# ETC Help

##  Overview

This is an online help for the Tauvex Exposure Time Calculator (ETC). Please note that ETC will only help you assess the feasibility of an observation. If you come across any inconsistent results, report to us. You may either file a bug report at the Tauvex Bugzilla or write to tauvex_AT_iiap.res.in.

In order to reduce the complexity of the inputs page, we use javascript to show only the relevent input fields. Javascript is also used to check if the entered values are of expected types and within range. For eg: if you leave any of the required inputs blank, or if you enter a wrong data type, the field will turn red. If the number in a field is out of range, it would turn the number red. Javascript works on the client-side, ie on your browser. Checking input values before submitting them helps to reduce data transfer to and from the server, and (more importantly) it can save you several minutes on slow connections. Therefore, for your own convenience we recommend javascript enabled browsers, though it won't affect the functionality of the ETC.

Given below is a brief description of the input fields and the backend calculations. Each of the user inputs should be within an allowed range. Note that these numbers have nothing to do with instrument capabilities. The allowed range is only to avoid "un-astronomical" values in input fields.

The principle behind an ETC is simple. First you select the source type, along with the parameters that define the spectrum of the source. ETC then generates a spectrum of the source and convolve with the filter response to get the expected count rate from the source. Next step is to estimate the background noise. We assume that most of the background photon count arise from sunlight scattered off from spacecraft body or otherwise. The count rate from the source and the instrument background noise is then used to estimate the time required to detect the source (or the s/n achieved in a given observing time). The basic idea is shown in the cartoon below.

##  The Source

Here you may choose the kind of source you are interested in. You may also choose to upload your own source spectrum - In which case, we can proceed without other inputs for calculations (you do have options to scale the spectrum and redshift it though). Brief notes on each types of sources are given in the following sections.

###  Star

If your choice of source is a star, then we require star specific inputs - the Spectral Type to generate a model spectrum using the Kurucz database (Dr. R. Kurucz, CD-ROM No. 13, GSFC). The backend calculation is based on Sujatha et al (BASI, 32, 151, 2004).

####  Spectral Type

For a star, its spectral type is required to estimate the source flux density at the instrument. Select a combination using the three drop down lists for spectral class and subclass. Please note that some of the combinations may not be valid, in which case, the ETC will try to make a guess for the closest match. While there are no known issues with finding a closest match, we would appreciate any feedback on it. Used only for Stellar sources.

###  Black Body

Astronomers often come across sources that can be approximated as a blackbody. Spectrum of a blackbody radiation is provided by Plank's law of radiation.

####  Temperature

Temperature of a blackbody decides the shape of its spectrum. This spectrum is then normalized and flux is scaled to match the source magnitude.

• Allowed Range: 0.0K to 108K
• Data type: integer or float

###  Galaxies

If your source is a galaxy, then we will require two more parameters to generate the source spectrum. 1) The type of galaxy and 2) the redshift. We use a set of template spectra from the Kinney-Calzetti spectral atlas of galaxies and scale it according to the magnitude of the source. However, before applying filter response, we need to shift the spectrum to account for the redshift of the source. NOTE:The template spectra starts from wavelengths of around 1200Å, which is close to the observing band of Tauvex/UVIT. Therefore, higher values of redshift can result in the spectrum shifting out of the instrument's bands.

####  Galaxy Types

These are the types of templates available in the Kinney-Calzetti spectral atlas of galaxies. Templates include various types of spirals and star burst galaxies. These are based on various optical observations and IUE for UV data. Used only when source type is galaxy.

###  AGNs

As in the case of galaxy, here too we use a set of template spectra to generate the source spectrum. The magnitude of the source is needed to scale the template spectrum. In addition, redshift is used to shift the profile in wavelength. The templates are from AGN atlas at CDBS, which consists of a few spectral templates of AGNs ranging from LINER to Seyfert and bright QSO. A brief description is given in the next subsection.

