COMMISSION 27 OF THE I.A.U.
                 INFORMATION BULLETIN ON VARIABLE STARS
                             Number 3257

                                                         Konkoly Observatory
                                                         Budapest
                                                         3 November 1988

                                                         HU ISSN 0374 - 0676


               ROTATION OF THE MAGNETTC Ap STAR 56 Ari.

The magnetic Ap star 56 Ari was investigated in the UBV system by several
authors: Provin (1953), Rakosch (1963), Hardie and Schroeder (1963), Blanco
and Catalano (1970) and Hildebrandt et al. (1985). Additional measurements
were made in the U band at the Bialkow Station of the Astronomical Institute
of the Wroclaw University. All the data cover the interval J.D. 2434322 -
2447176 and span 17660 rotational cycles. These data yield the mean rotational 
period P_0=0.72789761 days. Then trigonometric polynomials of the second
order were fitted to the individual data sets, by the least squares method:

   m=m_0 + summa Ak*cos(2pi*((JD-JD_0)*k*f_0-phi_k)).   (k=1,2)        (1)

   The frequency f_0=1/P_0=1.3738196 and the starting epoch JD=2437667.728 were
adopted in the calculations. Calculated phases of minimum brightness of the
first and second order components (phi_1 and phi_2) vs. Julian Date together with
the least squares fits of parabolas to these phases are exhibited in Figures 1
and 2. The fits indicate a decrease in the frequency. Calculated coefficients
of the parabolas yield the following mean relationship between the frequency
and JD:

         f = 1.3739186 - 2.42*10^-9 (JD-2400000).                     (2)

   Such decrease of frequency corresponds to an increase in the rotational
period of 4 seconds per 100 years.
   Magnetic braking may be the reason for the increase of rotational period.
The calculated time for the e-folding loss of angular momentum is equal to
1.6*10^6 years. This result is an accord with calculations of hydromagnetic
deceleration made by Fleck (1981). He gives estimate of the braking time equal
to 106 years for "perpendicular rotators". From the model of Borra and
Landstreet (1980) follows, that 56 Ari is a "perpendicular rotator" i.e. the
magnetic field axis is nearly perpendicular to the rotational axis (beta=80d).
   Another result is presented in Figure 3, which exhibits phases of maximum
index obtained in four observational runs vs. Julian Date. For comparison
the calculated phases of minimum light in the U band are also exhibited.


                             [FIGURE 1]

 Figure 1. The phases of minimum brightness of the first order
           component vs. Julian Date.

                             [FIGURE 2]

 Figure 2. The phases of minimum brightness of the second order
           component vs. Julian Date.


   The JD_0 and f_0 remain the same as those used for calculation of the data
presented in Figures 1 and 2. The B indices for the time interval
J.D. 2446307-2446746 were published by Musielok (1986), and by Musielok and
Madej (1988). Additional measurements were made between J.D. 2447028 and
2447239. The increase of phases of maximum & index in Figure 3 is steeper
than the calculated increase of phase of minimum light in U. This implies
that the period of Beta variations is larger than the period of light
variations in the U band. The period calculated from Beta measurements is equal
to 0.7279534d, whereas the period of light variations in U calculated from
equation 2 for the corresponding Julian Date is equal to 0.7279048d.
   Musielok and Madej (1988) suggest that nonhomogenities of the Beta index
over the surface of 56 Ari are a consequence of Lorenz forces, which arise
from interaction between macroscopic electric currents, which flow in the
atmosphere and the large scale dipole magnetic field measured by Borra and
Landstreet (1980). Variations of the Beta index reflect variations of the
visibility of regions, where the Lorenz forces are most effective -
"Beta-spot", during the rotational period. On the other hand, light variations
reflect variations of visibility of the chemical spot. The positions of the
photometric spot and the "Beta-spot" on the surface of 56 Ari are not the same


                             [FIGURE 3]

       Figure 3. The phases of maximum beta index vs. Julian Date.

because we observe a shift between the phases of maximum Beta and photometric
minimum (cf. Figure 3). The difference of both rotational periods could be
interpreted as a result of relative migration of these features on the surface
of 56 Ari.


                   B. MUSIELOK

         Department of Solid State Cryophysics
            Istitute of Experimental Physics
               of the Wroclaw University
                  ul. Cybulskiego 36
                    50-205 Wroclaw
                       Poland

                        and

           Universitatssternwarte Gottingen
                Giesmarlandstr. 11
               D-3400 Gottingen, BRD



References:

Blanco, C., Catalano, F.A., 1970 Astron. J. 75, 53. [BIBCODE 1970AJ.....75...53B ]
Borra, E.F., Landstreet, J.D., 1980, Astrophys. J. Suppl. Ser. 42, 421.  [BIBCODE 1980ApJS...42..421B ]
Fleck, R.C., 1981, 23 Coll. Liege, p. 341. [BIBCODE 1981LIACo..23..341F ]
Hardie, R.H., Schroeder, N.M., 1963, Astrophys, J. 138, 350. [BIBCODE 1963ApJ...138..350H ]
Hildebrandt, G., Schoeneich, W., Lange, D., Zelwanowa, E., Hempelmann, A.,
    1985, Publ. Astrophys. Obs. Potsdam, 112, 1. [BIBCODE 1985POPot..32.....H ]
Musielok, B., 1986, Acta Astron. 36, 131. [BIBCODE 1986AcA....36..131M ]
Musielok, B., Madej, J., 1988, Astron. Astrophys., in press. [BIBCODE 1988A&A...202..143M ]
Provin, S.S., 1953, Astrophys. J. 118, 281. [BIBCODE 1953ApJ...118..281P ]
Rakosch, K.D., 1963, Acta Phys. Austriaca 16, 70.