Determination of the Distance to NGC 4725 Using the Infrared Tully-Fisher Relation

Laura Rafferty

2002 June 3



Abstract

The Tully-Fisher relation is one the most widely used methods for determining the distances to galaxies independently of redshift. The distance to NGC 4725 was calculated using the published formula for the absolute magnitude (M) for I-band and the published value for HI line width and a measured value for the total apparent magnitude in I-band. The distance was found to be 10±2 Mpc.

1. Introduction

The Tully-Fisher relation (Tully and Fisher 1977) continues to be one of the better methods for determining galaxy distances independently of redshift. The first application of the Tully-Fisher (TF) relation was using B-band photometry of spiral galaxies (Tully and Fisher 1977). Later in the 1980's Aaronson and co-workers (1980) using a version of the TF relation that used H-band aperture photometry obtained a better distance indicator because the scatter in H-band is smaller, for three reasons:
  1. H magnitude is much less sensitive to the internal reddening characteristic of inclined galaxies
  2. It reflects more accurately the actual stellar mass of the galaxy since the light in H is dominated by low-mass giants
  3. It is less susceptible to sporadic excesses as the result of star formation.
The major improvements in the TF relation were achieved in the late 1980's using I or R (rather than H or K) CCD images because the detectors have high efficiency and large fields of view, and data acquisition is relatively fast even with small aperture telescopes (Bothun et al. 1987).

   The object of this project is to find the distance to NGC 4725 using the I-band TF relation. This galaxy is an Sb/SB(r)II barred spiral (Sandage 1996) with an isophotal inclination of 46 degrees (de Vaucouleurs et al. 1991). The absolute magnitude in I-band was calculated using the formula from Verheijen (2001):

M = -(2.73±0.34) - (7.5±0.1) log WR,Ii.

By Tully and Pierce (2000), the logarith of the width WR,Ii of the global HI profile, corrected for instrumental resolution (R), internal turbulent motion (I), and the inclination of the disk (i) is logWR,Ii = 2.624±0.004 km s-1. In order to accomplish the task of finding the distance to NGC 4725, the apparent magnitude was measured. This was done with multiple long exposures and the total apparent magnitude was found by extrapolating the aperture size to infinity and also calibrating with standard stars.

2. Observations

NGC 4725 (RA(2000)=12:50:26, Dec(2000)=25:30:01) was observed on 2002 May 15 UT using the 0.25 meter Great Ohio Telescope. Conditions were not photometric, especially after 7:30 UT when it began to be very cloudy. The observations were made with the ST8CCD camera at a temperature of -18 Celsius.

   For this project the exposures were done in I-band. The exposures taken for this project are: the calibration frame exposures, the standard star observations and the galaxy observations. The calibration frames include: 7x0.11s zeros ,4x30s plus 3x300s darks and 3 flats(1x60s, 2x3s) . The standard star observations are shown in Table 1. Standard stars were taken from Landolt (1983).
Table 1. Standard Star observations.

The galaxy observations include: 4x300s exposure in I-band beginning at 7:18UT until 7:45UT, a little too late for the last two when the zenith angle was more than 60 degrees (the last two were also in cloudy conditions).

3. Reductions

The basic reduction was done following Massey (1997). The 7 zero frames were combined and also the darks with the same exposure time were combined. These combined dark and zero correct the flat field and the object frames.

   By using the XEphem the airmasses were found for each exposure(standard star exposures and galaxy exposures). The airmasses for the galaxy exposures were: 1.91, 2.006, 2.237, 2.68. Because the last two are significantly above 2 airmasses, only the first two exposures were used.

   The standard star photometry was done following Massey et al.(1992). For this the aperture photometry the IRAF routine phot was run. First the aperture size used for measuring the standard stars was determined (40 pixels) by looking to the FWHM factor (around 10 pixels) and also the sky annulus (50-55 pixels). The various parameter files (datapars, centerpars, fitskypars, photpars) were set to the appropriate values. After this, the routine phot was run for each of the standard stars. The phot task calculates the instrumental magnitude inside the specified aperture and subtracts the sky in the specified annulus. The photcal package was used to find the transformation equations. For this the Landolt catalog (1983) was used. After this, the standard star observation file was made and the task fitparams from photcal package was run. This is the task that actually solves the transformation equations.

   For the galaxy the ellipse task from stsdas.analysis.isophote package was run with fixed center and fixed ellipticity (e = 1 - cos(46) = 0.305). The ellipse task creates ellipses with the given ellipticity and with the semi major axis varying from 1 to 400 pixels in one pixel increments. Next, the stars were subtracted with imedit. After this, each ellipse was used as an aperture for the polyphot task from the noao.digiphot.apphot package. The polyphot task computes the magnitude inside a given polygonal aperture. The total magnitude was estimated by extrapolating the aperture to infinity.

4. Results

The photcal package was run with the standard stars with the following transformation equation (the airmass and color terms were neglected due the low number of standard star observations):

mI = I+i1,

where mI is the instrumental magnitude and I is the apparent magnitude in the standard system. The value of the constant is i1 = 6.8±0.2.    After the standard star analysis was completed, the magnitude of the galaxy was found for the two images (n4021 and n4022). Figure 1 shows the image n4021 after IRAF reduction. This image, along with n4022, was used to find the magnitude with polyphot.
Figure 1. Final image (n4021) before polyphot task was run.