####  AGN Types

The following types of template spectra are available: The data are from optical observations, plus UV data from IUE.

• Liner
• Seyfert 1
• Seyfert 2
• QSO

The LINER template is basically the spectrum of M81 and the Seyfert 2 template is a spectrum of NGC 5548. Seyfert 1 and QSO were obtained from various spectra.

###  Flat Spectrum Source

Use this option if you know of a flat spectrum source and would like to observe it with TAUVEX. A flat spectrum means one constant value for flux density at all wavelengths.

###  Redshift

Source redshift. The source spectrum is corrected for the redshift, using the standard relation:

$\frac{\lambda_{obs}}{\lambda_{em}} = (1 + z)$

Where λobs is the observed wavelength, λem is the emitted wavelength and z is the redshift. This is used only if source type is galaxy or AGN.

• Allowed range: 0 to 6.0
• Data type: integer or real

Redshift is available as an option for galaxies, AGNs and for User defined Source.

###  Source Magnitude/Flux

Source spectrum for all sources except user defined and flat spectrum are normalized, before scaling to the magnitude of source or to the source flux at a given wavelength. Normalizing spectra is optional for user defined source.

####  Source Magnitude

Apparent magnitude of the source. Flux of source at the respective wavelength of the band is calculated first, which is then used to scale the normalized source spectrum.

#####  Band

Magnitude is expected in one of the vega based U/B/V/R band. You may choose AB also. In this case, the magnitude is first converted to V magnitude before calculations using the relation:

• V = V(AB) + 0.044 (Source: Patton)
• Allowed range: -26.0 to 30.0
• Data type: integer or real.

####  Source Flux

Type in the source flux value here. ETC will scale the normalized source spectrum to this value and proceed with calculations. Note that we do not require a separate field for source magnitude anymore.

Input flux may be specified in a number of units:

1. Watts m-2 Hz-1
• Allowed range: 6.2 x 10-36 to 1.6 x 10-13
2. Ergs s-1 cm-2 Hz-1
• Allowed range: 6.2 x 10-33 to 1.6 x 10-10
3. Ergs s-1 cm-2A-1
• Allowed range: 4.0 x 10-23 to 1.00
4. Jansky (10 x -26 Watts m-1 Hz-1)
• Allowed range: 6.2 x 10-10 to 1.6 x 1013

#####  Wavelength

Source Flux should be accompanied by a wavelength at which the flux is measured. Expected units is Angstroms.

###  User Defined Source

If you are not happy with any of our sources, you can upload your own source spectrum. Select "user defined" source and you will be presented with a file upload option.

NOTE:You need to make sure that source spectrum is defined over the filter response curve. Expect the unexpected if source spectrum and filter response do not overlap.

####  Redshift Spectrum

Ever felt the need to place your source in another part of the universe? Then check this option to apply a redshift to your source spectrum. You may also need to normalize the spectrum and scale it to a magnitude/flux.

####  Normalized Spectrum

This option is to scale the input source spectrum to a given magnitude or Flux at a specified wavelength. You may also apply Extinction to the spectrum.

ETC expects a two column ascii file as source spectrum. First column should be the wavelength (in angstroms) and second column, the flux density (in ergs s-1 cm-2 Å-1). Any lines that begin with a "#" are ignored as a comment. Please note that if your spectrum has negative flux values you will get an error message. An example of a valid spectrum is shown below.

 # My source's spectrum
#
# Wavelength     Flux density
# (angstroms)    (ergs/s/cm^2/Å)
1370.10144043    3.97418026e-09
1441.79272461    5.91593765e-09
1502.95971680    9.01411200e-09
1569.54650879    1.03960225e-08
1642.30700684    1.38279651e-08
1722.14147949    1.42179048e-08
1810.13403320    1.73137944e-08


###  Galactic Extinction

Contribution from Galactic extinction to the source flux. We begin with calculating AV, the extinction in V band (in magnitude). Various inputs used to calculate AV and their allowed ranges in their values are listed below:

####  RV

Observed extinction curve in the Galaxy is fairly well characterized by this single parameter RV. It is a measurement of the total extinction AV to selective extinction, E(B-V). RV = 3.1 is the standard value for interstellar medium.

