the Uppsala Astronomical Observatory. The parameter space of the MARCS subsets are listed the following tables. Note that not all models (referring to all possible combinations of parameters) actually exist.

 MARCS subset: Spherical Geometry Parameter Number of unique values Unique Values model 1 "st" [Fe/H] 4 -4.00,-2.00,-1.00,0.00 Teff/K 9 4000,4500,5000,5500,6000,6500,7000,7500,8000 log(g) 5 -0.50,0.00,1.00,2.00,3.50 geometry 1 "s" microturbulence 1 2 mass 2 1,5 total (product) 360 (this is the number of possible combinations, but only 87 models exist)

 MARCS subset: Plane Parallel Geometry Parameter Number of unique values Unique Values model 1 "st" [Fe/H] 6 -1.00,-2.00,-4.00,0.00,0.50,1.00 Teff/K 9 4000,4500,5000,5500,6000,6500,7000,7500,8000 log(g) 1 4.00 geometry 1 "p" microturbulence 1 2 total (product) 54 (this is the number of possible combinations, but only 50 models exist)

The user can upload a file representing the object spectral distibution to the ETC server. The framework supports FITS images and two-column ASCII files, with wavelength in nm units and ascending order, and a flux unit proportional to erg/cm2/s/A (e.g. W/m2/μm). The (red-shifted, if applied) spectrum must cover the spectral range of the intended instrument mode, but also the wavelength range of the photometric band in which the magnitude is given. The absolute flux scale is not significant since the spectrum will be scaled to the given magnitude in the given band.

• Blackbody

The target model is a Planck blackbody spectrum defined by the temperature T

• Power Law

The target model is a power law spectrum of the type F(λ) ∝ λp, where p is the spectral index.

• Object Magnitude

In all of the above cases, the object spectrum is scaled to the given broad-band magnitude after integration over the given photometric band, using photometric zeropoints and bandpass profiles as listed here. When a redshift is applied to the spectrum, it is redshifted before it is scaled. Magnitudes are given per arcsec2 for extended sources

• Emission Line

In this case the source is a single emission line of characteristic wavelength, FWHM, and Flux in 10-16 ergs/s/cm2 for point sources or 10-16 ergs/s/cm2/arcsec2 for extended sources.

• ### Spatial Distribution

• Seeing Limited

Seeing limited sources are point-like sources.

• Extended Source

The signal to noise for extended sources is given per wavelength bin on the detector (as indicated in the output table). The magnitude is given per square arcsecond. The detected counts reported on the output table integrates over the solid angle omega determined by the product of PSF (in arcsec) and the slit width (in arcsec).

• ### 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

##### Almanac 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.

• Sky Brightness

For the X-SHOOTER VIS arm, the sky background is reduced to correspond to the continuum between emission lines.
The offsets applied to the normal table of night sky brightness (mag/arcsec2) are: U:0 , B:0, V:0.242, R:0.139, I: 0.633, Z: 1.237.

• ### Instrument Setup

• Mirrors (M1 to M2/M3 Depending on location of Instrument on Telescope). UVES (M1,M2,M3).

The ETC allows the user to set the following:

• Pre Slit Optics: The pre slit filter is selected from a list with an option menu. The ETC allow the following settings: None (no pre-slit filter inserted), ADC (Atmospheric Dispersion Compensator), Depolarizer, Iodine cell.
• Image Slicers:

The UVES instrument can observe with or without inserting image slicers along the optical path. The use of image slicers is important for bad seeing conditions or the highest spectral resolution. The Image Slicers mode is selected from a list with an option menu. The ETC allow the following settings: None (no image slicer inserted), IS#1, IS#2, IS#3. The following table contains the characteristic image slicers data.

 IS IS width (arcsec) IS heigh (arcsec) slit width (arcsec) slit heigh (arcsec) #1 2.0 2.6 0.68 8 #2 1.8 1.9 0.44 8 #3 1.5 1.5 0.30 10

• Slit.

The ETC allow the user to select the slit width. The slit heigh is kept fixed at 10 arcsec. See below to know how the Obj, Sky, Imax and S/N is calculated.

• FLAMES Fiber Feed

Instead of a slit, the FLAMES Medusa fibers can be used to feed light to UVES. The fiber diameter is 1 arcsec, which then serves as the slit. The total sky aperture is 0.785398 arcsec2. ( = pi*(0.5 arcsec)2)

• HARPS

The echelle spectrograph HARPS (La Silla 3.6m) is basically very similar to UVES, but has a simpler set of configurations. The efficiency of Fiber A is factor ~ 1.6 higher than fiber B. For details see this web page. Note that the polarimeters are splitting the light in 2 channels (equally if the star is unpolarized), i.e. for a "lossless" polarimeter circ_A/no_pol_A = lin_A/no_pol_A = 0.5. You can also see page 18 of the user manual. The ETC applies measured polarimeter efficiency factors.