   The polyphot task gives the magnitude within an elliptical aperture of a given semi major axis (see Figure 2).
Figure 2. Plots of magnitude versus aperture semi major axis in pixels for the two exposures (n4021 and n4022) of NGC 4725. The errors in the data points are of order 0.01-0.02 mag, and are too small to be seen in the figure.

The next step was to find the total magnitude by extrapolating the aperture to infinity. The curves of Figure 2 were fit for values of the semi major axis between 200 - 400 pixels with the following equations:
mI21 = (14.312±0.002) e(10.35±0.04)/ a


mI22 = (14.322±0.007) e(10.15±0.14)/ a,

where a is the semi-major axis in pixels and mI is the instrumental magnitude. To find the uncertainties in the fitted coefficients, the least-squares fitting method was used for the above equations (mI = A eB/a), where A and B are the coefficients. After "linearization", and change of variables (z = logm, and w = 1/a), the equation will be:
z = ln A + Bw,

In this linear form, the equations are easy to solve for the uncertainties in the parameters using the least-squares fitting methods.

The total instrumental magnitudes found by extrapolating the aperture to infinity are:

mI21 = 14.312±0.002 mag


mI22 = 14.322±0.007 mag.

Now, the apparent magnitude is found by using the transformation equation given above. The resulting total apparent magnitudes are:

I21 = 7.49±0.16 mag


I22 = 7.50±0.16 mag.

The error in the apparent magnitude (I = mI - i1) was found using propagation of uncertainties for independent random errors. The errors that propagate here are the uncertainties in the instrumental magnitude that was found using the least-squares fitting method and the errors in the i1 coefficient given by the photcal package. The resulting error in the apparent magnitude was found by adding the errors in quadrature. The total apparent magnitude was found by averaging these values:
m = 7.5±0.1 mag.

   Next, the total absolute magnitude may be calculated using the equation from Verheijen (2001) given previously:

M = -(2.73±0.34) - (7.5±0.1) log WR,Ii,

with a value for the logarithm of the width of the global HI profile WR,Ii = 2.564±0.03 km s-1.

Thus,

M = -22.4±0.4 mag.

The distance to NGC 4725 was calculated using the distance modulus formula (m-M = 5 log d - 5):

d = 10±2 Mpc.

5. Discussion

The present result can be compared to the previous values for the distance to NGC 4725, listed in Table 2.
Table 2. Distances to NGC 4725 for comparison between the present study and the published values.

These previous distance determinations for NGC 4725 were done for the galaxy itself or indirectly through an association with the Coma I or II Groups within the Coma-Sculptor cloud. In 1985, Bottinelli et al., using the B-band TF-relation found a value of d = 9.9±1.0 Mpc; in 1988 Tully, by Coma cloud inventory found d = 12.4 Mpc (Gibson et al. 1999). In 1992, Tully, Shaya, & Pierce by adopting an H-band TF-relation with the zero point tied to M31, M33 and NGC 2403 found d = 16.1 Mpc; in the same paper the predicted distance from their mass model was 20 Mpc (Gibson et al. 1999). Later in 1997, Tully revised the TF distance to NGC 4725 by taking into account also B, R, and I-bands and found d = 12.6±2.1 Mpc (Gibson et al. 1999). In 1998, Tonry using SBF (Surface Brightness Fluctuations) found a distance of d = 13.1±2.2 Mpc, which agrees with the previous results and the Cepheid distance d = 12.6±1.0 (Gibson et al 1999). In conclusion from Table 2, the direct and indirect distance determinations to NGC 4725, generally associated with the classical Coma I and II groups, is between 10 - 20 Mpc.

   The value for the distance to NGC 4725 found with GOT is d = 10±2 Mpc, which agrees within errors with the range of distances in Table 2 (10 - 20 Mpc). The general result is dependent on the choice of TF relation that was used to calculate the absolute magnitude. The relation used in this study (from Verheijen et al 2001) used a sample of 49 galaxies to calibrate the zero point and the slope. Another source of discrepancy is in the determination of the apparent magnitude (7.5±0.1 mag). The accepted value of apparent magnitude is 7.8±0.12 mag found from the absolute magnitude of -22.77±0.09 mag (Sakai et al. 2000) and distance modulus of 30.57±0.08 mag (Gibson et al 2000). The error in the apparent magnitude is the result of below average photometry. In conclusion, to find the best value for the distance it is important to have a photometric night with a large number of standard star observations. This would result in a better calibration for the transformation equations and a better value for the apparent magnitude.

References

Aaronson, M., Huchra, J. R., & Mould, J. 1980, ApJ, 237, 655
Bothun, G. D. & Mould, J. R. 1987, ApJ, 313, 629
de Vaucouleurs, G.,de Vaucouleurs, A., Corwin, H., Buta, R., Paturel, A., & Fouque, P. 1991, Third Reference Catalogue of Bright Galaxies (ESA SP-310; Berlin:Springer)
Gibson, B. K., et al. 1999, ApJ, 512, 48
Gibson, B. K., et al. 2000, ApJ, 529, 723
Landolt, A. U. 1983, AJ, 88, 439
Massey, P. 1997, A User's Guide to CCD Reductions with IRAF
Massey, P. & Davis, N., 1992, A User's Guide to Stellar CCD Photometry with IRAF
Sakai, S., et al. 2000, ApJ, 529, 698
Sandage, A. 1996, AJ, 111, 18
Tully, R. B. & Fisher, J. R. 1977, A&A, 54, 661
Tully, R. B. & Pierce, M. J. 2000, ApJ, 533, 744
Verheijen, M. A. W. 2001, ApJ, 563, 694