• Allowed range: 0.0 to 10.0
• Data type: integer/float

####  E(B-V)

E(B-V) = AB - AV is the difference between extinction in the B band and V band.

AV = RV x E(B-V)

• Allowed range: 0.0 to 1000.0
• Data type: integer/float

####  NH

The hydrogen column density NH along the line of sight. Total extinction AV depends on the amount of interstellar dust, which in turn is proportional to the hydrogen column density along the line of sight. Input units are 1021 cm-2.

AV = (NH x RV/5.81)

• Allowed range: 0.00001 to 10000.0
• Data type: integer/float

####  Heliocentric Distance

As you span greater distances along any line of sight, you cover more dust which scatters starlight. AV can also be expressed as a function of heliocentric distance.

AV = 1.6 x distance(Kpc)

• Allowed range: 0.0 to 100.0 (kpc).
• Data type: integer/float

####  AV

Often we face situations where none of the above are required and you got AV is readily available. That brings us to an AV input option.

• Allowed range: 0.0 to 10.0
• Data type: integer/float

####  Calculations

Once we have AV, one need to correct the observed V magnitude for extinction. This corrected magnitude is used to scale source spectrum (in the case of galaxy, AGN and black body) or to generate spectrum (of stellar sources).

The next step is to calculate Aλ, extinction at a given wavelength. We use the Galactic Extinction model from Cardelli, Clayton & Mathis (ApJ, 345, 245, 1989):

Fig.1a Aλ/AV as a function of μm-1, for RV = 2.75
• Aλ = (a + b/RV) x AV
Where a and b are polynomial functions of wavelength.

Figure 1a shows Aλ/AV as a function of 1/λ (μm-1) for RV = 2.75.

Extinction spectrum is then applied on the simulated/uploaded source spectrum:

• flux(Obs) = flux(sim)/alog10(Aλ/2.5)

##  TAUVEX Specific Options

You can get more Tauvex specific information from your observing time estimates by using extra inputs. Recall that Tauvex is a secondary payload, attached to the east face of GSAT-4. The stray light (mainly sunlight scattered off spacecraft body, solar panels etc.) falling on detector is a function of daily orbital phase of the satellite and time of the year. Hence, we need the time of observation along with source coordinates, J2000 RA and Decl. to estimate background noise levels. This calculation uses stray light modelling software by Dr. Elhannan Almoznino (Tel-Aviv University).

###  Date of Observation

Observing date is used to calculate the background, which includes contributions from zodiacal light and sunlight scattered off the spacecraft. It is also used to calculate the sun angle and issue a warning if program source is too close to the sun.

###  Source Coordinates

Equatorial coordinates and date of observation is used to estimate the stray light zodiacal light contributions. This is based on the zodiacal light calculator. Input is expected in the format (RA, decl) = "hh mm ss.ss, +/-dd mm ss.ss" (without the quotes).

####  Intelligent Input

Client side javascript will ensure that input format is valid. If you are not sure about the coordinates, then it should be sufficient to type in the source name. Move out of the input field while an AJAX request is sent to fetch coordinates. Our name resolver is based on the Sesame from CDS. It will query Simbad, NED and VizieR databases for source coordinates.

NOTE: Name resolver will not check for source type and other properties like magnitude, Reddening etc. It will only return the coordinates.