• Observation Mode.

The instrument works in 4 instrument modes: Red Arm, Blue Arm, Dichroic1, and Dichroic2 where the dichroic modes allow the simultaneous exposure of the Red and the Blue Arm. The definition of an 'Observing Mode' requires the selection of the instrument mode, the crossdisperser to be used (Blue Arm: CD1 or CD2, Red Arm: CD3 or CD4), and the central wavelength.
If 'Standard Template' is selected, the predefined central wavelength as given in parentheses (lam_c) in the pull-down menu is used. This wavelength setting corresponds to the wavelength in the Standard Template as provided by the 'Phase 2 Proposal Preparation (P2PP)' tool.
If 'Free Template' is selected, the central wavelength can be set in the wavelength range as given in brackets [lam_0 < lam_c > lam_1] in the pull-down menu for the given instrument mode and crossdisperser. Note, that the suggested instrument mode, crossdisperser, and central wavelength combinations are predefined to allow senseful instrument setups only.

• Below Slit Filters.

The user can insert in the optical path no filter (option None) or set one of the the filters listed in the following table:

Filter Cross Disperser
BBS6-HER5 CD#1 or CD#2
BBS2-BG24 CD#1
RBS1-BG40 CD#3
RBS2-SHP700 CD#3
RBS9-BK7_5 CD#3 or CD#4
RBS3-OG590 CD#4
RBS12_HALPHA CD#3 or CD#4
RBS13_HBETA CD#3
RBS14_OIII5007 CD#3 or CD#4
RBS15_OIII4363 CD#3
RBS16_NII5755 CD#3
RBS17_OI6300 CD#3 or CD#4
RBS18_SII6724 CD#3 or CD#4
RBS19_HeII4686 CD#3

Recommnded combinations are colored yellow.

Detailed information on filters, optical components and detectors is available in the relevant instrument user manuals.

# Results

The ETC calculates as default the predicted spectral format. This is presented in a table format. The table reports for each order number the wavelength of the central column, its y position in pix units and arcseconds units, the Free Spectral Range (FSR) size, minimum and maximum wavelength, the order starting and ending wavelength and size: Template Spectra range (TS range).

The FSR is the wavelength range over which two adjacent orders are not overlapping, correspondent to the distance between wavelengths at which the Blaze function is 0.5.

The central wavelength of the FSR is

wc=2*sin(alpha_blaze)/Kech/m

where alpha_blaze is the echelle incidence angle at blaze wavelength, Kech is the echelle constant (grooves/mm) and m is the order number.

The size of the FSR it is approximatively given by

FSR_size=lambda_blaze/m

where lambda_blaze is the blaze wavelength and m the order number.

If required the ETC also calculates for each significative order (in the single line case only for the order where is detected the line) the total efficiency (% units), the Object, Sky and maximum expected counts (in electron units) and the Signal to Noise ratio for three points, the FSR minimum, and maximum and the central column wavelength. For the FSR central wavelength it is reported also the wavelength value and the spectral bin size (over which the Object, Sky, Imax counts are integrated).

To evaluate the total number of counts expected, the ETC use the following "zero order" formula:

For point sources:

N_point=F*D*T*E*S/P For extended sources:

N_extended=F*D*T*E*S*Omega/P

Where

F=Incident Flux (in ergs/s/cm2/A for point sources and ergs/s/cm2/arcsec2/A for extended sources).

D=wavelength bin

T=Exposure time

E=Total efficiency (atmosphere, telescope, optical components, filters, detector, slit losses in case of point sources)

S=Telescope Surface

P=Energy of one photon

Omega=Solid Angle subtended by a rectangle of size equal to the product of the slit width (in arcsecs) and the pre-slit PSF FWHM projected on the sky.

To evaluate the signal to noise ratio the ETC use the following expression:

S/N=N_Obj/sqrt(N_Obj+ S_Sky+ nPixY*n_dark*T/3600+ nBinY*n_RON2)

Where N_Obj and N_Sky are the number of predicted detected counts predicted for the object (using the appropriate expression if point source or extended one) and the sky (extended source).

nPixY is the number of pixels along the Y detector direction equivalent to twice the PSF FWHM (or to the appropriate size if an Image Slicer is inserted).

n_dark is the dark current (1e/pix/h).

T the exposure time in seconds.

nBinY is the number of bins equivalent to nPixY.

n_RON is the read out noise (for the particular chip used in the arm red or blue at the specified read out speed and gain).

The information contained in the spectral format table, relative to the central column wavelength value, can be displayed also in form of graphs selecting the appropriate check button in the input page. In this case the ETC generate applet graphs and links to the corresponding data in ASCII format and in gif images format.

### Version Information

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