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Topic: Variable Star--RR Lyrae

Team TYC-cepheids

Name :	Roll no:	Contribution :
Amrit Gupta	195120038	Observation Plan, Photometry, Distance to the RR-Lyrae
Anish Chaurasiya	180260007	Target selection, Photometry
Sudarshan Das	195120033	Target selection, Photometry
Koushik Das	195120031	Photometry, Period Verification

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Goals:

Our target is ASAS J094809+0000.1 star which is a variable star (RRab- Lyrae)

Our first goal is to plot the light curve for this star

We have assumed that we know the period of star for observation purpose
We consider that we know the apparent r-band magnitude of all the reference stars for zero point estimation

Second goal is to use the light curve to find the distance of star from earth.

We are considering that we know the luminosity of our star

Third goal is to estimate the period of our star using Lomb-Scargle Periodogram algorithm.

We are using the python codes from Growth Astronomy school.

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Target selection:

We used VSX the AAVSO variable stars search engine, to find a star having magnitude between 12-18 and a time period for which a complete phase can be covered in 4-5 nights.
We shortlisted 4 stars and then check for the number of hours they are visible in the night sky above altitude 25^o to the horizon and also their distance from moon is more than 30^o or not.
Based on these Criterias we finalised our target which has a visibility window of about 6.5 hours between 1 to 10 march.

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Pre data analysis:

-After selecting our target star, based on the period of star we uniformly spread our time of observation to get all the variability in star

-As asked we got our data, but due to some bad weather condition we missed our one day data which had 2 observations. In order to compensate we have been provided 2 observation on the next day.

-To check whether we covered the entire cycle we plotted them to see the phase coverage

-Since it was uniformly spread across its phase we were good to go.

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Softwares used:

Origin

Python- Jupyter Notebook

Aperture Photometry Tool (APT)

SAOImageDS9*

Google Sheets

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Data analysis: Major Steps (for single image)

-Reference stars - Zero point

-Checking: variable stars

-Eliminate Background sky noise

-Magnitude and uncertainty of ref stars

-Calculate final mag and error of target star

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Data analysis: SAOImageDS9

Used DS9 to see the image that we got
Identifying our star and noting the x,y coordinate of our star for that image
Now the next step is to do Zero point estimation
For this we have selected 9-10 reference star for each image
For each observation we got 3 images and for these set of images the x,y coordinate of star were unchanged. Since the time gap was very less
In DS9 we used SDSS release 7 catalog to point out all the stars in a particular image and their r-mag
We randomly selected clear visible star in that image noted down x-y coordinate and RA-Dec.
Along with it we also noted down the absolute mag of reference stars in r-band.
Finally we checked if by mistake we have chosen some variable stars as a reference, we eliminated them.

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Data Analysis: APT (Aperture Photometry Tool )

-Now the next step is to find the magnitude of all the star using APT

- Open the same image in APT

- The first thing is to subtract the background sky noise

- For this we have to select a sky annulus median subtraction (sky algorithm from ) more setting option

- Then we have to set the aperture overlay and sky annulus overlay , generally the radius of the inner circle of sky annulus should be 3 times the radius of aperture overlay

- The image below shows the image in APT with aperture overlay in red and inner and outer sky overlay annulus

-Then you have to also see the Radial profile of your image, in this you have to minimize the chi square value by choosing a good sigma value. From the value of FWHM you have to set the radius of red circle equal to FWHM and for green and yellow circles accordingly as mentioned

-Note that the above analysis we will do only for our target star, we will use the same parameters for all the reference stars

-Now as we know the x,y coordinate of stars we will read the magnitude and the errors for all the selected image

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Data analysis:

Now we have to calculate Zero point

Zero point mag = absolute r mag - calculated mag in APT

Apparent mag of target star = calculated mag + Zero point mag

Error in magnitude,

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Data Analysis:Magnitudes and errors of all the images we got:

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Plots:

Light Curve:

Simple Mag plot including error bars:

Light curve with 2 phase :

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Plots:

Light curve:

Magnitude plot with smooth curve:

Magnitude plot with smooth curve for two phase:

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Distance to star:

To calculate the distance of the star we need to know the absolute magnitude and average apparent magnitude of the star.
To calculate the average apparent magnitude we used ORIGIN pro to plot a light curve and calculate the area under that light curve, which will give the average of the apparent magnitude.
The absolute magnitude of an RR-Lyrae variable is between 0.5 to 0.75 magnitude.

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Absolute magnitude of star

To calculate the absolute magnitude we use the formula

Where M is absolute magnitude of star

M_SUN is absolute magnitude of Sun. M_SUN = + 4.74

L is luminosity of star

L_O is solar luminosity

We taken the luminosity of our star from the GAIA DR2 catalog.That is 56.749 L_O .

Using all these values, we have calculated the absolute magnitude of our star to be 0.355104 .

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Distance to star:

We calculate the distance to the star from the Earth using the formula,

Where m is apparent magnitude

M is absolute magnitude

d is distance from earth in parsec

Apparent magnitude is found to be 11.82008 magnitude from the area under the light curve.

Calculated value of distance of star from earth is 1963.3886 parsec.

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Results: Light curve

Actual Light curve:

Taken from ASAS-SN variable stars database

Plotted Light curve:

Using Python notebook

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Results : Period Estimation

Actual period:

Actual Period of this star is 0.833903 days (20.013672 hours), as taken from ASAS-SN variable star database.

Estimated Period:

Estimated period of the star using the Lomb-Scargle Periodogram algorithm is found to be 0.81314 days.

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Results: Distance

Actual Distance:

Actual Distance of this star is 1847.84 parsec , as taken from ASAS-SN variable star database.

Calculated Distance:

The distance of the star is found to be 1963.39 parsec.

Here we are not able to calculate the uncertainty in our calculation because the method we used to find the area of light curve (average apparent magnitude) does not give the uncertainty in the area.

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Error:

Period of star

The calculated period deviate from the value given in ASAS-SN variable star database by 2.49%.

Cause: It may be due to less number of observations available to us.

Distance of star

Our calculated distance deviates from the distance given in ASAS-SN by 6.25%.

Cause:It may be due to the error in estimation of area under the light curve.Also there are uncertainties in the calculated magnitude.