####  Declination

The declination of the source and the angular height of the source above the field center are two quantities which will decide the number of scans required to complete an observation. Since Tauvex is a scanning telescope, the time for which your source is within the field of view can be only a few minutes per day (or even less). These options are detailed below:

Tauvex operates in constant declination scanning mode from a geo-stationary orbit. Therefore, if a source is at the celestial equator (declination = 0o), time for which it is available within the field of view is:

• t0 = FOV/scan_rate
• FOV = 0.9o deg. for TAUVEX
• scan_rate = 360o/(24 x 3600) deg/s
• t0 = 216 seconds

The available time is infinite for a source at the celestial pole, since sources behave similar to circumpolar stars. In general, the variation of availability of source with declination can be expressed as:

• td = t0/cos(d)
• Where
• d is the declination of source
• t0 is the time for which a source at zero declination is available within the field of view
• td is the time for which a source at declination = do is available within the field of view

The source declination is used to express the calculated exposure time (section 4) as number of scans (one scan per day) required to complete the observation. This can be useful, in say, feasibility studies.

###  Source Location

In a similar manner as the variation of time of availability for a source with declination, the time of availability also depends on the location of the source within the field of view (FOV). If a source cut throught the center of FOV, along the diameter, and the declination is 0°, then time for which it is available is 216 seconds per day (See section: 2.7.1). If the source is at the edge of the FOV, this is reduced to one frame! In most cases we would expect the source to be at the center of the field and I don't know if this option has any practical use at all. Anyway, a brief description of the calculation is given below:

In the figure, if "r" is the radius of the field of view, time for which a source located at a height "h" above the field center is available, is given by:

t2 = 4(r2h2)

Where

• r = td /2
• td = Diameter of the circle - Available time on source per scan, for a source crossing FOV through the field center. td is a function of declination.
• h = Height of the source above the the field center
• t = Available time on source per scan, for a source crossing FOV at a height "h" above the field center

##  Instrument

Instrument specific inputs are listed here. Since the ETC will estimate the count rate of the source in all the filters, the only instrument parameter left is the dark counts on the detector. This value will be added to the stray light counts to obtain total background. Signal-to-noise is then calculated assuming photon statistics.

###  Dark Counts

The background noise in the detector. Input is counted as so many counts per second, over the detector area. The normal value for Tauvex is around 20 counts per second. Increase this value if you need to consider external contributions or if you expect a noisy detector

• Allowed range: 0.0 to 100.0
• Data type: integer or real

###  Filter

Tauvex is fitted with five filters, as seen in the figure below:

UVIT will go with 10 filtes, the responses of which are given below:

The flux from the source will be convolved with the filter response, and the background noise added to estimate what is "seen" by the detector. The ETC will calculate results for all filters.

##  Output

Once all the inputs are in place, you need to select the output mode. You can feed in an observing time for the ETC to estimate how much signal to noise is achieved in the stipulated time. Alternatively, you may specify a value for signal-to-noise, for the ETC to return the required observation time to reach that signal-to-noise.

The estimate is obtained in the following steps:

• Get the count-rate from source. Usually involves the following steps:
• Get the spectrum from Kurucz model/templates/uploaded file
• Consider extinction/redshift (if required)
• Apply filter response and convert it to count rate (Nsrc)
• Estimate the total background, which consists of
• Instrument dark counts
• Stray counts from sunlight scattered of spacecraft body
• Zodiacal light
• The Signal to noise (SnR) and the observing time t are related by:
SnR = Nsrc x t/(total_bkg)
(See next section for total_bkg calculation)

###  Estimating Background Noise

• Add the stray counts, zodiacal light contribution and instrumental dark counts to get total background
bkg_counts = dark counts + stray counts + zodiacal counts
• Get the background per pixel. Field of View is (npixels x npixels).
bkg_pixel = bkg_counts/(npixels2)
• pixel size in arc-seconds.
pixel_size = (fov x 3600.0/npixels)
• Area covered by PSF. Assuming a circular psf footprint,
fwhm_area = PI x (psf_fwhm/pixel_size)2
PI = 3.1415926...
• Assume poisson noise, square root of total expected events from source. Add that to the background counts to get total noise contribution. For a given time, t
total_bkg = (src_counts x t)-2 + fwhm_area x bkg_pixel

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